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Coulomb interactions and optically-active vibrations of ionic crystals. I. Theory and application to NaNO3
vi
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
Vol. 18, No. 5
peak in a Ill—V ternary alloy. This allows the most accutemperature interval (10—95°C)of the thermoelastic rate determination to date of both the composition martensitic transformation, were determined. From the dependence of the F band gap and the position of the experimental data, using ultrasonic techniques at hydroF—X crossover (x~= 0.72, 77°K;x~= 0.73, 300°K). static pressures (up to 5 kilobars), the temperature Absorption and photoluminescence spectra are corndependence of the isothermal equation of state of pared for both direct and indirect In 1_~Ga~P. In the cubic f3-phase was calculated. It was found that addition, absorption, photoluminescence, and lumithe low-temperature orthorhombic ~3’-phaseis elasticnescence lifetimes of In1_~Ga~P :N are examined, ally softer than the cubic [3-phase,consequently affectThese data suggest that the A-line is perturbed by alloy ing the [3~ [3’ transformation kinetics upon application disorder and merges with the NN pairs into a broad lumi- of hydrostatic pressure. The high values of the GrUneisen nescence band for x ~ 0.94. The observed Stokes shift p} arameter, calculated from the pressure derivatives of for the N-trap in the alloy is characteristic of an the sound veocities, in the orthorhombic f3’-phase are impurity strongly coupled to the lattice. The tempera~indicative of a high artharmonicity of interatomic potenture dependence of the N luminescence band is found to tial in the vicinity of the [3’ —~- [3phase transformation. be well described by the conventional configuration— Received 8 October 1975 coordinate model for phonon-coupled impurity luminescence. Implications of these results for light emitting 7. VACANCIES IN TRANSITION METALS: devices are mentioned. FORMATION ENERGY AND FORMATION Received 7 November 1975 5.
G. Allan and M. Lannoo, Physique des Solides, I.S.E.N., 3, rue F. Baës, 59046 Lille Cedex, France.
PSEUDOPOTENTIAL BAND STRUCTURE CALCULATIONS FOR [3-AgIAND y-AgI P.V. Smith Physics Department, University of New England Armidale N.S.W., 2351 Australia.
The pseudopotential calculations of Cohen and Bergstresser on the zinc-blende structures of Sn, InSb and CdTe, are extended to the 1—Vil compound, Ag!. The resulting band structure for the metastable phase with the zinc-blende structure, denoted y-AgI, is found to be in good agreement with that derived by a previous tight-binding calculation. The same pseudopotential form factors are used to calculate the band structure for [3-Agi which is the stable low temperature phase having the wurtzite structure. This band structure is shown to be consistent with the predictions of the earlier tight-binding analysis. Taken together, these band structures and pseudopotential form factors provide a suitable basis for calculating the electronic properties of these two silver iodide polytytpes.
.
This work describes a calculation ot the formation energy and volume for a vacancy in transition metals. One uses a tight-binding schem for the d band and a Born—Mayer type potential to account for the repulsive part of the energy at small distances. The results show that the relaxation energy is small in all cases, less than 0.1 eV. This seems to be coherent with the good agreement obtained for the theoretical and experimental values of the formation energy E1~’of the vacancy, without including relaxation. The center of the transitional series is found to give a contraction (formation volume of order -. 0.4 atomic volume) whereas the edges are found to produce dilatations. Received 20 February 1973 Revised 12 December 1975 ~.
COULOMB INTERACTIONS AND
THE ULTRASONIC EQUATION OF STATE IN TuE VICINITY OF THE MARTENSITIC TRANSFORMATION IN Au —47.5 at.%Cd
OPTICALLY-ACTIVE VIBRATIONS OF IONIC CRYSTALS. I. THEORY AND APPLICATION TO NaNO3 A. Yamarnoto. T. Utida and H. Murata, Department of Chemistry, Faculty of Science, Hiroshima University, Higashisenda-maciii.
Y. Gefen and M. Rosen, Nuclear Research Centre-Negev, P.O. Box 9001, Beer-Sheva. Israel; and Materials Engineering Department, Ben Gurion University, Beer-Sheva, Israel.
Hiroshima 730, Japan; and Y. Shiro. Shinonorne Branch School, Faculty of Education, Hiroshima University, Shinonome-3chome, Hiroshima 734, Japan.
Received 16 October ]975 6.
VOLUME
The isotropic elastic constants of Au — 47.5 at.% Cd, and their hydrostatic pressure derivatives, within the
A method is given for polarizable-ion model calculations of optically-active vibration frequencies of
Vol. 18, No. 5
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLiDS
vii
ionic crystals together with an illustrative application,
optical rotation in mixed crystals of NaClO3--NaBrO3 of
Frequency splittings originating from Coulomb inter-
different compositions.
actions between induced dipoles are explained satisfactorily by the calculations. Important discrepancies remaining in rigid-ion treatments are considerably reduced by taking into account the electronic polarizabilities. Some effects of anisotropy of the ionic polarizabilities on crystal vibrations are discussed briefly.
Received 21 August 1975 11.
P.W. Mirwald and G.C. Kennedy, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, U.S.A.
Received 5 September 1975 Revised 12 December 1975 9.
ETUDE DE L’AUTODIFFUSION sous PRESSION HYDROSTATIQUE DANS LA PHASE CUBIQUE A FACES CENTREES DU CERIUM G. Marbach, M. Fromont et D. Calais, CEA, DEcPu/SEAMA, Bt.19, B.P. 6, Fontenay aux
Roses, France. Comme dans la phase cubique centrée, l’autodiffusion s’accélère sons pression dans le cerium y cubique3 a faces centrées. Le volume d’activation (z~ V = plus —3 cm soit — 15% du volume molaire) est légèrement négatif que dans la phase cubique centrée comme le prévoyait la loi semi-empirique de Nachtrieb. Received 18 December 1974 Revised 19 September 1975
10.
OPTICAL ROTATION OF SOLID SOLUTIONS OF SODIUM CHLORATE AND SODIUM BROMATE V. Sivaramakrishnan and K.A. Arunkumar, Department of Physics, Indian Institute of Technology, Madras 600 036, India.
The optical rotary dispersion (ORD) data for a mixed crystal of sodium chlorate and sodium bromate have been analysed. It is found that the ORD exhibited by these solid solutions cannot be explained using Vegard’s law of additivity. Based on the model proposed by Wasastjerna, a special form of additivity of polarisability is assumed which the asymmetric distribution of the anions around the cation is considered. A formula has been proposed for the additivity of optical rotation in solid solutions and this is found to fit the data for
MELTING TEMPERATURE OF LEAD AND SODIUM AT HIGH PRESSURES
We have redetermined the melting temperatures of lead and sodium as a function of pressure in a new pressure cell made up of low strength materials. Many of the anomalies reported in a prior determination of the melting curve of lead have largely disappeared - The slope of our new melting curve for lead is in close agreement with the slope computed from thermochemical data.
Our new curve for sodium differs only slightly from
the prior published curves.
Received 11 November 1975
12.
EFFECTS OF PRESSURE ON OPTICAL
F-BANDS IN RUBIDIUM HALIDES K. Mamola and R. Wu, Department of Physics, Dartmouth College, Hanover, NH 03755, U.S.A. High pressure optical absorption measurements have been made on additively colored RbCl and RbBr at pressures up to 10 kbar and on electrolytically clored RbI up to 4 kbar. The pressure dependence of the F-band produced in RbCl by x-irradiation in the s.c. phase is also reported. Effects of the pressure induced structure transformation these salts are described. F-band pressure shifts are inrelated to a semi-empirical treatment which takes account of relative ion sizes. A new Ivey law for F-centers in host crystals having the s.c. structure is presented. This relation is established using all available F-band data including those for salts transformed to the s.c. structure by the application of high pressure. Received 15 May 1975 Revised 3 December 1975
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
Vol. 18, No. 5
peak in a Ill—V ternary alloy. This allows the most accutemperature interval (10—95°C)of the thermoelastic rate determination to date of both the composition martensitic transformation, were determined. From the dependence of the F band gap and the position of the experimental data, using ultrasonic techniques at hydroF—X crossover (x~= 0.72, 77°K;x~= 0.73, 300°K). static pressures (up to 5 kilobars), the temperature Absorption and photoluminescence spectra are corndependence of the isothermal equation of state of pared for both direct and indirect In 1_~Ga~P. In the cubic f3-phase was calculated. It was found that addition, absorption, photoluminescence, and lumithe low-temperature orthorhombic ~3’-phaseis elasticnescence lifetimes of In1_~Ga~P :N are examined, ally softer than the cubic [3-phase,consequently affectThese data suggest that the A-line is perturbed by alloy ing the [3~ [3’ transformation kinetics upon application disorder and merges with the NN pairs into a broad lumi- of hydrostatic pressure. The high values of the GrUneisen nescence band for x ~ 0.94. The observed Stokes shift p} arameter, calculated from the pressure derivatives of for the N-trap in the alloy is characteristic of an the sound veocities, in the orthorhombic f3’-phase are impurity strongly coupled to the lattice. The tempera~indicative of a high artharmonicity of interatomic potenture dependence of the N luminescence band is found to tial in the vicinity of the [3’ —~- [3phase transformation. be well described by the conventional configuration— Received 8 October 1975 coordinate model for phonon-coupled impurity luminescence. Implications of these results for light emitting 7. VACANCIES IN TRANSITION METALS: devices are mentioned. FORMATION ENERGY AND FORMATION Received 7 November 1975 5.
G. Allan and M. Lannoo, Physique des Solides, I.S.E.N., 3, rue F. Baës, 59046 Lille Cedex, France.
PSEUDOPOTENTIAL BAND STRUCTURE CALCULATIONS FOR [3-AgIAND y-AgI P.V. Smith Physics Department, University of New England Armidale N.S.W., 2351 Australia.
The pseudopotential calculations of Cohen and Bergstresser on the zinc-blende structures of Sn, InSb and CdTe, are extended to the 1—Vil compound, Ag!. The resulting band structure for the metastable phase with the zinc-blende structure, denoted y-AgI, is found to be in good agreement with that derived by a previous tight-binding calculation. The same pseudopotential form factors are used to calculate the band structure for [3-Agi which is the stable low temperature phase having the wurtzite structure. This band structure is shown to be consistent with the predictions of the earlier tight-binding analysis. Taken together, these band structures and pseudopotential form factors provide a suitable basis for calculating the electronic properties of these two silver iodide polytytpes.
.
This work describes a calculation ot the formation energy and volume for a vacancy in transition metals. One uses a tight-binding schem for the d band and a Born—Mayer type potential to account for the repulsive part of the energy at small distances. The results show that the relaxation energy is small in all cases, less than 0.1 eV. This seems to be coherent with the good agreement obtained for the theoretical and experimental values of the formation energy E1~’of the vacancy, without including relaxation. The center of the transitional series is found to give a contraction (formation volume of order -. 0.4 atomic volume) whereas the edges are found to produce dilatations. Received 20 February 1973 Revised 12 December 1975 ~.
COULOMB INTERACTIONS AND
THE ULTRASONIC EQUATION OF STATE IN TuE VICINITY OF THE MARTENSITIC TRANSFORMATION IN Au —47.5 at.%Cd
OPTICALLY-ACTIVE VIBRATIONS OF IONIC CRYSTALS. I. THEORY AND APPLICATION TO NaNO3 A. Yamarnoto. T. Utida and H. Murata, Department of Chemistry, Faculty of Science, Hiroshima University, Higashisenda-maciii.
Y. Gefen and M. Rosen, Nuclear Research Centre-Negev, P.O. Box 9001, Beer-Sheva. Israel; and Materials Engineering Department, Ben Gurion University, Beer-Sheva, Israel.
Hiroshima 730, Japan; and Y. Shiro. Shinonorne Branch School, Faculty of Education, Hiroshima University, Shinonome-3chome, Hiroshima 734, Japan.
Received 16 October ]975 6.
VOLUME
The isotropic elastic constants of Au — 47.5 at.% Cd, and their hydrostatic pressure derivatives, within the
A method is given for polarizable-ion model calculations of optically-active vibration frequencies of
Vol. 18, No. 5
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLiDS
vii
ionic crystals together with an illustrative application,
optical rotation in mixed crystals of NaClO3--NaBrO3 of
Frequency splittings originating from Coulomb inter-
different compositions.
actions between induced dipoles are explained satisfactorily by the calculations. Important discrepancies remaining in rigid-ion treatments are considerably reduced by taking into account the electronic polarizabilities. Some effects of anisotropy of the ionic polarizabilities on crystal vibrations are discussed briefly.
Received 21 August 1975 11.
P.W. Mirwald and G.C. Kennedy, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, U.S.A.
Received 5 September 1975 Revised 12 December 1975 9.
ETUDE DE L’AUTODIFFUSION sous PRESSION HYDROSTATIQUE DANS LA PHASE CUBIQUE A FACES CENTREES DU CERIUM G. Marbach, M. Fromont et D. Calais, CEA, DEcPu/SEAMA, Bt.19, B.P. 6, Fontenay aux
Roses, France. Comme dans la phase cubique centrée, l’autodiffusion s’accélère sons pression dans le cerium y cubique3 a faces centrées. Le volume d’activation (z~ V = plus —3 cm soit — 15% du volume molaire) est légèrement négatif que dans la phase cubique centrée comme le prévoyait la loi semi-empirique de Nachtrieb. Received 18 December 1974 Revised 19 September 1975
10.
OPTICAL ROTATION OF SOLID SOLUTIONS OF SODIUM CHLORATE AND SODIUM BROMATE V. Sivaramakrishnan and K.A. Arunkumar, Department of Physics, Indian Institute of Technology, Madras 600 036, India.
The optical rotary dispersion (ORD) data for a mixed crystal of sodium chlorate and sodium bromate have been analysed. It is found that the ORD exhibited by these solid solutions cannot be explained using Vegard’s law of additivity. Based on the model proposed by Wasastjerna, a special form of additivity of polarisability is assumed which the asymmetric distribution of the anions around the cation is considered. A formula has been proposed for the additivity of optical rotation in solid solutions and this is found to fit the data for
MELTING TEMPERATURE OF LEAD AND SODIUM AT HIGH PRESSURES
We have redetermined the melting temperatures of lead and sodium as a function of pressure in a new pressure cell made up of low strength materials. Many of the anomalies reported in a prior determination of the melting curve of lead have largely disappeared - The slope of our new melting curve for lead is in close agreement with the slope computed from thermochemical data.
Our new curve for sodium differs only slightly from
the prior published curves.
Received 11 November 1975
12.
EFFECTS OF PRESSURE ON OPTICAL
F-BANDS IN RUBIDIUM HALIDES K. Mamola and R. Wu, Department of Physics, Dartmouth College, Hanover, NH 03755, U.S.A. High pressure optical absorption measurements have been made on additively colored RbCl and RbBr at pressures up to 10 kbar and on electrolytically clored RbI up to 4 kbar. The pressure dependence of the F-band produced in RbCl by x-irradiation in the s.c. phase is also reported. Effects of the pressure induced structure transformation these salts are described. F-band pressure shifts are inrelated to a semi-empirical treatment which takes account of relative ion sizes. A new Ivey law for F-centers in host crystals having the s.c. structure is presented. This relation is established using all available F-band data including those for salts transformed to the s.c. structure by the application of high pressure. Received 15 May 1975 Revised 3 December 1975