Debye Characteristic Temperatures of Cubic Metals

1972 ◽  
Vol 50 (21) ◽  
pp. 2712-2714 ◽  
Author(s):  
B. S. Semwal ◽  
P. K. Sharma
Keyword(s):  
Shear Modulus ◽  
Numerical Integration ◽  
Elastic Constants ◽  
Characteristic Temperature ◽  
Debye Characteristic Temperature ◽  
Cubic Metals ◽  
Characteristic Temperatures ◽  
Metallic Element ◽  
Elastic Data ◽  
Direct Numerical Integration

The validity of Hill's formulas for the shear modulus of a polycrystalline cubic solid is examined by calculating the Debye characteristic temperature at 0 °K for a number of cubic metals using the measured elastic constants. The results are compared with calorimetric values and the numbers deduced from direct numerical integration of elastic data. Various methods give nearly similar results if the anisotropy of the metallic element is not excessively large.

ON THE CHARACTERISTIC TEMPERATURES OF SINGLE CRYSTALS AND THE DISPERSION OF THE "DEBYE HEAT WAVES”

1953 ◽  
Vol 31 (1) ◽  
pp. 112-119 ◽  
Author(s):  
E. J. Post
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Elastic Constants ◽  
Heat Waves ◽  
Lattice Structure ◽  
Characteristic Temperature ◽  
Normal Modes ◽  
Simple Calculation ◽  
Characteristic Temperatures ◽  
Elastic Data

A procedure for the calculation of the number of normal modes of a single crystal is proposed which takes an intermediate position between the methods of Debye and Born–von Karman. The method of Debye is extended to an anisotropic continuum, where the cutoff and dispersion phenomena, which are due to the lattice structure, are accounted for in a semiempirical way. It appears possible to define a finite number of characteristic temperatures (one for cubic crystals and at most three for crystals of low symmetry) independent of direction. This ensures a comparatively simple calculation from the phenomenological elastic constants of the crystal, as such retaining one of the pleasing features of Debye's theory, i.e., a straightforward correlation between thermal and elastic data.The method is applied to eight cubic monatomic crystals for which elastic data are available. The results provide some additional evidence to emphasize the significance of the dispersion of the Debye heat waves.An application to the hexagonal crystals of cadmium and zinc leads to results similar to those obtained by Grüneisen and Goens who produced with these crystals the first experimental evidence of the dispersion phenomenon using the concept of a characteristic temperature dependent on direction.In the last section the correlation between the elastic constants of single crystals and the corresponding quasi-isotropic materials is discussed and illustrated with data found in the literature. It is shown that the polycrystalline state is more "elastic" (sometimes very considerably) than the single crystal state. The consequences of this "boundary layer elasticity" for the calculation of θ values are discussed.

Note on the Characteristic Temperatures of Sphalerite-Structure Semiconductors

1972 ◽  
Vol 50 (11) ◽  
pp. 1220-1221 ◽  
Author(s):  
M. D. Aggarwal ◽  
V. Raju ◽  
J. K. D. Verma
Keyword(s):  
Characteristic Temperature ◽  
Sphalerite Structure ◽  
Debye Characteristic Temperature ◽  
Characteristic Temperatures

The characteristic temperatures of III–V sphalerite semiconductors have been calculated by using the Reeber–McLachlan relation. These values do not follow the same trend as obtained for II–VI solids. However, the agreement with the Debye characteristic temperature is fair.

ANHARMONIC CONTRIBUTIONS TO THE BULK MODULUS AND CHARACTERISTIC TEMPERATURES OF NEON AND ARGON AT T = 0 °K

1967 ◽  
Vol 45 (9) ◽  
pp. 2995-2997 ◽  
Author(s):  
J. S. Brown ◽  
G. K. Horton
Keyword(s):  
Bulk Modulus ◽  
Excellent Agreement ◽  
Characteristic Temperature ◽  
Experimental Results ◽  
Debye Characteristic Temperature ◽  
Characteristic Temperatures ◽  
Lennard Jones ◽  
Anharmonic Potential ◽  
Potential Parameters

Anharmonic contributions to the bulk moduli of Ne and Ar are calculated for Lennard-Jones (m–6) potentials and compared with the experimental results at T = 0 °K. We consider direct anharmonic contributions to the bulk moduli and the anharmonic contributions via the use of Brown's (1966) anharmonic potential parameters. Excellent agreement is found with the experimental results of Peterson, Batchelder, and Simmons (1966) and Batchelder, Losee, and Simmons (1967).We also study the effect of the anharmonic parameters on the Debye characteristic temperature obtained from Cν. Improved agreement with the experimental results is found.

ELASTIC PROPERTIES AND DEBYE CHARACTERISTIC TEMPERATURE OF PARTIALLY MELTED YBa2Cu3O7−x SUPERCONDUCTOR

1988 ◽  
Vol 02 (09) ◽  
pp. 1111-1117 ◽  
Author(s):  
D.F. LEE ◽  
K. SALAMA
Keyword(s):  
Debye Temperature ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Tetragonal Phase ◽  
Room Temperature ◽  
Characteristic Temperature ◽  
Shear Moduli ◽  
Debye Characteristic Temperature ◽  
Temperature Range ◽  
Free Material

The quasi-isotropic elastic constants are measured in a 85% dense partially melted YBa 2 Cu 3 C 7−x superconductor in the temperature range 80–300 K. The room temperature values of the longitudinal and shear moduli of the void-free material are found to be 168 and 59 GPa respectively, and no decrease in these constants is observed during the transition from normal to superconducting states. The Debye temperature is found to be 426 K which is comparable to that of the tetragonal phase polycrystalline BaTiO 3 (429 K).

scholarly journals Generalization of intrinsic ductile-to-brittle criteria by Pugh and Pettifor for materials with a cubic crystal structure

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
O. N. Senkov ◽  
D. B. Miracle
Keyword(s):  
Crystal Structure ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Single Crystal ◽  
Elastic Constants ◽  
Mechanical Analysis ◽  
Quantum Mechanical ◽  
Modulus Ratio ◽  
Cubic Crystal ◽  
The Difference

AbstractTwo classical criteria, by Pugh and Pettifor, have been widely used by metallurgists to predict whether a material will be brittle or ductile. A phenomenological correlation by Pugh between metal brittleness and its shear modulus to bulk modulus ratio was established more than 60 years ago. Nearly four decades later Pettifor conducted a quantum mechanical analysis of bond hybridization in a series of intermetallics and derived a separate ductility criterion based on the difference between two single-crystal elastic constants, C12–C44. In this paper, we discover the link between these two criteria and show that they are identical for materials with cubic crystal structures.

The crystal dynamics of cuprous halides

1982 ◽  
Vol 60 (11) ◽  
pp. 1589-1594 ◽  
Author(s):  
Manvir S. Kushwaha
Keyword(s):  
Phonon Dispersion ◽  
Characteristic Temperature ◽  
Force Model ◽  
Phonon Dispersion Curves ◽  
Debye Characteristic Temperature ◽  
Zinc Blende ◽  
Crystal Dynamics ◽  
Bond Bending ◽  
Dynamical Description ◽  
Good Agreement

The lattice dynamics of cuprous halides have been thoroughly investigated by means of an 8-parameter bond-bending force model (BBFM), recently developed and applied successfully to study phonons in various II–VI and III–V compound semiconductors having zinc-blende (ZB) structure. The application of BBFM is made to calculate the phonon dispersion relations, phonon density of states, and temperature variation of the Debye characteristic temperature [Formula: see text] of CuCl, CuBr, and CuI. The room-temperature neutron scattering measurements for phonon dispersion curves along three principal symmetry directions and calorimetric experimental data for the Debye characteristic temperature have been used to check the validity of BBFM for the three crystals. The overall good agreement between theoretical and experimental results supports its use as an appropriate model for the dynamical description of ZB crystals.

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