Lattice relaxation around impurity pairs in alkali halides

1976 ◽  
Vol 54 (19) ◽  
pp. 2010-2017
Author(s):  
T. L. Templeton ◽  
B. P. Clayman
Keyword(s):  
Nearest Neighbor ◽  
Molecular Model ◽  
Linear Chain ◽  
Alkali Halides ◽  
Lattice Relaxation ◽  
Resonant Absorption ◽  
Force Constants ◽  
Chain Model ◽  
Absorption Frequencies ◽  
Good Agreement

The rigid ion model is applied to the calculation of the relaxation of the lattice around single impurities and pairs of impurities in alkali halide host-defect systems. The calculated relaxation of nearest neighbors is typically a few percent of the host crystal lattice constant. Relaxation falls off with increasing distance from the defects. Nearest neighbor force constants derived from this calculation are, in some cases, in good agreement with those obtained by fitting the resonant absorption frequencies of the vibrational modes of these impurity centres to a molecular model. In other cases the extreme anisotropy of the relaxed force constants is seen to prevent the application of a simple molecular model. The calculated force constants, when used in a linear chain model, give good qualitative agreement with experiment.

Lattice relaxation around tetragonal and rhombic defects in alkali halides

1979 ◽  
Vol 57 (8) ◽  
pp. 1209-1215
Author(s):  
B. P. Clayman
Keyword(s):  
Nearest Neighbor ◽  
Alkali Halides ◽  
Nearest Neighbors ◽  
Lattice Relaxation ◽  
Force Constants ◽  
Tetragonal Symmetry ◽  
Model Calculations ◽  
Host Interactions ◽  
Rhombic Symmetry ◽  
Rigid Ion Model

The relaxation of the crystal lattice around impurity pair defects in alkali halides is calculated based on a rigid ion model. Pairs with tetragonal symmetry—fourth nearest neighbors along the [001] axis—and those with rhombic symmetry—second nearest neighbors along the [110] axis— are both considered, for all cases where experimental evidence exists for resonant or gap modes. These are: NaCl with F−, Li+, and Ag+; KI with Cl−, Br−, Na+, and Rb+; KCl with Na+; and NaBr with Li+. Relaxation spaces with 72 ions (tetragonal) and 50 ions (rhombic) are used and results reported for all ions within the spaces. The nearest neighbor central force constants coupling the impurity ions and their nearest neighbors are calculated in the rigid ion approximation and the results compared with earlier dynamical model calculations. Because the dynamical models assumed that only one perturbed force constant was needed to characterize all the impurity–host interactions, and significant directional inhomogeneity of the force constants was a result of the present calculations, only qualitative comparisions could be made.

Molecular Model Calculations of Pair–Modes in Alkali Halides

1974 ◽  
Vol 52 (16) ◽  
pp. 1492-1501 ◽  
Author(s):  
R. W. Ward ◽  
B. P. Clayman
Keyword(s):  
Short Range ◽  
Nearest Neighbor ◽  
Molecular Model ◽  
Alkali Halides ◽  
Nearest Neighbors ◽  
Local Mode ◽  
Relevant Parameter ◽  
Model Calculations ◽  
Short Range Force ◽  
Range Force

The molecular model, developed by Jaswal for [100] aligned impurity pairs, has been extended to account for [110] aligned pairs and used to study U center (H−H− and D−D−) pairs in KCl and (Cl−Cl− and Na+Na+)-induced pair–modes in the gap of KI. In this model the impurity ions in the pair and their nearest neighbors are allowed to vibrate while the rest of the lattice is held fixed. For [110] and [100] aligned pairs, this gives 12- and 17-ion molecules respectively. The potential energy is treated in the rigid ion approximation with short range forces between the nearest neighbors only. After the single relevant parameter of the model, the nearest neighbor force constant, is fitted to the U center local mode frequency, the model can account for the experimentally observed frequencies and polarizations of the three U center pairs in KCl. Similarly, after fitting to the single ion Cl− gap mode at 77 cm−1 in KI, the model predicts 3 infrared active pair–modes whose frequencies are in close agreement with experiment. In KI:Na+, where no single ion resonance has been observed, the calculated results suggest that the absorption lines are due to [110] aligned Na+ ions, with a large softening of the short range force constants occurring around the defect. The KI:Br− and NaCl:F− systems are also considered.

ABSENCE OF PHASE TRANSITIONS ON TREE STRUCTURES

1993 ◽  
Vol 07 (29n30) ◽  
pp. 1947-1950 ◽  
Author(s):  
RAFFAELLA BURIONI ◽  
DAVIDE CASSI
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Mean Field ◽  
Range Order ◽  
The Other ◽  
Long Range Order ◽  
Field Phase ◽  
Tree Structures ◽  
Bethe Lattices

We rigorously prove that the correlation functions of any statistical model having a compact transitive symmetry group and nearest-neighbor interactions on any tree structure are equal to the corresponding ones on a linear chain. The exponential decay of the latter implies the absence of long-range order on any tree. On the other hand, for trees with exponential growth such as Bethe lattices, one can show the existence of a particular kind of mean field phase transition without long-range order.

scholarly journals Erratum: Force constants of the metaborate ion in alkali halides

1973 ◽  
Vol 58 (4) ◽  
pp. 1782-1782
Author(s):  
J. C. Decius ◽  
C. R. Becker ◽  
W. J. Fredericks
Keyword(s):  
Alkali Halides ◽  
Force Constants

scholarly journals Local and electronic structure around Ga in CdTe: evidence of DX- and A-centers

2012 ◽  
Vol 20 (1) ◽  
pp. 166-171
Author(s):  
Vasil Koteski ◽  
Jelena Belošević-Čavor ◽  
Petro Fochuk ◽  
Heinz-Eberhard Mahnke
Keyword(s):  
Density Functional ◽  
Plane Waves ◽  
Lattice Relaxation ◽  
Defect Structures ◽  
Functional Theory ◽  
Edge Structure ◽  
X Ray ◽  
First Time ◽  
X Ray Absorption ◽  
Good Agreement

The lattice relaxation around Ga in CdTe is investigated by means of extended X-ray absorption spectroscopy (EXAFS) and density functional theory (DFT) calculations using the linear augmented plane waves plus local orbitals (LAPW+lo) method. In addition to the substitutional position, the calculations are performed for DX- and A-centers of Ga in CdTe. The results of the calculations are in good agreement with the experimental data, as obtained from EXAFS and X-ray absorption near-edge structure (XANES). They allow the experimental identification of several defect structures in CdTe. In particular, direct experimental evidence for the existence of DX-centers in CdTe is provided, and for the first time the local bond lengths of this defect are measured directly.

Temperature-Dependent Spectrum of an Antiferroelectric Linear Chain Model

1962 ◽  
Vol 128 (2) ◽  
pp. 638-645 ◽  
Author(s):  
B. D. Silverman
Keyword(s):  
Linear Chain ◽  
Chain Model ◽  
Temperature Dependent

NUCLEAR MAGNETIC RELAXATION IN GAS MIXTURES

1962 ◽  
Vol 40 (8) ◽  
pp. 1027-1035 ◽  
Author(s):  
D. Llewelyn Williams
Keyword(s):  
Room Temperature ◽  
Lattice Relaxation ◽  
Lattice Relaxation Time ◽  
Proton Spin ◽  
Spin Lattice Relaxation ◽  
Spin Lattice ◽  
Gas Molecules ◽  
De Broglie Wavelength ◽  
Diffraction Effects ◽  
Good Agreement

Measurements of the proton spin–lattice relaxation time using pulse techniques have been made on the hydrogen–nitrogen, hydrogen–neon, and hydrogen–helium systems from room temperature to 60° K. The results are in good agreement with the Oppenheim–Bloom theory and illustrate the importance of the radial distribution of the gas molecules and of diffraction effects associated with the de Broglie wavelength.

Linear-chain-model interpretation of resonant Raman scattering inGenSimmicrostructures

1996 ◽  
Vol 53 (23) ◽  
pp. 15871-15877 ◽  
Author(s):  
M. A. Araújo Silva ◽  
E. Ribeiro ◽  
P. A. Schulz ◽  
F. Cerdeira ◽  
J. C. Bean
Keyword(s):  
Raman Scattering ◽  
Linear Chain ◽  
Chain Model ◽  
Model Interpretation ◽  
Resonant Raman ◽  
Resonant Raman Scattering

Force constants and normal vibrational modes of a simplified molecular model of methyl thionitrite

1963 ◽  
Vol 11 (1-6) ◽  
pp. 331-339 ◽  
Author(s):  
Roger J. Philippe ◽  
John M. Ruth
Keyword(s):  
Molecular Model ◽  
Force Constants ◽  
Vibrational Modes ◽  
Normal Vibrational Modes

Nuclear Quadrupole Spin-Lattice Relaxation in Alkali Halides

1960 ◽  
Vol 118 (3) ◽  
pp. 631-639 ◽  
Author(s):  
E. G. Wikner ◽  
W. E. Blumberg ◽  
E. L. Hahn
Keyword(s):  
Alkali Halides ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Quadrupole Spin ◽  
Spin Lattice ◽  
Nuclear Quadrupole ◽  
Nuclear Quadrupole Spin
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