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Thermodynamic Modeling of Solid Phases


Thermodynamic Modeling of Solid Phases


1. Aufl.

von: Michel Soustelle

139,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 26.08.2015
ISBN/EAN: 9781119178521
Sprache: englisch
Anzahl Seiten: 266

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Beschreibungen

<p>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.</p>
<p>PREFACE ix</p> <p>NOTATIONS AND SYMBOLS xiii</p> <p><b>CHAPTER 1. PURE CRYSTALLINE SOLIDS 1</b></p> <p>1.1. Characteristic values of a solid 1</p> <p>1.2. Effect of stress and Young’s modulus 2</p> <p>1.3. Microscopic description of crystalline solids 4</p> <p>1.4. Partition function of vibration of a solid 5</p> <p>1.4.1. Einstein’s single-frequency model 5</p> <p>1.4.2. Debye’s frequency distribution model 6</p> <p>1.4.3. Models with more complex frequency distributions 9</p> <p>1.5. Description of atomic solids 10</p> <p>1.5.1. Canonical partition function of an atomic solid 10</p> <p>1.5.2. Helmholtz energy and internal energy of an atomic solid 11</p> <p>1.6. Description of molecular solids 13</p> <p>1.6.1. Partition function of molecular crystals 13</p> <p>1.6.2. Thermodynamic functions of molecular solids 14</p> <p>1.7. Description of an ionic solid 15</p> <p>1.7.1. Crosslink energy of an ionic solid 15</p> <p>1.7.2. Born/Haber cycle 22</p> <p>1.7.3. Vibrational partition function and internal energy of an ionic solid 23</p> <p>1.8. Description of a metallic solid 26</p> <p>1.8.1. Sommerfeld’s electron perfect gas model 27</p> <p>1.8.2. The metallic bond and band theory 37</p> <p>1.9. Molar specific heat capacities of crystalline solids 46</p> <p>1.9.1. Contribution of the vibrational energy to the specific heat capacity at constant volume 46</p> <p>1.9.2. Specific heat capacity of an atomic solid at constant volume 50</p> <p>1.9.3. Specific heat capacity of a molecularor ionic-solid at constant volume 54</p> <p>1.9.4. Conclusion as to the specific heat capacity of a crystalline solid 54</p> <p>1.10. Thermal expansion of solids 55</p> <p>1.10.1. Expansion coefficients 55</p> <p>1.10.2. Origin of thermal expansion in solids 58</p> <p>1.10.3. Quantum treatment of thermal expansion. Grüneisen parameter 62</p> <p>1.10.4. Expansion coefficient of metals 68</p> <p><b>CHAPTER 2. SOLID SOLUTIONS 71</b></p> <p>2.1. Families of solid solutions 71</p> <p>2.1.1. Substitutional solid solutions 72</p> <p>2.1.2. Insertion solid solution 75</p> <p>2.2. Order in solid solutions 82</p> <p>2.2.1. Short-distance order 83</p> <p>2.2.2. Long-distance order 87</p> <p>2.3. Thermodynamic models of solid solutions 94</p> <p>2.3.1. Determination of the Gibbs energy of mixing 94</p> <p>2.3.2. The microscopic model of the perfect solution 100</p> <p>2.3.3. Microscopic model of strictly-regular solutions 102</p> <p>2.3.4. Microscopic model of the ideal dilute solution 104</p> <p>2.3.5. Fowler and Guggenheim’s quasi-chemical model of the solution 106</p> <p>2.4. Thermodynamic study of the degree of order of an alloy 111</p> <p>2.4.1. Hypotheses of the model: configuration energy 112</p> <p>2.4.2. Expression of the configuration partition function 113</p> <p>2.4.3. The Gorsky, Bragg and Williams model 114</p> <p>2.4.4. The quasi-chemical model 120</p> <p>2.4.5. Comparison of the models against experimental results 127</p> <p>2.5. Determination of the activity of a component of a solid solution 132</p> <p>2.5.1. Methods common to solid solutions and liquid solutions 134</p> <p>2.5.2. Methods specific to solid solutions 140</p> <p><b>CHAPTER 3. NON-STOICHIOMETRY IN SOLIDS 147</b></p> <p>3.1. Structure elements of a solid 147</p> <p>3.1.1. Definition 148</p> <p>3.1.2. Symbolic representation of structure elements 149</p> <p>3.1.3. Building unit of a solid 151</p> <p>3.1.4. Description and composition of a solid 151</p> <p>3.2. Quasi-chemical reactions in solids 153</p> <p>3.2.1. Definition and characteristics of a quasi-chemical reaction between structure elements 153</p> <p>3.2.2. Homogeneous quasi-chemical reactions in the solid phase 156</p> <p>3.2.3. Inter-phase reactions 158</p> <p>3.3. Equilibrium states between structure elements in solids 158</p> <p>3.4. Thermodynamics of structure elements in unary solids 159</p> <p>3.4.1. Structure elements of a unary solid 159</p> <p>3.4.2. Global equilibrium of an isolated crystal – influence of temperature 162</p> <p>3.5. Thermodynamics of structure elements in stoichiometric binary solids 165</p> <p>3.5.1. Symmetrical disorders in stoichiometric binary solids 166</p> <p>3.5.2. Asymmetrical disorders in stoichiometric binary solids167</p> <p>3.6. Thermodynamics of structure elements in non-stoichiometric binary solids 169</p> <p>3.6.1. Deviations from stoichiometry and point defects 169</p> <p>3.6.2. The predominant defect method – the Wagner classification 171</p> <p>3.6.3. Equilibrium of a Wagner solid with one of its gaseous elements 174</p> <p>3.6.4. General equilibrium of a non-stoichiometric binary solid with one of its gaseous elements 175</p> <p>3.7. Representation of complex solids – example of metal oxy-hydroxides 180</p> <p>3.7.1. The pseudo-binary approximation 180</p> <p>3.7.2. The predominant-defect generalization 180</p> <p>3.8. Determination of the equilibrium constants of the reactions involving structure elements 181</p> <p>3.8.1. Recap on calculating the equilibrium constants using statistical thermodynamics 182</p> <p>3.8.2. Examination of the pre-exponential term in the quasi-chemical equilibrium constants 184</p> <p>3.8.3. Determination of the internal energy of transformation of quasi-chemical reactions 187</p> <p><b>CHAPTER 4. SOLID SOLUTIONS AND STRUCTURE ELEMENTS 195</b></p> <p>4.1. Ionic solid solutions 195</p> <p>4.1.1. Introduction of foreign elements into stoichiometric binary solids 197</p> <p>4.1.2. Influence of foreign elements introduced into a non-stoichiometric binary solid 200</p> <p>4.2. Thermodynamics of equilibria between water vapor and saline hydrates: non-stoichiometric hydrates 204</p> <p>4.2.1. Experimental demonstration of non-stoichiometry of a hydrate 204</p> <p>4.2.2. Equilibria between stoichiometric hydrates 207</p> <p>4.2.3. Equilibrium reactions in non-stoichiometric hydrates 207</p> <p>4.2.4. The limits of the domains of divariance 213</p> <p><b>APPENDICES 217</b></p> <p>APPENDIX 1. THE LAGRANGE MULTIPLIER METHOD 219</p> <p>APPENDIX 2. SOLVING SCHRÖDINGER’S EQUATION 223</p> <p>BIBLIOGRAPHY 227</p> <p>INDEX 231</p>
<b>Michel SOUSTELLE</b> is a chemical engineer and Emeritus Professor at Ecole des Mines de Saint-Etienne in France. He taught chemical kinetics from postgraduate to Master degree level while also carrying out research in this topic.

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