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Non‐Equilibrium Vacancy Concentrations in Metals Subject to Thermal Gradients and Electric Fields
Author(s) -
Blackburn D. A.
Publication year - 1967
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19670230116
Subject(s) - vacancy defect , electric field , lambda , physics , condensed matter physics , metal , electrical resistivity and conductivity , materials science , quantum mechanics , optics , metallurgy
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 E , parallel to a temperature gradient ∂ T /∂ x , should suffer a vacancy supersaturation given by q = C e r Lambda; 2 / k 2 T 4 [( E f ( E f + E m + E t ‐ 2 kT ) + E t ( E m ‐ 2 kT )) (∂ T /∂ x ) 2 ‐ Z e E T ( E f + E m ‐ kT ) ∂ T /∂ x ‐ Z e kT 3 ∂ E /∂ x + E t kT 2 ∂ 2 T /∂ x 2 ], where C e denotes the equilibrium vacancy concentration appropriate to the temperature T at any point x , and Lambda; is the mean free path of a vacancy during migration between source and sink. E f , E m , and E t are the energies for formation, motion, and transport of vacancies, Z e is the effective electrical charge carried by a vacancy when diffusing, and r is a geometrical constant (1/6 in f.c.c.).