Fluid Metals: The Liquid-Vapor Transition of Metals [Core Textbook ed.] 9781400865000

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FLUID METALS

PHYSICAL CHEMISTRY: SCIENCE AND ENGINEERING SERIES EDITORS: John M. Prausnitz Leo Brewer Debenedetti, Metastable Liquids: Concepts and Principles Hensel and Warren, Fluid Metals: The Liquid-Vapor Transition of Metals

Fluid Metals The Liquid-Vapor Transition of Metals FRIEDRICH HENSEL AND W I L L I A M W. W A R R E N , J R .

PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY

Copyright ©1999 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, Chichester, West Sussex All Rights Reserved

Library of Congress Cataloging-in-Publication Data Hensel, Friedrich, 1933Fluid metals : the liquid-vapor transition of metals / Friedrich Hensel and William W. Warren, Jr. p. cm. — (Physical chemistry) Includes bibliographical references and index. ISBN 0-691-05830-X (cl : alk. paper) 1. Liquid metals. I. Warren, William W., 1938II. Title. III. Series: Physical chemistry (Princeton, N.J.) QC173.4.L56H46 1999 530.4Ί4—dc21 This book has been composed in Times Roman and Times Roman Bold The paper used in this publication meets the minimum requirements of ANSI/NISO Z39.48-1992 (R1997) (Permanence of Paper) http://pup.princeton.edu Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

98-27753 CIP

Contents List of Figures List of Tables Preface Chapter 1 - Introduction

1.1 The Science of Fluid Metals 1.2 The Liquid-Vapor Critical Point Data of Fluid Metals and Semiconductors 1.3 Technological Considerations 1.4 Scope of the Book

Chapter 2 - Fluids with State-Dependent Electronic Structure

2.1 Fluid Metals 2.2 Fluid Semiconductors 2.3 Mechanisms of Electronic Transitions 2.4 Theories of the Metal-Nonmetal Transition and Phase Behavior in Fluids 2.5 Challenges for Experimentalists

Chapter 3 - Alkali Metals 3.1 3.2 3.3 3.4 3.5 3.6 3.7

Monovalent Fluid Metals Magnetic Properties Optical Properties Structure The Equation of State Electron Transport Hydrogen—The Lightest Alkali Metal?

Chapter 4 - Mercuiy

4.1 A Divalent Fluid Metal 4.2 Optical Properties 4.3 Magnetic Properties 4.4 Structure 4.5 The Equation of State 4.6 Electron Transport 4.7 The Metal-Nonmetal Transition in Mercury Clusters

vii xiii xv 3 3

6 8 9

11

11 19 24

37 49

54

54 54 69 77 92 99 107

114 114 115 125 129 134 142 152

vi -

CONTENTS

Chapter 5 - Chalcogens 5.1 5.2 5.3 5.4

Selenium; The Middle Chalcogen Structure Optical Properties Electronic Transport 5.5 Magnetic Properties 5.6 The Equation of State 5.7 Electronic Transitions in the Critical Region

Chapter 6 - Critical Fluctuations and Interfacial Phenomena 6.1 6.2 6.3 6.4 6.5

Fluctuations and the State-Dependent Interaction The Critical Region of Single-Component Fluids Critical Phenomena in Dilute Binary Mixtures Wetting Homogeneous Nucleation of Supersaturated Metal Vapor

Chapter 7 - High-Temperature/High-Pressure Techniques 7.1 ThelnternallyHeatedAutoclave

7.2 Equation-of-State and Electrical Measurements 7.3 Magnetic Measurements 7.4 Neutron Diffraction Studies 7.5 Optical Measurements 7.6 X-Ray Measurements

162 162 163 167 172 178 184 186 192 192 194 200 208 213 219 219 221 223 227 230 231

Appendix

235

Index

239

List of Figures Fig. 2.1 The effective pair interaction potentials of liquid argon and sodium near their triple points. 13 Fig. 2.2 Schematic phase diagrams for a metallic element in pressure-temperature plane (a) and density-temperature plane (b). 14 Fig. 2.3 Isothermal equation-of-state (a) and DC electrical conductivity (b) data for cesium at sub- and supercritical temperatures as functions of pressure. (Hensel et al., 1985, 1991) 17 Fig. 2.4 Isothermal equation of state (α) and DC electrical conductivity (b) data for mercury at sub- and supercritical temperatures as functions of pressure. (Gotzlaff, 1988) 18 Fig. 2.5 Schematic electronic energy level diagram for selenium showing valence electron states of the free atom, splittings due to interactions with a second atom, and energy bands in the condensed phases of selenium. 19 Fig. 2.6 Isothermal equation-of-state ( a ) and DC electrical conductivity ( b ) data for selenium at sub- and supercritical temperatures as functions of pressure. 22 Fig. 2.7 Pressure-temperature phase diagram of selenium showing solid, liquid, and vapor phases together with regions of semiconducting (SC), metallic (M), and insulator (I) behavior. 23 Fig. 2.8 Schematic electronic energy states of atoms ( a ) , small molecules (b ), large molecules (c), and condensed phases (d) either solid or liquid. 25 Fig. 2.9 Electronic wave function Ψ(Γ) for the case (a) when the mean free path λ is much larger than the mean interatomic distance a and (b) when λ is comparable with a (after Mott, 1974). 28 Fig. 2.10 Allowed energy values for an electron in crystalline mercury versus the reciprocal density. 30 Fig. 2.11 Schematic pressure-temperature (ρ — Τ) phase diagrams proposed by Landau and Zeldovich (1943): S = solid, L = liquid, G = gas, M = metal, NM — nonmetal. 38 Fig. 2.12 Calculated composition of cesium plasma (Redmer and Ropke, 1989) as a function of the total atom density NA at a constant temperature of 2000 K. 42 Fig. 2.13 Density of states N ( E ) versus energy from band calculations for mercury in a series of crystal structures with constant interatomic separations (Mattheiss and Warren, 1977). 45 Fig. 3.1 Total mass susceptibility xg of liquid rubidium and cesium as a function of temperature along the liquid-vapor coexistence curve. 58

viii - LIST OF FIGURES

Fig. 3.2 Electronic, paramagnetic volume susceptibility of liquid cesium (derived from data of Freyland, 1979) as a function of reduced density p/p . 59 Fig. 3.3 Effective mass ratio m * = m e f f / m 0 of liquid cesium as a function of 61 density (Knuth et al., 1997). Fig. 3.4 Relative fractions of free conduction electrons and electrons localized on neutral atoms, ionized dimers, and neutral dimers in cesium as a function of density (Redmer and Warren, 1993a, b). 62 Fig. 3.5 133Cs NMR Knight shift in liquid cesium (El-Hanany et al., 1983; Warren et al., 1989) as a function of temperature at constant pressures of 90 bar and 120 bar. 65 Fig. 3.6 133Cs Korringa enhancement ratio, defined in Eq. (3.13), as a function of density in liquid cesium at various constant pressures (El-Hanany et al., 1983; Warren et al., 1989). 68 Fig. 3.7 Optical reflectivity R of liquid cesium as a function of photon energy at various temperature-density points (Knuth and Hensel, 1990; Knuth et al., 1997). 72 Fig. 3.8 Absorption spectrum of cesium vapor (Muller, 1993) at 420°C (N = 1.4 χ IO17 cm-3). Inset, photoionization cross-section for formation of the dimer ion CsJ as a function of photon energy. 74 Fig. 3.9 Absorption spectra of cesium vapor (Knuth, 1990) at various tempera­ ture-atom density points. 75 Fig. 3.10 The pair distribution function g(R) of expanded liquid cesium at various temperature-density points near the liquid-vapor coexistence line. 78 Fig. 3.11 Experimentally determined liquid structure factor S(Q) of liquid cesium at various temperature-density points near the liquid-vapor coexistence 79 line (Winter et al., 1987, 1988). Fig. 3.12 Average number of nearest neighbors N1 for liquid cesium (Winter et al., 1987, 1988), rubidium (Franz et al., 1980b), and argon (Mikolaj and Pings, 1967), and the average distance of nearest neighbors R1 for liquid cesium as a function of the density relative to the liquid density pmp at the normal melting point. 82 Fig. 3.13 Experimentally determined dynamic scattering laws S(Q, ω) at Q = 1 . 0 A" 1 ( a ) a n d c u r r e n t c o r r e l a t i o n f u n c t i o n s J i i Q , ω ) a t Q — 1 . 3 A- 1 ( b ) for liquid rubidium at four different temperatures along the liquid-vapor coexistence line (Pilgrim et al., 1997). 86 Fig. 3.14 Dispersion curves obtained from the maxima hmm in the longitudinal current correlation function for liquid rubidium at various temperatures along the liquid-vapor coexistence line (Pilgrim et al., 1991). The data for 42°C are those of Copley and Rowe (1974a, b). 87 Fig. 3.15 Bond networks at (a) 50 C and (b) 1400 C obtained from reverse Monte Carlo computations (after Nield et al., 1991). 89 c

LIST OF FIGURES

- ix

Fig. 3.16 Test of Eq. (3.27) comparing the density- and wave number- derivatives of the liquid structure factor for cesium at three temperatures along the 91 liquid-vapor coexistence curve (Winter et al., 1988). Fig. 3.17 Isochores and vapor pressure curve of fluid cesium in the temperature and pressure range approaching the critical point (Hensel et al., 1986). 93 Fig. 3.18 Reduced plot of the internal pressure, ρ, = —(dU/dV)T of fluid cesium and rubidium at saturation conditions as a function of the liquidvapor equilibrium temperature. The corresponding densities can be taken from Tables A.1 and A.2. 94 Fig. 3.19 Isothermal compressibility χ τ of fluid cesium as a function of density at various constant temperatures (Jiingst, 1985). 100 Fig. 3.20 DC electrical conductivity of fluid cesium as a function of temperature along the liquid-vapor coexistence line. 102 Fig. 3.21 The absolute thermoelectric power of cesium as a function of temperature at various pressures (Freyland et al., 1974). 103 Fig. 3.22 DC electrical conductivity of fluid cesium (Hensel et al., 1985, 1991), rubidium (Freyland, 1981), and hydrogen (Weir et al., 1996), versus atomic density. 108 Fig. 4.1 Optical conductivity σ ( ω ) as a function of energy ( Κ ω ) of liquid mercury at various density/temperature points along the liquid-vapor coexistence line (Hefner et al., 1980). 116 Fig. 4.2 Optical absorption Κ ( ω ) as a function of energy ( Κ ω ) of fluid mercury at various densities (in g cm"3) at constant supercritical temperature 1550°C (Hensel and Yao, 1996). 117 Fig. 4.3 Density dependence of optical gap E g and the energy at which the absorption coefficient K is equal to 2 χ IO4 cm-1 for fluid mercury at constant 119 supercritical temperature 1550°C (Hensel and Yao, 1996). Fig. 4.4 Real part of the dielectric constant C1 (1.27 eV) as a function of density for fluid mercury at constant supercritical temperature 1570°C (Hensel, 1990). 121 Fig. 4.5 Excess pair polarizability Α β and calculated pair correlation function g(R) as a function of the interparticle separation for mercury vapor (Hensel, 1995). 125 199 Fig. 4.6 Hg NMR Knight shift as a function of density for liquid mercury close to the liquid-vapor coexistence line (El-Hanany and Warren, 1975; Warren and Hensel7 1982). 127 Fig. 4.7 Density of electronic states at the Fermi level as a function of density from LAPW band calculations for crystalline mercury in FCC (N1 = 12); BCC (N1 = 8); SC (N1 = 6); and diamond (N1 = 4) structures (Mattheiss and Warren, 1977). 129 Fig. 4.8 Pair correlation function g ( R ) as a function of R for liquid mercury (Tamura and Hosokawa, 1994). 130

χ - LIST OF FIGURES

Fig. 4.9 Average atomic coordination number N 1 and nearest-neighbor distance .R1 as a function of density for Uquid mercury. Inset, integration method used to determine N1, 132 Fig. 4.10 Pressure-temperature phase diagram of mercury with isochores at the indicated densities (Gotzlaff, 1988). 135 Fig. 4.11 Isothermal compressibility of mercury as a function of density at various supercritical temperatures approaching the critical temperature Tc = 1478°C (Gotzlaff, 1988). 136 Fig. 4.12 The isochoric thermal pressure coefficient, y v , of fluid mercury versus density along the liquid-vapor coexistence curve derived from isochores of Fig. 4.10. 137 Fig. 4.13 The internal pressure, p„ of fluid mercury versus density along the liquid-vapor coexistence curve derived from isochores of Fig. 4.10. 137 Fig. 4.14 Effective hard-sphere diameter, cr.//, for liquid mercury versus density along the liquid-vapor coexistence curve (Schonherr et al., 1979; Gotzlaff, 1988). 138 Fig. 4.15 Isothermal pressure derivative of the DC electrical conductivity of mercury, (