Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism
Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure t...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Franke, Peter [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© ASM International 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of phase equilibria and diffusion - Boston, Mass. : Springer, 2004, 35(2014), 6 vom: 02. Okt., Seite 780-787 |
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| Übergeordnetes Werk: |
volume:35 ; year:2014 ; number:6 ; day:02 ; month:10 ; pages:780-787 |
| Links: |
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| DOI / URN: |
10.1007/s11669-014-0348-0 |
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| Katalog-ID: |
SPR021697019 |
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| 520 | |a Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. | ||
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10.1007/s11669-014-0348-0 doi (DE-627)SPR021697019 (SPR)s11669-014-0348-0-e DE-627 ger DE-627 rakwb eng Franke, Peter verfasserin aut Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ASM International 2014 Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. CALPHAD (dpeaa)DE-He213 metals (dpeaa)DE-He213 thermodynamic modeling (dpeaa)DE-He213 thermodynamic stability (dpeaa)DE-He213 Enthalten in Journal of phase equilibria and diffusion Boston, Mass. : Springer, 2004 35(2014), 6 vom: 02. Okt., Seite 780-787 (DE-627)626050863 (DE-600)2552809-9 1863-7345 nnns volume:35 year:2014 number:6 day:02 month:10 pages:780-787 https://dx.doi.org/10.1007/s11669-014-0348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 35 2014 6 02 10 780-787 |
| spelling |
10.1007/s11669-014-0348-0 doi (DE-627)SPR021697019 (SPR)s11669-014-0348-0-e DE-627 ger DE-627 rakwb eng Franke, Peter verfasserin aut Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ASM International 2014 Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. CALPHAD (dpeaa)DE-He213 metals (dpeaa)DE-He213 thermodynamic modeling (dpeaa)DE-He213 thermodynamic stability (dpeaa)DE-He213 Enthalten in Journal of phase equilibria and diffusion Boston, Mass. : Springer, 2004 35(2014), 6 vom: 02. Okt., Seite 780-787 (DE-627)626050863 (DE-600)2552809-9 1863-7345 nnns volume:35 year:2014 number:6 day:02 month:10 pages:780-787 https://dx.doi.org/10.1007/s11669-014-0348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 35 2014 6 02 10 780-787 |
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10.1007/s11669-014-0348-0 doi (DE-627)SPR021697019 (SPR)s11669-014-0348-0-e DE-627 ger DE-627 rakwb eng Franke, Peter verfasserin aut Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ASM International 2014 Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. CALPHAD (dpeaa)DE-He213 metals (dpeaa)DE-He213 thermodynamic modeling (dpeaa)DE-He213 thermodynamic stability (dpeaa)DE-He213 Enthalten in Journal of phase equilibria and diffusion Boston, Mass. : Springer, 2004 35(2014), 6 vom: 02. Okt., Seite 780-787 (DE-627)626050863 (DE-600)2552809-9 1863-7345 nnns volume:35 year:2014 number:6 day:02 month:10 pages:780-787 https://dx.doi.org/10.1007/s11669-014-0348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 35 2014 6 02 10 780-787 |
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10.1007/s11669-014-0348-0 doi (DE-627)SPR021697019 (SPR)s11669-014-0348-0-e DE-627 ger DE-627 rakwb eng Franke, Peter verfasserin aut Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ASM International 2014 Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. CALPHAD (dpeaa)DE-He213 metals (dpeaa)DE-He213 thermodynamic modeling (dpeaa)DE-He213 thermodynamic stability (dpeaa)DE-He213 Enthalten in Journal of phase equilibria and diffusion Boston, Mass. : Springer, 2004 35(2014), 6 vom: 02. Okt., Seite 780-787 (DE-627)626050863 (DE-600)2552809-9 1863-7345 nnns volume:35 year:2014 number:6 day:02 month:10 pages:780-787 https://dx.doi.org/10.1007/s11669-014-0348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 35 2014 6 02 10 780-787 |
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10.1007/s11669-014-0348-0 doi (DE-627)SPR021697019 (SPR)s11669-014-0348-0-e DE-627 ger DE-627 rakwb eng Franke, Peter verfasserin aut Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © ASM International 2014 Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. CALPHAD (dpeaa)DE-He213 metals (dpeaa)DE-He213 thermodynamic modeling (dpeaa)DE-He213 thermodynamic stability (dpeaa)DE-He213 Enthalten in Journal of phase equilibria and diffusion Boston, Mass. : Springer, 2004 35(2014), 6 vom: 02. Okt., Seite 780-787 (DE-627)626050863 (DE-600)2552809-9 1863-7345 nnns volume:35 year:2014 number:6 day:02 month:10 pages:780-787 https://dx.doi.org/10.1007/s11669-014-0348-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 35 2014 6 02 10 780-787 |
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Enthalten in Journal of phase equilibria and diffusion 35(2014), 6 vom: 02. Okt., Seite 780-787 volume:35 year:2014 number:6 day:02 month:10 pages:780-787 |
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Enthalten in Journal of phase equilibria and diffusion 35(2014), 6 vom: 02. Okt., Seite 780-787 volume:35 year:2014 number:6 day:02 month:10 pages:780-787 |
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Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism CALPHAD (dpeaa)DE-He213 metals (dpeaa)DE-He213 thermodynamic modeling (dpeaa)DE-He213 thermodynamic stability (dpeaa)DE-He213 |
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modeling of thermal vacancies in metals within the framework of the compound energy formalism |
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Modeling of Thermal Vacancies in Metals within the Framework of the Compound Energy Formalism |
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Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. © ASM International 2014 |
| abstractGer |
Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. © ASM International 2014 |
| abstract_unstemmed |
Abstract The thermodynamics of thermal vacancies in pure metals is analyzed within the compound energy formalism. It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. The results of this analysis are illustrated by the example of thermal vacancies in tungsten. © ASM International 2014 |
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It is shown that depending on the choice of the compound energy of the vacancies two ranges with different solution behavior for the equilibrium state are available. In order to assure the existence of unique solutions for the vacancy concentrations the compound energy for vacancies must exceed a critical value. But if this compound energy is in the range between zero and the critical value additional metastable states with different vacancy concentrations become possible. However, if the compound energy for vacancies is set to zero then the Gibbs energy of the respective phase approaches infinitely negative values and no stable equilibrium can exist. A dataset containing such a phase cannot possess any stable state with a global minimum of the Gibbs energy. 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