The elastic constants of the alkali-metals

1976 ◽  
Vol 23 (3) ◽  
pp. 265-269 ◽  
Author(s):  
G. Fritsch
1970 ◽  
Vol 48 (10) ◽  
pp. 1270-1271 ◽  
Author(s):  
René Wanner

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%.


1978 ◽  
Vol 8 (5) ◽  
pp. 725-742 ◽  
Author(s):  
V G Vaks ◽  
S P Kravchuk ◽  
E V Zarochentsev ◽  
V P Safronov

1981 ◽  
Vol 106 (1) ◽  
pp. 309-314 ◽  
Author(s):  
T. Soma ◽  
S. Kagaya ◽  
H. Matsuo

1979 ◽  
Vol 22 (4) ◽  
pp. 370-372 ◽  
Author(s):  
L. V. Belan-Gaiko ◽  
V. I. Bogdanov ◽  
D. L. Fuks

1989 ◽  
Vol 135 (6-7) ◽  
pp. 368-372 ◽  
Author(s):  
N. Singh ◽  
N.S. Banger ◽  
S.P. Singh

2002 ◽  
Vol 16 (32) ◽  
pp. 4847-4864 ◽  
Author(s):  
S. M. MUJIBUR RAHMAN ◽  
ISSAM ALI ◽  
G. M. BHUIYAN ◽  
A. Z. ZIAUDDIN AHMED

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.


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.


Sign in / Sign up

Export Citation Format

Share Document