Anharmonic Thermal Vibrations in Germanium

Mair, S. L.; Barnea, Z.

doi:10.1143/jpsj.38.866

Cited by 13 publications

(18 citation statements)

References 15 publications

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“…Keffer & Portis (1957) (see also Jeffrey, Parry & Mozzi, 1956) have derived expressions for u, on the assumption that the bondstretching constants are much larger than the bondbending constants: Both (5a) and (5b) tend to underestimate the existing observed values of u which, with only one exception to our knowledge (ZnO; Kihara & Donnay, 1981), are based on harmonic refinements of the data. The value of u given by (5a) is always closer to the observed value and the difference between the two has been attributed to anharmonicity by Mair & Barnea (1975).…”

Section: The Refined Value Of the U Parametersupporting

confidence: 69%

“…Clearly, the right-hand-side of (8) is positive and so u~ is predicted to be greater than u~ for CdS, in contrast to the expectations of Mair & Barnea (1975). If the more realistic constraints of model III are substituted in (6), along with B~ = B33, which was assumed when deriving these constraints, then (z) = 0 for all atoms and u~t---u~, as discussed earlier in connection with (5a) and (5b).…”

Section: The Refined Value Of the U Parametermentioning

confidence: 74%

“…Mair & Barnea (1975) and WMB have derived equivalent expressions for the anharmonic temperature factor for wurtzite, expanding the OPP as a power series (to third order) in the atomic displacements from appropriate positions (Malt & Wilkins, 1981) within the restrictions imposed by the local site symmetry (3m). Fakineos, Stevenson & Barnea (1982) have also derived an equivalent expression, using a group-theory approach.…”

Section: Fj(s) =Fc J(s) + Ifaj(s)mentioning

confidence: 99%

“…When c/a> (8),/2 the value of u given by (5b) is greater than that given by (5a) and we suggest that both these values will be greater than any observed values derived from harmonic treatments of the data for such compounds, with the difference still attributable to anharmonicity. The sign and magnitude of the difference between the predicted and observed (harmonic) values of u depend on the forces binding the atoms in the solid, with the relative strength of the Coulomb interaction and the short-range interactions being an important consideration (Mair & Barnea, 1975). O' Keeffe & Hyde (1978) have pointed out that compounds which exist in both the wurtzite and zinc blende modifications have, for the wurtzite phase, c/a~(8) '/2.…”

Section: The Refined Value Of the U Parametermentioning

confidence: 99%

“…Nizzoli (1976) has discussed anharmonicity in h.c.p. crystals generally, as have Mair & Barnea (1975) for crystals with the wurtzite structure. Whiteley, Moss & Barnea (1977 have also discussed anharmonicity in wurtzite structures and reported some of the consequences of this effect for CdSe.…”

Section: Introductionmentioning

confidence: 99%

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Anharmonic thermal vibrations and the position parameter in wurtzite structures. I. Cadmium sulphide

Stevenson¹,

Milanko²,

Barnea³

1984

Acta Crystallogr Sect B

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Intensity measurements have been carried out with an extended-face single crystal of hexagonal CdS using Mo Ka X-radiation at room temperature. The Bragg intensities were analysed by using the oneparticle potential (OPP) within the framework of Dawson's [Proc. R. Soc. London Set. A (1967), 298, [255][256][257][258][259][260][261][262][263] generalized structure-factor formulation with allowance for cubic anharmonic effects. The position parameter in the wurtzite structure which is not determined by symmetry is evaluated, and its dependence on the temperature-factor model used is demonstrated. The most reliable determination of this position parameter, with allowance for cubic anharmonicity, is 0.37715(8). The observation of significant differences between the intensities of nonsymmetry-related reflections occurring at the same Bragg angle demonstrates the possibility of measuring the anharmonicity of thermal vibrations.

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Section: The Refined Value Of the U Parametersupporting

confidence: 69%

Section: The Refined Value Of the U Parametermentioning

confidence: 74%

Section: Fj(s) =Fc J(s) + Ifaj(s)mentioning

confidence: 99%

Section: The Refined Value Of the U Parametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Anharmonic thermal vibrations and the position parameter in wurtzite structures. I. Cadmium sulphide

Stevenson¹,

Milanko²,

Barnea³

1984

Acta Crystallogr Sect B

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Syntheses and ¹H NMR Spectra of Substituted Zintl Ions [Ge₉R_n]^(4–n)–: Crystal Structures of [Ge₉R]^3– (R = 2,4,6‐Me₃C₆H₂, CHCH₂) and Indication of Tris‐Vinylated Clusters

et al. 2011

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The introduction of a mesityl (Mes; 2,4,6‐Me3C6H2) ligand to a Ge9 polyanion is accomplished by the reaction of [Ge9]4– solutions with Ag4Mes4. The crystal structure investigation of its [K([2.2.2]crypt)] salt ([2.2.2]crypt: 4,7,13,16,21,24‐hexaoxa‐1,10‐diazabicyclo[8.8.8]hexacosane) shows that [Ge9Mes]3– comprises one exo‐bonded aryl ligand in accordance with the 1H NMR spectroscopic data. The formation of mono‐, bis‐, and tris‐substituted Zintl Ions [Ge9Rn](4–n)– (n = 1, 2, and 3; R = CHCH2) is investigated by 1H NMR spectroscopy. The mono‐ and bis‐vinylated Ge9 clusters, [Ge9(CHCH2)]3– and [Ge9(CHCH2)2]2–, were obtained by the reaction of K4Ge9 with Me3SiC≡CSiMe3 in ethylenediamine. In the presence of [18]crown‐6 (1,4,7,10,13,16‐hexaoxacyclooctadecane) and K(C5H5) crystals containing both cluster species were isolated and structurally characterized as[K([18]crown‐6)]2{(η5‐C5H5)[K([18]crown‐6)]2}[Ge9(CHCH2)]and [K([18]crown‐6)]{(η5‐C5H5)[K([18]crown‐6)]2}[Ge9(CHCH2)2], respectively. 1H NMR experiments hint for the tris‐vinylated cluster [Ge9(CHCH2)3]–.

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Determination of structure factors of germanium by the critical-voltage and convergent-beam diffraction methods

Shishido

Tanaka

1976

Phys. Stat. Sol. (a)

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The structure factors for the 111 and the “forbidden” 222 reflections of germanium are consistently determined by combining two independent electron diffraction measurements: 1. the critical voltage Ec = (908.5 ± 6.4) kV for the 333 reflection and 2. the rocking curves in convergent‐beam diffraction patterns taken at the 111 and 222 Bragg settings with incident electrons of 100 kV. The values obtained for these factors without thermal vibrations are F 1110 = −155.74 ± 0.07 and F 2220 = 1.24 ± 0.32. These correspond to the atomic scattering factor f111 = 27.53 ± 0.01 and the anti‐centrosymmetric component of f222, f 222a = −0.16 ± 0.04, respectively. The mean value of f111 is in good agreement with earlier X‐ray measurements and its percentage error, 0.04%, is much smaller than other published values.

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Anharmonic Thermal Vibrations in Germanium

Cited by 13 publications

References 15 publications

Anharmonic thermal vibrations and the position parameter in wurtzite structures. I. Cadmium sulphide

Anharmonic thermal vibrations and the position parameter in wurtzite structures. I. Cadmium sulphide

Syntheses and ¹H NMR Spectra of Substituted Zintl Ions [Ge₉R_n]^(4–n)–: Crystal Structures of [Ge₉R]^3– (R = 2,4,6‐Me₃C₆H₂, CHCH₂) and Indication of Tris‐Vinylated Clusters

Determination of structure factors of germanium by the critical-voltage and convergent-beam diffraction methods

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Anharmonic Thermal Vibrations in Germanium

Cited by 13 publications

References 15 publications

Anharmonic thermal vibrations and the position parameter in wurtzite structures. I. Cadmium sulphide

Anharmonic thermal vibrations and the position parameter in wurtzite structures. I. Cadmium sulphide

Syntheses and 1H NMR Spectra of Substituted Zintl Ions [Ge9Rn](4–n)–: Crystal Structures of [Ge9R]3– (R = 2,4,6‐Me3C6H2, CHCH2) and Indication of Tris‐Vinylated Clusters

Determination of structure factors of germanium by the critical-voltage and convergent-beam diffraction methods

Contact Info

Product

Resources

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Syntheses and ¹H NMR Spectra of Substituted Zintl Ions [Ge₉R_n]^(4–n)–: Crystal Structures of [Ge₉R]^3– (R = 2,4,6‐Me₃C₆H₂, CHCH₂) and Indication of Tris‐Vinylated Clusters