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Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields
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| Zeitschriftentitel: | physica status solidi (b) |
|---|---|
| Personen und Körperschaften: | |
| In: | physica status solidi (b), 23, 1967, 1, S. 177-183 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Wiley
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| Schlagwörter: |
| author_facet |
Blackburn, D. A. Blackburn, D. A. |
|---|---|
| author |
Blackburn, D. A. |
| spellingShingle |
Blackburn, D. A. physica status solidi (b) Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields Condensed Matter Physics Electronic, Optical and Magnetic Materials |
| author_sort |
blackburn, d. a. |
| spelling |
Blackburn, D. A. 0370-1972 1521-3951 Wiley Condensed Matter Physics Electronic, Optical and Magnetic Materials http://dx.doi.org/10.1002/pssb.19670230116 <jats:title>Abstract</jats:title><jats:p>Gradients of temperature and electric fields may be used to cause vacancy currents in metals. If vacancies are supposed to migrate between randomly distributed, fixed sources and sinks, a metal subject to an internal electric field <jats:italic>E</jats:italic>, parallel to a temperature gradient ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>, should suffer a vacancy supersaturation given by <jats:italic>q</jats:italic> = <jats:italic>C</jats:italic><jats:sub>e</jats:sub> <jats:italic>r</jats:italic> Lambda;<jats:sup>2</jats:sup>/<jats:italic>k</jats:italic><jats:sup>2</jats:sup> <jats:italic>T</jats:italic><jats:sup>4</jats:sup> [(<jats:italic>E</jats:italic><jats:sub>f</jats:sub>(<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>) + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> (<jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>)) (∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>)<jats:sup>2</jats:sup> ‐ <jats:italic>Z</jats:italic> e <jats:italic>E T</jats:italic> (<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ <jats:italic>kT</jats:italic>) ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic> ‐ <jats:italic>Z e kT</jats:italic><jats:sup>3</jats:sup> ∂<jats:italic>E</jats:italic>/∂<jats:italic>x</jats:italic> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> <jats:italic>kT</jats:italic><jats:sup>2</jats:sup> ∂<jats:sup>2</jats:sup><jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic><jats:sup>2</jats:sup>], where <jats:italic>C</jats:italic><jats:sub>e</jats:sub> denotes the equilibrium vacancy concentration appropriate to the temperature <jats:italic>T</jats:italic> at any point <jats:italic>x</jats:italic>, and <jats:italic>Lambda;</jats:italic> is the mean free path of a vacancy during migration between source and sink. <jats:italic>E</jats:italic><jats:sub>f</jats:sub>, <jats:italic>E</jats:italic><jats:sub>m</jats:sub>, and <jats:italic>E</jats:italic><jats:sub>t</jats:sub> are the energies for formation, motion, and transport of vacancies, <jats:italic>Z e</jats:italic> is the effective electrical charge carried by a vacancy when diffusing, and <jats:italic>r</jats:italic> is a geometrical constant (1/6 in f.c.c.).</jats:p> Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields physica status solidi (b) |
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10.1002/pssb.19670230116 |
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Physik Technik |
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| imprint |
Wiley, 1967 |
| imprint_str_mv |
Wiley, 1967 |
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0370-1972 1521-3951 |
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0370-1972 1521-3951 |
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English |
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1967 |
| publisher |
Wiley |
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ai |
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ai |
| series |
physica status solidi (b) |
| source_id |
49 |
| title |
Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_unstemmed |
Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_full |
Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_fullStr |
Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_full_unstemmed |
Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_short |
Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_sort |
non‐equilibrium vacancy concentrations in metals subject to thermal gradients and electric fields |
| topic |
Condensed Matter Physics Electronic, Optical and Magnetic Materials |
| url |
http://dx.doi.org/10.1002/pssb.19670230116 |
| publishDate |
1967 |
| physical |
177-183 |
| description |
<jats:title>Abstract</jats:title><jats:p>Gradients of temperature and electric fields may be used to cause vacancy currents in metals. If vacancies are supposed to migrate between randomly distributed, fixed sources and sinks, a metal subject to an internal electric field <jats:italic>E</jats:italic>, parallel to a temperature gradient ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>, should suffer a vacancy supersaturation given by <jats:italic>q</jats:italic> = <jats:italic>C</jats:italic><jats:sub>e</jats:sub> <jats:italic>r</jats:italic> Lambda;<jats:sup>2</jats:sup>/<jats:italic>k</jats:italic><jats:sup>2</jats:sup> <jats:italic>T</jats:italic><jats:sup>4</jats:sup> [(<jats:italic>E</jats:italic><jats:sub>f</jats:sub>(<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>) + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> (<jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>)) (∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>)<jats:sup>2</jats:sup> ‐ <jats:italic>Z</jats:italic> e <jats:italic>E T</jats:italic> (<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ <jats:italic>kT</jats:italic>) ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic> ‐ <jats:italic>Z e kT</jats:italic><jats:sup>3</jats:sup> ∂<jats:italic>E</jats:italic>/∂<jats:italic>x</jats:italic> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> <jats:italic>kT</jats:italic><jats:sup>2</jats:sup> ∂<jats:sup>2</jats:sup><jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic><jats:sup>2</jats:sup>], where <jats:italic>C</jats:italic><jats:sub>e</jats:sub> denotes the equilibrium vacancy concentration appropriate to the temperature <jats:italic>T</jats:italic> at any point <jats:italic>x</jats:italic>, and <jats:italic>Lambda;</jats:italic> is the mean free path of a vacancy during migration between source and sink. <jats:italic>E</jats:italic><jats:sub>f</jats:sub>, <jats:italic>E</jats:italic><jats:sub>m</jats:sub>, and <jats:italic>E</jats:italic><jats:sub>t</jats:sub> are the energies for formation, motion, and transport of vacancies, <jats:italic>Z e</jats:italic> is the effective electrical charge carried by a vacancy when diffusing, and <jats:italic>r</jats:italic> is a geometrical constant (1/6 in f.c.c.).</jats:p> |
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| description | <jats:title>Abstract</jats:title><jats:p>Gradients of temperature and electric fields may be used to cause vacancy currents in metals. If vacancies are supposed to migrate between randomly distributed, fixed sources and sinks, a metal subject to an internal electric field <jats:italic>E</jats:italic>, parallel to a temperature gradient ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>, should suffer a vacancy supersaturation given by <jats:italic>q</jats:italic> = <jats:italic>C</jats:italic><jats:sub>e</jats:sub> <jats:italic>r</jats:italic> Lambda;<jats:sup>2</jats:sup>/<jats:italic>k</jats:italic><jats:sup>2</jats:sup> <jats:italic>T</jats:italic><jats:sup>4</jats:sup> [(<jats:italic>E</jats:italic><jats:sub>f</jats:sub>(<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>) + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> (<jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>)) (∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>)<jats:sup>2</jats:sup> ‐ <jats:italic>Z</jats:italic> e <jats:italic>E T</jats:italic> (<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ <jats:italic>kT</jats:italic>) ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic> ‐ <jats:italic>Z e kT</jats:italic><jats:sup>3</jats:sup> ∂<jats:italic>E</jats:italic>/∂<jats:italic>x</jats:italic> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> <jats:italic>kT</jats:italic><jats:sup>2</jats:sup> ∂<jats:sup>2</jats:sup><jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic><jats:sup>2</jats:sup>], where <jats:italic>C</jats:italic><jats:sub>e</jats:sub> denotes the equilibrium vacancy concentration appropriate to the temperature <jats:italic>T</jats:italic> at any point <jats:italic>x</jats:italic>, and <jats:italic>Lambda;</jats:italic> is the mean free path of a vacancy during migration between source and sink. <jats:italic>E</jats:italic><jats:sub>f</jats:sub>, <jats:italic>E</jats:italic><jats:sub>m</jats:sub>, and <jats:italic>E</jats:italic><jats:sub>t</jats:sub> are the energies for formation, motion, and transport of vacancies, <jats:italic>Z e</jats:italic> is the effective electrical charge carried by a vacancy when diffusing, and <jats:italic>r</jats:italic> is a geometrical constant (1/6 in f.c.c.).</jats:p> |
| doi_str_mv | 10.1002/pssb.19670230116 |
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| imprint | Wiley, 1967 |
| imprint_str_mv | Wiley, 1967 |
| institution | DE-Zi4, DE-Gla1, DE-15, DE-Pl11, DE-Rs1, DE-14, DE-105, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-D161 |
| issn | 0370-1972, 1521-3951 |
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| physical | 177-183 |
| publishDate | 1967 |
| publishDateSort | 1967 |
| publisher | Wiley |
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| recordtype | ai |
| series | physica status solidi (b) |
| source_id | 49 |
| spelling | Blackburn, D. A. 0370-1972 1521-3951 Wiley Condensed Matter Physics Electronic, Optical and Magnetic Materials http://dx.doi.org/10.1002/pssb.19670230116 <jats:title>Abstract</jats:title><jats:p>Gradients of temperature and electric fields may be used to cause vacancy currents in metals. If vacancies are supposed to migrate between randomly distributed, fixed sources and sinks, a metal subject to an internal electric field <jats:italic>E</jats:italic>, parallel to a temperature gradient ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>, should suffer a vacancy supersaturation given by <jats:italic>q</jats:italic> = <jats:italic>C</jats:italic><jats:sub>e</jats:sub> <jats:italic>r</jats:italic> Lambda;<jats:sup>2</jats:sup>/<jats:italic>k</jats:italic><jats:sup>2</jats:sup> <jats:italic>T</jats:italic><jats:sup>4</jats:sup> [(<jats:italic>E</jats:italic><jats:sub>f</jats:sub>(<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>) + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> (<jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ 2 <jats:italic>kT</jats:italic>)) (∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic>)<jats:sup>2</jats:sup> ‐ <jats:italic>Z</jats:italic> e <jats:italic>E T</jats:italic> (<jats:italic>E</jats:italic><jats:sub>f</jats:sub> + <jats:italic>E</jats:italic><jats:sub>m</jats:sub> ‐ <jats:italic>kT</jats:italic>) ∂<jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic> ‐ <jats:italic>Z e kT</jats:italic><jats:sup>3</jats:sup> ∂<jats:italic>E</jats:italic>/∂<jats:italic>x</jats:italic> + <jats:italic>E</jats:italic><jats:sub>t</jats:sub> <jats:italic>kT</jats:italic><jats:sup>2</jats:sup> ∂<jats:sup>2</jats:sup><jats:italic>T</jats:italic>/∂<jats:italic>x</jats:italic><jats:sup>2</jats:sup>], where <jats:italic>C</jats:italic><jats:sub>e</jats:sub> denotes the equilibrium vacancy concentration appropriate to the temperature <jats:italic>T</jats:italic> at any point <jats:italic>x</jats:italic>, and <jats:italic>Lambda;</jats:italic> is the mean free path of a vacancy during migration between source and sink. <jats:italic>E</jats:italic><jats:sub>f</jats:sub>, <jats:italic>E</jats:italic><jats:sub>m</jats:sub>, and <jats:italic>E</jats:italic><jats:sub>t</jats:sub> are the energies for formation, motion, and transport of vacancies, <jats:italic>Z e</jats:italic> is the effective electrical charge carried by a vacancy when diffusing, and <jats:italic>r</jats:italic> is a geometrical constant (1/6 in f.c.c.).</jats:p> Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields physica status solidi (b) |
| spellingShingle | Blackburn, D. A., physica status solidi (b), Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields, Condensed Matter Physics, Electronic, Optical and Magnetic Materials |
| title | Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_full | Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_fullStr | Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_full_unstemmed | Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_short | Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| title_sort | non‐equilibrium vacancy concentrations in metals subject to thermal gradients and electric fields |
| title_unstemmed | Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields |
| topic | Condensed Matter Physics, Electronic, Optical and Magnetic Materials |
| url | http://dx.doi.org/10.1002/pssb.19670230116 |