Anharmonic contributions to the Debye–Waller factor for zinc

Albanese, G.; Deriu, A.; Ghezzi, Carlo

doi:10.1107/s0567739476001812

Cited by 11 publications

(6 citation statements)

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“…The effects of anharmonic thermal vibrations on the intensities of Bragg reflections have been investigated using neutrons, X-rays and y-rays in a number of structures (see, for example, Willis & Pryor, 1975;Tanaka & Marumo, 1983). The studies of anharmonicity in hexagonal structures include those of zinc (Albanese, Deriu & Ghezzi, 1976, Merisalo & Larsen, 1977Merisalo, J/irvinen & Kurittu, 1978; Kurki-Suonio, Merisalo & Peltonen, 1979;Vah-vaselkS., 1980), cadmium (Merisalo, Peljo & Soininen, 1978;Field, 1982), beryllium (Larsen, Lehmann & Merisalo, 1980) and Li3N (Zucker & Schulz, 1982). Nizzoli (1976) has discussed anharmonicity in h.c.p.…”

Section: Introductionmentioning

confidence: 99%

“…The studies of anharmonicity in hexagonal structures include those of zinc (Albanese, Deriu & Ghezzi, 1976, Merisalo & Larsen, 1977Merisalo, J/irvinen & Kurittu, 1978;Kurki-Suonio, Merisalo & Peltonen, 1979;VahvaselkS., 1980), cadmium (Merisalo, Peljo & Soininen, 1978;Field, 1982), beryllium (Larsen, Lehmann & Merisalo, 1980) and Li3N (Zucker & Schulz, 1982). Nizzoli (1976) has discussed anharmonicity in h.c.p.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…: number N of data points ðT i ; C i Þ minus number of independent fitting parameters] are also recorded. The standard error SE = f Albanese et al (1976). The B factors B axial ðTÞ (red solid curve) and B basal ðTÞ (blue solid curve) are defined by the mean-squared atomic displacements hu 2 axial ðTÞi (parallel to the hexagonal axis) and hu 2 basal ðTÞi in the basal plane, cf.…”

Section: Thermodynamic Functions and Debye-waller Factors Of Zinc 41 Regressed Lattice Heat Capacity Of The Zinc Structurementioning

confidence: 99%

“…In Section 4, the thermodynamic variables and meansquared vibrational amplitudes of the zinc structure are studied. Heat capacity measurements of zinc continuously extend from the low-temperature regime up to the melting point (Seidel & Keesom, 1958;Phillips, 1958;Eichenauer & Schulze, 1959;Garland & Silverman, 1961;Zimmerman & Crane, 1962;Martin, 1968Martin, , 1969Cetas et al, 1969;Mizutani, 1971;Grønvold & Stølen, 2002), converted from isobaric to isochoric values (Barron & Munn, 1967b;Arblaster, 2018), and B factors of vibrations in the basal plane and along the hexagonal axis have also been measured over a wide temperature range [see Skelton & Katz (1968), Albanese et al (1976), Pathak & Desai (1981) and earlier measurements reviewed by Barron & Munn (1967a) and Rossmanith (1977)]. We model the lattice heat capacity of the zinc structure with a multiply broken power-law density (Tomaschitz, 2020a(Tomaschitz, ,b, 2021b and perform a least-squares fit to the isochoric data sets, subtracting the electronic heat capacity (cf.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of lattice vibrations in non-cubic crystals: the zinc structure revisited

Tomaschitz¹

2021

Acta Cryst Sect A

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A phenomenological model of anisotropic lattice vibrations is proposed, using a temperature-dependent spectral cutoff and varying Debye temperatures for the vibrational normal components. The internal lattice energy, entropy and Debye–Waller B factors of non-cubic elemental crystals are derived. The formalism developed is non-perturbative, based on temperature-dependent linear dispersion relations for the normal modes. The Debye temperatures of the vibrational normal components differ in anisotropic crystals; their temperature dependence and the varying spectral cutoff can be inferred from the experimental lattice heat capacity and B factors by least-squares regression. The zero-point internal energy of the phonons is related to the low-temperature limits of the mean-squared vibrational amplitudes of the lattice measured by X-ray and γ-ray diffraction. A specific example is discussed, the thermodynamic variables of the hexagonal zinc lattice, including the temperature evolution of the B factors of zinc. In this case, the lattice vibrations are partitioned into axial and basal normal components, which admit largely differing B factors and Debye temperatures. The second-order B factors defining the non-Gaussian contribution to the Debye–Waller damping factors of zinc are obtained as well. Anharmonicity of the oscillator potential and deviations from the uniform phonon frequency distribution of the Debye theory are modeled effectively by the temperature dependence of the spectral cutoff and Debye temperatures.

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“…In particular, the RSMR makes possible the high precision determination of the mean square atomic displacement ͗u 2 ͘. 10,11 On the other hand, the temperature dependence of the elastic and inelastic intensities can be used to detect lattice instabilities and structural phase transitions. [12][13][14] The broadening of the resonance lines due to the diffusive atomic motion is another interesting effect allowing the study of those motions occurring at a time scale comparable to the lifetime of the Mössbauer isotope's excited level (10 Ϫ8 s for 57 Fe).…”

Section: Introductionmentioning

confidence: 99%