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Concentrations des lacunes dans les metaux soumis a un gradient de temperature
xl
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
Comparison of the Hall mobility and the drift mobility of holes measured under stationary conditions shows that at T> 200°Choles are trapped at silver ion vacancies, the trapping energy being E~= 0. 18 eV. The effective mass ratio for the holes m~’Jm= 0.6 0. 9. At T < 200°Ctrapping takes place either at silver ion vacancies at dislocations, or at iron impurities, leading to a center (FeA VA~ consisting of tnvalent iron and a silver ~on~acancy. -
(Received 28 February 1966) 13. THE ELASTIC CONSTANTS OF RUBIDIUM Carol A. Roberts and Robert Meister (Department of Electrical Engineering, The Catholic University of America, Washington 17,D.C.). The elastic constants of single crystal rubidiuni have been measured at 80 ±3°K using the ultrasonic pulse echo method at a frequency of 15 mc. The elastic constants (in units of 10~° 3) are cu = 2.96, C~ = 2.44, C~ = dynes/cm 1.60. Five wave velocities were measured, allowing the computation of the three independent elastic constants with two internal checks. Single crystal rubidium has an anisotropy indicated by the ratio (c 11 c~) /2c~ = 0.162. -
(Received 21 February 1966) 14. FORMATION OF VACANCY-DONOR ASSOCIATES DURING Cu AND Nt PRECIPITATION IN Ge. C. S. Fuller and K. B. Wo]fstirn (Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey). Acceptor levels at EV + 0. 07 ev and Ev + 0. 10 ev form when supersaturated solutions of Cu or Ni in As-doped Ge are quenched or are annealed in the temperature range 160-400°C. The 0. 07 eV acceptor is observed after a slow quench of Cu solutions or after a short anneal of Ni solutions. The 0. 10 eV acceptor is found after fast quench in the case of Cu or after long anneals in both the Cu or Ni solutions. The increase in hole mobility during annealing indicates that similar vacancy-donor associates are produced in both solutions. A tentative model to account for the results is presented. (Received 28 January 1966) (Revised 21 March 1966)
Vol. 4, No. 5
15. CONCENTRATIONS DES LACUNES DANS LES METAUX SOUMIS A UN GRADIENT DE TEMPERATURE. D. A. Blackburn (Centre d’Etudes Nucl4aires de Sac]ay, Gif-sur-Yvette, Seine et Olse, France).
a
Un metal soumis un gradient de tempJrature est le si~ged’une sursaturation de lacunes: q/C,=
E,(Ef+ Em ÷E~2kT)+E~
~
(E,
2 kT)J
-
et d’un flux de lacunes: DaC (Ef+Et)(1+q/C,) kT on E~, E~et E~sont les Lnergies de formation, migration et transport pour les lacunes. L’~cart~i.1’ ~qui1lbre est dii au parcours moyen fini, X = (g p)h/2, des lacunes: la concentration en un point donn~est une fonction des concentrations thus Ia r~gtonenvironnante d’un rayon de l’ordre de X. Des sursaturations et sons-saturations suivant le signe de (Ef + Es), de 0, 1 % semblent accessibles l’exp~rience haute temperature et l’effet est plus grand vers les temp4ratures plus basses.
a
a
A metal maintained in a temperature gradient will experience a vacancy supersaturation given by: q/C.=
gp [E#(Et+Em+Et~2kT)+Et k (E1
-
2 kT)
and a vacancy flow: D~ J
=
-
kT
(E
+
E ~)(1
+
q/C,)
where E~,Em and E~are the energies of formation, motion and transport for vacancies. The deviation from equilibri~iniis due to the finite mean free path, X = (g p) 1/2, of the vacandes: the concentration at any point is a complex average of the concentrations of the surrounding
VoL 4, No. 5
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
region to a distance X. Supersaturations or subsaturations, following the sign of (E, + E ~), of 0. 1 % are possible under reasonable experi-
xli
mental conditions at high temperature, and the effect is larger at lower temperatures. (Received 26 January 1966) (Revised 7 April 1966)
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
Comparison of the Hall mobility and the drift mobility of holes measured under stationary conditions shows that at T> 200°Choles are trapped at silver ion vacancies, the trapping energy being E~= 0. 18 eV. The effective mass ratio for the holes m~’Jm= 0.6 0. 9. At T < 200°Ctrapping takes place either at silver ion vacancies at dislocations, or at iron impurities, leading to a center (FeA VA~ consisting of tnvalent iron and a silver ~on~acancy. -
(Received 28 February 1966) 13. THE ELASTIC CONSTANTS OF RUBIDIUM Carol A. Roberts and Robert Meister (Department of Electrical Engineering, The Catholic University of America, Washington 17,D.C.). The elastic constants of single crystal rubidiuni have been measured at 80 ±3°K using the ultrasonic pulse echo method at a frequency of 15 mc. The elastic constants (in units of 10~° 3) are cu = 2.96, C~ = 2.44, C~ = dynes/cm 1.60. Five wave velocities were measured, allowing the computation of the three independent elastic constants with two internal checks. Single crystal rubidium has an anisotropy indicated by the ratio (c 11 c~) /2c~ = 0.162. -
(Received 21 February 1966) 14. FORMATION OF VACANCY-DONOR ASSOCIATES DURING Cu AND Nt PRECIPITATION IN Ge. C. S. Fuller and K. B. Wo]fstirn (Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey). Acceptor levels at EV + 0. 07 ev and Ev + 0. 10 ev form when supersaturated solutions of Cu or Ni in As-doped Ge are quenched or are annealed in the temperature range 160-400°C. The 0. 07 eV acceptor is observed after a slow quench of Cu solutions or after a short anneal of Ni solutions. The 0. 10 eV acceptor is found after fast quench in the case of Cu or after long anneals in both the Cu or Ni solutions. The increase in hole mobility during annealing indicates that similar vacancy-donor associates are produced in both solutions. A tentative model to account for the results is presented. (Received 28 January 1966) (Revised 21 March 1966)
Vol. 4, No. 5
15. CONCENTRATIONS DES LACUNES DANS LES METAUX SOUMIS A UN GRADIENT DE TEMPERATURE. D. A. Blackburn (Centre d’Etudes Nucl4aires de Sac]ay, Gif-sur-Yvette, Seine et Olse, France).
a
Un metal soumis un gradient de tempJrature est le si~ged’une sursaturation de lacunes: q/C,=
E,(Ef+ Em ÷E~2kT)+E~
~
(E,
2 kT)J
-
et d’un flux de lacunes: DaC (Ef+Et)(1+q/C,) kT on E~, E~et E~sont les Lnergies de formation, migration et transport pour les lacunes. L’~cart~i.1’ ~qui1lbre est dii au parcours moyen fini, X = (g p)h/2, des lacunes: la concentration en un point donn~est une fonction des concentrations thus Ia r~gtonenvironnante d’un rayon de l’ordre de X. Des sursaturations et sons-saturations suivant le signe de (Ef + Es), de 0, 1 % semblent accessibles l’exp~rience haute temperature et l’effet est plus grand vers les temp4ratures plus basses.
a
a
A metal maintained in a temperature gradient will experience a vacancy supersaturation given by: q/C.=
gp [E#(Et+Em+Et~2kT)+Et k (E1
-
2 kT)
and a vacancy flow: D~ J
=
-
kT
(E
+
E ~)(1
+
q/C,)
where E~,Em and E~are the energies of formation, motion and transport for vacancies. The deviation from equilibri~iniis due to the finite mean free path, X = (g p) 1/2, of the vacandes: the concentration at any point is a complex average of the concentrations of the surrounding
VoL 4, No. 5
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
region to a distance X. Supersaturations or subsaturations, following the sign of (E, + E ~), of 0. 1 % are possible under reasonable experi-
xli
mental conditions at high temperature, and the effect is larger at lower temperatures. (Received 26 January 1966) (Revised 7 April 1966)