Pattern Formation at Interfaces (CISM International Centre for Mechanical Sciences, 513) 3709101247, 9783709101247

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SpringerWienNewYork

CISM COURSES AND LECTURES

Series Editors: The Rectors Giulio Maier - Milan Jean Salençon - Palaiseau Wilhelm Schneider - Wien

The Secretary General Bernhard Schrefler - Padua

Executive Editor Paolo Serafini - Udine

The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.

INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 513

PATTERN FORMATION AT INTERFACES

EDITED BY PIERRE COLINET UNIVERSITE LIBRE DE BRUXELLES, BRUSSELS, BELGIUM ALEXANDER NEPOMNYASHCHY TECHNION-ISR. INST. OF TECHNOLOGY, HAIFA, ISRAEL

This volume contains 113 illustrations

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2010 by CISM, Udine Printed in Italy SPIN 12821907

All contributions have been typeset by the authors.

ISBN 978-3-7091-0124-7 SpringerWienNewYork




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26

Pierre Colinet

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Interfacial Patterns and Waves in Liquid Layers and Thin Films

27

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Nonlinear Dynamics of Fronts

87

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Thin Film and Droplet Patterns Shaped by Surface Forces

 

179

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182 

Len M. Pismen -2'-, "3# 2- 17++#207 -$ -,2!2 ,%*#1

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184

Len M. Pismen

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186

Len M. Pismen

MA> LBFIE>LM H? : I:BK H? =KHIE>ML L>I:K:M>= :M : =BLM:G 9 FNK MA:G MA>BK K:=BB %  HG> MA> +:IE: >JN:MBHG NLBG@ MA> ;BIHE:K LRLM>F PBMA MA> ?H =KHIE>M GM>KL 2A> L   K>LI>ER K>E:M>= MH MA> ":KM>LB:G L = > :L =

9 LBGA    BGBMB:E IHLBMBHGL :G= MA> LG >O>GML =HML F:KD >QMBGO>GML

L= ;R : EBG>:K DBG>MB< >JN:MBHG =-=;  3 - 3- PA>K> - BL MA> ;NED DBG>MB< E:MM>K BL :LLNF>= ?HK LBFIEB MA> L:F> BG MA> =KHIE>M :G= MA>  2:DBG@ BGMH :M MH ;> G>@EB@B;E> P> PKBM> MA> :=LHKIMBHG=BNLBHG >JN:MBHG ?HK MA> LNK?: HG MA> LN;LMK:M> BG MA> =BF>GLBHGE>LL ?HKF -   - -    



PA>K>   >JN:EL MH  HNMLB=> :G=  BGLB=> MA> =KHIE>M ?HHMIKBGM 2A> LNK?: - BL L= ;R MA> K:@> BG >JNBEB;KBNF PBMA MA> LNK ?: ;R MA> BGO>KL> =>LHKIMBHG K:M> G@MA ;R 3 PA>K>  BL MA> LNK?: LN;LMK:M> M E:M>K LM:@>L H? MA> IKHLL PA>G LNK?:M ;NED HG> MA> L:F> >JN:MBHG M:DBG@ BGMH

Thin Film and Droplet Patterns Shaped by Surface Forces

191

:K>G H? :=LHKIMBHG K:M>L HNMLB=> :G= BGLB=> MA> =KHIE>M BL BFIHKM:GM :G= K>IE: =B>K>G H? MA> K>LI> O:EN>L  2A> EH K:MBH H? MA> 8FBEH EHKFBG>L MA> BG N>G H? OBLLL>L HG MA> =KHIE>M LA:I> LNLM:BG>= ;R LNK?: M>GLBHG 2ABL BFIEB>L MA:M MA> K BL MA> MKN> LF:EE I:K:F>M>K H? MA> IKH;E>F =>OB:MBHGL H? MA> H? " ": MH CNLMB?R MA> I>KMNK;:MBHG :IIKH:K K>:EBLMB< >Q I>KBF>GM:E LA:I> H? FBEE>= =KHIE>ML BL HGER P>:DER =BLMHKM>= ;R OBLLL>L $JN:MBHG  MK:GL?HKF>= MH MA> ?K:F> FHOBG@ PBMA : =BF>GLBHGE>LL  O>EH = :QBL BL LHENMBHG H? MABL >JN:MBHG >QIK>LL>= PBMA MA> A>EI H? :G :IIKH IKB:M> &K>>GL ?NG@K:E HO>K MA> =KHIE>M ?HHMIKBGM :K>: :G= LN;L>JN>GMER MK:GL?HKF>= BGMH : @K:E PBMA MA> A>EI H? MA> &:NLL MA>HK>F /BLF>G    %HK : E> FH=NENL +  % 3 MA> KFBG>L MA> IKHI:@:MBHG LI>>= BL = BG MABL P:R :L  

   
        + > K>  :G=  ;>EHP :K> FH=B>= !>LL>E ?NG : EBG>:K ?NG LNK?:  
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

    = +    +   + LBG =   LBG   + =+ 

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194

Len M. Pismen 1
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198

Len M. Pismen

1

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206

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Thin Film and Droplet Patterns Shaped by Surface Forces

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+ B JW+ B JGBO B ZOB,"+Z 2W+ 8GJJG%+ .WUZGM +MWOGZ B JW+ K8GOZ!D+"+ " GOZJ
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B8J K8GOZ!D+"+ " GOZJ
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+ B8O= GO #%GZ -NN@



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2W+ K8GOZ!D+"+ " GOZJ
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OMW+= ZJ 8MJ8 + XO +.+ B  =+O= GJ+ M UZJ GZ ZWBO GO G7 /O=++=4 W+O .+ J8
JGBOZ B  M UZJ!+J GOJ+ M+  B O= =+! %+B. JW+U B +JP 
B8J JW+ GOGJG ZW.+ B JW+ 8OZJ
+ GOJ+ M+ XJ+

ZB+ JG+4 JW+ O+U B += GOJ+ M+
+MB+Z 8OZJ
+ GJZ+4
U JW+ Z+ +MWOGZ4 JW8Z +=GO JB JW+  BJW B JW+ Z+MBO= U ZJ 8MJ8 + 2WGZ . B! M+ZZ MBOJGO8+Z JB =Z JW+ B JGBO B J+ JG U O= 8 JG U ZJ 8MJ8 +Z4 +JM MW ZJ 8MJ8 +4 WB+%+ 4 WZ  MBBO +J8 +  . 
BGM!G"+ JG. B  O+
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Interfacial Phenomena in Materials Science

heat flows away here faster freezing

heat accummulates here slower freezing

235

MELT

CRYSTAL


   K+MWOGZ B JW+ K8GOZ!D+"+ " GOZJ
GGJU


   X =+O= GJ+ M UZJ B Z8MMGOBOGJ G+  B SG"ZO O= K ZW @ T+. GOJ+= GJW .+ GZZGBO B Z+%G+ DMG+OM+

236

Alexander A. Golovin

B JGBO O= . B.JGBO B JWGZ =+O= GJ+ JG. JWJ B Z JW+
ZGZ B JW+ WB+ =+O= GJGM ZJ 8MJ8 + [+J 8Z +O+ GC+ JW+ . B
+ B   BGO Z.W+ GM O8M+8Z =GZM8ZZ+= GO D+MJGBO - O= MBOZG=+ JW+  BJW B  M UZJ B O 
GJ  U ZW.+ GOJB O 8O=+ MBB+= +J [+J JW+ M UZJ ZW.+
+ =+ZM G
+=
U  8OMJGBO  + 0 N 2W+ +J J+.+ J8 +  U  B JW+ M UZJ4  4 GZ +ZZ JWO JW+ +8GG
G8 +JGO J+.+ J8 +  -   B ZG.GMGJU4 +J 8Z O++MJ JW+ SG

Z!2WBZBO +3+MJ B JW+ Z8 M+ +O+ U BO JW+ +8GG
G8 J+.+ J8 + J JW+ M UZJ!+J GOJ+ M+ /O JWGZ MZ+ JW+ J+.+ J8 + J JW+ G8G=!ZBG= GOJ+ M+ G
+ +8 JB JW+ +8GG
G8 +JGO J+.+ ! J8 +  O= B +B%+ 4 JW+ J+.+ J8 + #/1 JW+ M UZJ G
+ "#/# O= +8 JB  4 ZGOM+ BJW+ GZ+4 W+J ZB8 M+Z B ZGO"Z B8=
+ . +Z+OJ GOZG=+ JW+ M UZJ 2W+ . B
+ MO JW+ +B +
+ =+ZM G
+= MB.+J+U
U MBOZG=+ GO JW+ J+.+ J8 + ?+=   + GO JW+ +J4 O= JW+
B8O= U MBO=GJGBOZ J JW+ M UZJ!+J GOJ+ M+ =+ZM G
GO JW+ MBO=GJGBO B JW+ B! =UOGM +8GG
G8 O= JW+
OM+ B W+J ,8 / 0  

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A+ +  GZ JW+ JW+  =G38ZG%GJU4 6 GZ JW+ JW+  MBO=8MJG%GJU4 = GZ JW+ J+OJ W+J B +JGO .+ 8OGJ %B8+4 8 GZ JW+ OB  %+BMGJU B JW+  BGO M UZJ Z8 M+4 O=  GZ JW+ Z8 M+ OB  / O +%B%GO Z8 M+ GO JW ++!=G+OZGBO Z.M+ GZ G%+O
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8 0   IY   DGOM+ GO B8 . B
+ JW+ Z8 M+ B   BGO M UZJ GZ O /,14 G+ GJ GZ =+?O+=
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[+J 8Z OB 8Z+ JW+ BBGO J GM" GO%+OJ+=
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Interfacial Phenomena in Materials Science

237

Z  /&1 11# 1 # B  Q ZB%+ GJ O= ,1# ?O= '   JB ZJGZU +I@ [+J 8Z GOJ B=8M+  O+ 8OMJGBO4 



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244

Alexander A. Golovin

2W+ MBOZJOJZ  O=  + B8O=  B JW+ JB
B8O= U MBO=GJGBOZ J

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JGO #+

?N + 0   - >Y 

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+ B 1 @ @ 1   1 F 1 0 N

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1 N 0   -> 

$ 1 N 0 N

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+ B8O= GO J+ Z B WU.+ +B+J GM 8OMJGBO AB+%+ 4 GJ GZ B + MBO%+OG+OJ JB BB" B JW+ ZB8JGBO
U +OZ B  B
+OG8Z +JWB=4 GO JW+ B 
  1 0 @NN   

Interfacial Phenomena in Materials Science

245

D8
ZJGJ8J+ @NN GO $! JB B
JGO JW+ BBGO +M8

+OJ +JGBO B

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+ ?O= JWJ JW+ MB+MG+OJZ  J+O= JB C+ B 8GJ+ 8GM"U4 0 N7$N  0 @NNNN 0 N-$II  0 N  0 NNN$@ 0 N  0 NNNN-    2W+ +Z8JGO Z8 M+ ZW.+ WZ JW+ B  ZWBO GO G @N /J +WG
GJZ /"#/ GJW  =+MUGO .GJ8=+ O= JW+ %++OJW  BGO Z I#+  2W+ . +Z+OM+ B Z8 M+ BZMGJGBOZ GZ JW+ MW MJ+ GZJGM +J8 + B Z8 M+!=G38ZGBO!= G%+O Z8 M+ +JGBO JWJ BBZ  B JW+ B8 JW Z.JG =+ G%JG%+ MB

+Z.BO=GO JB JW+ [.MGO B JW+ +O M8 %J8 + 2W+ =+ G%JGBO B JW+ Z8 M+!=G38ZGBO +8JGBO O= JW+ ZB8JGBO B JW+  GO!
B8O= U  BB%+ . B
+ Z ? ZJ B
JGO+= GO JW+ MZZGM ..+


U K8GOZ K8GOZ 4 @Y74 WGMW JW+ =+ G%JGBO . +Z+OJ+= GO JWGZ Z+MJGBO MBZ+U BBZ

 ( (!  ( )
 (  ()"(()!   ( /O JWGZ Z+MJGBO + ZW =GZM8ZZ O G.B JOJ GOJ+ MG GOZJ
GGJU JWJ GZ

+J+= JB JW+ ?+= B OOBJ+MWOBBU O= +Z.BOZG
+ B JW+ B JGBO B GOJ+ +ZJGO OOB!ZM+ Z8 M+ ZJ 8MJ8 +Z M+= 8OJ8 =BJZP 6BOZG=+  ? B ZBG= M UZJGO+ J+ G =+.BZGJ+= BO  Z8 M+ B  Z8
ZJ J+ =+ B OBJW+ M UZJGO+ J+ G DBG=!BO!ZBG= =+.BZGJGBO GZ M+= +.GJU4 O= W+O JW+ =+.BZGJ+= J+ G GZ =G3+ +OJ  B JWJ B JW+ Z8
ZJ J+ GJ GZ M+= W+J+ B!+.GJU 2W+ =+.BZGJGBO . BM+ZZ GZ BJ+O =BO+
U +OZ B 
+ B JBZ B B+M8+Z WGJJGO JW+ Z8
ZJ J+4 JW+ ZB!M+= B+M8


+ +.GJU KH W+O JBZ  + =+.BZGJ+= BO  Z8
ZJ J+ JW+U ZJGM" JB JW+ JBZ B JW+ Z8
ZJ J+ ZB JWJ JW+ JBZ GOZG=+ JW+  BGO +.GJG ?  + 

O+= MMB =GOU DGOM+ JW+ M UZJ JJGM+ Z.MGOZ GO JB =G3+ +OJ J+ GZ 8Z8U =G3+  B BO+ OBJW+ "1 /",4 JW+ ?  BZ GO O +ZJGMU ZJ +ZZ+= ZJJ+4 O= WZ +ZJGM +O+ U ZJB += GO GJ /4 Z  +Z8J B ZB+ ,8MJ8JGBO4  Z .+ J8
JGBO GO JW+ B  B  Z WG ..+ Z BO JW+ ? Z8 M+4 JW+ + G
+ B + BB GOZG=+ JWGZ WG B JW+ JBZ B JW+ ? JB =58ZJ JW+G GOJ+ JBGM Z.MGO JB JW+ OB  +8GG
G8 %8+4 WGMW G += JB JW+ =+M +Z+ B JW+ +ZJGM +O+ U 2WGZ

246

Alexander A. Golovin

. BM+ZZ B JW+ WG B JGBO G JW+ +B +
+ +O+ +JGMU . ++ 
+4 WGMW G +Z8J GO O GOZJ
GGJU B  .O ? JWJ G =+MB.BZ+ GOJB  ZUZJ+ B GZO=Z 2W+ J OZ.B J +MWOGZ
U WGMW JW+ ? Z8 M+ +MBOZJ 8MJZ GJZ+ GOJB  ZUZJ+ B GZO=Z GZ Z8 M+ =G38ZGBO =GZM8ZZ+= GO JW+ . +%GB8Z Z+MJGBO 2WGZ +MWOGZ B JW+ GZO= B JGBO GZ ZMW+JGMU ZWBO GO G@@ Ge FILM Ge FILM

INSTABILITY Si SUBSTRATE

Si SUBSTRATE


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GGJU B O +.GJGU!ZJ GO+= ZBG= ? .+Z B Z8MW GZO=Z  + ZWBO GO G@- &O+ MO Z++ JWJ JW+U MO W%+ =G3+ +OJ ZW.+Z4 M+J+= B B8O=+= X JU.GM GZO= ZGC+ B JW+ B =+ B OOB+J+ Z4 WGMW GZ B JW+ Z+ B =+ B OGJ8=+ Z =+ H BG+ %++OJW B ++MJ BOZ GO Z+GMBO=8MJB Z 6BO?O+= GJWGO Z8MW Z8 M+ ZJ 8MJ8 +Z4 ++MJ BOZ +WG
GJ GOJ+ +ZJGO 8OJ8 . B.+ JG+Z JWJ MO
+ 8Z+= B 
GMJGBO B O+ ++MJ BOGM =+%GM+Z B JWGZ +ZBO Z8MW GZO=Z  + M+= # / #Z B +%G+Z B JW+ B JGBO O= . B.+ JG+Z B #Z Z++ DWMW8"GO O= HG
+  @Q HG
+  + -NN Q DJO + -NN  /O B =+ JB =+ZM G
+ JW+ =UOGMZ B JW+ B JGBO B #Z GO +.GJG ?Z BO+ ZWB8= 8Z+ JW+ Z8 M+ =G38ZGBO +8JGBO =+ G%+= GO JW+ . +%GB8Z Z+MJGBO AB+%+ 4 BO GJW JW+ Z8 M+ +O+ U4 JW+ Z8 M+ MW+GM .B! J+OJG ZWB8= GOM8=+ ZB JW+ +ZJGM +O+ U MM88J+= GO JW+ ? 2W8Z + W%+ ;  0   F )

@N- @ F ; W+ +  GZ  MBOZJOJ . B.B JGBO JB JW+ Z8 M+ =G38ZG%GJU B JBZ4 ) GZ JW+ Z8 M+ +O+ U4  GZ JW+ +O M8 %J8 +4 O=  GZ JW+ . J B Z8 M+ MW+GM .BJ+OJG MB

+Z.BO=GO JB JW+ +ZJGM +O+ U ZJB += GO JW+ +.GJG ? /J GZ MB.8J+= Z  BB W++Z O= BWOZBO 4 -NN   0

@  , 

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W+ +  GZ JW+ ZJ GO J+OZB 4 , GZ JW+ ZJ +ZZ J+OZB [O=8 O= [GZWGJZ 4 @$@4 O= JW+ 8Z8 MBO%+OJGBO B JW+ Z8JGBO B%+ JW+ +.+J+= GO=GM+Z

Interfacial Phenomena in Materials Science

247


   .+Z B 8OJ8 =BJZ 8..+ +J S+ #Z BO DGNN@ GGZ + @$  +. GOJ+= GJW .+ GZZGBO  B GGZ + @$4 M @$
U JW+ X+ GMO 6W+GM DBMG+JUQ 8..+ GWJ 
D+ #Z BO 
2+!BO!DG@@@ XMW
G + -NN  +. GOJ+= GJW .+ GZZGBO  B M XMW
G + -NN4 -NN
U JW+ X+ GMO WUZGM DBMG+JUQ B+ +J /OXZ #Z BO SXZNN@ S O=BZ + -NN  +. GOJ+= GJW .+ GZZGBO M  B S O=BZ + -NN4 -NN
U JW+ X+ GMO /OZJGJ8J+ B WUZGMZQ B+ GWJ MB Z+OGO B DGS+ #Z BO DGNN@  ?8 +
 MB

+Z.BO=Z JB J+ JG+ JWO  B B + -NNN  +. GOJ+= GJW .+ GZZGBO  B B B M + -NNN4 -NNN
U JW+ X+ GMO WUZGM DBMG+JU T+. GOJ+= GJW .+ GZZGBO  B D. GO+ 

248

Alexander A. Golovin

GO 8Z+= /O JW+ .. BGJGBO B GO+ +ZJGMGJU JW+B U4 , O=   + MBOO+MJ+=
U JW+ BBGO +JGBO [O=8 O= [GZWGJZ 4 @$@  
 , 0 - .  F 

@N  @F W+ +  GZ JW+ ZW+ B=88Z4  GZ JW+ BGZZBO*Z JGB4 O= . GZ JW+  BO+"+

=+J 2W+ ZJ GO J+OZB GZ =+J+ GO+=
U JW+ MB.BO+OJ B JW+ =GZ.M++OJ %+MJB  JWJ MW MJ+ GC+Z Z =+B JGBOZ B  ZBG=
B=U4  0

@ /  F /   -

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U JW+ +.GJG ZJ +ZZ M8Z+=
U JW+ JJGM+ GZJMW
+J++O JW+ ? O= JW+ Z8
ZJ J+ 6BOZG=+  JWGO ZBG= ? =+.BZGJ+= BO  Z+G! GO?OGJ+ ZBG= Z8
ZJ J+ 2W+ GOJ+ M+
+J++O JW+ ? O= JW+ Z8
ZJ J+ GZ .O O= JW+ !GZ GZ OB  JB GJ4 GJW   N MB

+Z.BO=GO JB JW+ Z8
ZJ J+ O= N    ; ? + MB

+Z.BO=GO JB JW+ ?Q  0 ; ? + =+ZM G
+Z JW+ ZW.+ B JW+ ?  ++ Z8 M+4 O= ?  + JW+ MBB =GOJ+Z GO JW+ .O+ . + JB JW+ Z8
ZJ J+ DGOM+ Z8 M+ =G38ZGBO . BM+ZZ+Z  + 8MW ZB+ JWO JW+ Z.++= B ZB8O= GO  M UZJGO+ J+ G JWJ =+J+ ! GO+Z JW+ MW MJ+ GZJGM JG+ B +ZJGM +JGBO4 + MO ZZ8+ JWJ J +MW B+OJ B JG+ JW+ + GZ +MWOGM +8GG
G8 GO JW+ ? O= GO JW+ Z8
ZJ J+ WGMW GZ =+ZM G
+=
U JW+ +8JGBO / , 0 N

@NI

+ ZWB8= ZB Z+J JW+ BBGO
B8O= U MBO=GJGBOZ G ZJ +ZZ! ++ ? Z8 M+4 , 7 0 N

@N7

W+ + 7  + JW+ MB.BO+OJZ B JW+ OB  JB JW+ ? Z8 M+Q GG MBOJGO8GJU B =GZ.M++OJ ?+= GO JW+ ? O= JW+ Z8
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@N$  0  F 9  ?  Q N

Interfacial Phenomena in Materials Science W+ + 90







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GZ JW+ JJGM+ GZJMW
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U JW+ M UZJ JJGM+ Z.MGOZ B JW+ MB

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G% =+MU B  =+B JGBOZ =++. GOJB JW+ Z+G!GO?OGJ+ Z8
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[+J 8Z ? ZJ MBOZG=+ JW+
ZGM ZJJ+P B JW+ +.GJG ?4 GO WGMW JW+ ZJ +ZZ+Z O= ZJ GOZ  + MBOZJOJ O= JW+ ?  ++ Z8 M+ GZ .O  &
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ZGM ZJJ+  + =+J+ GO+=
U JW+ JJGM+ GZJMW4     

0  0 9 @@- DGOM+ JW+ ?  ++ Z8 M+ GZ ZJ +ZZ! ++ O= JW+ ZJ +ZZ GZ MBOZJOJ4 JW+O JW+   %+ JGM ZJ +ZZ MB.BO+OJ 8ZJ
+ C+ B4 , 0 N 2W+O  B JW+ ZJ +ZZ! ZJ GO +JGBO @N  + ?O= JW+ %+ JGM MB.BO+OJ B JW+ ZJ GO GO JW+ ?4 -9    0  @@ @   2W+O4 GO  B @N  + ?O= JW+ WB GCBOJ MB.BO+OJZ B JW+ ZJ GO J+OZB 4

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0 , 0 -9 @   . +ZZGBOZ @@-!@@  + M+= +.GJG ZJ GO O= @@  GZ M+= +.G! JG ZJ +ZZ + MO Z++ JWJ
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250

Alexander A. Golovin

9BJ+ JWJ JWGZ +O+ U =B+Z OBJ =+.+O= BO JW+ ZGO B JW+ JJGM+ GZJMW4 G+ GJ =B+Z OBJ =+.+O= BO W+JW+ JW+ +.GJG ZJ GO GZ MB. +ZZG%+ B

J+OZG+ XZ =GZM8ZZ+= 
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+ 8OZJ
+ GJW +Z.+MJ JB JW+ 8O=8JGBOZ B JW+ ?  ++ Z8 M+ JWJ MO +Z8J GO JW+ B JGBO B B8O=Z O= GO JW+ =+M +Z+ B JW+ +ZJGM +O+ U ZJB += GO JW+ ? /O B =+ JB ZWB JWJ + O++= JB .+ B   GO+ ZJ
GGJU OUZGZ B JW+
ZGM ZJJ+ =+ZM G
+= 
B%+ 2WGZ OUZGZ GZ 8GJ+ M8
+ ZB+ O= JW+ =+JGZ MO
+ B8O= GO D.+OM+ + @@4 @ A+ + + ZW =+ZM G
+ JW+ GO ZJ+.Z B JWGZ OUZGZ + MBOZG=+ GO?OGJ+ZG .+ J8
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B8O= U MBO=GJGBOZQ  G
+ B
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JGO  0 5 9 +ZJGM MBOZJOJZ

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W+ + 5 GZ ZB+ M8
+ ZB+ 8OMJGBO B GJZ % G
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JGO JW+ =GZ.+ ZGBO +JGBO  0 5  9 +ZJGM MBOZJOJZ
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JGBOZ 2W+ MB.+JGJGBO B JW+ JB +3+MJZ

Interfacial Phenomena in Materials Science

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W

+=Z JB JW+ Z++MJGBO B  MW MJ+ GZJGM %++OJW B JW+  BGO ZJ 8M! J8 +4 6 0 -14 4 W+ + 4 MB

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+ G.B JOJ B JW+ B JGBO B #Z4 B +.+4 +JJGO GOJ+ MJGBOZ
+J++O JW+ ? O= JW+ Z8
ZJ J+ O= Z8 M+!+O+ U OGZBJ B.U &O+ MO += 
B8J JW+Z+ +3+MJZ Z + Z 
B8J OBOGO+

+%B8JGBO B JW+ 

UZ B #Z GO SBB%GO + 4 -NNI4 -NN Q [+%GO+ + 4 -NN7 O= GO ++ +OM+Z JW+ +GO

252

Alexander A. Golovin

 
&!  XMW
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BZGBO M M"GO 1 #/4 @7$@7I4 @7- # HG
+ 4 K S 8O=OO4 O= 99 [+=+OJZB% # ( 1& 1/"1/4 6WGMW+ZJ+  G+U4 @ DA #%GZ ,1%  "#4 6
G=+ OG%+ ZGJU  +ZZ4 -NN@ X B B4 KH DGOMG 4  6WZBO4 [H  +8O=4 T# 2+ZJ+O4 T AO4 O= SX [8M=B 9B%+ DGS+ GZO= MB Z+OGO "GO+JGMZ &ZJ! = G.+OGO O= +ZJGM GOJ+ MJGBOZ ,%/ '1* 014 $ 7N@7N 4 -NNN K SG"ZO O= D K ZW 2W+ =+O= GJ+ /O #2 A8 +4 +=GJB 4 #)  %/ $,4 Z+%G+ 4 @ 6 SB= +MW+4 +=GJB  /     6
G=+ OG%+ ZGJU  +ZZ4 @- XX SBB%GO4  BB W++Z4 O= DA #%GZ D+!ZZ+
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GGJU B JW+ Z+. JGBO
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ZJ J+ ,%/ '1*  7Y-NY@-4 -NN7

Interfacial Phenomena in Materials Science

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 K8GOZ 2W+B U B JW+   BB%GO ! -

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