Physica status solidi: Volume 8, Number 2 February 1 [Reprint 2021 ed.] 9783112497005, 9783112496992

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pliysica status solidi

VOLUME 8 . N U M B E R 2 • 1965

Contents Review Article

Page

P . GORLICH, H . KARRAS, G . K O T I T Z , a n d R . L E H M A N N

Spectroscopic Properties of Activated Laser Crystals (III) . . . .

385

Original Papers K . KIROV a n d V . Z H E L E V

Study of the Effect of an Electric Field on Trap Filling in CdS Single Crystals b y the Use of Thermally Stimulated Currents. . .

431

K . MEYER u n d F . POLLY

CH. SCHWINK

M. M.

SHUKLA

Tribolumineszenzuntersuchungen an Alkalihalogeniden und Bohrzucker

441

Über die Verfestigung homogener kubisch flächenzentrierter Vielkristalle bis zum Beginn dynamischer Erholungsvorgänge . . . .

457

Evaluation of Heat Capacities of Copper and Gold by Using Krebs's Model

475

A . SOSIN a n d K . GARR

Directional Effects in Electron Irradiated Cu Single Crystals. . .

481

K . THOMA a n d W . L U D W I G

G.

SCHOECK

Scattering of Sound Waves by Isotopes and Thermal Conductivity in the Simple Cubic Lattice

487

The Activation Energy of Dislocation Movement

499

S . CERESARA, H . E L K H O L Y , a n d T . F E D E R I G H I

Resistivity Increase in Polycrystalline Al Heavily Cold-Worked a t 78 °K

509

K . - H . P F E F F E R , P . SOBILLER u n d A . S E E G E R

Fehlstellenerzeugung durch aufgespaltene Versetzungssprünge in kubisch-flächenzentrierten Metallen

517

J . STUKE u n d K . W E N D T

L . MICHALOWSKY

Phonon-Drag in hexagonalen Se-Kristallen

533

Über den Einfluß der Anisotropiekonstanten auf den Perminvareffekt von Ferriten

543

W . BRODKORB, W . HATTBENREISSER u n d E . J Ä G E R

Berechnung der Anisotropiekonstanten eines kubisch und einachsig anisotropen Ferromagneten aus der freien Energie (Continued on cover three)

551

physica status solidi B o a r d of E d i t o r s P. A I G R A I N , Paris, S. A M E L I N C K X , Mol-Donk, W. D E K E Y S E R , Gent, W. F R A N Z , Münster, P. G Ö R L I C H , Jena, E. G R I L L O T , Paris, R. K A I S C H E W , Sofia, P. T. L A N D S B E R G , Cardiff, L. N É E L , Grenoble, A. P I E K A R A , Poznan, A. S E E G E R , Stuttgart, 0. S T A S I W , Berlin, M. S T E E N B E C K , Jena, F. S T Ö C K M A N N , Karlsruhe, G. S Z I G E T I , Budapest, J. T A U C . Praha Editor-in-Chief P. G Ö R L I C H Advisory Board M. B A L K A N S K I , Paris, P. C. B A N B U R Y , Reading, M. B E R N A R D , Paris, W. B R A U E R , Berlin, W. C O C H R A N , Cambridge, R. C O E L H O , Fontenay-aux-Roses, H.-D. D I E T Z E , Aachen, J. D. E S H E L B Y , Cambridge, G. J A C O B S , Gent, J . J A U M A N N , Köln, E. K L I E R , Praha, E. K R O E N E R , Clausthal-Zellerfeld, M. MATYAS, Praha, H. D. M E G A W , Cambridge, T. S. MOSS, Camberley, E. NAGY, Budapest, E. A. N I E K I S C H , Jülich, L. P A L , Budapest, M. R O D O T , Bellevue/Seine, B. Y. R O L L I N , Oxford, H. M. R O S E N B E R G , Oxford, R. V A U T I E R , Bellevue/Seine

Volume 8 • Number 2 • Pages 383 to 636 and K 77 to K 120 February 1, 1965

A K A D E M I E - V E R L A G

.

BERLIN

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Review Article phys. stat. sol. 8, 385 (1965) Jena, Carl-Zeifi-Strajie 1

Spectroscopic Properties of Activated Laser Crystals (III) By P. Gorlich, H . K a e e a s , G. K o t i t z , a n d R .

1.

Lehmann

Contents

Introduction

2. General remarks on the geometry and excitation of laser resonators of activated crystals 3. Theory 4. Spectroscopic emission

data on absorption,

spontaneous fluorescence,

and stimulated,

4.1 Group of Lanthanides 4.2 Actinide group 4.3 Transition metals 4.3.1 Nomenclature of the terms 4.3.2 Ruby, Al 2 0 3 :Cr 3 + 4.3.3 MgF 2 :Ni 2 + 4.4 Semiconductors 4.4.1 Survey of the laser materials 4.4.2 Production of diodes (GaAs) 4.4.3 Models for the mechanism of light emission in p—n semiconductors 4.4.4 Emission properties 4.4.5 Recombination radiation for optical pumping 4.4.6 Quartz glass 5. Instrumental

set-up

5.1 Laser arrangements 5.2 New developments in the field of pumping light sources 5.3 On modulation and determination of the input and output power 5.4 Testing instruments for absorption and fluorescence 6. General optical and thermal

properties

6.1 Refractive index, scattering, and strain 6.2 Nonlinear optical effects 6.3 Thermal properties 7. Problems 8. 25*

of crystal

Conclusion

growth

P. GÖRLICH, H. KARBAS, G. KOTITZ, and R. LEHMANN

386

4.2 Aetinide

group

Of all the actinides only uranium has so far come to be known as an activator for laser crystals. Absorption, fluorescence, and the properties of the paramagnetic resonance spectra of uranium-doped synthetic crystals have been investigated in many respects. Also the fluorescence spectra of the transuranium elements Np 3 + , Pu 3 + , Am 3+ , and Cm 3+ in LaCl2 crystals have already been investigated'[7]1), but the use of these ions as active media in host crystals has so far not been reported in literature. The emission and absorption spectra of the actinides consist of relatively sharp bands, even if the elements are incorporated in solids. The reason for this is that always transitions within an incomplete shell, the O-shell, are involved, which is screened by the partially occupied P and Q-shells against the host lattice. It should be noted for most actinides the electronic configuration and consequently also the ground term is still uncertain (see Table 10). The electronic configuration of some valencies of uranium, neptunium, and plutonium ions has been given in Table 11. The absorption and emission spectra are now methodically and systematically studied. These investigations are, however, impeded by radioactivity and the short lifetime of the isotopes. The first fundamental research work on the spectroscopic properties of U 3 + , which had been incorporated in alkaline earth fluorides, was performed by GALKIN and FEOFILOV [100] who showed that uranium is not only capable of fluorescence in the hexavalent state (U0 2 ) 2+ but also in a valency different from that. A more detailed presentation of the measurement results published in the aforeT a b l e 10 (according SUGANO [7]) Atomic number

Element

Ground term

89 90

Ac (Actinium) Th (Thorium)

91

Pa

92 93

U (Uranium) Np (Neptunium)

?

94

Pu (Plutonium)

9

Am Cm Bk Cf E Fm Mv

1

95 96 97 98 99 100 101

Dzl2

3

oder

(Protactinium)

(Americum) (Curium) (Berkelium) (Californium) (Einsteinium) (Fermium) (Mendelevium)

Electronic configuration Atomic 0-shell P-shell Q-shell radius

oder

oder oder

? •>

1 1 ?

? 1

?

•>

5/ 5/2 5/ 5 f3 5 /5 5/4 5 /« 5 /5 5 p 5 f 5/» 5 fw 5 /10 5 /" 5 f 12

6 s2 6 s2 6 s2 6 s2 6 Ä2 6 s2 6 s2 6 s2 6 s2 6 s2 6Ä2 6 s2 6 s2 6 s2 6 s2 6 s2 6 s2

6 p6 6 pe 6 p6 6 p6 6 p6 6 p» 6 p6 6 p6 6 p6 6 p6 6 p6 6 p6 6 p6 6 p6 6 p6 6 ps 6 p6

6d 6 d2 6d 6d 6 d2 6d 6d 6d

6d 6d 6d

Ts 2 Ts 2 7 s2 7 s2 7 s2 Ts 2 7 s2 7 s2 7 s2 7 s2 7 s2 7 s2 7 s2 7 s2 7 s2 7 s2 7 s2

1.80

1.57

!) The references [1] to [75] have been published in Part I of this article (phys. stat. sol. 5, 437 (1964)), the references [76] to [99] have been published in Part I I of this article (phys. stat. sol. 6, 277 (1965)).

387

Spectroscopic Properties of Activated Laser Crystals (III) Table 11 (according to J o r g e n s b n [125]) Atomic number

Electronic configuration O-shell P-shell Q-shell

Element XJ3 +

92

f3 512

XJ6 +

Np 3+ Np 4+ Np 7+ pu3+ Pu < +

93

94

6

5

XJ4 +

f3

5

F

6

6 s2

6

s2 6 s2 6 s2 6 s2 6 s2

6

1.05

6

0.97

p6

0.80

pe 6 pe dp6 6p*

6

5/2

p6

6 p

6 s2

4

5/ 5

s2

Ionic radius (after A h r e n s )

6

1.10 0.95 0.71 1.08

p6

0.93

mentioned work has already been given in the review article on the alkaline earth fluorides of the fluorite type [9]. In contrast with the green luminescence of the U 6 + ion [101] U 3 + incorporated in CaF2, SrF 2 , and BaF 2 shows a strong fluorescence in the region 2.0 to 2.6 ¡xm [102], The spectra for the measuring temperatures between + 2 0 °C and —150 °C are illustrated in Fig. 71. The variation of the spectral position and the general characteristic of the emission bands is insignificant when changing from CaF2 via SrF 2 to BaF. The individual bands are ascribed to transitions within the 5 f 1.0

Hh

0.8

J

i-

CaFrU +20%

i

0.6

1

OA J,

22

26

2A

Hh

2.8 °2.0 10 SrFz-U +20X

A

V

k

0.2 2.0 W

CaFrU -150X

j \

V

V

2£

2.4

2.2

h-

28

SrF2-U -150X

/

w

10 1.0 08

2.2

Hh

0£ OA 0.2 2j0

2.2

24

2.6

\ \

\

\

26 U X(jjLm) -

28 ZO 1.0 BaFz-U 08 *20X 0B OA 0.2 2.8°20

V M

2.2

2A

2.6

Hi-

t

L

2.2

BaFrU -1SOX

\ t /\

/

28

N

2A X(fim)-

2£

2.8

Fig. 71. Luminescence spectra of M F 2 : U , + at + 2 0 °C and —150 °C (after Galkjn and Feofilov [102])

388

P . GÖRLICH, H . KAKRAS, G . KOTITZ, a n d R . LEHMANN

CaFz /U Hl-

spectrat

, T-300°K slit

width

I S

§

S

tg

A ?xc

=

436

;?xc

=

564

^exc

2A X (¡jum) — » 1 0 6 0 n m , AJ

. =

1220 n m (after

GÖRLICH,

KARRAS, a n d KÖTITZ [ 1 0 4 ] )

Fig. 74. The excitation spectrum for the 3984 c m " 1 fluorescence of a 0.007 mole % U 8 + : CaF, crystal at 78 °K (liquid N„ temperature). Fluorescent intensity is plotted vs. wavelength of the exciting light for constant intensity of Jight incident upon the sample (after \VITTKE, K I S S , . DUNCAN, a n d MCCORMICK [ 1 0 5 ] )

1(A)-

shell, especially to the 4 / u/2 - 4 -^9/2 transition. The spectral position of the two short-wavelength emission bands at 2.14 [xm (4673 cm _1 ).and 2.22 ¡im (4504 cm - 1 ) is in agreement with the position of the two long-wavelength absorption bands,

Spectroscopic Properties of Activated Laser Crystals (III)

389

Fig. 75. The absorption of CaF 2 :lJ 3 + as a function of wavelength (after BOYD, COLLINS, PORTO,^ Y A R I V , a n d HARGREAVES [ 1 0 6 ] )

0.1 MOLE %CaF2 :U 3* AT 77°K

Fig. 76. Absorption spcctra of CaFa:XJ samples with varying ratios of U 1 + and U 3 + . Traces a and b are for the same sample at 5° and 77°K and show the relatively small line narrowing that occurs between 5° and 77 °K. All other traces were taken at 5 °K. The absorption coefficients are only approximately linear at wavelengths longer than 6000 A (after TITLE, SOROKIN, STEVENSON, P E T T I T , SCARDEFIELD,

and LANKARD [107])

Jk _l I 2.50 2M130

I LUOVO 100

j\

JL A i

\l.50l.W

^ - J k L

_l I I I I 190 1.80 170 1£0 1.50 W

-

^

i i i i i i i i i i ¿30 2.20 110 2.00 ISO 1.80 1.70 1.60 1.50 W

I I—; L 130 120 110 100 030 0.80 0.70

luta i i i i i i i 1.30 1.20 1.10 1.00 0S0 0.80 070 0.60

\

JL_ 2.50 UO 2.30 120 210 2.00 1.30 WO 1.70 WO

1.50 UO

X(fjun)

1.30 1.20 7.10 100 0.30 0.80 0.70 0.60 0.50

OM

390

P.

GÔRLICH, H .

KAKRAS,

G. KÔTITZ,

and

R.

LEHMAKN

i.e. that resonant transitions are involved in this case. Fig. 72 shows an energy level diagram of the U 3 + ion [103]. G Ô K L I C H and co-workers were able to show that the spectral response of the luminescence light clearly depends upon the frequency of the exciting light [104], which consequently results in different resolutions of the two resonant lines and a more or less well defined structure of the long-wavelength absorption bands (fcg. 73). A complete excitation spectrum for the fluorescence line 2.51 fxm (3984 cm 1 ) is shown in Fig. 74. The sample, which was illuminated with a constant light intensity, was a CaF2 crystal with 0.007 mole % U 3 + . I t is apparent from a comparison with Fig. 75 that the excitation spectrum essentially reflects the absorption spectrum, which implies that the fluorescent efficiency is almost independent upon the excitation wavelength [105].

iw

no

no

z.00 m

wo no

w

iso iw 130 1.20 no X (fjun)

100 aso aso a?o 0.60 aso aw

F i g . 7 7 . A b s o r p t i o n s p e c t r u m a t 5 ° K o f S r F ! : 1 0 0 % U I + , 0 % U » * ( a f t e r T I T L E , SOROKIN, STEVENSON, P E T T I T , SCARDEFIELD, a n d LANKARD [ 1 0 7 ] )

2.50ZW 2.30 220 2.10 2.00 730 1.80 W

W 150 W

1.30 1.20 1.10 1.00 OSO 0.80 0.70 0.60 0.500.40

1502.W 130 2.20 2.10 2.001.30 1.80 7.70 1.60 1.50 U0 130 1.20 1.10 1.00 030 0.80 0.70 060 0.50 0.W

2.502402302.202.70 200 7JO 7.80 770 7.60 7.50 IW 7.30120 1.10 100030080 0.70 0.60 0.50 OM -—X(fJLm) F i g . 78. Absorption s p e c t r a a t 5 ° K of S r F 2 : U samples with v a r y i n g r a t i o s of U 4 + a n d ( a f t e r T I T L E , SOROKIN, STEVENSON, P E T T I T , SCARDEFIELD, a n d LANKARD [ 1 0 7 ] )

U3f

Spectroscopic Properties of Activated Laser Crystals (III)

391

Fig. 79. Absorption and fluorescence spectra for three CaF 2 :U 3 + crystals at 78 °K, showing the effects of varying U 3 + concentration ( a f t e r W I T T K E , K I S S , DUNCAN, a n d MCCORMICK [ 1 0 5 ] )

Numerous i n vestigations du ring the last years have shown that uranium may be incorporated. in synthetic crystals (predominantly CaF 2 , SrF 2 , and BaF 2 ) in the form of U 3 + , U 4 + , and U 6 + . Substances with trivalent uranium have been found to be best suited for lasers; we shall revert to this in more detail below. The appearance of the absorption spectra clearly depends upon the valency of the incorporated uranium ion. Fig. 75 [106] illustrates a spectrum of CaF 2 crystal containing more than 9 5 % of uranium in the trivalent state. Furthermore, T I T L E , S O R O K I N , and co-workers [107]investigated the influence of the U 4 + i o n s on the absorption spectrum for different parts of U 3 + (Fig. 76). Corresponding spectra are shown in Fig. 77 and 78 for S r F 2 : U 4 + and SrF 2 : U 4 + , U 3 + , from which it is apparent that characteristic features in the case of U 3 + in SrF 2 are an absorption band at 1.88 ¡xm (CaF 2 shifted by a corresponding amount) and in the case of U 4 + in SrF 2 weak absorptions in the regions 2.2 to 2.5 ¡xm and 1.40 to 1.75 ¡xm. These results nearly agree with C O N W A Y ' S [108] measurements on C a F 2 : U 4 + . The absorption of U 4 + may be assigned to the 3 i i 4 - 3 i i 5 transition. The observed absorption and emission spectra very strongly depend upon concentration [105]. Fig. 79 shows that with an increase of the uranium concentration several new lines occur. The authors distinguish between spectra, which correspond to "isolat e d " uranium ions, and those that are characteristic of a higher uranium concentration and which can possibly be related to associated pairs of U 3 + ions. The integral intensity of the spectrum of the first type becomes saturated, as the uranium concentration is increased, while in the second case a square curve is obtained (Fig. 80). Absorption bands for B a F 2 : U 3 + , measured at 2 0 ° K , are reported by P O K T O and Y A B I V [ 1 0 9 ] to occur at the following wavelengths: 2 . 2 2 0 ¡xm ( 4 5 0 5 cm - 1 ), 2 . 2 8 5 ;xm (4376 cm" 1 ), 2.382 ¡xm (4198 cm" 1 ), 2.417 ¡xm (4139 cm" 1 ), 2 . 5 7 6 ¡xm (3882 cm" 1 ), a n d 2.488 ¡xm (4019 cm" 1 ).

The presence of U 3 + or U 4 + , respectively, is not only apparent from the characteristic absorption spectrum, but it is also at once obvious to the eye due to the colouration of the crystals. Thus, C a F 2 : U 3 + is deeply red, S r F 2 : U 3 + orange-red,

392

P . GÔRLICH, H . KARRAS, G . KÔTITZ, a n d R . LEHMANN

150

0

Fig. 80. Integrated absorption coefficients for absorption lines corresponding to the "isolated ion" (line A) and "high concentration" (line B) spectra of U 3 + in CaF„ as a function of concentration (after WITTKE, Kiss, DUNCAN, and MCCORMICK [105])

0.02 0M 0.06 0.08 L0.10 CONCENTRATION (MOLAR PERCENT)

0.12

and B a F 2 : U 3 + orange due to the strong absorption in the green region of the spectrum [100], while S r F 2 : U 4 + crystals develop a light green tint [107]. I t essentially depends upon the growth conditions, in which valency uranium is incorporated in the crystals. Under strongly reduced conditions and when the melt is kept for approximately 2 hours about 100 °C above the melting temperature, incorporation is predominantly effected in the trivalent from. If the process of crystal growing proceeds rather rapidly and if there is in addition no possibility for reduction (metal crucible, little graphite powder), then the U 4 + portion in the crystals will be predominant [110]. The crystal structure of the alkaline earth fluorides can be shown to be a cubic lattice of F ions with each second cube centre occupied by a Ca 2 + ion, which after the incorporation of uranium is isomorphously substituted by the latter. The resultant positive excess charge can be compensated in various ways dependent upon the valency of the uranium ion. For a trivalent cation B L E A N E Y et al. [ I l l ] suggest the following four possibilities: 1. M 3+ substitutes one M 2+ and one excess F ion resides in one of the nearest and otherwise empty cube centres in the [100] direction. 2. M 3+ substitutes one M 2+ and one O 2 - ion substitutes one F ion. 3. M 3+ substitutes one M 2+ and one M+ substitutes a second M 2+. 4. 2 M 3+ substitute 3 M 2+. Paramagnetic resonance measurements at 20 °K on CaF 2 and SrF a yielding a tetragonal symmetry of the resonance spectra induced the authors to assume that in this case an incorporation of U 3 + after model 1 is involved. The suggestion of this model also supports the investigations of Z I N T L and U D G A B D [ 1 1 2 ] on crystals with a preponderant fraction of trivalent ions. A very small fraction of U 3 + ions in CaF 2 is supposed by Vnsrcow and Low [113] to retain the original cubic symmetry. This assumption was corroborated by the exact measurements of T I T L E and co-workers [ 1 0 7 ] , who found approximately 1 0 % of all centres observed in cubic symmetry. In the same work also resonance spectra were reported with trigonal symmetry which have to be assigned to incorporated U 4 + ions, as was almost simultaneously stated by P O B T O and Y A B I V [ 1 1 4 ] , These centres were also found in CaF 2 , SrF 2 , and BaF 2 [110]. The charge compensation in the case of U 4 + substituting one Ca 2 + could according to Y A B I V [ 1 1 0 ] be accomplished in that two F ions lying on either side of the U 4 + ion on a cube diagonal are replaced by O2 ' ions. A less probable model, which must, however, not be

Spectroscopic Properties of Activated Laser Crystals (III)

393

L

Fig. 81. CI arge compensation in the case of the incorporation of I" 3 ' in CaF 2 by an interstitial F" ion in the second-nearest neighbour position AHIiAB, VOLTERRA, LOW, and YARIV [115]) (after IV Fig. 82. A

model of the luminescence centre in L i F : U crystals (after FEOFILOV ril61>

excluded is the one, in which one O 2 - ion occupies the nearest centre of the cube, which is otherwise vacant. In one of their recent works M A H L A B and co-authors [ 1 1 5 ] report an electron spin resonance spectrum of U 3 + in CaF 2 with orthorhombic symmetry. The model suggested by the authors for a charge compensation is shown in Fig. 81. The positive excess charge generated by the substitution of Ca 2 + by U 3 + is compensated by an F ion, which occupies the interstitial site in the second nearest empty centre of the fluorine cube. A charge compensation by 0 2 ~ ions is not likely to occur, since the orthorhombic system was also observed in crystals, which did not exhibit trigonal symmetry of U 3 + or U 4 + . Oxygen likewise plays an important role when incorporating hexavalent uranium. After comprehensive luminescence investigations on L i F : U 6 + in polarized light F E O E I L O V [ 1 1 6 ] suggests a model for the luminescence centre in L i F : U (Fig. 82): L i + is isomorphously substituted by U 6 + ; the positive excess charge is compensated in that 0 2 ~ ions take the position of five out of the six fluorine ions surrounding the U 6 + . K A P L Y A N S K I I and M O S K V I N [ 1 1 7 ] also suppose that uranium is incorporated in LiF and NaF in the form of different uranyl centres (U0 2 ) 2 + . Comprehensive investigations of laser emission have already been carried out on CaF 2 :TJ 3 + crystals; there are, however, discrepancies in the interpretation of the causes of the generation of different laser frequencies. At low concentration (0.05% nominal concentration) S O B O K I N and S T E V E N S O N [13] found laser emission at 2.5 (i.m. An extra band at 2.6 ¡im appeared when the nominal concentration was increased to 0.1 %. The authors suppose that the change of the laser frequency does not only result from the higher uranium content, but can possibly be explained by someother than the tetragonal symmetry position (possibly by uranium ions in trigonal symmetry position). In a recently published work by W I T T K E et al. [105] the laser emission measured at 2.51 ¡im (3984 cm - 1 ) is likewise assigned to "isolated" U 3 + ions. In this case transitions are involved between the lowest component of the l I n / 2 level and the highest component of the 4 / 9 / 2 level, which would have to lie 515 c m - 1 above the ground state. Further cooling of the laser down to 4 °K resulted in a shift of the 2.51 fi.m emission by 3.6 c m - 1 towards longer wavelengths. At higher concentration ( ~ 0.007 mole %) and low tem-

394

P . GÖHLICH, H . KARRAS, G . KOTITZ, a n d R . LEHMANN

0

10 20 SO PULSE ENERGY INPUT (ARBITRARY UNITS) —-

Fig. 84. Pulsed laser energy output (arbitrary units) from a CaF a :XJ 3+ crystal at 78 °K, exhibiting simultaneous oscillations at both 2.51 and 2.61 ixm (3984 and 3830 cm - 1 ) vs. energy input (arbitrary units) from the xenon flash lamp (after WITTKE, KISS, DUNCAN, a n d MCCORMICK [105])

« Total Resonator

8 12-10' Loss per cm -

Fig. 83. Variation of threshold energy with total resonator loss (after GOODWIN [120])

perature laser emission starts at 2.61 fim (3830 cm -1 ). However, crystals with higher concentration emitting radiation simultaneously at 2.51 and 2.61 ¡xm were likewise investigated. On a single sample a 2.57 ¡xm transition could be measured at room temperature. Data on a continuous CaF 2 :U 3 + laser were first presented by B O Y D , C O L L I N S , P O E T O , and Y A B I V [106]. On the strength of E S R measurements they ascribed the laser emission found at 2.613 ¡Am to U 3 + ions in tetragonal symmetry position. They found 0.88 to 0.92 ¡im to be the most favourable excitation region, in which relatively weak absorption lines with / fa 10" 6 and a half width of Av pa 15 cm" 1 occur. A smaller portion of the 2.613 [zm laser emission, about 15%, originates from absorption in the intense bands (/ ^ 10~3) in the region 0.5 to 0.6 ¡j.m. Laser emission is explained by the authors in terms of transitions between the lowest component of the 4 iii/2 level and a terminal state lying 609 cm - 1 above the ground state. P O E T O and Y A B I V [ 1 1 8 ] also found a laser emission at 2 . 5 ¡xm, when the fractions of the uranium ions in tetragonal or trigonal symmetry positions were comparable. If, however, the ratio of the trigonal to the tetragonal incorporation was 10:1, a laser emission was found at 2.24 ¡j.m, which was assigned to uranium ions in trigonal symmetry position. The values of the threshold energy of lasers very strongly depend upon the available measuring instruments and the quality of crystals, which accounts for the different data presented by various authors. K A I S E E and K E C K [ 1 1 9 ] point out that the internal losses in the crystal are in many cases greater than the reflection losses at the end surfaces of the laser rod and thus lead to considerable enhancements of the threshold. The internal losses may result from the scattering at included particles of different sizes. Investigations on CaF 2 :U 3 + lasers showed that in this case CaO particles are probably involved, but also uranium colloids must not be excluded. The stimulated emission radiation can be scattered and absorbed at defects of the host crystal. G O O D W I N [ 1 2 0 ] reports that the scattering and absorption coefficients together must not exceed 10~3 c m 1 ; otherwise the

Spectroscopic Properties of Activated Laser Crystals ( I I I )

395

threshold value will linearly increase with the density of the scattering particles. In Fig. 83 is seen that the threshold power is a linear function of the total resonator loss as governed by the scattering extinction coefficient. BOYD et al. [106] found that for CaF 2 :U the threshold energy is lowest, if the uranium ions are located in tetragonal symmetry positions. The following threshold values are reported for 2.6 ¡xm: 2 J (20 °K), 3.78 J (77 °K), 4.35 J (90 °K), and 1200 J (300 °K). According to WITTKE [105] the threshold energy for the 2.51 [IM emission decreases when cooling from 300 °K to 78 °K, while further cooling down to 4 °K again leads to an increase. The threshold value for 2.61 ¡xm decreases monotonously on cooling down to 4 °K. The striking difference of both lines is also apparent from Fig. 84, in which the radiated laser energy is plotted as a function of the incident energy (energy of the flash lamp) measured on a crystal, which simultaneously emitted radiation at 2.51 and 2.61 |xm. SOROKIN a n d STEVENSON [ 1 3 ] d e r i v e d a n o s c i l l a t o r s t r e n g t h o f / =

2.6 x l 0

_ 1

for the 2.5 ¡xm transition from the relation / =

by means of r-measure8n 2 e 2 v 2 r ments. For the 2.5 ¡am emission the lifetime of the metastable state was determined to be 136 ± 15 ¡xs at 4.2 °K. For the 2.613 [xm emission the following r-values were reported [106]: r = = 130 ± 13 (is (4.2°, 20°, and 77 °K), r = 95 ± 15 ¡xs (90 °K), T < 15 ¡xs (limit of the measuring system) for 300 °K. S t i m u l a t e d e m i s s i o n a t 2 . 4 0 7 (IM w a s m e a s u r e d b y PORTO a n d YARIV [ 1 2 1 ] o n

a SrF 2 : U 3 + laser. About 6 0 % of the excitation is concentrated in the region 1 to 1.3 ¡xm. where narrow absorption bands with oscillator strengths between 0.5 X10"® and 2 X 10" 5 appear, while the rest falls into the region 0.4 to 0.6 ¡xm, where intense bands occur (/ m 10~3). The 2.407 [xm laser emission corresponds to transitions from the lowest component of the 4 iii/ 2 level at 4489 c m - 1 to a component of the 4 / 9 /2 level lying 334 c m - 1 above the ground state (Fig. 85). The lifetimes of the metastable state were determined to be 1 1 0 |xs ( 2 0 ° K ) , 8 0 jxs (77 ° K ) , and 60 ¡xs (90 °K) with an accuracy of I 10 [xs. For the threshold energy the following values were obtained on a crystal sample with 0.1 mole % uranium: 38 J (90 °K), 32 J (77 °K), and 8 J (20 °K). The authors believe that the strong decrease of the threshold value at a temperature fall from

17

15

J 5

%/2

'NONRADIATIVE TRANSITIONS

-MASER TRANSITION AT 2. ¥)7fMm (3/2

3

F,

3

' A / 2

-D4

6

F S 2

3 l

2 V

Atomic radius

Electronic configuration 3d 3 d2 3 d3 3d5 3d5 3 d* 3 S> 3 d8 3d 1 0 3 dw

.

1.65 1.45 1.36 1.28 1.31 1.27 1.26 1.24 1.28 1.37

4 52 4 s2 4 s2 4 s1 4 s2 4 s2 4s2 4 «2 4Ä2 4 s2

T a b l e 13 (C. K . J 0 R G E N S E N " [ 1 2 5 ] )

Atomic number

Element

Electronic configuration

Atomic radius

24 25 27 28

Cr 3+ Mn 2 + Co 3 + Ni2+

3 d3 3d5 3 d* 3d8

0.55 0.80 0.47 0.68

According to T A N A B E and STJGANO [126] the narrow lines are assigned to transitions within the states of the same electronic configuration, which are termed tN-n en ( n 2 P ° - > 3p 2 2D

4128.09 A 24217.69 c m " 1 4/ 2F° -> 3d 2D

4130.88 A 24201.09 c m " 1 4/ 2F° -> 3d 2D

The above a u t h o r s associated t h e observed emission w i t h t h e m o s t l y f o r b i d d e n transitions of Si I I I (2541.83 A) a n d S i l l (remaining lines). E x c i t a t i o n of t h e laser emission was effected b y a m e r c u r y discharge in high v a c u u m . T h e lines a t 1213.9 A, 1213.90 A, 962.79 A, a n d 818.42 A are t a k e n as probable p u m p lines. Although an optically p u m p e d solid-state laser is involved, it was discussed in t h e section dealing with semiconductor lasers. T h e reason is t h a t t h e emission process does n o t t a k e place in an a c t i v a t o r e m b e d d e d in t h e q u a r t z glass. I t is r a t h e r assumed b y t h e above a u t h o r s t h a t t h e absorption a n d emission processes t a k e place in t h e silicon of t h e glass. This is c o r r o b o r a t e d b y t h e p u m p regions on t h e v e r y short wavelength side extending f a r i n t o t h e self-absorption region of t h e q u a r t z glass, so t h a t for t h e i n t e r p r e t a t i o n recourse m u s t possibly be h a d t o exciton processes. I n a n y case, an i m p u r i t y , which possibly escaped t h e experimenters' observation a n d which has t o be m a d e responsible for t h e emission, should n o t f r o m t h e first be ruled out. F a c t is t h a t t h e m a n y q u a r t z glass qualities considerably differ in their optical behaviour. Most q u a r t z glasses h a v e a s t r o n g selective absorption a t 0.248 ¡i,m, which is t h e cause of a strong blue fluorescence. F u r t h e r m o r e ,

414

P . GÖRLICH, H . KARBAS, G . KOTITZ, a n d R . LEHMANN

there are also glasses t h a t fluoresce green. I t is merely Suprasil, which neither exhibits a n y noticeable extrinsic absorption (edge of t h e electron absorption a b o u t 0.175 fi.m) nor a n y fluorescence. N o reference t o t h e t y p e of q u a r t z glass used is m a d e in t h e paper. 5. I n s t r u m e n t a l Set-up 5.1 Laser

arrangements

The simplest laser a r r a n g e m e n t s consist of a laser rod with F a b r y - P e r o t g e o m e t r y enclosed by a spiral flashlight l a m p (high-pressure xenon or m e r c u r y lamps). Laser rod a n d light source are arranged in t h e interior of a cylindrical reflector, t h e reflecting coating of which consists of MgO or other highly reflecting materials, whose reflecting powers despite high working rates m u s t n o t be allowed t o deteriorate. Owing t o its simplicity this a r r a n g e m e n t is most commonly used. I n spite of i n t e r m i t t i n g excitation (pulse operation) t h e cooling of t h e rod cannot completely be dispensed with, even for laser substances t h a t are suitable for lasing a t room t e m p e r a t u r e (ruby, h o s t : N d 3 + etc.). Cooling is effected by air circulation (possibly cooled air) or by heat conduction via t h e holder of t h e resonator. Materials, such as r u b y and C a W 0 4 , with excellent h e a t conduction, even a t r o o m t e m p e r a t u r e , have certain a d v a n t a g e s over CaF 2 , which is a poor h e a t conductor. As an arbitrarily chosen example of a commercial i n s t r u m e n t based on this principle reference is m a d e t o t h e solid-state laser of t h e Optische W e r k e J e n a [161] (Fig. 107). This i n s t r u m e n t consists of a resonator housing containing t h e resonator, t h e flashlight lamp, and t h e reflector a n d a power-supply u n i t . The inside components of t h e resonator housing can be cooled w i t h fresh air, if neces-

Fig. 107. Resonator housing of the solid-state laser from Jena. Reflector housing (left) and power-supply unit (right) after BERNDT, GRASSME, KOCH, and MEINEL [161])

Spectroscopic Properties of Activated Laser Crystals (III)

415

Fig. 108. Diagram of the experimental arrangement for flashlight operation of laser resonators cooled with liquid g a s e s ( 2 0 ° K ) ( a f t e r YAKIV, PORTO, a n d NASSAU [ 1 4 ] )

sary. Another possibility of cooling the resonator is provided by the evaporaQUARTZ tion of nitrogen. The power-supply unit LIGHT PIPE delivers a continuously variable lamp voltage from 1 kV to 3 kV which is CRYSTAL SUPPORTING equivalent to an excitation energy for AND LIGHT BAFFLE the flashlight lamp from 85 Ws to max. CONE 750 Ws. The pump light can manually ^ -INNER DEWAR be released with the aid of a key on the power-supply unit by optionally variable positive or negative voltage pulses (3 V to 100 V) as well as by a pulse generator (flash sequence continuously variable from 5 to 20 s). The CaWO+:PrZlL CONDENSER flash duration of the pump light lies CRYSTAL V^mrrp) BANK AND within the order of 1 to 2 ms. For actuPOWER SUPPLY ating indicating and measuring instru- Xe FLASH LAMP ments an impulse can in addition be obtained from the power-supply unit, which relative to the trigger pulse is continuously shiftable by i 2 ms. Laser materials having a small separation between the terminal state of the fluorescence and the ground state must be cooled with liquid gases, A frequently used flashlight arrangement is schematically shown in Fig. 108. The arrangement was used up to temperatures of 20 °K (hydrogen) [14]. Colour glass cylinders can be inserted between light source and Dewar vessel, if required, so that the most favourable spectral range for optical pumping can be filtered out. Materials other than quartz, e.g. corundum (A1203 colourless), CaF 2 , and others, are likewise requently used as light pipes. For continuous operation of laser resonators especially the arrangement developed by a research team under J O H N S O N [18, 106, 27, 26] at the suggestion of R . J . C O L L I N S has stood its test. The set-up is schematically shown in Fig. 109. A cylinder with elliptical cross-section serves as a reflector with the light-source (mercury arc lamp or xenon arc lamp) being arranged in one focal line and the laser resonator in the other. Undercooled liquid oxygen is directly flowing around the crystal. In order to avoid gas bubbles the liquid oxygen (boiling temperature at 760 Torr 90 °K) is undercooled by liquid nitrogen of 77 °K, thereby achieving a good heat contact between crystal and coolant, so that the temperature elevation of the crystal during operation should be kept to a minimum. A liquid (natrium nitrite solution) absorbing the short-wavelength light of the excitation light source below 0.4 ¡xm flows through the outer tube system. This arrangement was used to investigate CaW0 4 :Nd 3 + [18], C a F 2 : U 3 t [106], and CaF 2 :Dy 2 + [27], Of special importance for the operation (77 °K) of CaF 2 :Dy 2 + was the outer tube system, through which a solution of diluted K 2 Cr 2 0 7 solution (7 g per litre) flowed. With this liquid filter operation could be maintained for 30 min at 77 °K 27

physica

416

P . GÔBLICH. H . KAEKAS, G . KÔTITZ, a n d R . LEUMANN

—

LIQUID FILTER FOR ULTRAVIOLET AND INFRARED DROPPABLE HEAT SHIELD SHUTTER WATER

JACKET

DETECTOR

MASER BEAM

_ LI au ID OXYGEN FT 97 XENON FLASH TUBE ELLIPSE WATER COOLED

ELLIPSE CRYSTAL

MERCURY AH6 LAMP

SAMPLE

MICRO SWITCH

FOC/ OF ELLIPSE

DE WAR

LIQUID

F/LTER LIQU/D OXYGEN FLOW COOLED TO L/au/D N/TROGEN TEMPERATURE

F i g . 109. 4D i a g r a m of the experimental arrangement for continuous operation of laser resonators ( C a \ V 0 4 : X d s + , CaF„ rNd' -, C a F „ : D y 2 t ) (after JOHNSON, BOYD, NASSAU, and SODEN [18] and EOYD, COILINS, PORTO, YARIV, and HARGREAVES [106])

Spectroscopic Properties of Activated Laser Crystals (III)

417

•without a photochemical conversion of the divalent dysprosium into the trivalent one taking place. On the other hand the crystal was bleached within 10 min or so when no filter was used (colour change from green tint to colourless). For continuous operation of CaF 2 :Dy 2 + JOHNSON [ 2 6 ] did not require a circulation of the liquid gas. The resonator was embedded in a bath of liquid hydrogen (20 °K). Heat contact was excellent also during the operation of the laser, since no gas cushion formed between the resonator and the cooling bath. The liquid filter was deliberately dispensed with, since the radiation below 0.4 ¡xm considerably contributed to the optical pumping. An experimental arrangement (Fig. 110) differing from that described above was used by N E L S O N and B O Y L E [134] for the continuous excitation of ruby crystals. The laser resonator consists of a cylinder of ruby (Al 2 0 3 :Cr 3+ ) with a truncated cone of colourless corundum (A1203) at the one base end. The truncated cone serves as a light pipe for the pumping light. The pumping energy is axially fed to the activated cylinder. This type of excitation offers advantages especially for the three-level laser. For according to formula (47) it is favourable for achieving low pumping powers, when the concentration of the activators is small. At low

27«

418

P . GÖRLICH, H . KABRAS, G . KOTITZ, a n d R . LEHMANN

COMPACT (XENON ARC

PHOTOMULTI PU ER

Fig. 111. Continuous-wave laser arrangement with a chiseltype condenser (after KECK, REDMANN, WHITE, and BOWEN [162])

LASER CONDENSER

activator concentrations (1.6 X 10 18 Cr atoms per cm 3 ) the optical paths of the pumping light in the laser material must, however, be as large as possible. This is optimally achieved by the resonator geometry suggested by N E L S O N and B O Y L E . The resonator (cylinder: diameter 0.61 mm and length 11.5 mm; truncated cone: largest diameter 1.5 mm and length 10.5 mm) is provided with a transparent mirror on the outer circular face of the cone (external arrangement). The resonator is embedded in a bath of nitrogen. The laser oscillates at 77 °K with a wavelength of 0.6934 nm. The arc of a high-pressure mercury lamp is imaged into the truncated cone via two collector mirrors. For continuous laser operation (room temperature and water cooling, operating time more than one hour) of C a W 0 4 : N d 3 + ( 2 x 2 x 1 2 mm 3 ) K E C K , R E D M A N N , W H I T E , and B O W E N [162] used acommon type high-pressure xenon lamp. The optical set-up is shown in Fig. 111. Via an elliptical mirror the pumping light is directed to a condenser (straight-cone condenser or chisel-type condenser), which is directly cemented (Canada balsam) to the laser rod. With the straight-cone condenser the laser rod is arranged in the axis of the cone, with the chisel-type condenser at the prism edge. The condensers should, if possible, be made of a highly reflecting optical medium. Use was made of corundum (A1 2 0 3 without activator, n = 1.76). There is still a number of further arrangements in addition to those mentioned above. For continuous operation several elliptical mirrors are frequently mounted in cylindrical form such that all have one focal line in common, in which the laser resonator is arranged, while the light sources are positioned in the other focal lines, so that it is possible to excite a resonator by several light sources. 3 ) As an example of a resonator, whose transparent mirror is externally arranged, reference is made to Fig. 112 [163]. In this case excitation is effected with an elliptical reflector. One end face of the ruby rod is provided with a totally reflecting coating. The external transparent mirror (gold 3 % transparent) is placed in a distance of 5 to 15 m from the ruby rod. The required distance can be adjusted by means of the coated convex lens. Fig. 113 shows examples of the mirror arrangements of laser resonators [5], Resonators with small loss rates l/i„ or a large figure of merit Q must satisfy two conditions. First, there must be radiation beams which frequently traverse the resonator (20 to 100 times) without leaving it. Second, the condition

¡2 1 / d

must be fulfilled, so that diffraction losses are kept low (r, and r 2 radii of the mirrors, d separation of the mirrors). 3 ) Maser Optics (U.S.A.) developed four confocal elliptical mirrors with 40 kW flashlight lamps. At a total pumping power of 160 kW an output energy (ruby) of 1500 J is produced, which is sufficient for boring a 4 mm steel sheet with one pulse.

Spectroscopic Properties of Activated Laser Crystals (III) Fig. 112. Schematic path of rays for resonator lengths from 5 m (a) and up to 15 m (b): E elliptical reflector, B. rodtype flashlight lamp, It ruby rod, Sj nontransparcnt silver mirror on the ruby rod, S 2 weakly transparent concave mirror ( / = 370 cm), L convex lens ( / = 50 cm) (after GL'RS [163])

a

419

-^

In addition to these geometrical forms, resonators consisting of spheres, glass fibres, and cavities with the exciting light sources in the interior of the resonators have also been investigated. Stimulated emission was obtained by G A R R E T T , 2+ KAISER, and B O N D [ 1 6 4 ] on CaF 2 :Sm spheres of 1 to 2 mm diameter, which were cooled with liquid hydrogen. Investigations of dielectric waveguide modes in the visible spectrum were carried out by S N I T Z E R and O S T E R B E R G [ 1 6 5 ] on glass fibres. Ross [166] achieved stimulated emission on annular ruby crystals at 100 °K. He used an elliptical reflector with the axis of the ring in one focal line and the flashlight lamp in the other. For a toroid with lowest mode selection the ratio of the outer to the inner diameter must be equal to the refractive index, rn : rt = n. M,

M1

Mi

Mz

r H

PLANE

PARALLEL

Mi

Cy

Mz

C2

U

12

CONFOCAL

CONCENTRIC

Mz

Ci HIGH LOSS

C2

C7 HIGH LOSS

Fig. 113. Examples of mirror configurations for optical masers. All except the bottom two exhibit low-loss resonant modes (after YARIV and GORDON [5])

420

P . GÖHLICH, H . KABBAS, G . KOTITZ, a n d R . LEHMANN

TOP VIEW SEARCHLIGHT SIDE VIEW LIGHT SOURCE 355mm f/lOFRESNEL

LENS

PLANE MIRROR PLEXIGLAS

SEARCHLIGHT

MIRROR

DETONATOR -

Fig. 114. Optical arrangement for explosive light source laser pumping (after CROSBY and HONEY [168])

5J2 New

developments

in the field

of pumping

light

sources

New pumping light sources have recently been investigated. Instead of gas discharge lamps exploding wires were suggested for use as light sources. S T E V E N S O N , RETTTER, B B A S L A U , S O B O K I N , and L A N D O N [ 1 6 7 ] found optimum conditions for 100 to 500 [I.m flashes of light by exploding in air tungsten, tantalum, and molybdenum wires with diameters of 0.13 to 0.26 mm. The input energy was equal to or more than 3000 J . Wires exploding in a vacuum of 1 to 20 ¡I.m of Hg emitted a radiation which was almost comparable to that of a black body. However, their fraction of ultraviolet light is greater than that of a black body of comparable temperature. The spectral radiance of wires exploding in air is higher by 1 to 3 orders of magnitude than that of flashlight lamps. With wires exploding in vacuum the factor is equal to or greater than 8. Quartz tubes contain the wire. With the aid of these light sources ruby (300 °K) and CaF a :U 3 + (77 °K) were excited to stimulated emission. The laser oscillation of CaF 2 :U 3 + (2.61 ¡xm) began already 15 [i.s after the pumping pulse, whereas with the usual energetically weaker gas discharge flashlight lamps its onset could only be observed after 200 to 400 ¡jis. The excitation of laser resonators with exploding wires should be promising above all for those materials, whose spectral pumping region lies in the ultraviolet spectral range. The proposal to use the radiation of explosions for optical excitation was made by C B O S B Y and H O N E Y [ 1 6 8 ] (see Fig. 1 1 4 ) . With these light sources it should be possible to obtain a radiation in the shock wave, which corresponds to a temperature of 30000 °K of a black body.

421

Spectroscopic Properties of Activated Laser Crystals ( I I I ) .5.3 On modulation

and determination

of the input and output

power

For information on instrumental details of the modulation and determination of input and output power readers can only be referred to literature, although these fields, in particular the modulation, are of primary importance. Especially in view of the development of high power lasers (giant pulse technique) and with regard to special applications these fields of activity deserve preference in research and technology. In recent years communication engineering has become interested in the production of coherent light, so that also the optical modulation techniques have gained in importance. In most cases the linear electro-optical effect (POCKELS) of the crystals is utilized. Inertia phenomena and high dielectric losses make the Kerr substances less suitable. I t is further a great disadvantage that those substances showing Kerr effect have a quadratic electro-optical effect, so that the superposition of a steady field is necessary. Of special advantage are those substances having a linear electro-optical effect. The change of their dielectricity tensor is a linear function of the components of the applied field. An additional steady field need not be applied. Use of crystals is rather promising for the modulation of high frequencies. The linear electro-optical effect is possible in crystals having no centre of inversion, which is the case in 20 crystal classes. These also include crystals, which, when no electrical field is applied, are optically isotropic. For the most part, however, single crystals of the tetragonal system are used, which without an electrical field are optically uniaxial, e.g. ADP (ammonium dihydrogen phosphate) and K D P (potassium dihydrogen phosphate). The value of the upper modulation threshold of these crystals is taken to be about 10 12 Hz. A great number of works has been published on these themes, e.g. the modulation of optical masers with the aid of ADP [169] and K D P [229], piezoelectric modulation of optical masers with BaTi0 3 , ADP, K D P , Rochelle salt, quartz, CdS, and ZnO [170], electro-optical modulation with cubic crystals [171], modulation of light with the aid of ADP and K D P [172]. Use was made of electro-optical chutters for the stabilization of the ruby laser operation [173] as well as of ultrasonic diffraction shutters [174] and ultrasonic refraction shutters [175] for optical masers. The determination of the input and output energy is of great importance for the quantitative investigation of the processes. In proof of this we may refer to the numerous works [176, 177, 178, 179, 180, 181, 182, 183] dealing with the construction, testing, and calibration of calorimeters specially developed for laser radiation. 5.4 Testing

instruments

for absorption

and

fluorescence

Numerous commercial instruments are available for the investigation of absorption in the ultraviolet, visible, and infrared spectral regions. One of these instruments reaching particularly far into the ultraviolet region (165 nm) is a special version of the Beckman D K Spectrophotometer [184], The resolving power of these instruments is frequently not sufficient for optical maser investigation, so that several instruments made according to individual requirements have been used to carry out atom absorption spectroscopy [195]. Various versions of fluorescence instruments have been described, which were frequently developed from commercial instruments to meet individual require-

422

P . GORLICH, H . K A R R A S , G . K Ò T I T Z , a n d R . LEHMANN

ments. Such an instrument designed by us for crystal investigation [185] is schematically shown in Fig. 115 and 116. This instrument is suitable for exciting fluorescence in transmitted light and, in the case of strongly absorbing media, also in reflexion. Cryostats can likewise be used. For further instruments readers are referred to literature [186, 187, 188, 189, 190, 191]. 6. General Optical and Thermal Properties 6.1 Refractive

index, scattering,

and

strain

Regarding the optical media, which have already been known for decades and which are now used as host substances, reference is made to the relevant tabular works, as L A N D O L T - B Ò R N S T E I N , or to adequate monographs, e.g. A . S M A K U L A [ 1 9 2 ] . The refractive index of synthetic strontium molybdate single crystals was measured by LYLE

[193].

A highly unwanted phenomenon is the scattering of the light at colloids, bubbles, and other irregularities, which in the case of highly activated crystals can only with difficulty be avoided. Using C a F 2 : S m 2 + and C a F 2 : U 3 + crystals, K A I S E R and K E C K [194] investigated the magnitude of the loss the laser light is suffering at colloids. Polarization-optical and schlieren-optical methods are frequently employed for the analysis of large volume crystal defects, e.g. those caused by strains leading to optical birefringence. Especially the ruby crystals prepared after the Yerneuil method as well as the tungstate and CaF 2 crystals grown after the Czoehralski and melting zone techniques may have large defects of this kind. As readers are supposed to be well acquainted with the optical methods of investigation, a detailed description may be dispensed with. Applications are illustrated in many of the works cited, e.g. [210, 212, 218], 6.2 Nonlinear

optical

effects

A detailed description of wave propagation in nonlinear optical media is given by B L O E M B E R G E N [ 8 ] . Articles have been published by M I L L E R and S A V A G E [ 1 9 6 ] on the generation of the second harmonic and the mixing of CaW4 : Nd 3 and ruby emission radiation in piezoelectric crystals, by M I L L E R [ 1 9 7 ] on the generation of the second harmonic in quartz, by S L I K E R and B U R L A G E [ 1 9 8 ] on several dielectric and optical properties of K D 2 P 0 4 , by S O L I M I N I [ 1 9 9 ] on the mixing of light in nonlinear anisotropic mèdia, by A D A M S and S C H Ò F E R [ 2 0 0 ] on the continuous production of an optical frequency sum. An article on the structure of singularities and their motion in nonlinear electrodynamics was contributed by PELETMINSKY a n d YATSENKO

[201].

6.3 Thermal

properties

An extensive knowledge of the thermal properties, in particular of the thermal conductivity, is of great importance for the construction of high power lasers. The many applications of ruby are last not least based on its high thermal conductivity, which allows a rapid dissipation of the absorbed radiation energy not required for pumping. The thermal conductivity of ruby crystals grown after different techniques, and of CaW0 4 was measured by H O L L A N D [202] and compared with the thermal conductivity of copper. S L A C K determined the thermal conductivity of CaF 2 , MnF 2 , CoF 3 , and ZnF 2 crystals [203] and of MgO, A1 2 0 3 , MgAl 2 0 4 , FC 3 0 4 crystals in the temperature range between 3 ° K and 300 ° K [204]. The alkaline earth oxides were investigated by S U R P L I C E and J O N E S [205].

( a f t e r GÖRLICH, KARRAS, a n d KOTITZ [185])

424

P . GÖRLICH, H . K A K R A S , G . K O T I T Z , a n d R . L E H M A N N

7. Problems of Crystal Growth Synthetic crystals are an essential prerequisite for highly efficient optical products [206] such as spectroscopic apparatus, apochromatic corrected microobjectives, special precision photo-lenses, etc. But also the birefringent properties are utilized for the construction of optical compensators, polarizers, and modulators. Crystals have found a particularly large field of application in semiconductor engineering. The economic importance crystals gained in the semiconductor sector is expected to entail a large growth rate of investments and results in research and technology within the next few years. Nuclear engineering (scintillators), ultrasonic engineering, and piezoelectric oscillator elements have alike greatly benefited from the advances made in crystal growing. As a result of the numerous applications crystal growth became the object of methodic and systematic intensive research work, so that we dare say that crystal growth is on the point of developing into a theoretically founded science, while previously its results were predominantly gained empirically. Numerous monographs on crystal growth [192, 207, 208] may be cited in proof of this statement. An additional outcome of solid-state laser research was to give new impulses to the further development of crystal growth. The extreme demands to be made on the component "laser resonator" resulted in considerable improvements of known methods and procedures of crystal growing. Objects of this research work are the preparation of chemically very pure, optically homogeneous, and uniformly activated crystals. The material is completely available in the references cited and will only briefly be dealt with. Tungstate and molybdate crystals are of very great importance as hosts for neodymium. A vast bulk of literature deals with the growth and the properties of these crystals. Numerous articles by N A S S A U and co-workers [209, 210, 211, 212, 213, 214] are concerned with the growth of calcium tungstate crystals according to the Czochralski technique. V A N U I T B R T and co-workers [215] worked on the growth of lead and zinc molybdates. A systematic investigation of tungstate and molybdate systems was carried out by P R E Z I O S I , S O D E N , and V A N U I T E R T [216], This work deals with the growth of M n M o 0 4 crystals (M n = Ca, Sr, Ba) and Na 0 . 5 M™M I V O 4 crystals (M n I = La, Y, Gd; M I V = W, Mo). P E T E R S O N and B R I D E N B A U G H [217] used Nao.5Gdo.5WO4; Nao. 5 Pro. 5 W0 4 ; Na 0 5 Tb 0 . 5 WO 4 ; Na 0 5 Er 0 5 W0 4 crystals as host crystals. Na 0 5Gd0.5 - I Nd a .W0 4 crystals, of which a fraction (0.1 to 0.5) of gadolinium was replaced by neodynium, could be stimulated to pulsed laser operation at 77 °K. Of special importance were the coupling investigations Nd « R E (time-resolved excitation spectroscopy). An article on the growth of calcium tungstate crystals was contributed by G R A B M A I E R and Z A M I N E R [218]. The Bridgman-Stockbarger technique [ 2 1 9 ] , in which the crucible is lowered through a temperature field, has gained special importance for the growth of alkaline earth fluorides. This technique was used by L U D K E [ 2 2 0 ] , who produced large single crystals of more than 110 mm diameter and 100 mm length. The growth of activated CaF 2 crystals for the production of laser resonators requires additional working methods. The melting zone technique was employed by G U G G E N H E I M [ 2 2 1 ] to produce chemically very pure and at the same time activated calcium fluoride crystals. According to this method and the Czochralski technique CaF 2 crystals were grown

Spectroscopic Properties of Activated Laser Crystals (III)

425

by G R A B M A I E R and Z A M I N E R [ 2 1 8 ] . The Czochralski technique was likewise successfully used by N A S S A U [ 2 2 2 ] , A growth technique for the production of activated CaF 2 , SrF 2 , BaF 2 , CdF 2 , CeF 3 , PrF s , MgF2, and ZnF 2 crystals was elaborated by G U G G E N H E I M [ 1 2 4 ] , who described the preparation of the raw material and the growth in an atmosphere of hydrofluoric acid. Use was also made of Pt crucibles, which had been sealed. Articles on the growth of CdF 2 crystals were published by D . F. J O N E S and R. V. J O N E S [224], of MgF 2 by SCOTT [225], of Ca(Ni0 3 ) 2 by B A L L M A N , P O B T O , and Y A B I V [16] and of yttrium and rare earth borates by B A L L M A N [226].

8. Conclusion

The object of this review has been to bring together the scattered spectroscopic literature published in the field of laser crystals. It appeared advisable to deal briefly with the results of boundary fields, such as the optical phenomena and the growth of crystals. The general impression obtained by the rapid development of laser physics is very imposing. The gain of knowledge achieved within the last few years is quite astonishing. The growth rate of new publications is such that the coverage of all works is almost impossible for a small research team. We may conclude by stating that for some time stress has been laid less on the rapid examination of new substances but rather on the thorough investigation of individual phenomena. In our paper we have focused our attention on literature which is directly concerned with the laser effect or which is at least in some way related to this phenomenon. Reference has above all been made to papers published after 1958, although our contribution is far from being complete, especially as regards the literature published in 1964. Another deficiency our report shares with many others in the laser sector due to the vast bulk of material is the inadequate consideration of the earlier literature in the field of the atomic and ion spectra. However, these works have been of prime importance for the successful and rapid development of laser research. We feel therefore moved to mention at least a few names which, as it were, may stand for all those whose enumeration would go far beyond the scope of this article. G O B B E C H T (Yb 3 + , Er 3 + , Ho 3 + , Dy 3 + , Gd 3 + , Eu 3 + , Sm 3 + , Nd 3 + , Pr 3 + , Ce 3+ ) [ 2 3 0 ] - (Tu 3 + ) [ 2 3 2 ] - (Pr 3 + ) [ 2 4 9 ] , F B E E D and M E S I B O W (Yb 3 + ) [ 2 3 1 ] , M E E H A N and N U T T I N G ( T U 3 + , H O 3 + , Dy 3 + ) [ 2 3 3 ] , S E V E R I N (Er 3 + ) [ 2 3 4 ] - (Ho 3+ ) [ 2 3 5 ] , R O S A ( D V 3 + ) [ 2 3 6 ] , N U T T I N G and S P E D D I N G (Gd 3+ ) [ 2 3 7 ] , L A N G E ( E U 3 + ) [ 2 3 8 ] - (Pr 3+ ) [ 2 5 3 ] , S P E D D I N G , M O S S , and W A L L E R (Eu 3 + ) [ 2 3 9 ] , H E L L W E G E ( E U 3 + ) [ 2 4 0 ] , F B E E D and H A B W E L L (Sm 3 + ) [ 2 4 1 ] , S P E D DING and B E A B (Sm 3 + ) [ 2 4 2 ] , S P E D D I N G , H A M L I N , and N U T T I N G (Nd 3+ ) [ 2 4 3 ] , E W A L D (Nd 3+ ) [ 2 4 4 ] , M U K H E B J I E (Nd 3+ ) [ 2 4 5 ] , CHOW (Nd3+) [ 2 4 6 ] , K I N S E Y and K B U G E R (Nd 3+ ) [ 2 4 7 ] , B E N T O N and K I N S E Y (Nd 3+ ) [ 2 4 8 ] , S P E D D I N G , H O W E , and K E L L E B (Pr 3 + ) [ 2 5 0 ] , M E R Z (Pr 3 + ) [ 2 5 1 ] , L E H M A N N (Pr 3+ ) [ 2 5 2 ] , F B E E D (Ce 3+ ) [254] have considerably contributed to the explanation of the absorption spectra of the trivalent rare earths. This literature further includes numerous works on the emission analysis of the ions, which are suitable as laser activators. For space reasons we must likewise refrain from quoting these papers. The authors wish to express their sincere thanks to Dr. B I N D M A N N for his suggestions during the preparation of the English manuscript.

426

P . GÖRLICH, H . KAURAS, G . KOTITZ, a n d R . LEHMANN

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D . F . NELSON,

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Phys. Rev. Letters 9, 366 (1962).

T . J . SOLTYS,

and

R . O . CARLSON,

S p e c t r o s c o p i c P r o p e r t i e s of A c t i v a t e d L a s e r C r y s t a l s ( I I I )

427

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Spectroscopic Properties of Activated Laser Crystals (III)

429

[238] H. LANGE, Ann. Phys. (5) 32, 361 (1938). [ 2 3 9 ] P . H . SPEDDING, C. C. MOSS, a n d R . C. WALTER, J . c h e m . P h y s . 8, 9 0 8 ( 1 9 4 0 ) .

[240] K. H. HELLWEGE, Nachr. Ges. Wiss. Göttingen, math. phys. KL., 1947. [ 2 4 1 ] S. FREED a n d J . G . HARWELL, P r o c . A m s t e r d a m 3 5 , 9 7 9 ( 1 9 3 2 ) . [ 2 4 2 ] F . H . SPEDDING a n d R . S. BEAR, P h y s . R e v . 4 6 , 3 0 8 , 9 7 5 ( 1 9 3 4 ) . [ 2 4 3 ] F . H . SPEDDING, H . F . HAMLIN, a n d G. C: NUTTING, J . c h e m . P h y s . 5 , 1 9 1 9 ( 1 9 3 7 ) .

[244] H. EWALD, Ann. Phys. (5) 34, 209 (1939). [245] P. C. MUKHERJIE, Indian J . Phys. 11, 123 (1937). [246] Y. K. CHOW, Z. Phys. 124, 52 (1947). [ 2 4 7 ] E . L . K I N S E Y a n d R . W . KRUGER, P h y s . R e v . 6 2 , 8 2 (1942). [ 2 4 8 ] A . BENTON a n d E . L . K I N S E Y , P h y s . R e v . 75, 8 8 8 ( 1 9 4 9 ) .

[249] H. GOBRECHT, Phys. Z. 37, 549 (1936). [250] F. H. SPEDDING, J . P. HOWE, and W. H. KELLER, J . chem. Phys. 5, 410 (1937): [251] A. MERZ, Ann. Phys. (5) 28, 569 (1937). [ 2 5 2 ] P . LEHMANN, A n n . P h y s . (5) 3 4 , 3 8 9 (1939). [ 2 5 3 ] H . LANGE, A n n . P h y s . (5) 3 1 , 6 0 9 (1938).

[254] S. FREED, Phys. Rev. 38, 2122 (1931). (Received

November

5,1964)

Original

Papers

phys. stat. sol. 8, 431 (1965) Bulgarian

Academy of Sciences, Institute

of Physics,

Sofia

Study of the Effect of an Electric Field on Trap Filling in CdS Single Crystals by the Use of Thermally Stimulated Currents By

'

K . KIKOV a n d V . ZHELEV

Thermally stimulated currents (T.S.C.) in CdS are measured for electric fields of 10 t o 104 Y/cm and are found, in general, to change linearly. When t r a p filling is accomplished not by illumination, b u t with electrons injected from t h e cathode, t h e T. S. C.-maximum depends on the voltage, according t o t h e law Z m a x •—• Vn, where n varies from 3 to 6 for t h e various crystals. I t is concluded t h a t the fields at which measurements are made have n o significant effect on t r a p emptying. T.S.C. are also measured at various voltages a f t e r the initial application of a higher voltage, and these measurements show a strong increase in the dark current and a negative resistance. I t is, therefore, concluded t h a t the steep rise of the dark current is not due to t r a p emptying or to t h e complete filling of traps. The most probable cause for it is t h e injection of holes from t h e anode. Nous avons fait l'étude des courants thermostimulés en monocristaux de CdS sous champs électriques de 10 à 104 V/cm. E n général le courant varie suivant une loi linéaire. Lorsque les trappes sont remplies par une injection d'électrones par le cathode et non pas par illumination, le m a x i m u m du courant thermostimulé dépend de la tension appliquée suivant la loi 7 m a x ~ Un, où n varie de 3 à 6 pour les cristaux différents. A la base de ces résultats se f a i t la conclusion que les champs, sous lesquels nous avons mesuré ne provoquent pas le videment des trappes. De plus, les courants thermostimulés ont été mesurés sous des tensions diverses après qu'au cristal d'abord f u t appliquée une plus haute tension. E n ce cas le courant d'obscurité accroît vite et une resistance negative se manifeste. La conclusion qui suit est que l'accroissement rapide du courant d'obscurité n'est pas d û plus au videment des trappes qu'à leur emplissage complet. La cause la plus croyable c'est l'injection de trous p a r l'anode. 1. Introduction E l e c t r o l u m i n e s c e n c e a n d electrical b r e a k d o w n p h e n o m e n a i n CdS c r y s t a l s are o f t e n e x p l a i n e d b y e m p t y i n g of t r a p s d u e t o t h e h i g h field. B u t u p t o t h e p r e s e n t it s e e m s q u e s t i o n a b l e w e t h e r s u c h m e c h a n i s m really occurs. B Ô E B a n d K Ù M M E L [1, 2] u s e d t h e c u r v e s of t h e r m a l l y s t i m u l a t e d currents (T.S.C.) f o r a s t u d y of t h i s problem. T h e s e a u t h o r s h a v e s t a t e d t h a t t h e T.S.C. s t r o n g l y decrease if prior t o t h e m e a s u r e m e n t , for a certain period of t i m e , a h i g h v o l t a g e is applied t o t h e crystal. T h e y h a v e a t t r i b u t e d t h i s e f f e c t t o t h e electrical e x c i t a t i o n of e l e c t r o n s f r o m traps, d u e t o t h e h i g h v o l t a g e applied. I t will b e s h o w n t h a t t h e decrease of t h e T . S . C . can also be e x p l a i n e d f r o m a contrary p o i n t of v i e w , a d o p t e d i n [3 t o 5], according t o w h i c h e l e c t r o n s are i n j e c t e d f r o m t h e c a t h o d e i n t o t h e crystal. L e t a v o l t a g e TJ1 be applied t o t h e c r y s t a l w i t h a n electrode s e p a r a t i o n d. A n o h m i c c a t h o d e is a s s u m e d w h i c h is d e f i n e d t h e o r e t i c a l l y b y a n i n f i n i t e d e n s i t y of e l e c t r o n s a t t h e c o n t a c t . T h e d e n s i t y of electrons injected i n t o t h e crystal c a n b e d e t e r m i n e d 28

physica

432 from the theory of

K . KIROV a n d V . ZHELEV MOTT

and

and is

GUKNEY [6]

3« E^ n°

J_

- M x q d N *

' f

x

m

'

(

>

where x is the distance from the cathode, q the electron charge and e the dielectric constant. 1 ) The total space charge in the crystal is d n Q

=

J C

q

n Jo

d

x

3 =

- s ^U i- .

(2)

If we assume that a) the crystal is kept at low temperatures and b) the traps are already filled by a previous illumination, the total injected space charge will be captured mainly by deep-lying centres.2) Lowering the voltage from U1 to U alters the electric field distribution in the crystal which now depends on both voltages U and Uv

From the equations ~

dx

obtain E =

= — 4 7 t g w ° and f E dx = £

—T T+ — I( li — — 1 /— —I — I/ d

d

\

2

V A

Q

U we

(3)

with positive direction of the field from cathode to anode. The field is zero at a distance (4) from the cathode, as compared with the case without initial application of a higher voltage where this point lies at the cathode. If the crystal is homogeneously excited (for instance by homogeneous thermal release of electrons from traps (T.S.C.)) so that a electrons are created in 1 cm 3 per second, they move on both sides of .T0 in opposite directions towards the corresponding electrode. As a result the photoconductivity gain G= f

(5)

drops, (r is the lifetime of free electrons and tr the transit time for electrons from one electrode to the other.) A low current density is maintained in the circuit which is at the first moment equal to \2"1 i =

-^-ffl

q

d

(6)

This relation is obtained by assuming that all electrons reach the contact, i.e. capture is neglected. Due to the emptying of traps the space charge will gradually decrease and x0 shifts towards the cathode until a new equilibrium distribution of the charge, corresponding to the voltage U, is established. The current, however, does not reach that value which it would have at this temperature without ) Throughout this paper the CGS system is employed. ) If U1 is high enough, a complete filling of all centres with electrons occurs, and the crystal is homogeneously charged. This does not change these considerations. 1

2

Effect of an Electric Field on Trap Pilling in CdS

433

initial application of a higher voltage. In fact, until equilibrium of charges is established, the free electrons are extracted and their concentration is much lower than that which corresponds to an equilibrium between traps and conduction band. This leads to a more rapid emptying of traps. 2. Experimental High-resistivity, photosensitive crystals, grown by the French's technique were used for the measurements, with electrodes either on the same or on opposite crystal surfaces. The electrode distance was about 1 mm. Gold or indium electrodes were used, made by cathode sputtering or evaporation in high vacuum, respectively, after a treatment of the crystal surface in a gas discharge. Blocking contacts were obtained by evaporating gold without gas discharge treatment of the surface. The measurements were made in a special cryostat in which the crystal could be steeped in liquid nitrogen and then uniformly heated in a nitrogen atmosphere. This avoids difficulties arising with the cooling and control of the temperature of the crystal. The use of vacuum cryostats is unfavourable because of the low thermal conductivity of CdS. A heating rate of about 0.3°/s was usually employed. 3. Results Curves of theT.S.C. were measured under various conditions, where the voltage dependence was of the main interest. The standard measurements of theT.S.C. were carried out in the following manner: The crystals were illuminated at liquid nitrogen temperature with white light of high intensity, then they were kept in the dark at the same temperature for several minutes. Thereafter the voltage for the measurement of the T.S.C. was applied and after some minutes the heating was started. In general the shape of the curves of the T.S.C. was independent of voltage in the electric field range 10 to 104 V/cm. Fig. 1 shows the results of measurements, carried out with crystal No. 11 (thickness 7 X 10~3 cm and area 2 mm 2 ) with sputtered gold electrodes on the two surfaces ("sandwich" type). The curve of theT.S.C. of this crystal has only one maxmium at —78 °C. A trap energy of 0.31 eV below the conduction band, correponding to this maximum, is determined from the quasi-Fermi level at the maximum current [7]. With the area under the curve and the lifetime, a trap density of 2.5 x 1 0 u c m - 3 is obtained. Curve 1 in Fig. 1 indicates the dependence of the maximum of theT.S.C. on the voltage (the area under the curve of the T.S.C. is proportional to the current maximum). The traps have been filled by illumination at —196 °C. I t is evident that this dependence is linear for voltages ranging from 0.1 to 95 Y. With higher voltage the current becomes unstable and T.S.C. cannot be measured. For voltages higher than 2 to 3 Y initially a strong peak of the current is observed followed by a gradual decrease within several minutes. If it is assumed that electrons are injected from the cathode, the traps should be filled with these electrons. For a test of this hypothesis the crystal was illuminated at + 2 5 °C and kept in the dark at this temperature for 4 min. Thereafter the sample was cooled down to —196 °C within 10 to 15 min and the voltage applied. At low voltages, where no injection is expected, T.S.C. were not observed. At higher voltages T.S.C. can be measured which increase with voltage. Curve 2 shows the maximum value of theT.S.C. as a function of voltage. The slope of the 28*

434

K. Kirov and V. Zhelev Fig. 1. Experimental results of crystal No. 11: 1—Dependence of the maximum of the T.S.C. on the voltage, Im = / ( U); with traps filled by illumination at - 1 9 6 °C, 2 - Im=f(U) with traps filled by injected electrons, 3 - I-V dark curve Id = f(U) at - 1 9 6 °C with filled traps, 4 — Id — f(U) at - 1 9 6 °C with unfilled traps, 5 — im — f( U) with filled traps and previous application of 142 V at - 1 9 6 °C, 6 — Im = f(U) with unfilled traps and previous application of 142 V at - 1 9 6 °C

0.1

7

10

U(V)

100

curve is 5.7. The value of the T.S.C. depends strongly on the period between illumination and application of the voltage. The I — {/-characteristic of the stationary dark current at —196 °C with filled traps is shown by curve 3. I t exhibits a rapid rise for voltages above 70 V, and at 153 V a negative resistance is observed (not shown in the curve). Curve 4 denotes the I — [/-characteristic at —196 °C with unfilled traps (the crystal has been illuminated at + 2 5 °C and then cooled down to —196 °C). At higher voltages both curves merge. In order to study the effect of the voltage in the region of the steep rise of current on trap filling T.S.C. were measured at various voltages, after a voltage of 142 V has been applied to the crystal for 3 min at liquid nitrogen temperature ( I = 3.6 X 1 0 " 4 A). Curve 5 shows the dependence of the maximum of the T.S.C. on the voltage which has been chosen for the measurement of the T.S.C. The T.S.C. decrease with respect to the current measured without initial application of a high voltage. The decrease depends on the voltage which has been applied during the measurements of the T.S.C. The decrease becomes stronger with increasing voltages. Curve 6 indicates the same dependence as curve 5, but now the high voltage was applied to the crystal with empty traps. I n this case the trap filling is due to the application of the high voltage. If the steep rise of the dark current with voltage is due to a total filling of traps [5], curves 5 and 6 would merge. This is not the case. Nevertheless, curve 6 exhibits higher values than curve 2, which means that at high voltages trap filling is considerably high.

435

Effect of an Electric Field on Trap Pilling in CdS Fig. 2. Experimental results of crystal No 70: 1 — Dependence of the first maximum of the T.S.C. on the voltage, I m i = f(U), with traps filled by illumination at —196 °C, 2 — Dependence of the second maximum of the T.S.C. on the voltage, Im2 =f(U), with traps filled by illumination at —196 °C, 3 - 1 - 1 7 curve of the photocurrent at - 1 9 6 °C, 4 — I m i = f(U) with traps filled by injected electrons, with filled traps and previous 5 — I m i =f(U) application of 33 V, 6 — I m 2 = f ( U ) with filled trap and previous application of 33 V

l / J *

-in/u

10''

/J)

\

Fig. 2 shows the results of measurements made with crystal No. 70 (thickness 1.4 x 10" 3 cm and area 1 mm 2 ) with one gold -¡qand one indium electrode ("sandwich" type). The indium electrode was used as cathode. The curve of the T.S.C. of this crystal has a sharp and high peak at —128 °C and a second, lower one, at 70"' —26 °C. The two centres, cor0.7 10 responding to these maxima, U(vh lie 0.24 and 0.47 eV below the conduction band, the density of the centres at 0.24 eV is Nt = 5.3 X 1 0 1 3 c m - 3 . The dependence of both T.S.C. maxima on the voltage, which had been applied during the measurement of the T.S.C. is shown by curves 1 and 2 in Fig. 2. Up to 4 V the dependence is linear. Between 4 and 30 V the current is proportional to U0-7 and V0-9 for the first and the second maximum, respectively. To prove whether this deviation from linearity is due to trap emptying by the strong field the period between application of the voltage and starting of the heating was varied over a wide range. This, however, has no effect on the results obtained. The I — C-curve of the photocurrent at constant weak illumination and constant temperature was also measured. Curve 3 shows this relationship at —196 °C. The same deviation from linearity as mentioned above can be observed here. At room temperature the I — [/-characteristic of the photocurrent remains linear. From these data it can be concluded that the deviation from linearity is not due to emptying of traps. The dependence of the first T.S.C. maximum on the voltage, i.e. on trap filling with injected electrons, is indicated by curve 4. The crystal has been illuminated at —60 °C, kept in the dark for 3 min and cooled down to —196 °C. Then the voltage was applied. Up to 20 V the current is proportional to t/ 4 - 9 , whereas between 20 and 30 V it is proportional to U1-5. Curves 5 and 6 show the dependence of the first and second T.S.C. maximum, respectively. T.S.C. have been measured at various voltages after an initial application of 33 V for 3 min. This voltage corresponds to the negative resistance region (I = 4.2 x X 10" 4 A). I t is evident that with a voltage of 26 V, taken for the measurement of the T.S.C., the first maximum is lowered by about 25 percent, whereas with 2 V it is about 100-fold lower. The second maximum does not change at all at high voltages, but it is considerably lowered at low voltages.

/

/

436

K . KIROV a n d V . ZHELKV Fig. 3. Experimental results of crystal No 7 1 : A - I - U dark curve a t - 1 9 6 ° C with traps tilled by illumination at —196 °C, B — Dependence of the area S under the curve of the T.S.C., taken at 10 V, on the previously applied higher voltage. (On the /-^/-characteristic A-A' the cipher 5 must be added to the sixth point from the end of the curve)

A'

•V 10~-

I

Ji

10"

1

10'' B

i \ i \ \ i V \ \ \ \ \ i i i i i \ \ , \» \ \ \

10

103 to

\ *

\ >2 10l

w

1

A 1

w

0

10

20

30

U0 m-

50

Fig. 3 shows a series of measurements, carried out with crystal No. 71 (thickness 1.4 x 10~3 cm and area 1 mm 2 ). Curve A denotes the I - U characteristic in the dark at liquid nitrogen temperature. Before the measurement the crystal has been illuminated to fill the traps. (A currentlimiting resistance was in series with the crystal to avoid thermal destruction.) For voltages up to 50 V the current initially exhibits a strong peak and then gradually decreases. The lower branch of the curve was obtained with values of the dark current, measured 10 min after application of the voltage. For voltages higher than 50 V the current rises steeply and remains constant while the voltage at the crystal decreases.

The upper branch of curve A is formed from the values between points 2 and 3. Between points 3 and 4 the resistance is again positive, whereas at point 4 a region of negative resistance begins. At room temperature the I— U-cuvve has a similar character. Curve B , taken always at 10 V, denotes the area S under the curves of the T.S.C., plotted as a function of the initially applied higher voltage. The region 1 to 2 is obtained if the initially applied voltage is varied between 10 to 50 V, and corresponds to the lower branch of the I— U-ouvve. The region 2 to 4 to 5 of curve B represents the values of the T.S.C. with initially applied voltages, corresponding to the upper branch of the I — [/-characteristic. To show that no field emission of electrons from traps occurs (for field strengths used here) the following experiments were performed: A high voltage was first applied in the forward and then in the reverse direction to a crystal which had two gold contacts, an evaporated blocking one and an anti-blocking cathodesputtered one. Measurements made with crystal No. 64 (2 x 1 0 - 3 cm thick) have shown that the T.S.C. maximum measured in the forward direction at 4 V is lowered about three times if a voltage of 17 V has been initially applied to

Effect of an Electric Field on Trap Filling in CdS

437

the crystal in the same direction. When a voltage of 80 V is applied in the reverse direction, no change can be observed in the T.S.C. measured in the forward direction. 3 ) 4. Discussion Let us assume for simplicity t h a t the crystal has two types of centres in the band gap: recombination centres which can be partially or completely filled with electrons at equilibrium and trapping centres which are free from electrons at equilibrium. If the crystal is illuminated at low temperatures the traps are filled with electrons, whereas the holes are captured at the recombination centres or, otherwise speaking, the electrons are transferred from the recombination centres to the traps. If now a low voltage is applied to the crystal, so t h a t no space charge is injected, T.S.C. flow, as is well known, when the temperature is raised. If the cathode is ohmic and the voltage U high, electrons are injected from the cathode and a space charge limited current flows through the crystal. The injected electrons recombine with holes, captured by the recombination centres, and if the concentration of these holes is higher than t h a t of the injected electrons the current drops to zero (in the experiment a very weak current is maintained due to a quite insignificant emptying ef traps at this temperature). The negative space charge of a density q = q n 0 is captured by the recombination centres. The electric field distribution corresponding to this charge is

The gain for this case is n

T

T

=

/

dx

=

3 tu V '

(8)

¡TË

i.e. we obtain only 75 per cent of the gain without space charges. As the initial t r a p filling does not depend on the voltage, the area under the curve of the T.S.C. is proportional to U. This conclusions hold only if the lifetime x is independent of the voltage. As was shown, the injected electrons are captured by empty recombination centres and thus cause a decrease of their concentration, which results in an increase of r. This increase will be insignificant if the concentration of the injected electrons is much lower t h a n t h a t of the free recombination centres, which is believed to be fulfilled because, as shown for example in [8], the equilibrium concentration of the empty recombination centres is about 0.2 of their total concentration. From these considerations it can be concluded t h a t the T.S.C. must be proportional to the applied voltage. Our experiments confirme this relationship at least up to fields of the order of 10 4 V/cm. If t r a p emptying due to the high field would really occur, a decrease or even vanishing of the T.S.C. at high voltages must be observed. The slight deviation from the linear relationship between the current maximum and voltage in some crystals is probably not due to t r a p 3 ) Nevertheless, it proved necessary that no thermal emptying of traps occurs at the temperature at which the reverse voltage is applied, because, as already mentioned, the rate of trap emptying may be largely increased, due to the extraction of electrons from the conduction band.

438

K . KIROV a n d V . ZHELEV

emptying because this behaviour is also observed for the stationary photoconductivity. Some authors [9 to 13] have investigated the intial current peak. They called it "electrically stimulated current" and consider the peaks as caused by trap emptying and subsequent recombination of the excited electrons with captured holes. In our experiments, a strong current was also observed with the application of fields higher than 3 X 102 V/cm. I t decreased within some minutes. The total charge flowing through the crystal may, especially at higher voltages, largely exceed that of the T.S.C. As already mentioned, no decrease of the T.S.C. was observed at these voltages, which confirmes the assumption that the current, at these voltages, must be attributed to electrons injected from the cathode. The illumination of the crystal 4 ) at a temperature much higher than that of the T.S.C. maximum and keeping it in the dark for several minutes at this temperature should not result in a trap filling. In fact, when such a crystal was cooled down to —196 °C, the application of a low voltage and constant heating gives no T.S.C. At higher voltages electrons will be injected from an ohmic cathode and captured by traps and recombination centres. If the capture cross section of the traps for free electrons is much greater than that of the recombination centres, all electrons are captured by traps. The concentration of the electrons in the traps is equal to that of the injected electrons 5 ) and, as follows from (1), proportional to the voltage applied. The strength of the electric field is in that case given by (7) and the gain by (8). Upon heating the traps are gradually emptied and the electrons recombine with holes at the recombination centres. The gain and the trap filling are proportional to the voltage. Therefore we expect that the T.S.C. are proportional to the square of the voltage / ~ U2 .

(9)

If at a given voltage the traps are completely filled, the T.S.C. then depends linearly on the voltage. If in our experiments the traps were empty before application of the voltage the T.S.C. maximum increased more rapidly with voltage than according to (9), e.g. for crystal No. 11 (curve 2 in Fig. 1) the T.S.C. maximum was proportional to U5-7. The deviation from the square law dependence can be caused by various effects. One can suggest that only a part of the injected electrons is captured by traps whereas the rest is captured by deep-lying levels and the ratio between these two parts depends probably on the voltage. Another cause may be due to the contacts. If the cathode is not completely ohmic, less charge will be injected into the crystal than required by (2). Thus, at U = 50 V, the ratio of the charge calculated according to (2) to that obtained from the T.S.C. curve is 9.2, whereas at U = 120 V it is nearly unity. Crystal No. 70 was illuminated at —60 °C in order to fill only deep-lying centres so that the injected electrons are only captured by shallow traps. But also with this crystal no square law dependence is obtained. The initial part of curve 4 in Fig. 2 has a slope of 4.9 and the second part a slope of 1.5. As the concentration of these centres is found to be 5.3 X 10 13 c m - 3 complete filling should occur (with an ideal ohmic cathode) at 9.4 V, and at that voltage curves 1 and 4 should merge. The experimental data show that up to 30 V no complete filling of traps can be ) Illumination was necessary to achieve electrical neutrality in the crystal. ) This is not true for the immediate vicinity of the cathode because the concentration of the injected electrons is there much higher than the concentration of the traps. 4 5

Effect of an Electric Field on Trap Filling in CdS

439

observed, but the tendency of complete filling is noted as the slope of the curve approaches unity. In this crystal probably also less charge is injected than required by the theory with an ideal ohmic cathode. In spite of imperfections of the contacts, it is evident that electrons are injected and the traps are filled. The assumption that an electric field of strength 104 V/cm releases electrons from the traps could hardly explain the last mentioned results. Our experiments, in which T.S.C. were measured with low voltages after an initially applied high voltage show that the T.S.C. decrease. (This has been also found in [1] and [2].) This decrease can hardly be attributed to trap emptying because it occurs also at voltages much lower than those at which the dark current strongly increases (see for instance the regions 1 to 2 of curve B, Fig. 3). If the T.S.C. are measured without an initial application of a high voltage they depend, at these voltages, linearly on voltage. The hypothesis of a trap emptying by the high voltage implies a linear dependence of the T.S.C. on the low voltage taken for the measurements. It is evident from the experimental data that this relationship is super linear. The phenomenon described above can be better explained by the assumption that the decrease of the T.S.C. is due to the excess of space charges injected by the application of the high voltage. The space charge increases with increasing difference between the two voltages. Our experiments show that the decrease oftheT.S.C. is stronger in thinner crystals. In crystals with an electrode distance of the order of 1 mm hardly any effect can be observed. Such a behaviour was expected. The decrease of the T.S.C. increases with increasing ratio between the concentration of space charge and trap concentration. The space charge concentration varies within the crystal, but if the mean concentration is taken as a measure for the injected space charge we obtain from (2) =

3 6 U

,,m (10)

where U is the voltage previously applied. In crystals with one blocking and one anti-blocking contacts (e.g. crystal No. 64), up to fields of 4 x l 0 4 V/cm no field emission of electrons from traps occurs. But traps can also be emptied by impact ionization or heating of the crystal, which results in a strong increase of the current at high voltages. According to our opinion, however, the strong increase of the current at high voltages cannot be explained only with trap emptying because the excited electrons recombine and the current must decrease in time, whereas in the experiment the high current remains constant. Furthermore, if the initial strong current peak after application of the high voltage and the decrease of the T.S.C. measured at lower voltages would be due to trap emptying the decrease of the T.S.C. should depend strongly on the current measured with the high voltage. As shown in Fig. 3 such dependence could not be observed. On the other hand the steep rise of the current with voltage cannot be explained (as already mentioned) by complete filling of traps, which is evident from curve 6 in Fig. I. Moreover the voltage for a complete filling of traps in this crystal should be 1100 V which considerably exceeds the actually applied voltage. According to our opinion, the strong rise of current at high voltages, as well as the negative resistance, are best explained with the injection of electrons and holes

440

K. KIROV and V. ZHELEV : Effect of an Electric Field on Trap Tilling in CdS

from cathode and anode, respectively [14]. Adopting this assumption implies t h a t the electron concentration in the traps probably decreases due to recombination with free holes. But on the other hand, the empty traps will capture electrons from the conduction band until an equilibrium is established. I t is worth noting t h a t in our experiments I— U-characteristics with negative resistance were observed with electrodes which manifest themselves as hole- as well as electron-injecting contacts. Nevertheless, the contacts have a certain effect, because the I—[/-characteristics of a crystal are in general different for different polarities of the voltage. Negative resistances are usually accompanied by luminescence emission [15 t o 19]. Such phenomenon, however, was not observed visually. I t has been found [20] t h a t the T.S.C. decrease if a high a.c. voltage is applied to high-voltage electrodes, isolated from the crystal. I t is also established [21] t h a t in a crystal, treated in the same manner, the rise of photocurrent is strongly retarded. I n both papers the effect is explained by field emission of electrons from traps. In these experiments the strengh of the electric field in the crystal is probably higher than 105 V/cm. With such fields it is quite possible that a fieldemission of electrons from traps really occurs. References [1] K. W. BÖEB und U. KÜMMEL, Ann. Phys. (Germany) 14, 341 (1954). [ 2 ] K . W . BÖEK u n d U . KÜMMEL, A n n . P h y s . ( G e r m a n y ) 1 6 , 1 8 1 ( 1 9 5 5 ) .

[3] R. W. SMITH and A. ROSE, Phys. Rev. 97, 1531 (1955). [ 4 ] A . ROSE, P h y s . R e v . 9 7 , 1 5 3 8 ( 1 9 5 5 ) . [ 5 ] M . A . LAMPERT, P h y s . R e v . 1 0 3 , 1 6 4 8 ( 1 9 5 6 ) .

[6] N. P. MOTT and R. W. GURNEY, Electronic Processes in Ionic Crystals, Oxford University Press, New York 1940. [7] R. H. BUBE, Photoconductivity of Solids, John Wiley and Sons, Inc., New York, London 1960. [8] E. A. SaLKOV and M. K. SIIEINKMAX, Fiz. tverd. Tela 5, 397 (1963). [ 9 ] M . BORISOV, ST. KANEV, I . GUEORGUIEVA, a n d E . VATEVA, D o k l . B u l g . A k a d . N a u k 1 1 , 25 (1958). [ 1 0 ] M . BORISOV, ST. KANEV, I . GUEORGUIEVA, a n d E . VATEVA, A n n u a i U n i v . S o f i a ( p h y s . )

53, 72 (1958/1959). [ 1 1 ] M . BORISOV, ST. KANEV, E . VATEVA, a n d I . GTTEORGUIEVA, D o k l . B u l g . A k a d . N a u k 13, 23 (1960).

[12] M. BORISOV, M. MILASHEV, and V. MINKOVA, Izv. F I A N E B Bulg. Akad. Nauk 10, 5 (1962).

[13] ST. KANEV, Abhandl. Deutschen Akad. Wiss. Nr. 7 (1960). [ 1 4 ] M . A . LAMPERT, P h y s . R e v . 1 2 5 , 1 2 6 ( 1 9 6 2 ) .

[15] R. W. SMITH, Phys. Rev. 105, 900 (1957). [16] M. KIKUSHI and S. IIZIMA, J. Phys. Soc. Japan 14, 852 (1959). [17] G. A. MALOR and J. WOODS, Proc. Phys. Soc. 81, 1013 (1963). [ 1 8 ] C. W . LITTON a n d D . C. REYNOLDS, P h y s . R e v . 1 3 3 , A 5 3 6 ( 1 9 6 4 ) .

[19] P. N. KEATING, J. Phys. Chem. Solids 24, 1101 (1963). [ 2 0 ] K . W . BOER a n d U . KÜMMEL, Z . N a t u r f . 1 3 a , 6 9 8 ( 1 9 5 8 ) .

[21] ST. KANEV and M. K. SHEINKMAN, Fiz. tverd. Tela 3, 3539 (1961). (Received

September

28,

1964)

K . MEYER u n d F . POLLY :

Tribolumineszenzuntersuchungen

441

phys. stat. sol. 8, 441 (1965) Deutsche Akademie, der Wissenschaften zu Berlin, Forschungsgemeinschaft, Institut für Physikalische Chemie

Tribolumineszenzuntersuchungen an Alkalihalogeniden und Rohrzucker Von K. MEYEB und F.

POLLY

Die bisherigen Vorstellungen über Ursache und Mechanismus der Tribolumineszenz werden einer N a c h p r ü f u n g unterzogen. Durch Schaffung definierter Versuchsbedingungen mit physikalisch und kristallographisch klarer Fragestellung ergeben sich Zusammenhänge zwischen der Art des mechanischen Eingriffs und der Tribolumineszenz. Dabei werden die Lichtblitze synchron mit jedem einzelnen mechanischen Impuls beobachtet. Folgende F a k t o r e n werden in ihrem Einfluß auf die I n t e n s i t ä t der Tribolumineszenz quantitativ u n t e r s u c h t : Gasart, Gasdruck, Intensität der mechanischen Bearbeitung u n d Temperatur. Die Dauer der Lichtblitze wird bestimmt und liegt in der Größenordnung von 10 - 7 Sekunden. U n t e r den gegebenen Bedingungen ist eine eindeutige Zuordnung der Lichtblitze zu bestimmten morphologischen Veränderungen möglich. Unter Berücksichtigung der beobachteten Verformungsmechanismen sowie der E r k e n n t nisse über die Bewegung geladener Versetzungen in Ionenkristallen bei mechanischer Beanspruchung wird ein neuer Mechanismus f ü r die untersuchten Stoffgruppen diskutiert. Die bisherigen Vorstellungen, wonach als Ursache der Tribolumineszenz elektrische E n t ladungen zwischen Bruchflächen m i t elektrischen Potentialdifferenzen anzusehen sind, treffen nicht zu. Die Tribolumineszenz wird auf Entladungsprozesse ohne erkennbaren Einfluß von Bruchvorgängen zurückgeführt. Der Aufbau von Potentialdifferenzen ist bei rein plastischen Stoffverschiebungen möglich und wird auf geladene jogs u n d kinks zurückgeführt. The existing ideas on t h e mechanism and cause of triboluminescence are re-examined. Using physical and crystallographic arguments to treat t h e particular experimental conditions, t h e type of mechanical t r e a t m e n t can be related to t h e triboluminescence. The light flashes and the mechanical impulses are observed simultaneously. The effects of different gases, gas pressure, degree of mechanical t r e a t m e n t , and temper a t u r e on t h e triboluminescence are investigated. The length of t h e light flashes is found to be of t h e order of 10~7 s. Under given conditions t h e light flashes can be uniquely related t o particular morphological changes. T a k i n g into account the observed deformation mechanism and knowledge of the movem e n t of charged dislocations in ionic crystals due to mechanical t r e a t m e n t , a new mechanism is discussed for the materials investigated. The existing ideas attributing t h e triboluminescence t o electrical discharges between fracture planes with electrical potential differences are incorrect. The new mechanism attributes triboluminescence t o discharge processes which do n o t involve f r a c t u r e planes. The necessary potential differences arise f r o m pure plastic t r a n s p o r t of material due t o charged jogs and kinks.

1. Einleitung Lichtemission, die häufig beim Ritzen, Spalten oder Pressen von Kristallen auftritt und als Tribolumineszenz bezeichnet wird, ist an einer großen Zahl von Substanzen beobachtet worden. Es wurden jedoch bis jetzt keine bedeutenden

442

K. MEYER und F.

POLLY

Fortschritte zum Verständnis dieses Phänomens gemacht. Insbesondere liegt eine große Zahl einander widersprechender Beobachtungen vor. Die Gründe dafür liegen in erster Linie in der Schwierigkeit, exakte Meßmethoden für die Registrierung der sehr kurzen und in ihrer Intensität sehr schwachen Lichtblitze zu entwickeln und in der Wahl unkontrollierbarer Bearbeitungsveifahren, durch die nur Leuchterscheinungen als Summe zahlreicher, zeitlich und örtlich dicht überlagerter Einzelprozesse beobachtbar sind und die keine eindeutigen Rückschlüsse auf die Entstehungsursachen und die Beeinflussung durch verschiedene äußere Parameter zulassen. Durch Schaffung definierter experimenteller Bedingungen bei der Bearbeitung der Kristalle und bei der Registrierung der Lichtblitze wurden Versuchsergebnisse erhalten, die das Phänomen der Tribolumineszenz bei Alkalihalogeniden und Rohrzucker als elektrische Gasentladung in der umgebenden Atmosphäre des bearbeiteten Kristalls zu beschreiben gestatten. 2. Experimenteller Teil Für die Erzeugung definierter mechanischer Eingriffe wurde eir.e Eindruckvorrichtung innerhalb eines evakuierbaren Rezipienten mit Simmerring-Durchführungen aufgebaut, so daß die Bewegung der Kristalle von außen möglich ist. Daher erfolgt jeder Einschlag stets auf einer unbearbeiteten Stelle des Kristalls ohne Änderung der Versuchsbedingungen. Die Eindruckvorrichtung selbst besteht aus einem mit verschiedenen Gewichten belastbaren Hebelarm mit einer auswechselbaren Korundnadel, die aus 10 mm Fallhöhe auf die Probe schlägt. Damit ergeben sich reproduzierbare mechanische Eingriffe mit einstellbaren Energien von 0,4 bis 25 mmp, entsprechend 2 • 10 13 bis 150 • 10 13 eV. Mittels eines Heizbleches kann der Kristall auf 300 °C erhitzt werden. Unter diesen Bedingungen ist die Wahl sehr verschiedenartiger Arbeitsbedingungen gegeben: leichte Wiederholbarkeit und Summierung der Einzelvorgänge, freie Wahl der Proben und der Werkzeugnadeln und beliebiger Paarungen, leichte Bestimmbarkeit der Umgebung, z. B . Vakuum, Gasatmosphäre und Gasdruck, Einfluß der Temperatur sowie die Rezipientmit

Photomultiplier

Impulsverst.

Verzögerungs-

Fig. 1. Schematische Darstellung der Versuchsanordnung zur Messung der Tribolumineszenz

Tribolumineszenzuntersuehungen an Alkalihalogeniden und Rohrzucker

443

mikroskopische Erfassung morphologischer Veränderungen von Probe und Nadel bei gleichzeitiger und eindeutiger Zuordnung von Lichtblitz und mechanischem Eingriff. Die Registrierung der Lichtblitze erfolgte mit einem Multiplier, Verstärker und Oszilloskop. Der schematische Aufbau der Versuchsanordnung ist in Fig. 1 wiedergegeben. Die auf dem Oszilloskop sichtbaren Licht blitze wurden mit einer Kamera aufgenommen, die mit dem Nockenrad NR 2 über einen Schaltkontakt mit elektromagnetischem Auslöser gekoppelt ist. Die Auswertung der einzelnen Lichtblitze nach ihrer Intensität erfolgte durch Ausmessen der Amplitude. Als relative Maßeinheit der Tribolumineszenz-Intensität diente daher die elektrische Spannung am Ausgang des Vorverstärkers, wobei 1 V einem Skalenteil entspricht und in den folgenden Figuren als Einheit auf der Ordinate aufgetragen wurde. Unter vereinfachenden Annahmen läßt sich aus den Herstellerdaten des Photomultipliers die Photonenausbeute grob abschätzen: Ein Skalenteil entspricht ungefähr 2 • 103 Photonen. Die zeitliche Auflösung der einzelnen Lichtblitze wird durch die Zeitkonstante des Verstärkers begrenzt, die bei 5 • 10~7 s liegt. Daher werden Lichtimpulse mit kurzer Dauer durch die Zeitkonstante der elektronischen Schaltung verfälscht und nur längere maßstabgetreu wiedergegeben. Die in den folgenden Kurven eingetragenen Punkte stellen jeweils Mittelwerte einer großen Zahl von Einzelmessungen dar. 3. Experimentelle Ergebnisse Einfluß verschiedener Faktoren auf Intensität und Dauer der Lichtblitze 3.1

Gasdruck

Untersuchungen über den Einfluß des Gasdruckes von Luft auf die Intensität der Tribolumineszenz für verschiedene Alkalihalogenide und Rohrzucker ergaben, daß die Lichtemission bei etwa 1 Torr einsetzt, in Richtung höherer Drucke steil ansteigt, ein Maximum erreicht und allmählich wieder abfällt (Fig. 2). Die

Fig. 2. Abhängigkeit der Tribolumineszenz verschiedener Alkalihalogenide und des Ilohrzuckers vom Gasdruck (Luft)

444

K . MEYER u n d F . POLLY

Gasdruck ( Torr) l f i g . 3. Abhängigkeit der Tribolumineszenz des L i F vom Gasdruck für verschiedene Gase

Messungen wurden bei 10" 5 Torr begonnen. Die dargestellte Druckabhängigkeit änderte sich für die untersuchten Substanzgruppen grundsätzlich nicht mit der Temperatur, der Intensität der mechanischen Bearbeitung und der Gasart.

3.2 Gasart Der Einfluß verschiedener Gase auf die Intensität wurde mit L u f t , C 0 2 , Ar und H e untersucht. Grundsätzlich wurde die gleiche Druckabhängigkeit bei Veränderungen in der Intensität gemessen (Fig. 3). B e i den Edelgasen wurde eine schwache Verschiebung der Maxima in Richtung höherer Drucke bei gleichzeitiger schwacher Verbreiterung beobachtet. Die K u r v e n der Fig. 3 wurden mit derselben Nadel erhalten. Außerdem verändern sich die Intensität der Lichtblitze und die Schärfe des Maximums mit der Geometrie der Nadeln. B e i gleicher Belastung zeigen spitze Nadeln größere Intensitäten als abgerundete. 3.3 Intensität der mechanischen Bearbeitung U m die Abhängigkeit der Tribolumineszenz von der zugeführten mechanischen Energie zu untersuchen, wurde dieselbe Nadel mit verschiedenen Gewichten belastet (Fig. 4 und 5). Die K u r v e n zeigen, daß mit kleinen Belastungen die Intensität stetig abnimmt, ohne daß ein Sprung im Intensitätsabfall erkennbar wird. D a sich die Druckabhängigkeit mit der mechanischen Bearbeitung nicht ändert und das Maximum bei ungefähr 10 Torr liegt, wurden weitere Untersuchungen über den Einfluß der mechanischen Bearbeitung bei 10 Torr durchgeführt. Fig. 6 zeigt die Abhängigkeit der Tribolumineszenz von der zugeführten mechanischen Energie für KCl, L i F und Rohrzucker. Diese Abhängigkeit genügt der Gleichung E = E0e k' n , wobei E die kinetische Energie, n die Zahl der emittierten Photonen bedeutet und 1 ¡k dem Anstieg der Geraden entspricht und ein Maß für die Lumineszenzausbeute

Tribolumineszenzuntersuchungen an Alkalihalogeniden und Rohrzucker

Gasdruck (Torr)

445

-

Fig. 4. Abhängigkeit der Tribolumineszenz des L i F vom Gasdruck (Luft) für verschiedene Belastungen

darstellt. Aus der Gleichung geht weiterhin hervor, daß die Tribolumineszenz erst oberhalb einer Energieschwelle E0 einsetzt und dann logarithmisch mit der zugeführten mechanischen Energie ansteigt. Als Konstanten wurden für die verschiedenen Substanzen folgende Werte bestimmt: Tabelle 1 Substanz KCl LiF Rohrzucker

E 0 (eV) 4,8 21 22

10 13 10 13 10 13

1/k (Photonen) 16,8 16,8 8

103 103 10 3

446

K . MEYER und F.

POLLY

Fig. 6. Abhängigkeit der Tribolumineszenz von der zugeführten kinetischen Energie für KCl, L i F und Rohrzucker; p y .. =* 10 Torr

70* 10'' mech. Energie (eV)3.4 Verformungsstrukturen und ihre Abhängigkeit von der mechanischen Bearbeitung

Ein wesentlicher Gesichtspunkt für die Deutung der Tribolumineszenz schien uns die gleichzeitige Beobachtung morphologischer Veränderungen zu sein. Dieser Faktor wurde bisher völlig vernachlässigt und erst kürzlich von B E L J A J E W et al. [3] berücksichtigt. Daher wurden ausführliche Untersuchungen an LiF und KCl gemacht, die sich wesentlich in ihren plastischen Eigenschaften unterscheiden. L i F zeigt bei Normaltemperatur starke Neigung zur Rißbildung, während KCl ausgeprägte plastische Eigenschaften aufweist. Zur Sichtbarmachung der beim Stoßvorgang erzeugten Versetzungen außerhalb der unmittelbaren Eindruckstelle wurden die Kristalle anschließend geätzt, LiF mit einer Fe-Ionen enthaltenden Eisessig-Flußsäure-Lösung [5] und KCl mit Ba-haltiger Propionsäure [6]. Die Fig. 7 und 8a zeigen den mit einer Korundnadel erzeugten Eindruck in LiF mit dazugehörigem Tribolumineszenz-Impuls. Die systematische Auswertung der bei verschiedenen Belastungen erzeugten Eindrücke zeigt, daß bei LiF bis zu kleinsten Belastungen herab Risse auftreten, die in [110]-Richtung verlaufen und seltener in [100]-Richtung. Fig. 8 gibt eine Auswahl von Eindrücken wieder, die bei verschiedenen Belastungen erzeugt wurden. Die zugehörigen Tribolumineszenz-Kurven gehen aus Fig. 4 hervor. Bei den Belastungen 0,18 p und 0,091 p wurden keine meßbaren Lichtausbeuten beobachtet. Wesentlich andere Ergebnisse wurden hinsichtlich der morphologischen Veränderungen beim KCl beobachtet. Die Auswertung der Eindrücke bei verschie-

Fig. 7. Zur Fig. 8 a gehöriger Tribolumincszenz-Impuls. Ordinate: 1 Einheit (ca. 12,5 mm) = 4 Skt. (Intensität der T L ) ; Abszisse: 1 Einheit S 5 • 1 0 " ' s (Dauer der T L )

Tribolumineszenzuntersuchungen an Alkalihalogeniden und Rohrzucker

Stimm

0,1 mm

A

Qfimm

0,1mm

fttmm Fig. 8. Eindrücke auf einer LiF-Oberfläche mit verschiedenen Belastungen, geätzt. a : 2 , 7 p ; c: 0,7 p; d : 0,35p; e: 0,18 p; f : 0,091 p

29

physica

b:l,4p;

447

448

K . MEYER und F. POLLY Fig. 9. Eindrücke auf einer KCl-Oberfläche mit verschiedenen Belastungen, a: 0,18 p: b: 0,056 p

denen Belastungen — die entsprechenden Tribolumineszenz-Kurven sind in Fig. 5 wiedergegeben — ergab Rißbildungen nur oberhalb von 0,7 p. Bei geringeren Belastungen wurden ausschließlich plastische Deformationen beobachtet, die sich beim geätzten Kristall im Auftreten von sogenannten Rosetten äußern und die durch Bewegung von Schrauben- und Stufenversetzungen in den (llO)-Gleitebenen zustande kommen (Fig. 9). Zusammenfassend ergibt sich, daß beim LiF Rißbildungen im gesamten Belastungsbereich auftraten und Lichtblitze nur oberhalb 0,35 p beobachtet wurden. Beim KCl traten Risse nur oberhalb 2,7 p auf, unterhalb dieser Belastung wurden ausschließlich plastische Stoffverschiebungen beobachtet. Vergleichbare Belastungen ergeben beim KCl größere Intensitäten als beim LiF.

50/um

Um die gegenseitige Beeinflussung verschiedener Eindrücke auf die Tribolumineszenz zu untersuchen, wurden mehrere Einschläge auf derselben Stelle SQjum ! des Kristalls gemacht, d.h., jeder Stoß erfolgte an einer Stelle, an der das Material durch den vorhergehenden Eindruck schon weitgehend zerstört wurde. Bei dieser Art der Bearbeitung wird die ursprüngliche Größe und Form der ersten Trefferstelle durch die nachfolgenden Eindrücke nur unwesentlich beeinflußt. Insbesondere wurde nur eine geringfügige Änderung der Rißlängen beobachtet. Für K J und LiF wurde festgestellt, daß bei wiederholter mechanischer Bearbeitung desselben Eindruckes im Rahmen der normalen Schwankungen keine systematische Änderung in der Intensität auftritt (Fig. 10).

15. 20. Einschlag —

Fig. 10. Einfluß einer wiederholten mechanischen Bearbeitung desselben Eindruckes auf die Tribolumineszenz beim KJ

Tribolumineszenzuntersuchungen an Alkalihalogeniden und Rohrzucker

Gasdruck ( TorrJ

449

-

Fig. 11. Abhängigkeit der Tribolumineszenz des LiF vom Gasdruck (Luit) bei verschiedenen Temperaturen

3.5

Temperatur

Die Abhängigkeit der Tribolumineszenz von der Temperatur wird für LiF durch die Fig. 11 wiedergegeben. Sie zeigt, daß die Tribolumineszenz bei gegebenem Druck mit steigender Temperatur abnimmt, die Gasdruckabhängigkeit im untersuchten Temperaturintervall aber erhalten bleibt. Für die weitere Untersuchung des Temperatureinflusses wurde die Tribolumineszenz bei einem Gasdruck von 10 Torr gemessen (Fig. 12). Die Darstellung zeigt, daß sich die Intensität bis etwa 110 °C nicht ändert und danach rasch abfällt. Wiederholte Messungen an verschiedenen Kristallplatten desselben Kristalls zeigten weitgehende Übereinstimmung (Fig. 12). Wurden jedoch LiF-Kristalle verschiedener Herkunft mit unterschiedlichem Reinheitsgrad verwendet, ergaben sich starke Verschiebungen des Intensitätsabfalls in Richtung höherer und tieferer Temperaturen. In einzelnen Fällen wurde sogar ein Minimum vor dem Abfall bei höherer Temperatur beobachtet. Diese Unterschiede werden auf die Anwesenheit von Fremdionen, insbesondere der höherwertigen Kationen, zurückgeführt und sind Gegenstand

Fig. 12. Abhängigkeit der Tribolumineszenz des LiF von der Temperatur; PLuft = 1 0 T o r r 29*

100

120

Temperatur (%}

M

-

Fig. 13. Tribolumineszenz-Impuls bei der Bearbeitung von KCl; pLuf^ = 2 Torr. Ordinate: 1 Einheit Ä 2 Skt. (Intensität der TL); Abszisse: 1 Einheit — 5 • 10"' s (Dauer der TL)

weiterer Untersuchungen. Tribolumineszenz-Unterschiede wurden auch bei anderen Alkalihalogeniden in Abhängigkeit von der Fremdionenkonzentration gefunden. 3.6 Der zeitliche

Verlauf

der

Tribolumineszenz

Wie bereits im experimentellen Teil angedeutet, kann der zeitliche Verlauf der kurzen Lichtblitze durch die Zeitkonstante der elektronischen Schaltung beeinflußt u n d m u ß bei der Diskussion der Leuchtdauer beachtet werden. F ü r die Bestimmung der Intensität blieb der schaltungsbedingte exponentielle Abfall (z. B. in Fig. 7) der Lichtblitze unberücksichtigt. Bei der genauen Bestimmung eines Tribolumineszenz-Impulses geht die Anstiegszeit des Impulsverstärkers ein. Daraus ergeben sich Werte f ü r die Dauer eines Lichtblitzes von ca. 5 • 10" 8 s, die in ausgezeichneter Übereinstimmung mit einem kürzlich von B E L J A J E W et al. [3] angegebenen Wert von 5 bis 7 • 10~8 s sind. Die Dauer der Lichtblitze bei der Bearbeitung von Alkalihalogeniden u n d Rohrzucker liegt in der gleichen Größenordnung. Die Emissionsdauer wird vom Gasdruck u n d von der Gasart beeinflußt. Bei niedrigen Drucken wird die Dauer der Lichtblitze vergrößert, so daß die Zeitkonstante der Schaltung vernachlässigt werden kann (Fig. 13). Die Lichtemission dauert in diesem Fall etwa 2 bis 4 • 10~6 s. Durch Verwendung der Edelgase Ar u n d H e anstelle von L u f t wird die Leuchtdauer ebenfalls erhöht. Die Emissionsdauer ist in allen Fällen von der K o n t a k t d a u e r des mechanischen Impulses unabhängig. 4. Theoretischer Teil 4.1 Bisherige

Vorstellungen

über den Mechanismus

der

Tribolumineszenz

Als Ursache der Tribolumineszenz wurden bisher folgende Mechanismen angegeben: Chemilumineszenz [9 bis 14], direkte mechanische Anregung [12, 13, 16 bis 18], Elektro- u n d Kathodolumineszenz [26, 27], elektrischer Festkörperdurchschlag [19 bis 21], direkte oder indirekte Anregung durch Gasentladung [13, 17, 18, 22 bis 25] sowie verschiedene andere [7, 8, 15]. Die Dauer eines einzelnen Lichtblitzes versuchten erstmals S T R A N S K I et al. [1,2] zu bestimmen, allerdings mit 10"3 bis 10 4 s zu lang. Genaue Angaben auf Grund verfeinerter Untersuchungsmethoden machten inzwischen B E L J A J E W et al. [3] mit 5 bis 7 • 10" 8 s. Auch der Einfluß des Druckes der umgebenden Gasatmosphäre wird unterschiedlich eingeschätzt [2, 8, 18, 25, 28],

Tribolumineszenzuntersuchungen an Alkalihalogeniden und Rohrzucker

451

Weitgehende Übereinstimmung besteht in folgenden P u n k t e n : 1. Mit steigender Temperatur nimmt die Tribolumineszenz ab bzw. verschwindet vollständig [12, 15, 18, 23], 2. Mit abnehmender Korngröße n i m m t die Tribolumineszenz ab bzw. verschwindet unterhalb einer minimalen Korngröße [2, 15, 24, 30, 31]. 3. Die Tribolumineszenz ist mit dem Auftreten von Bruch verbunden [13, 24, 28, 31]. 4.2 Die Erzeugung

elektrischer

Ladungen

bei der mechanischen

Bearbeitung

Die Untersuchungen ergaben, daß die Tribolumineszenz bei den Alkalihalogeniden nicht an das Auftreten von Brüchen gebunden u n d auch bei rein plastischen StoffVerschiebungen möglich ist. Dies zeigten besonders die Beobachtungen an den plastischen KCl-Kristallen. Versuche über die Belastungsabhängigkeit zeigen weiterhin, daß ein Sprung im Tribolumineszenz-Veihalten beim t i b e r g a r g von Rißbildungen zu rein plastischen Deformationen nicht a u f t r i t t . Darüber hinaus ergab die Auswertung von etwa 350 Aufnahmen von Eindrücken mit den dazugehörigen Tribolumineszenz-Kurven keinen Zusammenhang zwischen der Intensität u n d den beim Eindruck erzeugten Rissen. Somit ergibt sich die Frage nach der H e r k u n f t elektrischer Ladungen als Folge der mechanischen Bearbeitung von Kristallen. Die von S T R A N S K I et al. [1] u n d LONGCHAMBON [24] vertretene Meinung, die mit der Bruchbildung in Alkalihalogeniden erzwungene Ladungstrennung für den Leuchtvorgang verantwortlich zu machen, steht im Widerspruch zu den experimentellen Beobachtungen. Betrachtet m a n verschiedene einfach indizierte Ebenen in der NaCl-Struktur, so ist ein Überschuß von positiven oder negativen Ladungen u n d damit die E n t stehung von Potentialdifferenzen auf korrespondierenden Spaltflächen nur bei ( l l l ) - E b e n e n möglich. Die Trennung von (100)- u n d (llO)-Ebenen f ü h r t nicht zum Aufbau von Potentialdifferenzen. Auf Grund gittertheoretischer Betrachtungen ist es jedoch unwahrscheinlich, daß gerade Brüche nach (111) auftreten, da die Oberflächenenergie z. B. von NaCl für (111) wesentlich höher als f ü r (100) bzw. (110) ist: ff(ioo) = 150 erg/cm 2 , ff(no) = 375 erg/cm 2 , ff(in) = 872 erg/cm 2 [32], Die erschwerte Bildung von (lll)-Rissen wird auch experimentell bestätigt [33]. Von M E Y E R et al. [4] wurden bei detaillierten Untersuchungen über die räumliche Verteilung von Rissen bei der Stoßbearbeitung von NaCl durch sukzessives Abtragen u n d Ätzen keine Hinweise f ü r das Auftreten von (111 )-Brüchen erhalten. Eine andere Möglichkeit der Trennung von Ladungen in Ionenkristallen besteht in der Bewegung von Versetzungen, die einen Sprung aufweisen und zu einem Überschuß positiver bzw. negativer Ladungen führen, worauf zuerst S E I T Z [34] aufmerksam machte. I n den letzten J a h r e n wurden dazu zahlreiche experimentelle Ergebnisse bekannt [36 bis 41], u. a. auch Ladungseffekte bei der inhomogenen Deformation durch Eindrücken einer Stahl- bzw. Diamantspitze in NaCl [36, 37], Obwohl hinsichtlich Vorzeichen u n d Betrag der durch mechanische Beanspruchung erzeugten Ladungseffekte Meinungsverschiedenheiten bestehen, sind durch Bewegung von Versetzungen u n d damit bei rein plastischer Verformung grundsätzlich Ladungstrennungen möglich. Auch in homöopolaren Kristallen können StufenverSetzungen elektrische Ladungen trennen [35], was bei der mechanischen Bearbeitung von Rohrzucker kristallen in Betracht gezogen werden muß. Es lag daher nahe, Tribolumineszenzerscheinungen bei Alkalihalogeniden auf die Entstehung von Potentialdifferenzen durch Bewegung geladener Versetzungen zurückzuführen, worauf bereits in [42] erstmals hingewiesen wurde. Inzwischen

452

K . MEYER u n d F . POLLY Fig. 14. Nachweis v o n Ladungen auf einer bearbeiteten K J - O b e r f l ä c h e durch B e s t a u b u n g m i t Mennige u n d Schwefel. Obere R e i h e : Bestäub u n g im H o c h v a k u u m ; bevorzugte Abscheidung v o n Mennigeteilchen im Z e n t r u m der E i n d r ü c k e . Untere Reihe: B e s t ä u b u n g bei einem Druck von 5 Torr; keine bevorzugte Abscheidung von Teilchen u n d d a m i t keine elektrische A u f l a d u n g

Fig. 15. Nachweis v o n Ladungen auf einer bearbeiteten K J - O b e r f l ä c h e durch B e s t ä u b u n g m i t Mennige u n d Schwefel. Keine bevorzugte Abscheidung von Teilchen a n Rissen, die durch Pfeile m a r k i e r t sind

wurden auch von BELjAJEwet al. [3] elektrisch geladene Versetzungen mit der Tribolumineszenz in Verbindung gebracht, jedoch ohne nähere Ausführungen u n d Begründungen. Allerdings messen die Autoren auch den Brüchen besondere Bedeutung bei. Der Ladungsnachweis unter den gegebenen Bearbeitungsbedingungen erfolgte durch Bestäubung der Eindrücke im Hochvakuum mit einem Gemisch von Pb 3 0 4 , Schwefel u n d Lycopodium [43] unmittelbar nach dem Eindruck. Fig. 14 (obere Reihe) zeigt bestäubte Trefferstellen auf einer KJ-Oberfläche. Die roten Mennigeteilchen haben sich bevorzugt im Zentrum angelagert u n d die gelben Schwefelteilchen am Rande. Die Eindrücke sind also gegenüber der Umgebung negativ geladen. Erfolgt die Bestäubung bei Gasdrucken oberhalb 5 Torr, ist keine elektrische Aufladung der Eindrücke festzustellen (untere Reihe der Fig. 14). Das ist aber gerade der Druckbereich, in dem die Tribolumineszenz einsetzt u n d zu einem Ausgleich der elektrischen Ladungen f ü h r t . Die Bestäubung von LiF-Eindrücken mit ihren starken Rißbildungen in der Umgebung ergaben ebenfalls nur Ladungsanhäufungen im plastisch verformten Zentrum des Einschlages, ohne daß bevorzugte Ablagerung von Pb 3 0 4 - oder S-Teilchen erfolgte. I n der Fig. 15 sind die Risse durch Pfeile markiert. I m Gegensatz zu K J konzentrieren sich die S-Teilchen beim LiF im Zentrum, so daß eine umgekehrte Aufladung vorlag. Die Aufladung der Eindrücke n a h m mit steigender Belastung zu.

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Versuche m i t L i F u n d KCl ergaben, daß die Tribolumineszenz erst o b e r h a l b einer mechanischen Mindestenergie einsetzt (Fig. 6). L i F zeigt a u c h u n t e r h a l b dieser Energieschwelle noch starke Brucherscheinungen, w ä h r e n d das plastischere KCl erst weit oberhalb dieser Energieschwelle geringeren B r u c h aufweist, wobei sich die Tribolumineszenz-Intensität keineswegs m i t a u f t r e t e n d e m B r u c h sprungh a f t ä n d e r t . D e r Vergleich verschiedener Alkalihalogenide zeigt, d a ß die plastischeren im allgemeinen stärker emittieren als die spröden. Die Brucherscheinungen h a b e n also keinen e r k e n n b a r e n E i n f l u ß auf die Tribolumineszenz. Dieser Zusamm e n h a n g wird noch deutlicher, w e n n m a n wiederholte E i n d r ü c k e auf der gleichen Kristallstelle m a c h t , wobei die Risse im wesentlichen beim ersten E i n d r u c k entstehen, ohne sich bei weiteren Beanspruchungen zu v e r ä n d e r n , w ä h r e n d aber die Tribolumineszenz k o n s t a n t bleibt (Fig. 10). Eine schwache B e d a m p f u n g der Kristalloberflächen m i t Cu im Sinne einer Dekoration (inselförmige Abscheidung) schwächt die Tribolumineszenz b e t r ä c h t lich. Sie k a n n auf ein Zehntel des ursprünglichen W e r t e s zurückgehen. E i n geschlossener Metallfilm verhindert die Tribolumineszenz vollständig. E s m u ß a n g e n o m m e n werden, d a ß sich die erzeugten elektrischen L a d u n g e n beim ersten Versuch n u r teilweise ausgleichen k o n n t e n . Diese B e o b a c h t u n g spricht f ü r eine L a d u n g s t r e n n u n g d u r c h Versetzungsbewegung, d a die frisch gebildeten B r u c h flächen d u r c h die Cu-Schicht k a u m beeinflußt werden d ü r f t e n . Auch die T e m p e r a t u r a b h ä n g i g k e i t der L a d u n g s t r e n n u n g d u r c h bewegte Versetzungen spricht f ü r einen Z u s a m m e n h a n g m i t der Tribolumineszenz. Diese ist praktisch t e m p e r a t u r u n a b h ä n g i g bis zu einem b e s t i m m t e n Grenzwert, d e r z. B. f ü r LiF-Kristalle verschiedener H e r k u n f t zwischen 70 u n d 110 °C liegt. Auch das elektrische Signal bewegter Versetzungen in NaCl-Kristallen ist zwischen 30 u n d 90 °C t e m p e r a t u r u n a b h ä n g i g , während oberhalb dieser T e m p e r a t u r plötzlich kurze Ströme a u f t r e t e n [38], N a c h C A F F Y N et al. [44] liegt diese T e m p e r a t u r grenze bei 180 °C. Die elektrischen E f f e k t e werden oberhalb dieser T e m p e r a t u r schwächer u n d verschwinden bei 250 °C. Es darf somit als gesichert gelten, d a ß die Tribolumineszenz. der Alkalihalogenide u n d des Rohrzuckers elektrische Ursachen h a t . Sie ist eine Folge des Ausgleichs elektrischer L a d u n g e n , die d u r c h W a n d e r u n g geladener Versetzungen getrennt w u r d e n . 4.3 Gasentladungen

als Ursache der

Tribolumineszenz

I n diesem A b s c h n i t t sollen der Ausgleich elektrischer L a d u n g e n bei I o n e n kristallen u n d R o h r z u c k e r sowie der, Mechanismus der Gasentladung d i s k u t i e r t werden. F ü r den Ausgleich elektrischer L a d u n g e n gibt es grundsätzlich drei Möglichkeiten: 1. Festkörperdurchschlag. E r e r f o r d e r t bei den Alkalihalogeniden elektrische F e l d s t ä r k e n von 5,7 • 10 5 V/cm beim K J u n d bis 31 • 10 s V/cm beim L i F [29]; 2. E n t l a d u n g ü b e r den Gasraum, w o f ü r wesentlich geringere F e l d s t ä r k e n n o t wendig sind; 3. strahlungsloser Ausgleich infolge Störstellenleitung der Kristalle. D a die experimentellen B e o b a c h t u n g e n Festkörperdurchschlag ausschließen, k o m m e n n u r die beiden letzten Mechanismen in B e t r a c h t , die sich aber voneinander t r e n n e n lassen, d a n u r der zweite Vorgang u n t e r Lichtemission a b l ä u f t . E i n u n m i t t e l b a r e r experimenteller Nachweis f ü r die T r e n n u n g beider E f f e k t e besteht darin, d a ß m a n E i n d r ü c k e u n t e r H o c h v a k u u m m a c h t , wobei keine Lichtemission b e o b a c h t e t wird. E r h ö h t m a n den Gasdruck im Rezipienten, so

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K . MEYER u n d F . POLLY

t r i t t gleichzeitig mit dem Gaseinlaß (bei etwa 5 Torr) Lichtemission auf. Die Zeit zwischen Eindruck u n d Gaseinlaß, die gerade noch zur E n t s t e h u n g eines Lichtblitzes f ü h r t , beträgt bis zu einigen Minuten u n d wird wesentlich von der Reals t r u k t u r der verwendeten Kristalle beeinflußt. Nach längeren Zeiten t r i t t bei entsprechendem Gaseinlaß keine Lichtemission mehr auf. Die Ladungen haben sich vorher ausgeglichen. Dieses Ergebnis zwingt dazu, die Tribolumineszenz als ein Gasentladungsphänomen aufzufassen. Sie kann zeitlich vom mechanischen Eingriff getrennt werden. Diese Zeit ist dadurch begrenzt, daß durch eine geringe elektrische Leitfähigkeit der Kristalle sich die Ladungen ausgleichen u n d die Zündspannung f ü r den E n t ladungsmechanismus nicht erreicht wird. Durch Erhöhung der Ionenbeweglichkeit (z. B. Temperatur) oder der Zahl der Kationenleerstellen (z. B. Dotierung) k a n n die Leitfähigkeit so weit erhöht werden, daß die Zeit des Ladungsausgleiches kleiner als die Zündverzögerung der Gasentladung wird u n d die Gasentladung deshalb ausbleibt. F ü r die Annahme eines Gasentladungsmechanismus sprechen weiterhin folgende Beobachtungen: 1. Das Auftreten der Tribolumineszenz ist an eine Gasatmosphäre mit bestimmtem Druckbereich gebunden. I m Hochvakuum wird keine Lichtemission beobachtet. 2. Bei den plastischen Materialien, wie KCl u n d K J , welche die Eindrucknadel dicht umschließen, wird häufig erst beim Abheben der Nadel Tribolumineszenz beobachtet. Die Ladungstrennung m u ß aber schon beim Stoß erfolgt sein, d a die Nadel einige Minuten nach dem K o n t a k t abgehoben werden muß, damit eine Lichtemission erfolgt. 3. Elektrisch leitende Stahlnadeln schließen die „Gasstrecke" kurz, so daß keine Tribolumineszenz auftritt. Charakteristisch f ü r Gasentladungen ist weiterhin ihre Druckabhängigkeit, die durch das Paschen-Gesetz beschrieben wird: Uz = F (p d), wobei Uz die Zündspannung, p den Gasdruck u n d d den Elektrodenabstand bedeuten. U n t e r bestimmten Voraussetzungen können die beobachteten Ergebnisse über die Druckabhängigkeit der Tribolumineszenz direkt auf das Paschen-Gesetz zurückgeführt werden, woraus sich folgende Konsequenzen ergeben: 1. Die Tribolumineszenz wird erst oberhalb einer Mindestenergie E0 beobachtet (Fig. 6), wenn die durch den mechanischen Eingriff erzeugte Potentialdifferenz größer als die Zündspannung ist, bei der die Gasentladung unter Lichtemission einsetzen kann. 2. Der Einfluß verschiedener Gasarten ordnet sich diesem Zusammenhang ein (Fig. 3), da das Paschen-Gesetz f ü r alle Gase Gültigkeit besitzt. 3. Das Maximum der Tribolumineszenz entspricht nach dem Paschen-Gesetz dem Minimum der Zündspannung u n d ist von der freien Weglänge der Elektronen in verschiedenen Gasen abhängig. Die Vergrößerung der freien Weglänge verschiebt das Maximum nach höheren Gasdrucken und umgekehrt. Damit d ü r f t e n f ü r die besprochenen Stoffgruppen als Ursache der Tribolumineszenz Chemilumineszenz oder Lumineszenz infolge Neuordnung der durch mechanische Bearbeitung getrennten Bindungen der Kristalle ausgeschlossen sein. Folgende Tatsachen sprechen dagegen: 1. Das Tribolumineszenz-Spektrum des Rohrzuckers bei Bearbeitung in L u f t •entspricht dem N 2 -Spektrum einer Gasentladung [18, 24], 2. Die chemische N a t u r der umgebenden Atmosphäre hat keinen nachweisbaren Einfluß (z. B. Edelgase - Luft).

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3. Die chemische Natur der Kristalle spielt eine untergeordnete Rolle für die Tribolumineszenz (Rohrzucker — Alkalihalogenide); 4. Die zeitliche Dauer der Tribolumineszenz ist u m 5 Größenordnungen kleiner als die mechanische Kontaktdauer. 5. Das Maximum der Tribolumineszenz liegt im Druckbereich von 5 bis 20 Torr. Herrn Prof. Dr. P. A. verpflichtet.

THIESSEN

sind wir für zahlreiche Diskussionen zu Dank

Literatur [1] G . WOLFF, G . GROSS u n d I . N . STRANSKI, Z. E l e k t r o c h e m . 5 6 , 4 2 0 (1952).

[2] I . N . STRANSKI, E . STRATJSS u n d G. WOLFF, Z. E l e k t r o c h e m . , Ber. Bunsenges. p h y s .

Chem. 59, 341 und 346 (1955). [3] L. M. BELJAJEW und Ju. N. MARTYSCHEW, Kristallografiya (USSR) 9, 117 (1964). [4] K. MEYER und E. GRAGERT, phys. stat. sol. 6, 803 (1964). [5] J . J . GILMAN und W. G. JOHNSTON, Dislocations and Mechanical Properties of Crystals, New York 1957 (S. 119). [6] J . S. COOK, J . appl. Phys. 32, 2492 (1961). [7] M . GUICHANT, C . R . A c a d . Sei. ( F r a n c e ) 1 4 0 , 1 1 0 1 u n d 1 1 7 0 ( 1 9 0 5 ) .

[8] [9] [10] [11] [12]

J. BURKE, Nature 58, 533 (1898). E. BANDROWSKI, Z. phys. Chem. 17, 234 (1895). W. D. BANCROFT, J . Franklin Inst. 175, 129 (1913). H. B. WEISER, J . phys. Chem. 22, 480 und 576 (1918). C. S. BEALS, Proc. Trans. Roy. Soc. Canada 17, Sect. ILL, 125 (1923).

[ 1 3 ] G . WOLFF, I . SCHÖNEWALD u n d I . N . STRANSKI, Z . K r i s t . 1 0 6 , 1 4 6 (1954).

[14] P. J. BUTJAGIN, Ber. Akad. Wiss. USSR 140, 145 (1961). [ 1 5 ] S. S. BHATNAGAR, K . G . MATHUR u n d K . L . BTJTHIRAJA, Z . p h y s . C h e m . A 1 6 3 , 8 ( 1 9 3 3 ) .

[16] A. KARL, C.R. Acad. Sei. (France) 146, 1104 (1908).

[17] F. G. WICK, J . Opt. Soc. Amer. 80, 91 und 302 (1940). [ 1 8 ] T . INOTJE, M . KUNITOMI u n d E . SHIBATA, J . C h e m . S o c . J a p a n 6 0 , 149 ( 1 9 3 9 ) .

[19] [20] [21] [22]

W. J. WERNADSKI, Bull. Acad. Sei. Saint Petersbourg, Ser. 6, 42, 1037 (1910). B. A. LINDENER, Bull. Acad. Sei. Saint Petersbourg, Ser. 6, 42, 999 (1910). M. TRAUTZ, Ion 2, 77 (1910). P. LENARD, Sitzungsber. Heidelberger Akad. Wiss., Abh. 28, S. 39, Anm. 67 (1914).

[23] H . SCHMIDT, P h y s . Z . 1 9 , 3 9 9 (1918).

[24] H. LCNGCHAMBON, C.R. Acad. Sei. (France) 176, 691 (1923); Bull. Soc. Fran t . Mineral. 48, 130 (1925). [25] J . W. OBREIMOFE, Proc. Roy. Soc. A 127, 294 (1930). [ 2 6 ] M . CURIE u n d M . PROST, C . R . A c a d . Sei. ( F r a n c e ) 2 2 3 , 1 1 2 5 ( 1 9 4 6 ) . [ 2 7 ] G . ALZETTA, N . MINNAJA u n d S. SANTUCCI, NUOVO C i m e n t o [ 1 0 ] 2 3 , 9 1 0 ( 1 9 6 2 ) . [ 2 8 ] L . M . BELJAJEW, W . W . NATATOW u n d J u . N . MARTYSCHEW, K r i s t a l l o g r a f i y a ( U S S R )

7, 579 (1962). [29] GRIMSEHL, Lehrbuch der Physik, Bd. IV, Leipzig 1959 (S. 594). [30] K. A. BECKER und I. SCHÖNEWALD, Z. phys. Chem. N.F. 33, 241 (1962). [31] A. IMHOF, Phys. Z. 18, 78 und 374 (1917). [32] M. BORN u n d M. GÖPPERT-MAYER, H a n d b u c h der P h y s i k B d . 24, 1933 (S. 623).

[33] S. WIEDERHORN, J. appl. Phys. 34, 2125 (1963). [34] F. SEITZ, Rev. mod. Phys. 23, 328 (1951). [35] W. DEKEYSER, Reactivity of Solids, Amsterdam 1961 (S. 376). [ 3 6 ] F . RUEDA u n d W . DEKEYSER, A c t a m e t a l l . 1 1 , 3 5 (1963). [ 3 7 ] F . RUEDA u n d W . DEKEYSER, P h i l . M a g . [8] 6 , 3 5 9 ( 1 9 6 1 ) .

[38] D. B. FISCHBACH u n d A. S. NOWICK, J . P h y s . Chem. Solids 5, 302 (1958). [ 3 9 ] J . E . CAFFYN u n d T . L . GOODFELLOW, P h i l . M a g . 7, 1 2 5 7 ( 1 9 6 2 ) .

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Tribolumineszenzuntersuchungen

[40] J . E . C A F F Y N und T. L. G O O D F E L L O W , Proc. Phys. Soc. 7 9 , 1285 (1962). [41] J . E. C A F F Y N und T. L. G O O D F E L L O W , J . appi. Phys. 23, 2567 (1962). [42] K . MEYER, Vortrag zum 5. Absolvententreffen des I n s t i t u t s f ü r Mineralogie der Humboldt-Universität zu Berlin vom 5. 4. 1963 über „Elektrische Vorgänge bei der mechanischen Bearbeitung von Kristalloberflächen". [ 4 3 ] BTTRKER, Drudes Ann. Phys. 1 , 4 4 7 ( 1 7 0 0 ) . [ 4 4 ] J . E. C A F F Y N und T. L. G O O D F E L L O W , N a t u r e 1 7 6 , 8 7 8 ( 1 9 5 5 ) . (Reeeived

October

3,

1964)

CH. SCHWINK: Verfestigung homogener kubisch flächenzentrierter Vielkristalle

457

phys. stat. sol. 8, 457 (1965) I I . Physikalisches

Institut der Universität

München

Über die Verfestigung homogener kubisch flächenzentrierter Yielkristalle bis zum Beginn dynamischer ErholungsVorgänge Von CH. SCHWINK

Die Verformung von kfz Vielkristallen geschieht von Anfang an durch eine Zunahme der Zahl aktiver Versetzungsquellen. Inhomogenität der Gleitung sowie Streckgrenzenanisotropie machen eine quantitative Formulierung des Gleitbeginns sehr schwierig, bestehende Ansätze [13] sind fehlerhaft. — Eine elektronenmikroskopische Definition des Gleitbeginns, die sich quantitativ ausdrücken läßt, wird gegeben u n d mit dem Experiment verglichen. — F ü r die plastischen Vorgänge oberhalb etwa 0,1% Dehnung bis zum Einsatz der Quergleitung wird eine Beschreibung gegeben und eine Versetzungstheorie entwickelt, die sich an die von SEEGER [6] f ü r Einkristalle aufgestellte anlehnt. Damit gelingt es, die makroskopischen Verfestigungsgrößen q u a n t i t a t i v auf P a r a m e t e r zurückzuführen, die sich aus licht- und elektronenmikroskopischen Daten gewinnen lassen. The mechanism for the beginning of deformation of f. c. c. polycrystals is by an increase in the number of activated dislocation sources. Inhomogeneous glide and anisotropy of yield stress make a quantitative description of the first stages of deformation very difficult; existing formulas [13] are not correct. — An electron-microscopic definition of "glide beginning", leading t o an analytical formulation, is given and compared with experiments. — The processes following t h e initial stage of deformation u p to the onset of cross glide are described, and a theory analogous to Seeger's theory for single crystals [6] is developed. The macroscopic work-hardening curve is deduced f r o m equations containing only d a t a given b y microscopic and electron-microscopic observations.

1. Einleitung Unsere derzeitige Kenntnis über die plastische Verformung von Vielkristallen wurde kürzlich von MACHERAUCH [ 1 ] in erschöpfender Weise zusammenfassend dargestellt. Dabei geht MACHERAUCH auch auf die bestehenden Versuche zu einer theoretischen Beschreibung der Verfestigungskurve homogener Vielkristalle ein. Wir können uns deshalb darauf beschränken, hier nur diejenigen Arbeiten und Punkte hervorzuheben, die für die eigenen Ausführungen unmittelbare Voraussetzung sind. Mehreren Ansätzen früherer Verfasser [2, 3, 4] zur rechnerischen Beschreibung der Vielkristallverformung war die Annahme gemeinsam, daß es eine EinkristallVerfestigungskurve gibt, die von der Orientierung der Einkristalle unabhängig ist. Das Problem der Vielkristallverfestigung reduziert sich dann auf das einer geeigneten Mittelung über die Einzelkörner der vielkristallinen Probe. Die Voraussetzung dieser Vereinfachung erwies sich jedoch in der Folgezeit als unzulässig, die Einkristalle besitzen in Wirklichkeit eine ausgeprägte Orientierungsabhängigkeit ihrer Verfestigung [5, 6]. Man hat nun versucht, die genannte Möglichkeit zur Vereinfachung des Problems dadurch zu retten, daß man den früheren Mittelungsverfahren eine ganz bestimmte aus der Schar der Einkristall-Verfestigungskurven zugrunde legte [7]. Diesem Vorgehen war jedoch nur ein beschränkter

CH. SCHWINK

458

Erfolg beschieden, wie Arbeiten von HOWE und ELBAUM [ 8 ] sowie K N Ö L L und MACHERAUCH [ 1 ] zeigten. Die berechtigte Anwendung der Mittelungsmethoden über die Korn Verteilung würde voraussetzen, erst einmal die für die plastischen Vorgänge zutreffende gemittelte Einkristallkurve zu finden. Das dürfte aber, will man auf deduktivem Weg vorgehen, eine sehr schwierige, wenn nicht aussichtslose Aufgabe sein. KRÖNER [ 9 ] schlug deshalb einen ganz anderen Weg ein. E r stellte die Kenntnis der gewöhnlichen Einkristallkurven bewußt beiseite und zeigte, wie man bei Kenntnis anderer — fiktiver, aber wohldefinierter — „Einkristall-Dehnungskurven" den gesamten Spannungszustand einer vielkristallinen Probe exakt berechnen kann. Das in den früheren Theorien nur mangelhaft behandelte Mittelungsproblem über die Einzelkörner ist also bei KRÖNER vollständig gelöst, übrig bleibt hier das Problem der Bestimmung der „Einkristall-Dehnungskurven". Die Schwierigkeit seiner Bewältigung, die vor allem vom experimentellen Standpunkt groß erscheint, rührt wieder von der Orientierungsabhängigkeit dieser Kurven her, die ganz analog zu derjenigen der gewöhnlichen Einkristall-Verfestigungskurven auftreten muß. Die Frage nach den mikroskopischen Vorgängen in den Kristalliten während der Verformung wird zwar auch von KRÖNER [ 9 ] besprochen, ist aber für seine Theorie ohne Belang. In der vorliegenden Arbeit wird versucht, gerade diese mikroskopischen Vorgänge in den Vordergrund zu stellen und zum Ausgangspunkt einer theoretischen Beschreibung zu machen. Das heißt, daß die Bewegung und gegenseitige Beeinflussung von Versetzungen in systematischer Weise als der Grundvorgang der plastischen Verformung auch des Vielkristalls betrachtet und eingeführt werden soll, so wie das für den mittelorientierten, kubisch-flächenzentrierten Einkristall mit großem Erfolg gelungen ist [6]. Die Möglichkeit hierzu scheinen uns Experimente zu geben, die in jüngerer Zeit angestellt wurden [10, 11] und dazu geführt haben, die Verfestigungskurve vielkristallinen Nickels bis zu mittleren Verformungsgraden in verschiedene Bereiche so einzuteilen, daß jedem Bereich bestimmte Vorgänge zugeordnet werden können, die von ZANKL [ 1 1 ] insbesondere aus elektronenmikroskopischen und magnetischen Messungen geschlossen wurden. Die von ZANKL aufgestellte Einteilung ist, soweit wir sie in dieser Arbeit benötigen, in Tabelle 1 zusammengefaßt. Sie wird den Ausführungen der weiteren Kapitel zugrunde gelegt, in denen das Versetzungsmodell, mit dem die Einteilung interpretiert wird, kurz dargestellt und theoretisch gefaßt wird. Tabelle 1 Bereich Dehnung (ungefähre Werte) Spannung

Einleitungsbereich

10 . . . £„ . . . £, jo . . . 5- 10~5. . . 10-3 0 . . . m co* (i + Em) « r = 2 < P T " K or 2 { - M(Oi8mn6ij nj

nj

+ 0rnn}un

=

nj

{0™n

_ 0'ntn)

+

Mm

H m b m n d i } } W > , (2.3b)

where M (1 + e m ) is the mass of the atom at position r m and are new coupling parameters. The deviation from the ideal lattice appears as an inhomogeneity. (2.3b) can be formally solved by «R=«Ra + s g t ? H > np

J

?

i

=

-

®

w


oa'%'\ 2 A gUm' - co - to") {(V T, k + k' + fc")}* a a' a" com'to" sinh (1/2 /S h to) sinh (1/2 /S h to') sinh (1/2 ph co") ' (4.12)

A contribution is obtained only for fc + fc' -f- fc" = g =(= 0. We choose for g those lattice vectors which occur in £ (fc + fc' + k" — g ) for the case of a simple cubic lattice, namely ®

g = ^ ( ± 1,0,0)

\g\2=^r-

etc.;

(4.13)

Since x does not depend on the direction of V T, we average over all directions and take { ( g , V T ) 2 } as 1/3 (4 ji 2 )/a 2 | V T\ 2 in front of the sum. Following a paper b y L E I B F K I E D a n d SCHLOEMANN [ 2 3 ] w e '

\tfvz?

A ; = • F

M(0i

put

j;Vzf,

- V )

Ai.

2

(4.14)

y g is the Griineisen constant with an assumed value of 2. This approximation was derived from a f . c. c.-lattice with central forces and neaiest neighbour interaction only. I t should be good for all lattices, however, because the structure of the lattice has practically been eliminated. Furthermore, according to [23], the ¿-function ¿(co' — co — co") = d(co* +k ' — co* — coa"') gives a contribution only for 13 of the 27 combinations of ( a , a ' , a " ) . Because of this ¿-function, we put co' = co + co" and eliminate co' from (4.12). The ¿-function is then replaced by 1 lcoD and smeared out into the whole volume. The sum over k' is cancelled by / \ g and k' is treated as — fc — fc". The condition fc -j- fc' + fc" = g =}= 0 can be approximately accounted for by k. + k ' + k"

(4.15a)

= ^

which amounts, in the Debye approximation, to m

I w"• sg a ; a>D

t0£>1

a= c

no a ojj) ¡3» 0.8 .

2 71 1

/a(4.15b) 1 eu

Of all these approximations the treatment of the ¿-functions is likely to be the worst. Inserting all these approximations into (4.12) we get (r, ¿ a n h r ) = 413

,V

T ?

,

(4.l6)

1 J

_ / / J ~ J J

o

J "

^

X

X

sinh (1/2 6/T x ) sinh (1/2 6 j T x " ) sinh (1/2 0/!T ( x + x " ) )

g.

X ( X

' '

X+X"

The coefficient of thermal conductivity is given by (4.3), (4.6) T* (y, r) 2

V t IV T I (r, A b r) 2

32 physlca

+ (r,

r) + (r, Am r) '

(4.17)

496

K . THOMA a n d W . L U D W I G

Numerical examples for x will be shown for a KC1 crystal doped with K J , NaCl andCaCl 2 . This system has been investigated experimentally by W A L K E R and P O H L [3]. KC1 is a non-primitive lattice with m K = 39.1 amu, m c l = 35.457 amu. Because of this relatively small mass difference it will be treated as a cubic primitive lattice with m = 37.3 amu ^ 6.2 x 10"23 gr, a ^ 3.12 A, 6 = 240 °K ([24], p. 403 and 423). The mean velocity of sound is therefore c = 2.52 x 10s cm/s. rb depends on the size of the sample to be measured and is usually determined from the x ~ T3 law at very low temperatures. We choose 1/rb = 5.8 X 108 s _ 1 which corresponds roughly to a size of 4 0 x 5 x 5 mm. I n order to evaluate (4.17) numerically one has to make various approximations in the integrals J0 (4.10), J1 (4.11) and J2 (4.16). Confining ourselves to a temperature range T 0.3 6 72 °K we can expand (4.10) easily into powers of Tj6. In J2 (4.16) we replace sinh - 1 u by e"uju. The resulting integral can be evaluated in closed form. J j (4.11) contains 1/|1 — a>2eg00!2. For large s (e = 5 for example, Fig. 1) this function has a pronounced peak at small values of x (x m 0.25). We put therefore 1/| 1 - a f i e g j * '

1 1 " ( 3 ^ (u - u0f + r 2 '

un =

1 3s'

(4.18)

71 6e/3

x2 is taken as the variable of integration, the rest of the integrand is taken out of the integral with its value at the peak of the resonance. For small e (s = 0.1; Fig. 1) the resonance has disappeared. I n this case we simply put |1 — to2 e ^ l - 2 equal to 1. Fig. 2 shows x(T) for e = 5 and different concentrations. 4 ) The mass of the

•10 M

y'10

3

0.1

I 20

40

T(°K)Fig. 2. Temperature dependence of the thermal conductivity for different concentrations of defects and e = 5 (solid line) and e = 2.4 (dotted line), e = 2.4 corresponds to J-defects in a KC1-crystal

i

4

i i i

6 810

i

20

i i

40 60

Tf'K) Fig. 3. The same as Fig. 2 for e = 0.075, which corresponds to Ca-defects in XC1

4 ) In KC1 this corresponds to the insertion of a mass of 224 amu in the region of Fr. In LiF the inserted mass would have to be 77.8 amu (Rb or Br).

Scattering of Sound Waves by Isotopes and Thermal Conductivity

497

doped atom has to be substantially larger than the mass of the host atoms, the configuration of electrons around the impurity is therefore altered, which changes certainly the coupling parameters. The discussion of an isotope with e ^ 5 is therefore somewhat unrealistic. In order to see the dependence of x on e, an example for e = 2.4 is given in Fig. 2. The influence of the isotopes is smaller in this case, the treatment, however, of the integral J1 (4.11) becomes questionable because the rest of the integrand, that has been taken out of the integral is not "slowly varying". The case of small e is given by KC1 doped with CaCl2 (e = 0.0751). The atomic number of Ca is 20, of K 19. Ca contains only one more electron in the outer shell, it is therefore reasonable to describe this impurity by an isotope. Fig. 3 gives x(T) for different concentrations of impurities. A comparison with the measurements of W A L K E R and P O H L [ 3 ] shows a qualitative and order-ofmagnitude agreement between our curves and the measurements. The case s = 5 is not realized in [3] but in KC1 doped with K J one has e = 2.40. The measured curves do not show the strong minima of x at T m 8 °K for large e. Possible reasons for this are the rough numerical approximations which were based on a strong resonance in |1 — co2 e (fool -2 - In any case the minimum is a lower limit to x because of the variational method. A better calculation will give no relative minimum but only a depression in the curve. The resonance for e = 2.40 is perhaps not pronounced enough to justify our treatment. Furthermore, because of the finite concentration y of isotopes, one should consider interactions of the scattering centres, which will broaden the resonance additionally. There is also additional scattering from changed coupling parameters, as has been discussed by K L E I N [6], Better calculations of the integrals J0, Jlt J2 are desirable, but can only be done on machines. The Ansatz /JJ = (V T, k) does not take into account the resonance at all. According to (4.17) /|f has to be chosen such as to make the denominator (r, A r) as small as possible. This can be accomplished by making small in the region co cores. A better Ansatz would, for example, be (V T, k)

for

I co - co0| ^ 180% eine lineare Beziehung zwischen AQ und y gefunden. Für y-Werte zwischen 0 und 70% können die Ergebnisse durch die Saada-Gleichung für die Erzeugung atomarer Fehlstellen beschrieben werden.

1. Introduction During the last ten years, the study of resistivity changes in metals as a function of plastic strain has been recognized as a very efficient tool for investigating the concentration and the nature of cold-work induced defects (for a review on this topic see VAST B U E B E N [1] and references quoted there). For polycrystalline materials, the following empirical equation, valid for low strains, was shown to be verified by most of the f.c.c. metals [1, 2]: AQ = Lorentzsche Linienform und Linienbreiten von 100 und 300 Gauß numerisch mit der elektronischen Rechenmaschine ZUSE Z 22 berechnet. Mit der obigen Gleichung für die Winkelabhängigkeit des gr-Faktors wurde eine große Zahl von ¡/-Faktoren von 0 = 0 bis tü/2 und 0 = 0 bis n\2 erhalten. Die Schrittweite A0 war konstant nj90. Die Schrittweite von 0 mußte wegen der Bedingung gleich großer Kugeloberflächenelemente, F = sin 0 AG A

+ a>' = a>0, ce qui impose co0 < 2 coD, tandis que la sommation sur les phonons se limite aux phonons dont les-énergies h a) satisfont à (co0 — o>D) m ^ a>D . D'autre part, on ne donnera pas à la distribution des phonons optiques sa valeur classique, parce qu'on n'a pas en général h œ0 < k T. L'intégration fera donc intervenir u n facteur R * = / ! + _ _ ! I " exp1 — kT

x

\(4_I)(6î!!._4_4). 1 \co3, / \ mD wb/

(6)

Dans cette expression, le premier terme est la probabilité d'avoir u n état d'énergie h OJ0 vide. Ce terme est responsable de la variation de W opt avec la température qui, à température élevée, est peu différente de la dépendance linéaire. Le second et le troisième terme sont introduits par l'expression de dS' et par les limites de l'intégration sur dq. Ce sont ces facteurs qui limitent le nombre de processus pour 2 Ed,

s= 1

for

T the activation energy Q for rotation or one elementary displacement and the value of r 0 . 2. A stored energy (SE)-peak or a residual resistivity (RR)-annealing maximum may be produced by the migration and annealing out of several types of defects,

Magnetic After Effects in Iron after Irradiation with Neutrons

611

which in general will contribute in different amounts to the S E or R R . As an example we note that within the second S E and RR-peak at 150 to 180 °K defect types 2 and 3 anneal out. 3. Certain defect types are produced within a S E or R R annealing stage. A striking example is annealing stage I (80 °K to 130 °K), which is accompanied by the build up of defect types 1 and 4, whereas no annealing of any magnetic after effect could be detected, in contrast to the findings of MOSEB, and DAUT B E P P E [2]. This is particularly surprising in view of the fact that the internal friction peaks I„ and I b anneal out within the temperature range of stage I . A possible explanation for this behaviour would be that internal friction peaks I a and I 6 are due to the interaction of magnetically inactive point defects with dislocations. This mechanism appears reasonable since the peaks I a and I 6 anneal out at the temperature of the maximum. 4. The build up of peak 3 and the annealing of peaks 1 and 4 are only reflected in the S E and not in the R R (the difference in heating rate between the R R and the S E is far too small to account for a shift of about 15 to 20 °K in stage I). I t appears that defect reactions without change in concentration take place in this temperature interval. We wish to thank Prof. H . MATER-LEIBNITZ and Prof. N. R I E H L for the support of this work. Special thanks are due to Dr. W. SCHILLING and Dr. H . - D . D I E T Z E for stimulating discussions. Referecnes Q ] E . BALTHESEN, K . ISEBECK, and H. WENZL, phys. s t a t . sol. 8, 5 9 3 (1965).

[2] P. MOSER and D. I). DATITREPPE, J . Phys. Radium 24, 516 (1963).

[3] E . BALTHESEN, phys. s t a t . sol. 3, 2 3 2 1 (1963). [4] I). BAUTREPPE, V. HIVERT, P . MOSER, and A. SALVI, C . R . A c a d . Sci. ( F r a n c e ) 2 5 8 , 4 5 3 9 (1964).

[5] E . BONJOTO and P. MOSER, C.R. Acad. Sci. (France) 2 5 7 , 1 2 5 6 (1963).

[ 6 ] G. BURGER., K . ISEBECK, H . MEISSNER, W . SCHILLING, and H . WENZL, t o be published. (Received

December

7,

1964)

B.H.HBaHOB-OMCKHftetal.: TajibBaHOMarHHTHbieCBOiicTBaTejuiypnnapTyra613 phys. stat. sol. 8, 613 (1965)

0U3UKO-TexnuuecKuu uucmumym, Jleiiimzpad TajibBaHOMarHMTHbie c s o f t c T s a TeiiJiypHfla pTyTH B . H . MBaHOB-OMCKHfi, B . T . KojioMHeix, A . A . M a n b K O B a , B . K . Oropoj(HHKOB H K . n . C M e K a j i o B a IIpOBOUHMOCTb, K03(J)9-6-0

S2

8 6

io3

10 l

103 ¡,9-5-0

%

£

13-18-0 -

13-1-0

Aa

10

10' •

5-1-0 28-1

\ v \ > \ \ \ V \ \+

13-1-0

%~7— 5-1-0 100

101

\

28-1

—

11-7 I I I I WO

PIIC. 2 .

100 -T(°K)

50

r 10

3aBHCHMOCTb K03((I(J)iimieiiTa X o . i . i a o r TeMnepaTypbi, H g T e p-Tima

70"

n'ai

0.5

1.0

5

10

H(lid) ~ PHC. 3 . 3aBiicHMOCTb K03(I>(J>HiuieiiTa X o . i . i a OT nanpiiHîënirocTii M a r i n m i o r o n o i m , H g T e p - r a n a , T — 4,2 " K . — CnpaBa-iiacniTaS a.iH o6pa3uo 28-1, 14-7

rajibBaHOMarHHTHbie CBOftcTBa Tenjiypuna ptyTH

615

pa3ua K o6pa3uy npn hh3khx TeMnepaiypax cooTBeTCTByeT yMeHbineHHK» H36biT0iH0H KOHijeHTpaijHH aKijenTopoB. Kan nerKo BHjieTb Ha P h c . 1, yBenHTOHHe KOHijeHTpaiiHH aKiiemopoB npHBOHHT k y B C J i H H e H H i o H H T e p B a n a TeMnepaTyp, b K O T o p o M n p o B O HHMOCTb H e 33BHCHT OT TeMnepaTypbl. HeMOHOTOHHOe H 3 M e H e H H e K O 3(|)(|)HHiHeHTa X o j i j i a c TeMnepaTypon b oßnacra ot 20 ho 60 ° K huh Hanöojiee ^ h c t h x 06pa3U0B He HaxoHHT b HacTOHmee BpeMH 0j;H03HaiHoro o6i.HCHeHHH h T p e ô y e T HononHHTejibHoro H c c j i e j j O B a H H H . H a Phc. 3 h 4 npencTaßjieHbi 3aBHCHM0CTH npoBojuHMocTH h ko3(|)$hHHeHTa X o n j i a ot HanpHHîëHHOCTH MarHHTHoro n o n n npn 4,2 ° K . J^jih Bcex o6pa3u;oB, He HMeiomnx HHBepcHH 3Hana Ha TeMnepaTypHOñ 3aBHCHMOCTH K03(|)(|)HHHeHTa

Xonna,

HOCTH M a r H H T H o r o n o j i H .

nocjieHHHH

najjaeT

c pocTOM

HanpHHtëH-

H3MeHeHHe c o n p o T H B j i e H H H b MarHHTHOM

none

pacTëT ot o6pa3Ha k o6pa3uy c yBejin^eHHeM OTpHuaTenbHoro K03(|)(f>HHHeHTa Ha

Xojijia. Phc.

n-THna

h

5

npencTaBJieHbi

TeiinepaTypHbie

3aBHCHMOCTH

npoBonn-

Xonna HJiH HgTe n - T H n a c hsômtohhoh KOHijeHT p a n n e Ë H O H o p o B n = 4,5 x l O 1 6 cm - 3 , a H a Phc. 6 hx 3 a B H C H M 0 C T H o t H a n p H H î ë H H O C T H M a r H H T H o r o noun n p w p a 3 H b i x T e M n e p a T y p a x . B nojib3y MOCTH

K09(|)(|)HUHeHTa

npoBOHHMOCTH

CBHHeTenbCTByiOT,

OÖJiaCTH, B K O T O p O H K03l) BAOJIb

HanpaB.neHHH

pOCTa

OnpeneneHHe opneHTauHH KpncTajuioB ojiOBa He noKa3ajio HiiKaKoñ npennoHTHTejibHoii opneHTauHH OTHocHTejibHo HanpaBjieHHH pocTa. MoHOKpHCTanjiH OjiOBa hmôiot opHeHTauHK), JieJKamyio Memgy HanpaBJieHHHMH H B nJIOCKOCTH (001), IipHMBpHO Ha CepejüHHe CTOpoHbi cTaHgapTHoro cTepeorpai|>HHecKoro TpeyronbHHKa o t och ho < 1 1 0 ) . 3tO Ba>KHOe HJIH HaCTOHmerO HCCJießOBaHHH OÖCTOHTeUbCTBO, nocKOJibKy oho HCKHionaeT bjihhhhc opHeHTanHOHHoro 3(J)(|)eKTa Ha H3MepneMyK) b paßoTe xapaKTepncTHKy CTeneHH coBepmeHCTBa KpncTajiJIHHeCKOH pemeTKH. Pe3yjibTaTbi HccnenoBaHHH h3M6hchhh CTeneHH CoBepmeHCTBa mohoKpncTanjia ojioBa Bßonb HanpaBjieHHH KpHCTàJiJiH3anHH CBeneHbi b r p a Horo TpaBJieHHH BbiHBjieHO pacnpenejieHHe HHCJioKaunfi BOKpyr oTnenaTKOB H napanHH Ha nocJieayiomHx rpaHHx A ( l l l ) H B ( l l l ) . The anisotropy of micro-solidity in GaP monocrystals is investigated by a process of surface scratching. The anisotropy of the impressions is determined and found to correspond to the symmetry of the side (111). B y means of selective etching the distribution of dislocations around the imprints and scratches on the next sides A (111) and B (111) is determined. 1.

BseAemic

B n o c j i e n H e e BpeMH coejjHHemiH - r a n a A n i B v HauuiH c e 6 e m n p o K o e npHM6HeHHe b nojiynpoBOHHHKOBOM npn6opocTpoeHnn [ 1 , 2 ] . Tpe6oBaHHH ycTOHHHBOH p a S o T H b uiHpoKOM HHTepBajie T e M n e p a T y p n p n BneKjiH BHHMaHHe K BhicoKOTeMnepaTypHOMy coeHHHeHHio 9 T o r o K n a c c a — (|ioc(|)Hny r a j i n H f l , T e M n e p a T y p a nnaBjieHHH K O T o p o r o p a B H a 1 4 6 7 ± ± 3 °C n p n naBjieHHH n a p o B oc• The mean values of a for the Ag-Sb alloys are plotted in Pig. 1 along with the data for similarly deformed Ag-Sn alloys due to CAHN and DAVIBS (6). The variation of a with 9 in the Ag-Sb alloys is similar to the trends observed for other copper and silver solid solutions. The other earlier finding, viz., the increase of Ot , at a given electron-concentration (p), with increasing solute valency, is borne out again on comparison with the Ag-Sn data. It is logical to expect that the surfaoe energy of a staoking fault (y) is determined by the difference in free energy between the face-centred cubic (f.c.o.) and hexagonal

Short Notes

K97

olose-packed (h.o.p.) phases, since the f.c.c. stacking fault represents a thin layer of the h.c.p. phase. This free-energy difference can be ezpeoted to diminish as q increases, as the stability of the f.c.o. phase decreases with increasing y . Furthermore, SPREADBOROUGH (4) has shown that the relative contributions of s, p, and d orbitals to the cohesion of the solid solution should alter in such a manner as to increase the h.c.p. stability as y increases. According to this theory, the first appearance of the h.c.p. phase (if any) in the various phase diagrams can be expected at a lower p for higher solute valenoy. The intermediate phase (?) that follows the f.c.c. primary solid solution in the Ag-Sb equilibrium diagram (11) at 5.5 atomic $ is h.c.p. The fact that the c/a ratio of this h.o.p. phase (1.632) is very olose to the ideal value (1.633) points again to a still smaller free-energy difference between .the two close-packed structures which constitute the first two phases in this binary system, as compared to that of Ag-Sn, and this explains the observed steeper rise (Pig. 1) in the a -values of Ag-Sb alloys as the f.c.c. phase-boundary composition is approached. The authors are grateful to Prof. A.E. VERMA, Head of the Department of Physics, Banaras Hindu University, for his kind permission to use their Diffractometer. References (1) M.S. PATERSON, J. appl. Phys. 23, 805 (1952). (2) L.F. VASSAMILLBT, J. appl. Phys. ¿2, 778 (1961). (3) R.E. SMALLMAN and K.H. WESTMACOTT, Phil. Mag. 12, 669 (1957). (4) J. SPREABB0R0UGH, Phil. Mag. 2, 1167 (1958). (5) R.P.I. ABLER and C.N.J. WAGNER, J. appl. i>hys.

3451

(1962). (6) R.G. BAVIES and R.W. CAHN, Acta metall. 10, 621 (1962). (7) J.H. FOLEY, R.W. CAHN, and G.V. RAYNOR, Acta metall. 1±, 355 (1963). (8) P. RAMA RAO and T.R. ANANTHARAMAN, unpublished work. (9) A. PAPOULTS, Rev. sci. Instrum. 26, 423 (1955).

physica status solidi 8

K98

(10) C.N.J. WAGNEE, Acta metall.

427, 477 (1957).

(11) M. HANSEN, Constitution of Binary Alloys, McGraw Hill, New York 1958. (Received January 4, 1965)

Pre-printed

Titles and

Abstracts

Papers to be published in "physica status solidi" Vol. 8, No. 3 Review Article H. WONK, Institut für Theoretische Physik der Technischen Universität Dresden, Zum gegenwärtigen Stand der Theorie der Supraleitung Original Papers ff.E. SPBAR and G.W. BRADBERRY, Physics Department, University of Leicester, The Edge Bmission in CdS Crystals In this paper the mechanism of the green edge emission in pure, undoped CdS crystals is investigated. First, a systematic study of photoconductive, transport and luminescent properties and their dependence on heat treatment (350 °C) has been carried out. The photoconductive measurements between 77 °K and 130 °K indicate that a class II centre (S p » S n ) lies 0.13 to 0.15 eV above the valence band. The experimental results are then compared with calculations based on a three centre model and carried out by electronic oomputer over a range of temperatures and centre densities. The observed luminescent properties can be predicted in agreement with experiment, but only if the radiative recombination takes place between a free electron and a hole trapped in the above centre (Schön-Klasens Model). The effect of heat treatment and the nature of these centres sire briefly discussed. A. TRUTIA and H. MUSA, Institute of Physics of the Rumanian Academy of Sciences, Buoharest, Absorption Spectra of Solid State (Polycrystalline) and Liquid Compounds of Bivalent Cobalt Measurements are made of the visible spectra of pure CoClg, CoBr2 polycrystalline layers, and C0CI26H2O and CoBr 2 6H 2 0 monoorystals between 77 and 1050 °K. A good degree of correspondence is established between the spectral oompo-

K100

Titles and Abstracts, phys. stat. sol.

nents of polycrystalline CoClg and CoBrg. The spectra of the two hydrates also show similarities which lead to the conclusion that the first coordination sphere around C o + + at 77 °K has an octahedral-type symmetry with two halide ions and four water molecules. Modification of the CoClg and CoBrg speotra when passing from the solid to liquid phase (melt) is also investigated. This indioates a transformation from octahedral to tetrahedral symmetry. H. HESSE, Institut für Experimentalphysik der Technischen Universität Dresden, Ober die Beobachtung einer Korngrenzenwanderung auf der Wolframkathode im Feldelektronenmikroskop Es wird über eine Korngrenzenwanderung auf einer WolframSpitzenkathode bei ca. 2600 °K beriohtet, die im Feldelektronenmikroskop beobaohtet wurde. Die beiden Kristallite sind um [011] um ca. 71° gegeneinander verdreht. Diese Orientierung stimmt mit dem Koinzidenzgitter-Modell überein. Die Abweichung der Korngrenze von einer dichtgepackten Ebene des Koinzidenzgitters wird duroh Stufenbildung gedeutet. Die Entstehung eines speziell orientierten zweiten Kristallbereichs im Wolframeinkristall ist eine besondere Form der Rekristallisation. 0. BEÜMMER, W. SCKÖLKE und H. BÖHHEL, Institut für experimentelle Physik der Martin-Luther-Universität Halle-Wittenberg, Untersuchung der Verteilung von Versetzungen in plastisch deformierten Cu-Elnkristallen mit Gitterquellen-Interferenzen (Kossel-Interferenzen) Es wird mit Hilfe von Gitterquelleninterferenzen (Kossel-Interferenzen) gezeigt, daß bei plastischer Deformation von Cu-Einkristallen im Bereioh I und II der Verfestigungskurve für vorliegende Orientierungen eine anisotrope Verbreiterung der Kossel-Linien auftritt. Diese richtungsabhüngige Verbreiterung kann mit der Wirkung einer [112]und [111]-Vorzugsdrehachse der Gitterrotation (senkrecht zur Gleitrichtung bzw. senkrecht zur Gleitebene des Hauptgleitsystems) erklärt werden. Es wird bereohnet, daß diese beiden Drehaohsen dann bevorzugt auftreten, wenn die Versetzungsdiohte in den tfebengleitsystemen zwar kleiner, aber von gleioher Größenordnung ist wie die Versetzungsdiohte in dem Hauptgleitsystem. Die Möglichkeit eines Aufstaus von primären Versetzungei

Titles and Abstracts, phys. stat. sol.

K101

gleichen Vorzeichens wird ebenfalls diskutiert. J.L. KOLOPUS and L.V. HOLROYD, Department of Physics, University of Missouri, Columbia, Higher Order Transitions in the E P E Spectrum of P e ^ + in MgO

The spectrum of the

¿ 1 . = 3, 4, and 5 transitions of F e ^ + in single crystals of MgO has been measured. A computer was used to solve the secular equation of the spin Hamiltonian appropriate for F e ^ + in a cubic site in MgO. A table of the angular dependence of the energy levels as a function of magnetic field in the dimensionless quantities ff/a vs

gßH/2a is given for gßH/2a between

1.30 and 2.50. The experimental data for the angular dependence of these lines is compared with the calculated values and the agreement found to be within experimental error. K.H. HERRMANN, R. LINZ und W.-D. RENTSCH, II. Physikalisches Institut der Humboldt-Universität zu Berlin, Thermische Akzeptoren in einkristallinem Tellur

Die Eigenschaften ab-

geschreckter Tellurproben werden untersucht. Durch schnelle Abkühlung von 150 °C bis 360 °C auf -196 °C werden thermische 1h A Fi o Akzeptoren in Konzentrationen zwischen 4-10 und 2«10 cm eingefroren. Parallel dazu erfolgt eine Erhöhung der Gitterbeweglichkeit. Die experimentellen Aussagen deuten auf eine Analogie im Verhalten abgeschreckter Proben zu Proben Vinter hydrostatischem Druck. CH. SCHWIHK und D. KNOPPIK, II. Physikalisches Institut der Universität München, Experimentelle Untersuchungen zum plastischen Verhalten von vielkristallinem Nickel

Es wird

die Verfestigung bis zu rund 10 96 Dehnung mit mechanischen u n d magnetischen Messungen verfolgt, mechanisch durch Bestimmung von Dehnung und Dehnungszunähme und durch Temperaturwechselversuche, magnetisch durch Messung v o n Koerzitivkraft und Anfangspermeabilität. Für letztere wird eine Meßanordnung näher erläutert. Eine früher für Zimmertemperatur angegebene Einteilung der Verfestigungskurve (1) läßt sich bis zur Temperatur der flüssigen Luft nachweisen, der Temperaturgang der charakteristischen ÜbergangsSpannungen wird angegeben und besprochen. Temperaturwechselvorgänge

zeigen die Bedeutung

von Schneidvorgängen vor allem im Anfangsstadium der Verfor-

K102

Titles and Abstracts, phys. stat. sol.

mung, wo auoh die Abweichungen vom Cottrellschen Gesetz am größten sind. (1) Gr. ZAMKL, Z. Naturf. 18a. 795 (1963). W. ZAWADZKI, Institute of Physics, Polish Academy of Sciences, Warsaw, Thermomagnetic Phenomena in Cubic Semiconductors Possessing Non-Parabolic Energy Bands

Thermomagnetio

phenomena are considered in a semiconductor crystal having cubic symmetry and an arbitrary relation between energy and wave-number. The theory is formulated in terms of three basic transport tensors. Expressions are obtained for thermomagnetic effects in the limiting cases of weak and strong magnetic fields. The influence of anisotropy and non-parabolicy of the energy bands is considered. The results apply both to the many-ellipsoid cubic energy bands of Si and Ge and to the non-parabolic band structure of III-V compounds. E.H. IIWHEC u H.H. TYMEH, XapLKOBCKHft rocyaapcTBeHUü yHOepCHTOT HM. A.M. TOPCKOBO, MarHHTOCTPHKUHH HHKejH» - KOÖaJIBTOBHX

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OT pasjiHiHHX TeimepaTyp. |*B| aHouajiBHO B03pacTaeT y Bcex $epPHTOB (KpoMe MMCTO HHKßjieBoro) nocjie 3aKajiKH OT TeMnepaTyp Jieacamux HecKOJitKo Hiixe TOVKK Kapn, n p m e u OSHOBpeueHHO nojiyqaeTCH yu6HBiii6Hii6 nocTosHHoi! penieiKH /lg«

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a nocjie 3aicajiKH HaÖJiioaaioTCH y $eppHTOB Handojiee Ö o r a -

Tbix KOÖajiLTOM, a y IHCTO HHKejieBoro $eppHTa OHH oÖpamaioTCH B Hyjii». OTJIHIHH oöycjioBJieHbi pa3HHM KOJIH^CCTBOU KHCJiopo^a pacTBopeHHoro B peiueTKe $eppnTOB pa3Horo c o c T a B a .

PeHTreHorpa$M-

wecKHM nyTeM Ha nojiHKpHCTajuiimecKMX o(5pa3ijax onpeaejieHa nepBaH KOHCTaHTa MarHHTOCTpHKIiHH ^

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^ „ „ l y $eppnTOB pa3JimiHoro cocTaBa niu 2Ariooi + W [in] pacc^HTaHa c noMomtio $opiayjiu A s « — — • F. FRÖHLICH und P. GRAU, Institut für experimentelle Physik der Universität Halle, Bildung und Ausheilung v o n Punktdefekten in KCl-Kristallen.gemessen mit Hilfe der Verfärbbarke it durch F-Zentren

Es wird die Bildung von punkt-

förmigen Gitterdefekten in KCl-Einkristallen naoh Abschrecken von 530 °C, naoh plastischer Deformation und naoh intensiver

Titles and Abstracts, phys. stat. sol.

K103

BöntgenvorbeStrahlung mit Hilfe der Höntgenverfärbbarkeit durch F-Zentren untersucht. Die Vorbehandlungen führen zu e.iner Erhöhung der Verfärbbarkeit, die duroh die charakteristischen Parameter der F-Zentren-Bildungskurve erfaßt werden kann. Dabei wird eine bevorzugte Zunahme der Konzentration von Anionenleerstellen gefunden, die in der Umgebung von Gitterstörungen lokalisiert sind. Die Ausheilung der fUr die Verfärbbarkeitserhöhung verantwortlichen Defekte wird im Anfangsteil der FZentren-Bildungskurve verfolgt. Die Defekte nach Abschrecken heilen mit einer diskreten Aktivierungsenergie von 1,6 eV aus und sind offenbar verbunden mit der Art des Einbaues der als Verunreinigungen vorliegenden 2-wertigen Kationen. Bei deformierten und röntgenvorbestrahlten Proben ergeben sich diskrete Werte zwischen 1,6 eV und 2,0 eV. Daraus wird geschlossen, daß die für die Verfärbbarkeitserhöhung verantwortlichen zusätzlichen Anionenleerstellen sicher nicht isoliert, sondern wahrscheinlich in Form von relativ kleinen Leerstellen-Clustern ziemlich einheitlicher Größe nach diesen Vorbehandlungen im Kristall'zurückbleiben. Ihr Abbau erfolgt über die Diffusion von isolierten Anionenleerstellen zu geeigneten Senken im Kristall. r.M. ryCEBA h n . C . 3HPHH0B, MHCTHTyT $H3HKK MeTaJMöB

A.H. CCCP, CBepflJiOBCK, K KBaHTOBOfl TeopHK TepMorajiBBaHQMarHHTHMX HBJieHHft B MeTajuiax H nojiynpoBQflHHKax ( I I I ) npoH3BeseHo cpaBHeHwe TeopwH ( 1 ,

2 ) c SKcnepmieHTaMH CTWJIA H EAEMCKHHA ( 3 ) ,

nyPH HfllEBJIJIA(4) no H3yqeHH» TepMorajiBB'aHOMarHHTHux HBJieHHM B KBaHTyiomeu MarHHTHOM nojie. (1 ) n.C. 3MPHH0B, phys. stat. sol. 6, 401 (1964). (2) n.C. 3HPHH0B, phys. stat. sol. 7, 223 (1964)$ $H3. MeTajiaoB H MeTanitOBeaeHHe

16., 13 (1963).

(3) M.C. STEELE and J. BABISKIN, Phys. Rev. 98, 359 (1955). (4) S.M. PURI and T.H. GEBALLE, Phys. Rev. Letters 9, 378 (1962). M. NACHMAN, L.N. COJOCAEU, and L.V. RIBCO, Institute for Atomio Physics, Bucharest, Electrical Properties of NonStoichiometric Nickel Oxide The temperature dependence of the electrical conductivity and of the Seebeck coefficient of

K104

Titles and Abstracts, phys. stat. sol.

NiO samples with various

concentrations is determined.

These samples are obtained from a nickel salt, using various decomposition temperatures. The temperature dependence of the hole concentration, ptt , is calculated from the Seebeck coefficient. Since p a is constant up to about 500 °K, the exponential temperature variation of the conductivity must be attributed to the temperature dependence of the mobility. It seems, therefore, that at least up to the N6el temperature non-stoichiometric NiO exhibits a similar conduction mechanism to Li2+

doped NiO, with holes hopping between Ni ions. The discrepancies between the values of the hole concentration determined from the Seebeck coeffioient and those given by the chemical analysis are discussed in terms of a simplified model, taking into account the non-uniform distribution of the excessoxygen atoms throughout the volume of the NiO grains. The results confirm that for NiO samples of high excess-oxygen content the electrical conduction is mainly due to grain boundarie L. STA1S and J. NIHOUL, Solid State Physics Departement, S.C.K. - C.E.N., Mol, Stage III Recovery in Cold-Worked Niobium Stage III recovery in niobium, cold-worked at room temperature, is investigated by means of electrical resistivity measurements The associated activation energy is found to be constant in the temperature range from 80 to 180 °C and equal to 1.20 + 0.04 eV Furthermore, the results indicate that the reoovery process can be described as a diffusion*oontrolled bimolecular reaction which follows Waite kinetics (1). It is concluded that this recovery is caused by recombination of intrinsic point defects. On the basis of the presently available data the possibility of this recovery being caused by migration of vacancies to trapped interstitials cannot be excluded. In view, however, of the relatively small activation energy found for this stage, and of the direct analogy with stage III reoovery in the f.c.c. metals, it is tentatively proposed that stage III recovery in b.c.c. metals is due to interstitial migration to vacancies. (1) T.R. WAITE, Phys. Rev. 107, 463 (1957). I. KOVACS and E. NAGY, Institut for Experimental Physics, Lor^nd EbtvBs University, Budapest, Plastic Properties of Poly-

Titles and Abstracts, phys. stat. sol.

K105

crystalline FCC Metals For polycrystalline f.c.c. metals, deformed by simultaneous torsion and extension, it is shown that the specifio resistivity change depends only on the total strain, as reported in (1), but is independent of the ratio of the individual strains. Further it is shown that the relation A ? = fty) cannot be characteristic for a metal, since its form is very sensitive to the sample history. However, a relation independent of sample history can be established between the resistivity change and the instantaneous flow stress. Under the condition that the resistivity due to the point defeots is assumed to be half of the total resistivity, this relation gives directly the resistivity due to the unit length of a •dislocation, in good agreement with previous experimental and theoretical estimates. (1) P. FELTHAM, Phil. Mag. 8, 989 (1963). F. BBLEZNAY and G. PATAKI, Research Institute for Technical Physics of the Hungarian Academy of Sciences, Budapest, On the Theory of Radiative Reoombination in High Magnetic Field in Semiconductors The effect of a high magnetic field on the recombination of electrons between conduction band and acceptor states is examined. It is found that at magnetic fields which correspond to the "quantum limit" for the conduction band but give no "deformation" of the aoceptor states, the transition matrix element does not depend on the magnetic field. The assumptions for the magnetic field are fulfilled for the case of laser radiation in magnetic field. In the range of validity of the hydrogen-like model, the field dependence of the threshold current must be determined by the change of the density of states. A. KITZ, Institut ftir Theoretisohe Physik der JustusLiebig-Universität, Gießen, Über die irreduzlblen Darstellungen der Raumgruppen und die Strahldarstellungen der kristallographischen Punktgruppen Es wird ein Verfahren beschrieben, wie man aus den Strahldarstellungen der kristallographisohen Punktgruppen die irreduziblen Darstellungen der Raumgruppen findet. Diese Methode läßt sich ebenso auf die doppelten Raumgruppen anwenden. Da man hierbei die Strahldarstellungen der doppelten

K106

Titles and Abstracts, phys. stat. sol.

kristallographischen Punktgruppen braucht, werden sämtliche, voneinander verschiedene Strahldarstellungen dieser Gruppen aufgestellt. H. KELLER und J. STUKE, Institut ftir angewandte Physik der Technischen Hochschule Karlsruhe, Elektrische und optische Eigenschaften von amorphem Tellur An aufgedampften amorphen Te-Schichten wurde die Temperaturabhängigkeit der spezifischen Leitfähigkeit gemessen. Bei hohen Temperaturen ( > 200 °K) ist die Eigenleitung mit 4 E