Volume forces in simple metals

1979 ◽  
Vol 57 (11) ◽  
pp. 1870-1883 ◽  
Author(s):  
S. H. Taole ◽  
H. R. Glyde
Keyword(s):  
Bulk Modulus ◽  
Elastic Constants ◽  
Alkali Metals ◽  
Lattice Dynamic ◽  
Second Order ◽  
Reliable Estimate ◽  
Dynamical Matrix ◽  
Volume Dependence ◽  
Long Wave ◽  
Cauchy Relation

Within the local pseudopotential model taken to second order, the metallic energy, U, is a sum of a volume dependent and a structure dependent term. Only the second term, expressed as a volume independent, effective ion–ion interaction, is usually retained for lattice dynamic calculations. Here we firstly evaluate the contribution from the volume dependence of U to the longitudinal elastic constants c11and c12 and the bulk modulus B for a variety of models. This contribution, Δbs, which is due to the volume dependence of the screening, was identified by Wallace, Brovman and Kagan, Pethick, and by Finnis but its magnitude is in dispute. We find Δbs is important and very model dependent, ranging from −10 to−50% of B in the alkali metals and Al (but is +50% in Pb for one model) depending on both the pseudopotential and screening employed. Secondly, the usual dynamical matrix is generalized to incorporate this volume dependence. The volume effects are important for long wave phonons only and for most practical purposes may be neglected otherwise. The volume contributions to the pressure and the deviation of the Cauchy relation are also evaluated suggesting that the observed deviation of the Cauchy relation does not provide a reliable estimate of Δbs.

Analysis of elastic constants and thermal energy of ionic materials

2011 ◽  
Vol 89 (11) ◽  
pp. 1111-1117
Author(s):  
S.K. Srivastava
Keyword(s):  
Bulk Modulus ◽  
Temperature Dependence ◽  
Linear Relationship ◽  
Elastic Constants ◽  
Thermal Energy ◽  
Room Temperature ◽  
Isothermal Bulk Modulus ◽  
Volume Dependence ◽  
Ionic Materials ◽  
Different Temperatures

Expressions for the temperature dependence of elastic constants have been formulated by taking into account volume dependence of the Anderson–Grüneisen parameters. These expressions have been applied to ionic materials such as NaCl, KCl, MgO, and CaO to determine elastic constants at different temperatures. It is found that the linear relationship between isothermal bulk modulus and thermal energy (Eth) is also applicable to other elastic constants. This linear relationship is valid, starting from room temperature.

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.

Volume Dependence of the Bulk Modulus in Alkali Metals

1981 ◽  
Vol 104 (1) ◽  
pp. 307-312 ◽  
Author(s):  
J. M. López ◽  
J. A. Alonso
Keyword(s):  
Bulk Modulus ◽  
Alkali Metals ◽  
Volume Dependence

Temperature dependence of elastic constants using thermal energy for geophysical minerals

2017 ◽  
Vol 31 (13) ◽  
pp. 1750103
Author(s):  
M. Panwar ◽  
S. K. Sharma ◽  
S. Panwar
Keyword(s):  
Experimental Data ◽  
Bulk Modulus ◽  
Temperature Dependence ◽  
Elastic Constants ◽  
Thermal Energy ◽  
Alternative Formulation ◽  
Thermal Pressure ◽  
Limit Formula ◽  
Volume Dependence ◽  
Good Agreement

In this paper, we have developed relationship to predict temperature dependence of elastic constants for geophysical minerals by using a formulation for volume dependence of isothermal Anderson–Grünesien parameter which is valid up to extreme compression limit [Formula: see text] or [Formula: see text]. An alternative formulation based on thermal pressure or thermal energy has also been used for determining elastic constants as a function of temperature. The basic idea used in this study is to generalize the expression of bulk modulus for determining temperature dependence of elastic constants. The results thus obtained for MgO, CaO, Mg2SiO4 and Al2O3 from the two different methods are very close to each other and also experimental data. The good agreement reveals the validity of the formulations given in this study.

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.

scholarly journals High temperature and pressure effects on the elastic properties of B2 intermetallics AgRE

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Lili Liu ◽  
Xiaozhi Wu ◽  
Weiguo Li ◽  
Rui Wang ◽  
Qing Liu
Keyword(s):  
High Temperature ◽  
Intermetallic Compounds ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Second Order ◽  
Pressure Effects ◽  
High Temperature And Pressure ◽  
Normal Behavior ◽  
Temperature And Pressure ◽  
Temperature And Pressure Effects

AbstractThe high temperature and pressure effects on the elastic properties of the AgRE (RE=Sc, Tm, Er, Dy, Tb) intermetallic compounds with B2 structure have been performed from first principle calculations. For the temperature range 0-1000 K, the second order elastic constants for all the AgRE intermetallic compounds follow a normal behavior: they decrease with increasing temperature. The pressure dependence of the second order elastic constants has been investigated on the basis of the third order elastic constants. Temperature and pressure dependent elastic anisotropic parameters A have been calculated based on the temperature and pressure dependent elastic constants.

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