The elastic constants of the alkali-metals

1976 ◽  
Vol 23 (3) ◽  
pp. 265-269 ◽  
Author(s):  
G. Fritsch
Keyword(s):  
Elastic Constants ◽  
Alkali Metals

Debye temperature of 24 cubic elements from elastic constants

1970 ◽  
Vol 48 (10) ◽  
pp. 1270-1271 ◽  
Author(s):  
René Wanner
Keyword(s):  
Numerical Integration ◽  
Debye Temperature ◽  
Elastic Constants ◽  
Alkali Metals ◽  
Approximation Methods

Approximation methods for calculating the Debye temperature are compared with an exact numerical integration by computer to complement a paper by Konti and Varshni. Except for the alkali metals the agreement is about 0.1%.

Temperature dependence of the elastic constants in alkali metals

1978 ◽  
Vol 8 (5) ◽  
pp. 725-742 ◽  
Author(s):  
V G Vaks ◽  
S P Kravchuk ◽  
E V Zarochentsev ◽  
V P Safronov
Keyword(s):  
Temperature Dependence ◽  
Elastic Constants ◽  
Alkali Metals

Temperature Dependence of the Isothermal Elastic Constants of Alkali Metals

1981 ◽  
Vol 106 (1) ◽  
pp. 309-314 ◽  
Author(s):  
T. Soma ◽  
S. Kagaya ◽  
H. Matsuo
Keyword(s):  
Temperature Dependence ◽  
Elastic Constants ◽  
Alkali Metals

Calculation of Gr�neisen parameter and temperature dependence of elastic constants in alkali metals

1979 ◽  
Vol 22 (4) ◽  
pp. 370-372 ◽  
Author(s):  
L. V. Belan-Gaiko ◽  
V. I. Bogdanov ◽  
D. L. Fuks
Keyword(s):  
Temperature Dependence ◽  
Elastic Constants ◽  
Alkali Metals

Dynamical treatment for elastic constants and phonon spectra of alkali metals

1989 ◽  
Vol 135 (6-7) ◽  
pp. 368-372 ◽  
Author(s):  
N. Singh ◽  
N.S. Banger ◽  
S.P. Singh
Keyword(s):  
Elastic Constants ◽  
Alkali Metals ◽  
Phonon Spectra ◽  
Dynamical Treatment

PHASE STABILITY OF ALKALI METALS UNDER PRESSURE: PERTURBATIVE AND NON-PERTURBATIVE TREATMENTS

2002 ◽  
Vol 16 (32) ◽  
pp. 4847-4864 ◽  
Author(s):  
S. M. MUJIBUR RAHMAN ◽  
ISSAM ALI ◽  
G. M. BHUIYAN ◽  
A. Z. ZIAUDDIN AHMED
Keyword(s):  
Bulk Modulus ◽  
Elastic Constants ◽  
Phase Stability ◽  
Alkali Metals ◽  
Structural Phase ◽  
Stable Structure ◽  
Spherical Waves ◽  
Pair Potentials ◽  
Effective Pair ◽  
Minimum Criteria

We have investigated the structural phase stability of crystalline alkali metals under external pressure in terms of their pair potentials, structural free energies, thermomechanical properties viz. the elastic constants and the density-of-sates [DOS] at the Fermi level. The pair potentials are calculated using amenable model potentials, the structural energies and the elastic constants are calculated in terms of the effective pair potentials and the DOS for the systems are calculated by employing the augmented-spherical-waves [ASW] method. The matching between the minima of the pair potentials and the relative positions of the first few lattice vectors of the relevant structures gives a qualitative impression on the relative stability of a crystal phase. Similarly the appearance of a minimum in the energy difference curves between relevant crystal structures manifests a relatively stable structure. On the contrary, a maximum in the bulk modulus indicates a stable structure; these maximum-minimum criteria are controlled by the profile of the effective pair interactions of the constituent atoms. If the relevant lattice vectors are populated in and around the minimum of the respective pair potential the corresponding bulk modulus shows a maximum trend. The same situation gives rise to a minimum in the free energy. Both of these tendencies favor a particular crystalline phase against other relevant structures. Similarly a maximum in the DOS curves gives rise to a minimum in the energy curve manifesting a stable structure. The population of electronic states plays the responsible role here. To treat the two entirely different methods, namely, the perturbative pseudopotential theory and the non-perturbative ASW method on the same footing, we have used the same metallic density in both the methods for the respective element. The calculated results show a qualitative trend in support of the observed structures for these elemental systems.

scholarly journals The elastic constants and specific heats of the alkali metals

1936 ◽  
Vol 157 (891) ◽  
pp. 444-450 ◽  
Keyword(s):  
Potential Energy ◽  
Large Deviations ◽  
Theoretical Calculation ◽  
Elastic Constants ◽  
Alkali Metals ◽  
The Body ◽  
Left Hand ◽  
Specific Heats ◽  
Cubic Structure

In a recent paper the author has given a theoretical calculation of the elastic constants of copper and of the alkali metals. The purpose of this note is: firstly, to correct some mistakes in the calculation for the alkali metals (that for copper is correct); secondly, to compare these results with a recent experimental determination of the elastic constants for sodium ; and thirdly, to attempt an explanation of the observed fact that the specific heats of the alkalis show abnormally large deviations from the Debye form. The corrections are as follows: the formulae in Table II, p. 630, for the body centred cubic structure should read A I - 16/3 ρ dw / d ρ 2B I = 8/9 ρ 2 d 2 w / d ρ 2 + 16/9 ρ dw / d ρ. In formulae (17a) and (18) a factor 2 should be inserted on the left-hand side, since w is defined as the potential energy per ion, whereas Born and Mayer’s values relate to the energy per pair of ions.

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