Application of Houston's Method to the Sum of Plane Waves over the Brillouin Zone. I. Simple‐Cubic and Face‐Centered‐Cubic Lattices

1966 ◽  
Vol 7 (1) ◽  
pp. 139-147 ◽  
Author(s):  
Maria Miasek
Keyword(s):  
Brillouin Zone ◽  
Plane Waves ◽  
Face Centered Cubic ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Face Centered

ON HOUSTON'S METHOD OF EVALUATING INTEGRALS OVER THE BRILLOUIN ZONE: NORMALIZATION FACTOR IN A SIMPLE CUBIC LATTICE

1962 ◽  
Vol 40 (9) ◽  
pp. 1153-1165 ◽  
Author(s):  
S. Ganesan ◽  
R. Srinivasan
Keyword(s):  
Brillouin Zone ◽  
Anisotropy Parameter ◽  
Face Centered Cubic ◽  
Normalization Procedure ◽  
Normalization Factor ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Face Centered

In evaluating integrals over the Brillouin zone by Houston's method, a normalization factor has to be used. A wave-vector-dependent normalization factor nj(q + Δq/2) is calculated by equating the volume common to a spherical shell of radius q and thickness Δq and the simple cubic Brillouin zone to the expression given by a j-direction Houston method. Some sample integrals are evaluated using this (GS) normalization procedure and Horton and Schiff's (HS) normalization procedure, originally developed for face-centered cubic lattices. The superiority of the GS method, especially with highly anisotropic functions, is demonstrated. From an evaluation of the moments of the frequency distribution function in a simple cubic lattice for various values of the anisotropy parameter, it is concluded that, when high accuracy is desired, the GS procedure is applicable over a wider range of anisotropy parameter than the HS procedure. The θ–T curve calculated by using the correct normalization procedure in a simple cubic lattice is in good agreement with that calculated by Blackman's method.

Zero-Point Effects in Heisenberg Antiferromagnets with Arbitrary Range of Interaction

1972 ◽  
Vol 50 (23) ◽  
pp. 2991-2996 ◽  
Author(s):  
M. F. Collins ◽  
V. K. Tondon
Keyword(s):  
Ground State ◽  
State Energy ◽  
Correction Term ◽  
Zero Point ◽  
Face Centered Cubic ◽  
Heisenberg Antiferromagnet ◽  
Body Centered Cubic ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Face Centered

The ground state energy, spin-wave energy, and sublattice magnetization have been calculated for a Heisenberg antiferromagnet at the absolute zero of temperature. The treatment extends the earlier work of Anderson, Kubo, and Oguchi to apply for any two-sublattice antiferromagnet with arbitrary range of interaction. It is shown that for each exchange interaction there is a different characteristic correction term to the energies. Explicit calculations are made of these terms for the simple cubic, body-centered cubic, and face-centered cubic lattices, with both first- and second-neighbor interactions. Applications are also made to NiO and MnO. An extra term in the magnetization series beyond that given by earlier workers is derived.

Equilibration of kinetic temperatures in face-centered cubic lattices

2020 ◽  
Vol 102 (4) ◽  
Author(s):  
Vitaly A. Kuzkin ◽  
Sergei D. Liazhkov
Keyword(s):  
Face Centered Cubic ◽  
Cubic Lattices ◽  
Face Centered

scholarly journals Pressure-Induced Dimerization of C60 at Room Temperature as Revealed by an In Situ Spectroscopy Study Using an Infrared Laser

Crystals ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 182 ◽  
Author(s):  
Bing Li ◽  
Jinbo Zhang ◽  
Zhipeng Yan ◽  
Meina Feng ◽  
Zhenhai Yu ◽  
...  
Keyword(s):  
Room Temperature ◽  
Infrared Laser ◽  
Face Centered Cubic ◽  
X Ray Diffraction ◽  
Simple Cubic ◽  
Excitation Laser ◽  
Face Centered ◽  
830 Nm Laser ◽  
Structure Evaluation

Using in situ high-pressure Raman spectroscopy and X-ray diffraction, the polymerization and structure evaluation of C60 were studied up to 16 GPa at room temperature. The use of an 830 nm laser successfully eliminated the photo-polymerization of C60, which has interfered with the pressure effect in previous studies when a laser with a shorter wavelength was used as excitation. It was found that face-centered cubic (fcc) structured C60 transformed into simple cubic (sc) C60 due to the hint of free rotation for the C60 at 0.3 GPa. The pressure-induced dimerization of C60 was found to occur at about 3.2 GPa at room temperature. Our results suggest the benefit and importance of the choice of the infrared laser as the excitation laser.

Theory of ordering in ternary alloys with face-centered-cubic lattices

1968 ◽  
Vol 11 (12) ◽  
pp. 56-63
Author(s):  
V. P. Fadin ◽  
Yu. A. Khon ◽  
V. E. Panin
Keyword(s):  
Ternary Alloys ◽  
Face Centered Cubic ◽  
Cubic Lattices ◽  
Face Centered
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