Anharmonic vibration in fluorite structures

Dawson, B.; Hurley, A. C.; Maslen, V. W.

doi:10.1098/rspa.1967.0104

Cited by 65 publications

(31 citation statements)

References 6 publications

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“…-0"001 -0.2 0"002 0"2 4 0 0 -0"048 -1-7 -0-074 -2-5 3 3 1 -0"022 -1"1 -0"086 -4-1 4 2 2 -0"121 -4"0 -0"002 -0"1 3 3 3 -0"049 -2"2 -0"035 -1"9 5 1 1 -0"032 -1"6 0"007 0"3 4 4 0 -0"010 -0"4 -0"039 -1"8 4 4 2 -0"028 -7"9 -0"031 -8"9 6 2 2 -0"021 -10"3 -0"022 -10"9 4 4 4 -0"015 -0"8 0"008 0-3 5 5 1 -0'012 -0"5 -0"024 -1"3 6 4 2 0"006 0"1 0"047 0"8 8 0 0 -0"068 -2"1 -0"003 -0"1 6 6 0 0"022 1"4 0-039 2-6 5 5 5 0"063 3-3 0"055 2"1 8 4 4 0-022 1"0 0"030 1"1 8 8 0 0"083 3"8 0.015 0"6 that the measurements off by Deutsch & Hart (1984) are appropriate, and the description of anharmonicity within the one-particle-potential approximation of Dawson et al (1967) holds at room temperature, it is plausible that these small systematic residuals are due to polarization of the L shell, which, although small, necessarily exists. The typical residuals summing to give these features are of the order of one to two e.s.d.'s.…”

Section: Analyses Of the Datamentioning

confidence: 99%

“…The temperature factor is due both to harmonic and anharmonic atomic vibrations. In view of the 43m site symmetry of the Si atoms the harmonic term, exp[-B(sin 0/A)2], is isotropic, and the dominant anharmonic effect is the cubic term (Dawson, Hurley & Maslen, 1967;Willis & Pryor, 1975). The data were corrected for anharmonic effects in the manner described in detail by PMM and Fehlmann (1979).…”

Section: The Data Setsmentioning

confidence: 99%

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The electron distribution in silicon. A comparison between experiment and theory

Spackman¹

1986

Acta Cryst Sect A

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T. JANSSEN 271 would give the 12 vertices of an icosahedron and locally icosahedral symmetry, which is, of course, in conflict with periodicity, but as we have seen not with quasi-periodicity. I thank J. C. Toledano, R. Struikmans and the referee for pointing out relevant references. AbstractDeformation and valence-electron densities in silicon are derived via Fourier summation and multipole refinement of highly accurate measurements of X-ray structure factors. These results provide a new perspective for the comparison between theory and experiment. The model electron density derived from experiment is in quantitative agreement with recent solid-state calculations, but not with earlier experimental results reported by Yang & Coppens [Solid State Commun. (1974), 15, 1555-1559.

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Section: Analyses Of the Datamentioning

confidence: 99%

Section: The Data Setsmentioning

confidence: 99%

The electron distribution in silicon. A comparison between experiment and theory

Spackman¹

1986

Acta Cryst Sect A

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“…In this structure the anion has a tetrahedral environment which allows an anharmonic contribution to the thermal vibration of the anion, consistent with the introduction of a cubic teim pxyz in the potential, where x, y and z are the coordinates defining the instantaneous displacement of the anion (see Dawson, Hurley & Maslen, 1967). The magnitude of the anharmonicity parameter/?…”

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confidence: 99%

Anharmonic thermal vibrations in Mg₂Si

Cooper¹,

Panke²

1970

Acta Cryst Sect A

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9) show systematic differences in the structure factors from those predicted by a model which assumes harmonic thermal vibration of the atoms. These differences indicate an anharmonic component in the thermal vibration of the magnesium atoms, consistent with their tetrahedral site symmetry. An analysis of these data has therefore been carried out in terms of a model which includes anharmonic thermal vibration and a least-squares refinement gave a value of the anharmonicity parameter (/~g=-2"39 x 10-1a erg./~-3) which is similar in magnitude to those found for other systems with the fluorite structure.The significance of anharmonic thermal vibrations in materials with the fluorite structure has been established by a series of recent accurate neutron diffraction studies on UO2 (Rouse, Willis & Pryor, 1968), BaF2 (Cooper, Rouse & Willis, 1968 and CaFz and SrFz (Cooper & Rouse, 1970). In this structure the anion has a tetrahedral environment which allows an anharmonic contribution to the thermal vibration of the anion, consistent with the introduction of a cubic teim pxyz in the potential, where x, y and z are the coordinates defining the instantaneous displacement of the anion (see Dawson, Hurley & Maslen, 1967). The magnitude of the anharmonicity parameter/? in these materials is of the order of -3 x 10-12 erA A,-3 and the anharmonic component of the thermal vibration results in significant deviations in the Bragg intensities from those predicted by a harmonic model. For X-ray diffraction the angular dependence of the scattering factors and the predominance of the cation scattering result in the X-ray Bragg intensities for these matelials being less dependent on the anharmonic effects, although a detailed analysis of recent accurate X-ray diffraction measurements on CaFa (Cooper, 1970a) has shown that these also are consistent with an anharmonicity of this magnitude. Panke & W61fel (1969) have recently carried out a careful X-ray diffraction study of Mg2Si, which also has the fluorite structure and which has a more favourable scattering factor ratio. It is interesting to note, therefore, that their results show systematic differences from the predictions of a model which assumes harmonic thermal vibration of the atoms, for example the different values obtained for the structure factors of the 933, 771 and 755 reflexions are indicative of anharmonic effects as described above, whereas a harmonic model would require these three reflexions to have equal structure factors. Because of these apparent systematic effects we have therefore reconsidered the experimental data in terms of an anharmonic model. The X-ray measurements on Mg2Si were made on both single crystals and powder samples and a comprehensive correction for extinction was carried out. Care was also taken to minimize errors due to multiple diffraction (Panke & W~51fel, 1968). No correction was made for the contribution of thermal diffuse scattering, but it is most probable that such a correction would result only in a change in the derived temperature f...

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“…Thus, it may not be adequate for accurate EDD researches. The method based on Boltzmann statistics (Dawson et al 1967, Willis, 1969 was employed,…”

Section: Anharmonic Vibration (Ahv)mentioning

confidence: 99%