ON THE PHASE STABILITY OF ALKALI METALS UNDER EXTERNAL PRESSURE

1993 ◽  
Vol 07 (01n03) ◽  
pp. 305-308
Author(s):  
BEKIR KARAOGLU ◽  
S. M. MUJIBUR RAHMAN
Keyword(s):  
Phase Stability ◽  
Alkali Metals ◽  
Structural Phase ◽  
Pair Potential ◽  
External Pressure ◽  
Simultaneous Application ◽  
Pseudopotential Theory ◽  
Spherical Waves ◽  
Total Energies ◽  
The Stability

Structural phase stability of certain alkali metals under external pressure is investigated in terms of the pseudopotential and augmented-spherical-waves (ASW) methods. The pair potential trend and the free energy differences between structures — both treated in a second-order pseudopotential theory — are invoked to explain qualitatively some aspects of the stability of the underlying phases at various pressures. Simultaneously, the ASW method is employed to compute the total energies and density-of-states (DOS) at the Fermi level for the phases concerned. The calculated differences in total energies between structures and the DOS curves shade some light in understanding the phase stability of the alkali metals under pressure. The simultaneous application of a perturbative and a nonperturbative treatment on the same footing has brought along some unified concluding remarks in dealing with this particular problem of phase stability.

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.

COORDINATION AND STRUCTURAL ENERGETICS OF VARIOUS PHASES OF Ni

2001 ◽  
Vol 15 (14) ◽  
pp. 2067-2073
Author(s):  
T. M. A. KHAJIL ◽  
S. M. MUJIBUR RAHMAN ◽  
G. M. BHUIYAN
Keyword(s):  
Dominant Role ◽  
Distribution Functions ◽  
Free Energies ◽  
Pseudopotential Theory ◽  
Coordination Numbers ◽  
Transition Series ◽  
Einstein Model ◽  
Total Energies ◽  
The Stability ◽  
Pair Distribution Functions

Nickel is one of the most versatile metals in the transition series of the periodic table. We have investigated the coordination and the cohesion of Ni corresponding to its various phases. The neighboring distances and the coordination numbers are estimated from the observed and simulated pair distribution functions (PDF) g(r) relevant to the various phases. Since the profiles of these functions are not symmetric, we have used the concept of minimum-to-minimum positions of the PDFs to estimate the successive coordination numbers for the solid amorphous and microcrystalline phases. The approximate values of the pseudo-lattice vectors estimated from the peak positions of the PDFs are employed to calculate the total energies for the amorphous and the microcrystalline phases of Ni in terms of the pseudopotential theory. The roles of the s- and d-electrons in the cohesion of Ni have been investigated by calculating the free energies for the relevant phases. The calculated energetics reveal the relative stability of the various phases in a qualitative manner. It is noted that the d-electrons play the dominant role in predicting the stability of the various phases; the s-electrons merely supplement the d-electron trend. Since the formalism corresponds to very low temperature, the lattice vibrations [Einstein model] do not seem to play any visible role in the prediction.

STRUCTURAL AND THERMODYNAMIC PROPERTIES OF 3d TRANSITION METALS: PSEUDOPOTENTIAL THEORY REVISITED

1995 ◽  
Vol 09 (09) ◽  
pp. 553-564 ◽  
Author(s):  
S. M. OSMAN ◽  
S. M. MUJIBUR RAHMAN
Keyword(s):  
Transition Metals ◽  
Thermodynamic Properties ◽  
Electron Density ◽  
Density Of States ◽  
Phase Stability ◽  
Structural Phase ◽  
Second Order ◽  
Pseudopotential Theory ◽  
Electron Density Of States ◽  
Almost All

Structural and thermodynamic properties of 3d transition metals are calculated in terms of the pseudopotential theory. The s − p and d electrons are treated in a pseudoadiabatic approximation in such a way that the s − p and d electrons are treated separately under the same footing. The s − p electrons are treated in terms of the conventional second order pseudopotential theory, while the tightly bound d electrons are treated in terms of the Wills–Harrison prescription that makes use of the Friedel rectangular electron density of states (DOS) model. The predictions of the structural phase stability and other relevant thermodynamic properties are found to be consistent with experiments for almost all of the metals.

PHASE STABILITY OF RANDOM BRASSES: PSEUDOPOTENTIAL THEORY REVISITED

1988 ◽  
Vol 02 (03n04) ◽  
pp. 301-354
Author(s):  
S. M. MUJIBUR RAHMAN
Keyword(s):  
Phase Stability ◽  
Theoretical Development ◽  
Band Model ◽  
Stability Criteria ◽  
Atom Ratio ◽  
Pseudopotential Theory ◽  
The Subject ◽  
The Stability ◽  
Introductory Discussion ◽  
Static Lattice

We review the theoretical development concerning the phase stability of random brasses. The introductory discussion of the subject embraces the rules of metallurgy in general, but we emphasize the roles of electron-per-atom ratio in the major bulk of our discussion. Starting from the so-called rigid-band model the discussion goes up to the recent higher-order pseudopotential theory. The theoretical refinements within the pseudopotential framework are discussed briefly. The stability criteria of the random phases are analysed both in the static lattice and dynamic lattice approximations.

The Temperature Dependent Elastic Moduli of Liquid Potassium

2013 ◽  
Vol 209 ◽  
pp. 220-224
Author(s):  
Amit B. Patel ◽  
A.Y. Vahora ◽  
Nisarg K. Bhatt ◽  
Brijmohan Y. Thakore ◽  
P.R. Vyas ◽  
...  
Keyword(s):  
Alkali Metals ◽  
Memory Function ◽  
Pair Potential ◽  
Delta Function ◽  
Damping Factor ◽  
Simple Liquid ◽  
Small Momentum Transfer ◽  
Pseudopotential Theory ◽  
Different Temperatures ◽  
Elastic Reaction

Near the melting point liquid alkali metals show positive dispersion, which can be described within generalized hydrodynamics as a visco-elastic reaction of the simple liquid. To understand an upward bending of the dispersion relation at small momentum transfer, treatment of pseudopotential theory on liquid potassium is performed at different temperatures in entire liquid regime. In the present study, we used the modified empty core potential due to Hasegawa et al. along with a local field correction due to Ichimaru-Utsumi (IU) to explain an electron-ion interaction. The potential used is composed of a full electron-ion interaction and a repulsive delta function to incorporate the orthogonalisation effect due to the s-core states. The temperature dependence of pair potential is calculated by using the damping term, exp(-πkBTr/2kF). While the expression for phonon dispersions are derived within the memory function formalism. Results for longitudinal phonon frequencies, and thus derived sound velocities and elastic modulii are compared with recent inelastic X-ray scattering experiment. It is found sufficient to carried temperature effect into the description only via the damping factor, keeping the volume of normal melting.

Tuning the phase stability and surface HER activity of 1T′-MoS2 by covalent chemical functionalization

2020 ◽  
Vol 8 (44) ◽  
pp. 15852-15859
Author(s):  
Jiu Chen ◽  
Fuhua Li ◽  
Yurong Tang ◽  
Qing Tang
Keyword(s):  
Phase Stability ◽  
Chemical Functionalization ◽  
The Stability

Chemical functionalization can significantly improve the stability of meta-stable 1T′-MoS2 and tune the surface HER activity.

Interionic Pair Potential, hard sphere diameter and entropy of mixing of NaCd compound forming binary molten alloys under the framework of Pseudopotential theory

2014 ◽  
Vol 10 (6) ◽  
pp. 2843-2852
Author(s):  
Sujeet Kumar Chatterjee ◽  
Lokesh Chandra Prasad ◽  
Ajaya Bhattarai
Keyword(s):  
Nearest Neighbor ◽  
Effective Interaction ◽  
Pair Potential ◽  
Sphere Diameter ◽  
Compound Formation ◽  
Pseudopotential Theory ◽  
Energy Of Mixing ◽  
Asymmetric Behaviour ◽  
Statistical Mechanical ◽  
Free Energy Of Mixing

The observed asymmetric behaviour of mixing of  NaCd liquid alloys around equiatomic composition with smaller negative values for free energy of mixing at compound forming concentration, i.e. GMXS = -4.9KJ at Ccd =0.66 has  aroused our interest to undertake a theoretical investigation of this system.A simple statistical mechanical theory based on compound formation model has been used to investigate the energetics of formation of intermetallic compound Cd2Na in the melt through the study of entropy of mixing.Besides, the interionic interactions between component atoms Na and Cd of the alloys have been understood through the study of interionic pair potential фij(r), calculated from pseudopotential theory in the light of CF model.Our study of фij(r) suggest that the effective interaction between Na-Na atoms decreases on alloying with Cd atom, being minimum for compound forming alloy( Cd 0.66 Na 0.34 ).The nearest neighbor distance between Na-Na atoms does not alter on alloying. Like wise Na-Na,  effective interaction between  Cd-Cd atom decreases from pure state to NaCd alloys, being smaller at compound forming  concentration Cd 0.66 Na 0.34.The computed values of SM from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterisation of σ3 and Ψcompound.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

Correct Structural Phase Stability of FeS2, TiO2, and MnO2 from a Semilocal Density Functional

2021 ◽  
Vol 125 (7) ◽  
pp. 4284-4291
Author(s):  
Bikash Patra ◽  
Subrata Jana ◽  
Lucian A. Constantin ◽  
Prasanjit Samal
Keyword(s):  
Phase Stability ◽  
Density Functional ◽  
Structural Phase

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

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