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Expansion of the free energy near a phase transition
iv
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS Laboratories, N.y. Philips’ Gloeilampenfabrieken Eindhoven— Netherlands
The compound /3-Ga2 03 shows at least three different emission bands depending on the choice of the dope. At room temperature, an efficient blue emission is found for undoped Ga203 and Ga203 containing cations with a charge higher than three. Greenish emission is found for Ga2 03 doped with Be or with a combination of Li (or Be) and one of the ions causing the blue emission. At liquid nitrogen temperature an ultra-violet emission band is observed for practically all compOsitions. Received 8 August 1969 Revised 28 October 1969
11.
A THEORY OF THE FIRST ORDER RAMAN SCATTERING OF LIGHT BY POLARITONS IN CRYSTALS OF THE ROCKSALT STRUCTURE A.A. Maradudin and S. Ushioda, Department of Physics, University of California, Irvine, California 92664, U.S.A.
via the magneto-optic effect, and estimate the intensity of the light scattered by this mechanism. Received 8 September 1969 Revised 27 October 1969
12.
THERMODYNAMIC PROPERTIES OF DILUTE MAGNETIC ALLOYS C.S. Ting, Department of Physics, University of California, San Diego, La Jolla, California
The free energy of a dilute magnetic alloy is obtained on the basis of Suhi’s theory from which the temperature dependent entropy and specific heat of the system are calculated at all temperature ranges. The zero temperature entropy we obtain is in agreement with Zittartz’s calculation, which is based upon Nagaoka’s formulation, and our specific heat results are in qualitative agreement with the experimental data given by Daybell and Steyert. Received 19 August 1969 13.
In crystals of the rocksalt structure the electro-optic coefficient as well as the first derivative of the electronic polarizability with respect to an ionic displacement vanishes because every ion is at a center of inversion. Consequently, the zone center optical phonons are inactive in first order Raman scattering. However, these phonons are infrared active, and the transverse optical (TO) phonons form polaritons when the retardation of the Coulomb interaction is taken into account. Because of the axial vector character of the magnetic field, the first derivative of the electronic polarizability with respect to the macroscopic magnetic field associated with the polaritons does not vanish in rocksalt type crystals. Thus the polaritons in crystals of the rocksalt structure can give rise to first order Raman scattering. In this note we present a theory of the Raman scattering intensity by polaritons
Vol. 7, No. 24
EXPANSION OF THE FREE ENERGY NEAR A PHASE TRANSITION
J. Daniel,
Amit, Department of Physics, Brandeis University, Waltham, Massachusetts 02154 A phenomenological theory describing the uniform and non-uniform properties of a system near a critical point is proposed. This theory allows for quite general exponents satisfying certain relations e.g. scaling relations. The form of the expansion in powers of the orderparameter is different from previous attempts to generalize the Landau—Ginzburg theory. This change in the form of the expansion allows for the allocation of a well defined region in the order-parameter temperature plane in which the theory is expected to be a good approximation. The expectation is reinforced by a recent experiment of Ho and Litster.
Vol. 7, No. 24
ABSTRACTS OF PAPERS TO APPEAR IN
The proposed expansion includes in a natural way a possible logarithmic divergence in the specific heat without affecting other properties with logarithm terms. The determination of the parameters in the theory is discussed both for cases in which the
J. PHYS.
CHEM. SOLIDS
order-parameter is experimentally accessible and for cases, like the superfluid, in which it is not accessible. Received 30 June 1969 Revised 21 October 1969
v
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS Laboratories, N.y. Philips’ Gloeilampenfabrieken Eindhoven— Netherlands
The compound /3-Ga2 03 shows at least three different emission bands depending on the choice of the dope. At room temperature, an efficient blue emission is found for undoped Ga203 and Ga203 containing cations with a charge higher than three. Greenish emission is found for Ga2 03 doped with Be or with a combination of Li (or Be) and one of the ions causing the blue emission. At liquid nitrogen temperature an ultra-violet emission band is observed for practically all compOsitions. Received 8 August 1969 Revised 28 October 1969
11.
A THEORY OF THE FIRST ORDER RAMAN SCATTERING OF LIGHT BY POLARITONS IN CRYSTALS OF THE ROCKSALT STRUCTURE A.A. Maradudin and S. Ushioda, Department of Physics, University of California, Irvine, California 92664, U.S.A.
via the magneto-optic effect, and estimate the intensity of the light scattered by this mechanism. Received 8 September 1969 Revised 27 October 1969
12.
THERMODYNAMIC PROPERTIES OF DILUTE MAGNETIC ALLOYS C.S. Ting, Department of Physics, University of California, San Diego, La Jolla, California
The free energy of a dilute magnetic alloy is obtained on the basis of Suhi’s theory from which the temperature dependent entropy and specific heat of the system are calculated at all temperature ranges. The zero temperature entropy we obtain is in agreement with Zittartz’s calculation, which is based upon Nagaoka’s formulation, and our specific heat results are in qualitative agreement with the experimental data given by Daybell and Steyert. Received 19 August 1969 13.
In crystals of the rocksalt structure the electro-optic coefficient as well as the first derivative of the electronic polarizability with respect to an ionic displacement vanishes because every ion is at a center of inversion. Consequently, the zone center optical phonons are inactive in first order Raman scattering. However, these phonons are infrared active, and the transverse optical (TO) phonons form polaritons when the retardation of the Coulomb interaction is taken into account. Because of the axial vector character of the magnetic field, the first derivative of the electronic polarizability with respect to the macroscopic magnetic field associated with the polaritons does not vanish in rocksalt type crystals. Thus the polaritons in crystals of the rocksalt structure can give rise to first order Raman scattering. In this note we present a theory of the Raman scattering intensity by polaritons
Vol. 7, No. 24
EXPANSION OF THE FREE ENERGY NEAR A PHASE TRANSITION
J. Daniel,
Amit, Department of Physics, Brandeis University, Waltham, Massachusetts 02154 A phenomenological theory describing the uniform and non-uniform properties of a system near a critical point is proposed. This theory allows for quite general exponents satisfying certain relations e.g. scaling relations. The form of the expansion in powers of the orderparameter is different from previous attempts to generalize the Landau—Ginzburg theory. This change in the form of the expansion allows for the allocation of a well defined region in the order-parameter temperature plane in which the theory is expected to be a good approximation. The expectation is reinforced by a recent experiment of Ho and Litster.
Vol. 7, No. 24
ABSTRACTS OF PAPERS TO APPEAR IN
The proposed expansion includes in a natural way a possible logarithmic divergence in the specific heat without affecting other properties with logarithm terms. The determination of the parameters in the theory is discussed both for cases in which the
J. PHYS.
CHEM. SOLIDS
order-parameter is experimentally accessible and for cases, like the superfluid, in which it is not accessible. Received 30 June 1969 Revised 21 October 1969
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