The Anharmonic Temperature Factor in Crystallographic Structure Analysis

Kuhs, Werner F.

doi:10.1071/ph880369

Cited by 43 publications

(39 citation statements)

References 13 publications

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“…The so-called Kuhs's rule of thumb (Kuhs, 1988) is fulfilled in the present data at 755, 805 and 855 K along a Pbnm , which is the direction of the largest ADP. Slightly higher resolutions are required to firmly probe anharmonicity for lower temperatures.…”

Section: Figurementioning

confidence: 79%

Crystal structure and phase transition of thermoelectric SnSe

Sist

Zhang

Iversen

2016

Acta Crystallogr B Struct Sci Cryst Eng Mater

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Tin selenide-based functional materials are extensively studied in the field of optoelectronic, photovoltaic and thermoelectric devices. Specifically, SnSe has been reported to have an ultrahigh thermoelectric figure of merit of 2.6 ± 0.3 in the high-temperature phase. Here we report the evolution of lattice constants, fractional coordinates, site occupancy factors and atomic displacement factors with temperature by means of high-resolution synchrotron powder X-ray diffraction measured from 100 to 855 K. The structure is shown to be cation defective with a Sn content of 0.982 (4). The anisotropy of the thermal parameters of Sn becomes more pronounced approaching the high-temperature phase transition (∼ 810 K). Anharmonic Gram-Charlier parameters have been refined, but data from single-crystal diffraction appear to be needed to firmly quantify anharmonic features. Based on modelling of the atomic displacement parameters the Debye temperature is found to be 175 (4) K. Conflicting reports concerning the different coordinate system settings in the low-temperature and high-temperature phases are discussed. It is also shown that the high-temperature Cmcm phase is not pseudo-tetragonal as commonly assumed.

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Section: Figurementioning

confidence: 79%

Crystal structure and phase transition of thermoelectric SnSe

Sist

Zhang

Iversen

2016

Acta Crystallogr B Struct Sci Cryst Eng Mater

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“…The relative effect of anharmonicity or disorder on the DWF is increasing with Q, however the greatest absolute change of the DWF is expected at some finite value of Q. It may be calculated by taking the derivatives of the generalized DWF expressions (Kuhs, 1988a) and is given in the Gram-Charlier case by Qn = 2nl/Z(2,n-)-l/2(21n 2)l/2(u2) -1/2…”

Section: The Case Of X-raysmentioning

confidence: 99%

Generalized atomic displacements in crystallographic structure analysis

Kuhs¹

1992

Acta Crystallogr A Found Crystallogr

195

159

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“…The real power of electron-beam methods now lies in their accuracy for structure-factor phase measurement and in their ability to study microcrystals from which large synthetically grown single crystals cannot be grown. In analyzing CV data, the following sources of error must be considered: (1) off-systematics reflections, if not included in computations; (2) errors in the absorption potential used (the CV is independent of this for centric crystals in first-order perturbation theory); (3) the influence of anharmonic vibrations (Kuhs, 1988); and (4) errors in the temperature factors used. Errors in the determination of Fx by CV have generally been in the range 0.1-1%.…”

Section: Fn(o) = [47rme2z/3h2](r2)mentioning

confidence: 99%

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Spence¹

1993

Acta Cryst Sect A

138

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A review is given of research into the measurement of crystal structure-factor amplitudes and phases by transmission electron diffraction. Accuracies for amplitudes are commonly a fraction of a percent (after conversion to X-ray structure factors) while phases may now be measured in favorable cases using three-beam electron diffraction to an accuracy of much better than 1 °. Following a brief review of theory, the main techniques are outlined. These include quantitative convergent-beam electron diffraction, the critical-voltage method, the intersecting K_ikuchi-and HOLZ-Iine methods and methods based on weak high-order reflections in wide-angle patterns. Enantiomorphs and polarity are discussed. Summaries are given of measurements of the mean inner potential and of structure factors generally. A brief review of the implications of this work for studies of crystal bonding and ordering in alloys is given, and its use to test ab initio computations of charge density. The mean inner potential is found to be the quantity most sensitive to the bonding distribution of valence electrons and sensitively constrains accurate X-ray structure-factor measurements. Electron diffraction techniques are to be preferred for studies of individual microcrystals or artificially formed structures and for the very accurate measurement of structure-factor phases in acentric crystals with small unit cells.

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The Anharmonic Temperature Factor in Crystallographic Structure Analysis

Cited by 43 publications

References 13 publications

Crystal structure and phase transition of thermoelectric SnSe

Crystal structure and phase transition of thermoelectric SnSe

Generalized atomic displacements in crystallographic structure analysis

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

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