Irradiation-induced formation of metastable phases: a master-equation approach
A new formalism, based on a master equation, for elaborating criteria of phase stability under irradiation is proposed. This technique is applied to the order--disorder transition in Ni sub 4 Mo, where an irradiation-induced inversion of the respective stability of two ordered states has been report...
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| Veröffentlicht in: | Phys. Rev. B: Condens. Matter; (United States) 1988-08, Vol.38 (4), p.2570-2582 |
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| creator | BELLON, P MARTIN, G |
| description | A new formalism, based on a master equation, for elaborating criteria of phase stability under irradiation is proposed. This technique is applied to the order--disorder transition in Ni sub 4 Mo, where an irradiation-induced inversion of the respective stability of two ordered states has been reported, and a temperature domain where bistability is observed. The technique consists in describing the time evolution of the configuration of the system at the atomistic level and writing a master equation for the probability distribution of configurations defined at a mesoscopic level. The transition probabilities of the former are expressed in terms of the atomic jump frequencies which enter the atomistic description, to a level of sophistication compatible with a simple mean-field description of the thermodynamics of the system outside irradiation. The identity between the thermodynamical equilibrium states and fluctuations on the one hand and the dynamical steady states outside irradiation on the other hand is thus built into the formalism. Irradiation effects are then introduced by enhancing the overall atomic mobility (defect supersaturation) and by adding to the atomic exchange frequencies a ballistic contribution which forces mixing whatever the local configuration (infinite-temperature dynamics). The same formal expression for the probability of the various dynamical steady states is obtained, but with some potential replacing the free energy. The former has no simple intuitive meaning but may be evaluated numerically. The probabilities of various steady-state configurations can then be assessed. When applied to Ni sub 4 Mo under high-energy-electron irradiation, the technique fully reproduces the sequence of behaviors which has been observed experimentally in the whole irradiation temperature range. The temperature thresholds where stability inversion or bistability are observed may be fitted reasonably well, despite the crudeness of the mean-field description underlying the treatment. 35 ref.--AA |
| doi_str_mv | 10.1103/PhysRevB.38.2570 |
| format | Article |
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This technique is applied to the order--disorder transition in Ni sub 4 Mo, where an irradiation-induced inversion of the respective stability of two ordered states has been reported, and a temperature domain where bistability is observed. The technique consists in describing the time evolution of the configuration of the system at the atomistic level and writing a master equation for the probability distribution of configurations defined at a mesoscopic level. The transition probabilities of the former are expressed in terms of the atomic jump frequencies which enter the atomistic description, to a level of sophistication compatible with a simple mean-field description of the thermodynamics of the system outside irradiation. The identity between the thermodynamical equilibrium states and fluctuations on the one hand and the dynamical steady states outside irradiation on the other hand is thus built into the formalism. Irradiation effects are then introduced by enhancing the overall atomic mobility (defect supersaturation) and by adding to the atomic exchange frequencies a ballistic contribution which forces mixing whatever the local configuration (infinite-temperature dynamics). The same formal expression for the probability of the various dynamical steady states is obtained, but with some potential replacing the free energy. The former has no simple intuitive meaning but may be evaluated numerically. The probabilities of various steady-state configurations can then be assessed. When applied to Ni sub 4 Mo under high-energy-electron irradiation, the technique fully reproduces the sequence of behaviors which has been observed experimentally in the whole irradiation temperature range. The temperature thresholds where stability inversion or bistability are observed may be fitted reasonably well, despite the crudeness of the mean-field description underlying the treatment. 35 ref.--AA</description><identifier>ISSN: 0163-1829</identifier><identifier>EISSN: 1095-3795</identifier><identifier>DOI: 10.1103/PhysRevB.38.2570</identifier><identifier>PMID: 9946567</identifier><identifier>CODEN: PRBMDO</identifier><language>eng</language><publisher>Woodbury, NY: American Physical Society</publisher><subject>360106 - Metals & Alloys- Radiation Effects ; ALLOYS ; COLLISIONS ; Condensed matter: structure, mechanical and thermal properties ; Cross-disciplinary physics: materials science; rheology ; ELECTRON COLLISIONS ; ENERGY ; ENERGY LEVELS ; Equations of state, phase equilibria, and phase transitions ; EQUILIBRIUM ; Exact sciences and technology ; EXCITED STATES ; FLUCTUATIONS ; FREE ENERGY ; IRRADIATION ; MATERIALS SCIENCE ; MEAN-FIELD THEORY ; Metals, semimetals and alloys ; METASTABLE STATES ; MOLYBDENUM ALLOYS ; NICKEL ALLOYS ; ORDER-DISORDER TRANSFORMATIONS ; Phase diagrams and microstructures developed by solidification and solid-solid phase transformations ; PHASE TRANSFORMATIONS ; PHYSICAL PROPERTIES ; PHYSICAL RADIATION EFFECTS ; Physics ; POTENTIALS ; RADIATION EFFECTS ; Specific materials ; Specific phase transitions ; STABILITY ; THERMAL EQUILIBRIUM ; THERMODYNAMIC PROPERTIES ; THERMODYNAMICS ; VARIATIONS</subject><ispartof>Phys. 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Rev. B: Condens. Matter; (United States)</title><addtitle>Phys Rev B Condens Matter</addtitle><description>A new formalism, based on a master equation, for elaborating criteria of phase stability under irradiation is proposed. This technique is applied to the order--disorder transition in Ni sub 4 Mo, where an irradiation-induced inversion of the respective stability of two ordered states has been reported, and a temperature domain where bistability is observed. The technique consists in describing the time evolution of the configuration of the system at the atomistic level and writing a master equation for the probability distribution of configurations defined at a mesoscopic level. The transition probabilities of the former are expressed in terms of the atomic jump frequencies which enter the atomistic description, to a level of sophistication compatible with a simple mean-field description of the thermodynamics of the system outside irradiation. The identity between the thermodynamical equilibrium states and fluctuations on the one hand and the dynamical steady states outside irradiation on the other hand is thus built into the formalism. Irradiation effects are then introduced by enhancing the overall atomic mobility (defect supersaturation) and by adding to the atomic exchange frequencies a ballistic contribution which forces mixing whatever the local configuration (infinite-temperature dynamics). The same formal expression for the probability of the various dynamical steady states is obtained, but with some potential replacing the free energy. The former has no simple intuitive meaning but may be evaluated numerically. The probabilities of various steady-state configurations can then be assessed. When applied to Ni sub 4 Mo under high-energy-electron irradiation, the technique fully reproduces the sequence of behaviors which has been observed experimentally in the whole irradiation temperature range. The temperature thresholds where stability inversion or bistability are observed may be fitted reasonably well, despite the crudeness of the mean-field description underlying the treatment. 35 ref.--AA</description><subject>360106 - Metals & Alloys- Radiation Effects</subject><subject>ALLOYS</subject><subject>COLLISIONS</subject><subject>Condensed matter: structure, mechanical and thermal properties</subject><subject>Cross-disciplinary physics: materials science; rheology</subject><subject>ELECTRON COLLISIONS</subject><subject>ENERGY</subject><subject>ENERGY LEVELS</subject><subject>Equations of state, phase equilibria, and phase transitions</subject><subject>EQUILIBRIUM</subject><subject>Exact sciences and technology</subject><subject>EXCITED STATES</subject><subject>FLUCTUATIONS</subject><subject>FREE ENERGY</subject><subject>IRRADIATION</subject><subject>MATERIALS SCIENCE</subject><subject>MEAN-FIELD THEORY</subject><subject>Metals, semimetals and alloys</subject><subject>METASTABLE STATES</subject><subject>MOLYBDENUM ALLOYS</subject><subject>NICKEL ALLOYS</subject><subject>ORDER-DISORDER TRANSFORMATIONS</subject><subject>Phase diagrams and microstructures developed by solidification and solid-solid phase transformations</subject><subject>PHASE TRANSFORMATIONS</subject><subject>PHYSICAL PROPERTIES</subject><subject>PHYSICAL RADIATION EFFECTS</subject><subject>Physics</subject><subject>POTENTIALS</subject><subject>RADIATION EFFECTS</subject><subject>Specific materials</subject><subject>Specific phase transitions</subject><subject>STABILITY</subject><subject>THERMAL EQUILIBRIUM</subject><subject>THERMODYNAMIC PROPERTIES</subject><subject>THERMODYNAMICS</subject><subject>VARIATIONS</subject><issn>0163-1829</issn><issn>1095-3795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1988</creationdate><recordtype>article</recordtype><recordid>eNp9kctLxEAMxgdRdH3cvQhFRLx0nUc7D2-6-IJFRbwP6TRlK32sM63gf--su3o0OYQkvy8EPkKOGZ0yRsXly-IrvOLnzVToKc8V3SITRk2eCmXybTKhTIqUaW72yH4I7zQGl2aX7BqTyVyqCXl69B7KGoa679K6K0eHZVL1vv2ZJH2VtDhAGKBoMFkuIGC4SiBp4wh9ih_jmoPl0vfgFodkp4Im4NGmHpC3u9u32UM6f75_nF3PUye0GFItZVXlhiqnwFAh0IAoyjIvkHFwlKvMoYwNQhETqHOVBFroUnGuIBcH5HR9tg9DbYOrB3QL13cdusEqlknGWITO11B87WPEMNi2Dg6bBjrsx2B5ZozKFI_gxb8g07lhWmcZjShdo873IXis7NLXLfgvy6hdOWJ_HbFC25UjUXKyuT4WLZZ_go0FcX-22UNw0FQeOleHP0zRjMU3xTf1xJYZ</recordid><startdate>19880801</startdate><enddate>19880801</enddate><creator>BELLON, P</creator><creator>MARTIN, G</creator><general>American Physical Society</general><general>American Institute of Physics</general><scope>IQODW</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>OTOTI</scope></search><sort><creationdate>19880801</creationdate><title>Irradiation-induced formation of metastable phases: a master-equation approach</title><author>BELLON, P ; MARTIN, G</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c383t-866ff5907c7a9033e9a3bdd5be12ac0274ce6be1eababaa0ccf6a0b8d7227a53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1988</creationdate><topic>360106 - Metals & Alloys- Radiation Effects</topic><topic>ALLOYS</topic><topic>COLLISIONS</topic><topic>Condensed matter: structure, mechanical and thermal properties</topic><topic>Cross-disciplinary physics: materials science; rheology</topic><topic>ELECTRON COLLISIONS</topic><topic>ENERGY</topic><topic>ENERGY LEVELS</topic><topic>Equations of state, phase equilibria, and phase transitions</topic><topic>EQUILIBRIUM</topic><topic>Exact sciences and technology</topic><topic>EXCITED STATES</topic><topic>FLUCTUATIONS</topic><topic>FREE ENERGY</topic><topic>IRRADIATION</topic><topic>MATERIALS SCIENCE</topic><topic>MEAN-FIELD THEORY</topic><topic>Metals, semimetals and alloys</topic><topic>METASTABLE STATES</topic><topic>MOLYBDENUM ALLOYS</topic><topic>NICKEL ALLOYS</topic><topic>ORDER-DISORDER TRANSFORMATIONS</topic><topic>Phase diagrams and microstructures developed by solidification and solid-solid phase transformations</topic><topic>PHASE TRANSFORMATIONS</topic><topic>PHYSICAL PROPERTIES</topic><topic>PHYSICAL RADIATION EFFECTS</topic><topic>Physics</topic><topic>POTENTIALS</topic><topic>RADIATION EFFECTS</topic><topic>Specific materials</topic><topic>Specific phase transitions</topic><topic>STABILITY</topic><topic>THERMAL EQUILIBRIUM</topic><topic>THERMODYNAMIC PROPERTIES</topic><topic>THERMODYNAMICS</topic><topic>VARIATIONS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BELLON, P</creatorcontrib><creatorcontrib>MARTIN, G</creatorcontrib><creatorcontrib>Centre d'Etudes de Chimie Metallurgique du Centre National de la Recherche Scientifique, 15 rue Georges Urbain, 94407 Vitry-sur-Seine Cedex, France</creatorcontrib><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>OSTI.GOV</collection><jtitle>Phys. Rev. B: Condens. Matter; (United States)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BELLON, P</au><au>MARTIN, G</au><aucorp>Centre d'Etudes de Chimie Metallurgique du Centre National de la Recherche Scientifique, 15 rue Georges Urbain, 94407 Vitry-sur-Seine Cedex, France</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Irradiation-induced formation of metastable phases: a master-equation approach</atitle><jtitle>Phys. Rev. B: Condens. Matter; (United States)</jtitle><addtitle>Phys Rev B Condens Matter</addtitle><date>1988-08-01</date><risdate>1988</risdate><volume>38</volume><issue>4</issue><spage>2570</spage><epage>2582</epage><pages>2570-2582</pages><issn>0163-1829</issn><eissn>1095-3795</eissn><coden>PRBMDO</coden><abstract>A new formalism, based on a master equation, for elaborating criteria of phase stability under irradiation is proposed. This technique is applied to the order--disorder transition in Ni sub 4 Mo, where an irradiation-induced inversion of the respective stability of two ordered states has been reported, and a temperature domain where bistability is observed. The technique consists in describing the time evolution of the configuration of the system at the atomistic level and writing a master equation for the probability distribution of configurations defined at a mesoscopic level. The transition probabilities of the former are expressed in terms of the atomic jump frequencies which enter the atomistic description, to a level of sophistication compatible with a simple mean-field description of the thermodynamics of the system outside irradiation. The identity between the thermodynamical equilibrium states and fluctuations on the one hand and the dynamical steady states outside irradiation on the other hand is thus built into the formalism. Irradiation effects are then introduced by enhancing the overall atomic mobility (defect supersaturation) and by adding to the atomic exchange frequencies a ballistic contribution which forces mixing whatever the local configuration (infinite-temperature dynamics). The same formal expression for the probability of the various dynamical steady states is obtained, but with some potential replacing the free energy. The former has no simple intuitive meaning but may be evaluated numerically. The probabilities of various steady-state configurations can then be assessed. When applied to Ni sub 4 Mo under high-energy-electron irradiation, the technique fully reproduces the sequence of behaviors which has been observed experimentally in the whole irradiation temperature range. The temperature thresholds where stability inversion or bistability are observed may be fitted reasonably well, despite the crudeness of the mean-field description underlying the treatment. 35 ref.--AA</abstract><cop>Woodbury, NY</cop><pub>American Physical Society</pub><pmid>9946567</pmid><doi>10.1103/PhysRevB.38.2570</doi><tpages>13</tpages></addata></record> |
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| ispartof | Phys. Rev. B: Condens. Matter; (United States), 1988-08, Vol.38 (4), p.2570-2582 |
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| subjects | 360106 - Metals & Alloys- Radiation Effects ALLOYS COLLISIONS Condensed matter: structure, mechanical and thermal properties Cross-disciplinary physics: materials science rheology ELECTRON COLLISIONS ENERGY ENERGY LEVELS Equations of state, phase equilibria, and phase transitions EQUILIBRIUM Exact sciences and technology EXCITED STATES FLUCTUATIONS FREE ENERGY IRRADIATION MATERIALS SCIENCE MEAN-FIELD THEORY Metals, semimetals and alloys METASTABLE STATES MOLYBDENUM ALLOYS NICKEL ALLOYS ORDER-DISORDER TRANSFORMATIONS Phase diagrams and microstructures developed by solidification and solid-solid phase transformations PHASE TRANSFORMATIONS PHYSICAL PROPERTIES PHYSICAL RADIATION EFFECTS Physics POTENTIALS RADIATION EFFECTS Specific materials Specific phase transitions STABILITY THERMAL EQUILIBRIUM THERMODYNAMIC PROPERTIES THERMODYNAMICS VARIATIONS |
| title | Irradiation-induced formation of metastable phases: a master-equation approach |
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