THERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONS
A multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: {Mathematical expression} ap...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer-Verlag
1978
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| _version_ | 1797077601786789888 |
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| author | Wood, B Nicholls, J |
| author_facet | Wood, B Nicholls, J |
| author_sort | Wood, B |
| collection | OXFORD |
| description | A multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: {Mathematical expression} applies. Even for the case in which mixing on each of the individual sublattices is ideal, ΔG0 contributes terms of the following form to the activity coefficients of the constituent components: {Mathematical expression} (XJi refers to the atomic fraction of J on sublattice i). The above equation, which assumes complete disorder on (A, B) sites and on (X, Y) sites is extended to the general n-component case. Methods of combining the "cross-site" or reciprocal terms with non-ideal terms for each of the individual sites are also described. The reciprocal terms appear to be significant in many geologically important solid solutions, and clinopyroxene, garnet and spinel solid solutions are all used as examples. Finally, it is shown that the assumption of complete disorder only applies under the condition: {Mathematical expression} where z is the number of nearest-neighbour (X, Y) sites around A and n1 is the number of (A, B) sites in the formula unit. If ΔG0 is relatively large, then substantial short range oder must occur and the activity coefficient is given by (ignoring individual site terms): {Mathematical expression} where X′Y2 is the equilibrium atomic fraction of Y atoms surrounding A atoms in the structure. The ordered model may be developed for multicomponent solutions and individual site interactions added, but numerical methods are needed to solve the simultaneous equations involved. © 1978 Springer-Verlag. |
| first_indexed | 2024-03-07T00:20:26Z |
| format | Journal article |
| id | oxford-uuid:7c5c6bc8-9ddd-4274-83f4-9f9a86d604cc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:20:26Z |
| publishDate | 1978 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | oxford-uuid:7c5c6bc8-9ddd-4274-83f4-9f9a86d604cc2022-03-26T20:56:31ZTHERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONSJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7c5c6bc8-9ddd-4274-83f4-9f9a86d604ccEnglishSymplectic Elements at OxfordSpringer-Verlag1978Wood, BNicholls, JA multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: {Mathematical expression} applies. Even for the case in which mixing on each of the individual sublattices is ideal, ΔG0 contributes terms of the following form to the activity coefficients of the constituent components: {Mathematical expression} (XJi refers to the atomic fraction of J on sublattice i). The above equation, which assumes complete disorder on (A, B) sites and on (X, Y) sites is extended to the general n-component case. Methods of combining the "cross-site" or reciprocal terms with non-ideal terms for each of the individual sites are also described. The reciprocal terms appear to be significant in many geologically important solid solutions, and clinopyroxene, garnet and spinel solid solutions are all used as examples. Finally, it is shown that the assumption of complete disorder only applies under the condition: {Mathematical expression} where z is the number of nearest-neighbour (X, Y) sites around A and n1 is the number of (A, B) sites in the formula unit. If ΔG0 is relatively large, then substantial short range oder must occur and the activity coefficient is given by (ignoring individual site terms): {Mathematical expression} where X′Y2 is the equilibrium atomic fraction of Y atoms surrounding A atoms in the structure. The ordered model may be developed for multicomponent solutions and individual site interactions added, but numerical methods are needed to solve the simultaneous equations involved. © 1978 Springer-Verlag. |
| spellingShingle | Wood, B Nicholls, J THERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONS |
| title | THERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONS |
| title_full | THERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONS |
| title_fullStr | THERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONS |
| title_full_unstemmed | THERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONS |
| title_short | THERMODYNAMIC PROPERTIES OF RECIPROCAL SOLID-SOLUTIONS |
| title_sort | thermodynamic properties of reciprocal solid solutions |
| work_keys_str_mv | AT woodb thermodynamicpropertiesofreciprocalsolidsolutions AT nichollsj thermodynamicpropertiesofreciprocalsolidsolutions |