| Preface |
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ix | |
| Notations and Symbols |
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xiii | |
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Chapter 1 Pure Crystalline Solids |
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1 | (70) |
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1.1 Characteristic values of a solid |
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1 | (1) |
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1.2 Effect of stress and Young's modulus |
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2 | (2) |
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1.3 Microscopic description of crystalline solids |
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4 | (1) |
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1.4 Partition function of vibration of a solid |
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5 | (5) |
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1.4.1 Einstein's single-frequency model |
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5 | (1) |
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1.4.2 Debye's frequency distribution model |
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6 | (3) |
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1.4.3 Models with more complex frequency distributions |
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9 | (1) |
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1.5 Description of atomic solids |
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10 | (3) |
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1.5.1 Canonical partition function of an atomic solid |
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10 | (1) |
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1.5.2 Helmholtz energy and internal energy of an atomic solid |
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11 | (2) |
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1.6 Description of molecular solids |
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13 | (2) |
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1.6.1 Partition function of molecular crystals |
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13 | (1) |
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1.6.2 Thermodynamic functions of molecular solids |
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14 | (1) |
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1.7 Description of an ionic solid |
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15 | (11) |
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1.7.1 Crosslink energy of an ionic solid |
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15 | (7) |
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22 | (1) |
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1.7.3 Vibrational partition function and internal energy of an ionic solid |
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23 | (3) |
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1.8 Description of a metallic solid |
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26 | (20) |
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1.8.1 Sommerfeld's electron perfect gas model |
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27 | (10) |
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1.8.2 The metallic bond and band theory |
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37 | (9) |
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1.9 Molar specific heat capacities of crystalline solids |
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46 | (9) |
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1.9.1 Contribution of the vibrational energy to the specific heat capacity at constant volume |
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46 | (4) |
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1.9.2 Specific heat capacity of an atomic solid at constant volume |
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50 | (4) |
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1.9.3 Specific heat capacity of a molecular- or ionic-solid at constant volume |
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54 | (1) |
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1.9.4 Conclusion as to the specific heat capacity of a crystalline solid |
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54 | (1) |
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1.10 Thermal expansion of solids |
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55 | (16) |
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1.10.1 Expansion coefficients |
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55 | (3) |
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1.10.2 Origin of thermal expansion in solids |
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58 | (4) |
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1.10.3 Quantum treatment of thermal expansion. Gruneisen parameter |
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62 | (6) |
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1.10.4 Expansion coefficient of metals |
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68 | (3) |
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Chapter 2 Solid Solutions |
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71 | (76) |
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2.1 Families of solid solutions |
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71 | (11) |
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2.1.1 Substitutional solid solutions |
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72 | (3) |
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2.1.2 Insertion solid solution |
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75 | (7) |
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2.2 Order in solid solutions |
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82 | (12) |
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2.2.1 Short-distance order |
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83 | (4) |
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2.2.2 Long-distance order |
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87 | (7) |
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2.3 Thermodynamic models of solid solutions |
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94 | (17) |
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2.3.1 Determination of the Gibbs energy of mixing |
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94 | (6) |
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2.3.2 The microscopic model of the perfect solution |
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100 | (2) |
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2.3.3 Microscopic model of strictly-regular solutions |
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102 | (2) |
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2.3.4 Microscopic model of the ideal dilute solution |
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104 | (2) |
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2.3.5 Fowler and Guggenheim's quasi-chemical model of the solution |
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106 | (5) |
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2.4 Thermodynamic study of the degree of order of an alloy |
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111 | (21) |
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2.4.1 Hypotheses of the model: configuration energy |
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112 | (1) |
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2.4.2 Expression of the configuration partition function |
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113 | (1) |
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2.4.3 The Gorsky, Bragg and Williams model |
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114 | (6) |
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2.4.4 The quasi-chemical model |
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120 | (7) |
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2.4.5 Comparison of the models against experimental results |
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127 | (5) |
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2.5 Determination of the activity of a component of a solid solution |
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132 | (15) |
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2.5.1 Methods common to solid solutions and liquid solutions |
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134 | (6) |
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2.5.2 Methods specific to solid solutions |
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140 | (7) |
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Chapter 3 Non-stoichiometry in Solids |
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147 | (48) |
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3.1 Structure elements of a solid |
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147 | (6) |
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148 | (1) |
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3.1.2 Symbolic representation of structure elements |
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149 | (2) |
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3.1.3 Building unit of a solid |
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151 | (1) |
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3.1.4 Description and composition of a solid |
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151 | (2) |
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3.2 Quasi-chemical reactions in solids |
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153 | (5) |
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3.2.1 Definition and characteristics of a quasi-chemical reaction between structure elements |
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153 | (3) |
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3.2.2 Homogeneous quasi-chemical reactions in the solid phase |
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156 | (2) |
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3.2.3 Inter-phase reactions |
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158 | (1) |
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3.3 Equilibrium states between structure elements in solids |
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158 | (1) |
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3.4 Thermodynamics of structure elements in unary solids |
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159 | (6) |
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3.4.1 Structure elements of a unary solid |
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159 | (3) |
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3.4.2 Global equilibrium of an isolated crystal -- influence of temperature |
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162 | (3) |
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3.5 Thermodynamics of structure elements in stoichiometric binary solids |
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165 | (4) |
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3.5.1 Symmetrical disorders in stoichiometric binary solids |
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166 | (1) |
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3.5.2 Asymmetrical disorders in stoichiometric binary solids |
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167 | (2) |
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3.6 Thermodynamics of structure elements in non-stoichiometric binary solids |
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169 | (11) |
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3.6.1 Deviations from stoichiometry and point defects |
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169 | (2) |
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3.6.2 The predominant defect method -- the Wagner classification |
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171 | (3) |
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3.6.3 Equilibrium of a Wagner solid with one of its gaseous elements |
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174 | (1) |
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3.6.4 General equilibrium of a non-stoichiometric binary solid with one of its gaseous elements |
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175 | (5) |
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3.7 Representation of complex solids -- example of metal oxy-hydroxides |
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180 | (1) |
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3.7.1 The pseudo-binary approximation |
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180 | (1) |
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3.7.2 The predominant-defect generalization |
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180 | (1) |
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3.8 Determination of the equilibrium constants of the reactions involving structure elements |
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181 | (14) |
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3.8.1 Recap on calculating the equilibrium constants using statistical thermodynamics |
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182 | (2) |
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3.8.2 Examination of the pre-exponential term in the quasi-chemical equilibrium constants |
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184 | (3) |
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3.8.3 Determination of the internal energy of transformation of quasi-chemical reactions |
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187 | (8) |
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Chapter 4 Solid Solutions and Structure Elements |
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195 | (22) |
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4.1 Ionic solid solutions |
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195 | (9) |
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4.1.1 Introduction of foreign elements into stoichiometric binary solids |
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197 | (3) |
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4.1.2 Influence of foreign elements introduced into a non-stoichiometric binary solid |
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200 | (4) |
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4.2 Thermodynamics of equilibria between water vapor and saline hydrates: non-stoichiometric hydrates |
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204 | (13) |
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4.2.1 Experimental demonstration of non-stoichiometry of a hydrate |
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204 | (3) |
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4.2.2 Equilibria between stoichiometric hydrates |
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207 | (1) |
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4.2.3 Equilibrium reactions in non-stoichiometric hydrates |
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207 | (6) |
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4.2.4 The limits of the domains of divariance |
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213 | (4) |
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217 | (10) |
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Appendix 1 The Lagrange Multiplier Method |
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219 | (4) |
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Appendix 2 Solving Schrodinger's Equation |
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223 | (4) |
| Bibliography |
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227 | (4) |
| Index |
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231 | |
