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Electromigration and permeation of hydrogen and deuterium in silver
viii
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
We have also considered the possibility of antisymmetric and symmetric exchange between nearest neighbours only, using a group theoretical approach. The high ratios of antisymmetric to symmetric exchange which would be necessary to explain the observed helical structures preclude however antisymmetric exchange as a dominant factor. Received 1 February 1973 Revised 10 December 1973 12.
ELECTROMIGRATION AND PERMEAT ION OF HYDROGEN AND DEUTERIUM IN SILVER RE. Einziger and H.B. Huntington, Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12181, U.S.A.
A steady state flow technique was used to measure the effective charge number (Z*) and permeability (N) of hydrogen and deuterium m silver. Over the range of temperature (485—720°C)and pressure (220—750 Torr) the effective charge number is a constant. The interstitial impurity migrates in the direction of the electron wind withZ~ —6.8 andZ~= —18. The values of Z* are of the same order as seif-electromigration but the size of the isotope effect is surprising. The quantum theories used to explain the isotope effect for hydrogen electromigration in Fe and Ni appear to fail here. In order to determine the effective charge number it was necessary to measure the perrneabiity. For both H 2 and D2, the permeability in silver follows the equation N = N0 exp(—Q/R T) where 300,NOH = 2.86 NOD 2.39 ± 0.40, QD = 14400 ± ±0.70 and QH = 14200 ±500. Here Q is in units of cal/mole and Nis in units of cc(ntp) / (sec-at~-cm.) The isotope effect ratio NH /ND = 1 .25 was smaller than the classically expected value of(2)~,but could be explained by the theory of Ebisuzaki, Kass and 0’ Keeffe. Received 2 October 1973 13.
ON THE VOLUME DEPENDENCE OF THE TOTAL ENERGY AND THE EQUATION OF STATE FOR COPPER J. Kollér andG. Solt Central Research Institute for Physics, Solid State Physics Department, 1525 Budapest, Hungary, 114. POB 49.
Vol. 14, No. 10
The total energy of metallic copper as a function of the atomic radius is calculated. The model assumes that in copper one has nearly free s-electrons in OPW states and d-electrons localized at the ions in atomiclike orbitals. The coulomb interactions in the energy are calculated by using the model of neutral spheres, while the kinetic and exchange contributions to the s2 -energy are approximated by the exchange charge model. Instead of the familiar Born—Mayer repulsion, which was found to lead to controversies in the case of copper, the d-type interaction energy shows a more complex behaviour having a minimum near the equilibrium atomic radius. The prediction for the cohesive energy and the equation of state is reasonable, the calculated value for the Ashcroft radius for s-electrons agrees remarkably with the ‘ab initio~ estimate. The atomic-like orbitals minimizing the total energy are somewhat more extended than the real atomic wave-functions. Received 24 October 1973
14.
OPTIMUM ACOUSTIC WAVE SECONDHARMONIC GENERATION IN P1EZOELECTRIC SEMICONDUCTORS Anti K. Agarwal and Satish K. Sharma, Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi-I 10029, India
The phenomenological approach has been used to study analytically the acoustic wave second harmonic generation in piezoelectric semiconductors in the presence of the d.c. electric and an oscillating electromagnetic field (OFF). It has been suggested that the second harmonic acoustic flux (SHAF) can be enhanced considerably by the application of an OEF polarized in the direction of the propagating acoustic wave. The SHAF exhibits a maximum at ~2 = w, where ci is the frequency of the OEF and w is the frequency of the acoustic wave. The SHAF also shows a maximum at d.c. electric fields for which the average drift veIocit~ of the carriers is equal to the velocity of sound. It is found that for a typical case of n-type nondegenerate InSb (77°K,n = 2.5 X l0’4cni3) that the SHAF is enhanced by a factor of lO3over its value in the
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
We have also considered the possibility of antisymmetric and symmetric exchange between nearest neighbours only, using a group theoretical approach. The high ratios of antisymmetric to symmetric exchange which would be necessary to explain the observed helical structures preclude however antisymmetric exchange as a dominant factor. Received 1 February 1973 Revised 10 December 1973 12.
ELECTROMIGRATION AND PERMEAT ION OF HYDROGEN AND DEUTERIUM IN SILVER RE. Einziger and H.B. Huntington, Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12181, U.S.A.
A steady state flow technique was used to measure the effective charge number (Z*) and permeability (N) of hydrogen and deuterium m silver. Over the range of temperature (485—720°C)and pressure (220—750 Torr) the effective charge number is a constant. The interstitial impurity migrates in the direction of the electron wind withZ~ —6.8 andZ~= —18. The values of Z* are of the same order as seif-electromigration but the size of the isotope effect is surprising. The quantum theories used to explain the isotope effect for hydrogen electromigration in Fe and Ni appear to fail here. In order to determine the effective charge number it was necessary to measure the perrneabiity. For both H 2 and D2, the permeability in silver follows the equation N = N0 exp(—Q/R T) where 300,NOH = 2.86 NOD 2.39 ± 0.40, QD = 14400 ± ±0.70 and QH = 14200 ±500. Here Q is in units of cal/mole and Nis in units of cc(ntp) / (sec-at~-cm.) The isotope effect ratio NH /ND = 1 .25 was smaller than the classically expected value of(2)~,but could be explained by the theory of Ebisuzaki, Kass and 0’ Keeffe. Received 2 October 1973 13.
ON THE VOLUME DEPENDENCE OF THE TOTAL ENERGY AND THE EQUATION OF STATE FOR COPPER J. Kollér andG. Solt Central Research Institute for Physics, Solid State Physics Department, 1525 Budapest, Hungary, 114. POB 49.
Vol. 14, No. 10
The total energy of metallic copper as a function of the atomic radius is calculated. The model assumes that in copper one has nearly free s-electrons in OPW states and d-electrons localized at the ions in atomiclike orbitals. The coulomb interactions in the energy are calculated by using the model of neutral spheres, while the kinetic and exchange contributions to the s2 -energy are approximated by the exchange charge model. Instead of the familiar Born—Mayer repulsion, which was found to lead to controversies in the case of copper, the d-type interaction energy shows a more complex behaviour having a minimum near the equilibrium atomic radius. The prediction for the cohesive energy and the equation of state is reasonable, the calculated value for the Ashcroft radius for s-electrons agrees remarkably with the ‘ab initio~ estimate. The atomic-like orbitals minimizing the total energy are somewhat more extended than the real atomic wave-functions. Received 24 October 1973
14.
OPTIMUM ACOUSTIC WAVE SECONDHARMONIC GENERATION IN P1EZOELECTRIC SEMICONDUCTORS Anti K. Agarwal and Satish K. Sharma, Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi-I 10029, India
The phenomenological approach has been used to study analytically the acoustic wave second harmonic generation in piezoelectric semiconductors in the presence of the d.c. electric and an oscillating electromagnetic field (OFF). It has been suggested that the second harmonic acoustic flux (SHAF) can be enhanced considerably by the application of an OEF polarized in the direction of the propagating acoustic wave. The SHAF exhibits a maximum at ~2 = w, where ci is the frequency of the OEF and w is the frequency of the acoustic wave. The SHAF also shows a maximum at d.c. electric fields for which the average drift veIocit~ of the carriers is equal to the velocity of sound. It is found that for a typical case of n-type nondegenerate InSb (77°K,n = 2.5 X l0’4cni3) that the SHAF is enhanced by a factor of lO3over its value in the