Polarity determination by diffraction from planes inclined to an extended crystal face

Accurate X-ray integrated-intensity data collected from an extended-face crystal of GaAs are analysed to provide detailed information on the thermal vibrations of atomic species, including cubic anharmonicity, at room temperature. The values obtained for the thermal parameters are BGa = 0.622 (3) A 2, B s = 0.483(5)A 2 and ~GaAs'-" --0.6(1) X 10-18jX -3 (defined in the text). The inclusion of cubic anharmonic thermal vibrations is shown to be highly significant. In order to interpret the data collected for certain low-angle Bragg reflections for which m h + k + l = 4n + 2 (in particular, 200, 222 and 222), it is necessary to consider bonding effects. It is shown that there is a net transfer of electron charge from gallium to arsenic [Q --0.12 (3) e] and that the inclusion of bonding effects in the least-squares analysis is highly significant. The analysis includes allowance for the extremely severe extinction effects present for such a perfect sample (minimum extinction factor 0.286). The refined value of the mean radius of © 1994 International Union of Crystallography Printed in Great Britain -all rights reserved perfect-crystal domains is 4.6 (2)I~m. The final fit, for 153 independent Bragg reflections, is excellent, as indicated by the weighted R factor of 0.683% and the goodness-of-fit parameter of 1.083. The results of the least-squares analysis are compared for the cases of relativistic Hartree-Fock, Thomas-Fermi-Dirac and relativistic Dirac-Slater atomic scattering factors, the former being favoured.

Section: Methodsmentioning

confidence: 99%

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Stevenson¹

1994

“…The absorption corrections, which take into account the variation of inclination angles between the normals of different reflecting planes and the normal of the extended crystal face, were calculated after Mair, Prager & Barnea (1971).…”

Section: Methodsmentioning

confidence: 99%

Anharmonicity of atomic vibrations in magnesium by measurement of almost-forbidden reflections

Järvinen¹,

Soininen²,

Merisalo³

1987

BRAGG AND DIFFUSE SCATTERING INTENSITIESto believe that Bragg intensities fitted with a split-atom model necessarily correspond to a static distribution of atoms about fractionally occupied sites. In the present model, for example, the atoms are continuously hopping across the potential barrier for T> Tc and even below Tc some hopping occurs until the temperature is low enough for the ordering to be complete. Nevertheless, a split-atom model would give a reasonable fit to the corresponding Bragg scattering [see Mair (1983b), where a split-atom model is used to fit probability densities for a onedimensional analogue of the present data].A CSIRO Cyber 205 grant is gratefully acknowledged.References COWLEY, J. M. (1975 AbstractThe X-ray intensities of almost-forbidden reflections 301 and 303 in a single crystal of magnesium have been measured at 293 K. Effective monochromatization by appropriate electronics was utilized to increase the observability of these weak reflections. The data are interpreted in terms of atomic vibrations by application of a quantum-statistical one-particle formalism that allows anharm0nic contributions to the atomic temperature factor. A value of -0.43 (3)eV~ -3 is obtained for the third-order anharmonic parameter, the negative sign being deduced from the coordination. This outcome is in accordance with earlier results concerning anharmonic vibrations.

“…The intensities were measured by the extended-face crystal technique described in previous papers (Mair, Prager & Barnea, 1971; on a XRD-4 General Electric manual diffractometer (powered by a stabilized Philips PW 1320 generator) with Mo K<t radiation. Balanced zirconiumyttrium oxide filters were placed in the diffracted beam before the scintillation counter.…”

Section: Methodsmentioning

confidence: 99%

Generalized temperature-factor formulation with application to cadmium selenide and other wurtzites

Whiteley¹,

Moss²,

Barnea³

1978

Self Cite

The generalized temperature factor is formulated within the framework of the one-particle potential in terms of functions derived from the harmonic functions of Stewart. This formulation is then applied to the wurtzite structure and projection analysis is used to eliminate one component of the potential. Inclusion of the generalized temperature factor in the structure-factor expression for wurtzitc leads to the appearance of harmonically forbidden reflections and the loss of equivalence of non-symmetry-related reflections which occur at the same Bragg angle. The results of a room-temperature X-ray experiment with cadmium selenide are interpreted within the above model to yield cubic anharmonic parameters 1fl3321 = 1fl3371 = lfl3131 (0.13 _+ 0.01) x 10 -12 erg A -3. These are used to estimate the anharmonic effect on the position parameter u. Some general conclusions are drawn regarding the possibility of observing similar effects in other wurtzitc structures.