Anharmonic thermal vibrations in wurtzite structures

Mair, S. L.; Barnea, Z.

doi:10.1107/s056773947500040x

Cited by 26 publications

(25 citation statements)

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“…Equations (8) and (9) can be shown to be equivalent to the expressions of Mair and Barnea (1975) and Whiteley et al (1978). In particular, we have…”

Section: Anharmonic Temperature Factormentioning

confidence: 96%

“…If equation (14) is expressed in the notation of Mair and Barnea (1975) and the sign conventions of Table 3 are used the result is (17) which should be the same as equation (7) of Mair and Barnea (1975). The discrepancy between the two equations is due to an error made by these authors, which is rectified ifihe three terms in -their-equation are multiplied by a\ a 2 e and c 3 respectively.…”

Section: Constraints Between Cubic Anharmonic Parametersmentioning

confidence: 99%

“…The expansion, to third order, is (3) where the single first-order term has been omitted. This omission is equivalent to making a Taylor expansion of the OPP about the positions defining the minima of that potential, in contrast to an expansion about the thermodynamic equilibrium positions, where a first-order term does occur (Mair and Wilkins 1981). Mair and Wilkins have shown that it is not possible to refine simultaneously both for the effect of the coefficient of the first-order term in the temperature factor and for the equilibrium position.…”

Section: Anharmonic Temperature Factormentioning

confidence: 99%

“…The approach used differs from that of Mair and Barnea (1975) and Whiteley et al (1978), who expanded the one-particle potential (OPP) as a power series in the atomic displacements from appropriate positions (Mair and Wilkins 1981) within the restrictions imposed by the local site symmetry. In the present paper we use a group theory approach, demonstrated by Nizzoli (1976) for zinc.…”

Section: Introductionmentioning

confidence: 99%

“…The refinements in Section 4 below were actually carried out with I P3321 = I P3321' because of the high correlation between these parameters. For convenience to those readers familiar with the notation of Mair and Barnea (1975), Table 3 contains the relationships in that notation.…”

Section: Constraints Between Cubic Anharmonic Parametersmentioning

confidence: 99%

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The Anharmonic Temperature Factor for Crystals with the Hexagonal Wurtzite Structure and Its Inclusion in Models for Least-squares Refinement of Intensity Data

Fakineos¹,

Stevenson²,

Barnea³

1982

Aust. J. Phys.

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The anharmonic temperature factor for binary compounds of the A N B8-N type possessing the wurtzite structure is derived as a perturbation expansion about the harmonic case. The terms in this expansion are obtained from combinations of spherical harmonics. The derivation utilizes group theory and follows the treatment of Von der Lage and Bethe (1947) and Nizzoli (1976). A set of constraints between the cubic anharmonic coefficients in the one-particle potential (OPP), which appear in the temperature factor, is then derived, enabling least-squares refinements to be carried out successfully. The use of the anharmonic temperature factor, with these constraints, is shown to result in a significant reduction in Hamilton's R factor for two extensive data sets.

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“…Equations (8) and (9) can be shown to be equivalent to the expressions of Mair and Barnea (1975) and Whiteley et al (1978). In particular, we have…”

Section: Anharmonic Temperature Factormentioning

confidence: 96%

Section: Constraints Between Cubic Anharmonic Parametersmentioning

confidence: 99%

Section: Anharmonic Temperature Factormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Constraints Between Cubic Anharmonic Parametersmentioning

confidence: 99%

See 3 more Smart Citations