Thermodynamic Modeling of Solid Phases E-Book

Michel Soustelle

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 274

Veröffentlichungsjahr: 2015

Beschreibung

This book offers advanced students, in 7 volumes, successively characterization tools phases, the study of all types of phase, liquid, gas and solid, pure or multi-component, process engineering, chemical and electrochemical equilibria, the properties of surfaces and phases of small sizes. Macroscopic and microscopic models are in turn covered with a constant correlation between the two scales. Particular attention is given to the rigor of mathematical developments.  This book focuses on solid phases.

Leseprobe

Table of Contents

Cover

Title

Copyright

Preface

Notations and Symbols

1: Pure Crystalline Solids

1.1. Characteristic values of a solid

1.2. Effect of stress and Young’s modulus

1.3. Microscopic description of crystalline solids

1.4. Partition function of vibration of a solid

1.5. Description of atomic solids

1.6. Description of molecular solids

1.7. Description of an ionic solid

1.8. Description of a metallic solid

1.9. Molar specific heat capacities of crystalline solids

1.10. Thermal expansion of solids

2: Solid Solutions

2.1. Families of solid solutions

2.2. Order in solid solutions

2.3. Thermodynamic models of solid solutions

2.4. Thermodynamic study of the degree of order of an alloy

2.5. Determination of the activity of a component of a solid solution

3: Non-stoichiometry in Solids

3.1. Structure elements of a solid

3.2. Quasi-chemical reactions in solids

3.3. Equilibrium states between structure elements in solids

3.4. Thermodynamics of structure elements in unary solids

3.5. Thermodynamics of structure elements in stoichiometric binary solids

3.6. Thermodynamics of structure elements in non-stoichiometric binary solids

3.7. Representation of complex solids – example of metal oxy-hydroxides

3.8. Determination of the equilibrium constants of the reactions involving structure elements

4: Solid Solutions and Structure Elements

4.1. Ionic solid solutions

4.2. Thermodynamics of equilibria between water vapor and saline hydrates: non-stoichiometric hydrates

APPENDICES

Appendix 1: The Lagrange Multiplier Method

A.1.1. Statement of the problem

A.1.2. Solution by the multiplier method

A.1.3. Determination of the values of the multipliers

Appendix 2: Solving Schrödinger’s Equation

Bibliography

Index

End User License Agreement

Guide

Cover

Table of Contents

Begin Reading

List of Illustrations

1: Pure Crystalline Solids

Figure 1.1. Cylindrical test tube a) under traction; b) under compression

Figure 1.2. Strain/stress curve under traction

Figure 1.3. Frequency distribution according to Debye

Figure 1.4. Frequency distributions: a) Born and Karman; b) Blackman

Figure 1.5. Born–Haber cycle for a compound A

a

B

b

Figure 1.6. Energy distribution of the free electrons in a metal at 0 K

Figure 1.7. Diagrammatic representation of a one-dimensional metal

Figure 1.8. Combination of levels into bands

Figure 1.9. Diagram of bands for metals, insulators and semi-conductors

Figure 1.10. Energy band structure in a metal

Figure 1.11. Distribution of states of s and p bands, with overlap, for a centered cubic crystal (data from [FOW 49])

Figure 1.12. Occupation of states in a) a monovalent metal; b) a divalent metal; c) a semi-conductor; d) an insulator

Figure 1.13. Comparison of the curves of the Einstein and Debye contributions for the specific heat capacity

Figure 1.14. Debye curve and specific heat capacities at constant volume for a number of atomic solids

Figure 1.15. Potential energy curves for a) the harmonic oscillator, and b) an anharmonic oscillator

Figure 1.16. Shape of the curve of the expansion coefficient with temperature in the context of the Debye approximation

Figure 1.17. Grüneisen parameter for a few alkali halides (data from [WHI 65])

Figure 1.18. Variation of the Grüneisen parameter for copper with the volume (data taken from [GIR 00])

Figure 1.19. Expansion of copper at low temperature, according to [PER 70]

2: Solid Solutions

Figure 2.1. Insertion sites in a compact lattice: a) octahedral site and b) tetrahedral site

Figure 2.2. Octahedral sites in a cubic lattice with centered faces

Figure 2.3. Tetrahedral sites in a cubic system with centered faces

Figure 2.4. Octahedral sites in a centered cubic system

Figure 2.5. Tetrahedral sites in a centered cubic system

Figure 2.6. Octahedral sites in a hexagonal compact structure

Figure 2.7. Tetrahedral sites in a hexagonal compact lattice

Figure 2.8. Diagrammatic representation: a) completely disordered solution; b) ordered solution and; c) solution with single-component clusters

Figure 2.9. Order in the alloy CuAu

Figure 2.10. Order in the alloy Fe

3

Al

Figure 2.11. Comparison of the excess Gibbs energy values

Figure 2.12. Variation of the degree of order as a function of the composition of a binary solution in the quasi-chemical model (data taken from [DES 10])

Figure 2.13. Variations in Helmholtz energy as a function of the degree of order, according to the GBW model for a solid AB with different values of the ratio –w

AB

/2k

B

T

Figure 2.14. Variations of the degree of order with temperature: a) solid of type AB and b) solid of type A

3

B

Figure 2.15. Dependence of pairs situated on four sites adjacent to a plane

Figure 2.16. Comparison of the models with experiments

Figure 2.17. Critical temperature as a function of the composition. Comparisons between models and experience. a) Case of CuZn and b) case of Fe

3

Al (according to [SYK 37])

Figure 2.18. Specific heat capacity (per atom) of CuZn – comparison of the models and the experimental results [SYK 37]

Figure 2.19. Determination of Henry’s constant

Figure 2.20. Determination of the equilibrium constant between carbon, CO and CO

2

Figure 2.21. Obtaining the activity of an element of an alloy

3: Non-stoichiometry in Solids

Figure 3.1. Representation of the electron reaction on the band diagram

Figure 3.2. Representation of ionization reactions in the band diagram

Figure 3.3. Representation of a Kröger–Vink diagram

Figure 3.4. 2D representation of the crystal, showing a) the relaxation of the ions around the vacancy; b) Mott and Littleton’s calculation zones

4: Solid Solutions and Structure Elements

Figure 4.1. Diagram of potassium chloride a) in the pure state and b) doped with calcium ions

Figure 4.2. Concentrations of vacancies in calcium-doped potassium chloride

Figure 4.3. Diagram of iron oxide a) in the pure state and b) doped with lithium

Figure 4.4. Kröger-Vink diagrams for lithium-doped zinc oxide

Figure 4.5. Equilibrium isotherm between water vapor and a) a stoichimetric hydrate and b) a non-stoichiometric hydrate

Figure 4.6. Pressure–temperature diagram for a stoichiometric hydrate

Figure 4.7. Equilibrium isotherms between water vapor and a non-stoichiometric hydrate with non-localized water molecules

Figure 4.8. Isothermal curves showing the equilibrium between water vapor and a non-stoichiometric hydrate with localized water molecules

Figure 4.9. Domain of divariance limited by precipitation of the inferior hydrate into a new solid phase

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Thermodynamic Modeling of Solid Phases

Chemical Thermodynamics Set

Volume 3

Michel Soustelle

First published 2015 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com

© ISTE Ltd 2015The rights of Michel Soustelle to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2015944961

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-84821-866-6

Preface

This book – an in-depth examination of chemical thermodynamics – is written for an audience of engineering undergraduates and Masters students in the disciplines of chemistry, physical chemistry, process engineering, materials, etc., and doctoral candidates in those disciplines. It will also be useful for researchers at fundamental- or applied-research labs dealing with issues in thermodynamics during the course of their work.