Point, Debye Temperature

The compounds MSe melt congruently, see for example, Yarembash [5], Bucher et al. [6]. Selected values of experimentally obtained melting points and those values tabulated by Mills [4] are, in K  

For additional experimental values, see sections on individual M-Se systems. 

Melting points and Debye temperatures 0q have been calculated from the linear dependence of 0D on the average atomic weight of the monoselenides. The values for some compounds were determined both experimentally, based on the heat capacity, and from known melting points on applying Lindemann s equation. Values are given in K with uncertainty ranges of Tm 100 and 0d 5, Tikhonov et al. [13]. 

LaSe CeSe PrSe NdSe GdSe TbSe DySe HoSe ErSe TmSe 

For melting points and Debye temperatures of rare earth chalcogenides, estimated from crystal chemical literature data for the NaCl type, see Kuz micheva et al. [14]. 

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Melting point Boiling point Debye temperature... 

Zhu YF, Lian JS, Jiang Q (2009) Modeling of the melting point, Debye temperature, thermal expansion coefficient, and the specific heat of nanostructured materieds. J Phys Chem... 

Melting Point 2870°C (decomposes by melting incongruently) WC has a large stability domain but reacts with W or W Debye Temperature 493K... 

Lattice Parameter a = 0.452 nm Space Group Fm3m Pearson Symbol cF8 Composition HfNo 7510 HFNj 12 Molecular Weight 192.497 Color greenish yellow X-ray Density 13.8 g/cm Melting Point 3387°C Debye Temperature 421 K... 

To separate the effects of static and dynamic disorder, and to obtain an assessment of the height of the potential barrier that is involved in a particular mean-square displacement (here abbreviated (x )), it is necessary to find a parameter whose variation is sensitive to these quantities. Temperature is the obvious choice. A static disorder will be temperature independent, whereas a dynamic disorder will have a temperature dependence related to the shape of the potential well in which the atom moves, and to the height of any barriers it must cross (Frauenfelder et ai, 1979). Simple harmonic thermal vibration decreases linearly with temperature until the Debye temperature Td below To the mean-square displacement due to vibration is temperature independent and has a value characteristic of the zero-point vibrational (x ). The high-temperature portion of a curve of (x ) vs T will therefore extrapolate smoothly to 0 at T = 0 K if the sole or dominant contribution to the measured (x ) is simple harmonic vibration ((x )y). In such a plot the low-temperature limb is expected to have values of (x ) equal to about 0.01 A (Willis and Pryor, 1975). Departures from this behavior indicate more complex motion or static disorder. 

However, most of the examples quoted in these earlier papers do not include the higher melting-point elements such as W, where a detailed treatment shows that the total entropy (at least of the solid phases) must include many other components such as the electronic specific heat, anharmonicity terms and the temperature dependence of 9d (Grimwall et al. 1987, Moroni et al. 1996). An estimate for the Debye temperature of the high-temperature 0 phase was included in the seminal... 

Figure 6. Compilation of step-mobilities derived from several experiments on Si(OOl) and Ge(OOl). The temperatures for the two data points for Ge(OOl) (filled triangles) have been scaled by the ratio of the cohesive energy of Si to Ge, 1.20. The dashed line shows a thermally activated process with an activation energy of 1.8 eV and a prefactor b kQ/k, 0 is the Debye temperature of Si, 650 K, and b = 0.38 nm.

As for graphite, its zero-point energy, ZPE = R6 + jR0 , is most conveniently deduced from Debye s theory [197,198] by separating the lattice vibrations into two approximately independent parts, with Debye temperatures (in plane) and 6j (perpendicular). A balanced evaluation gives ZPE 3.68 kcal/mol [199]. 

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