Elastic anomalies of Hg2X2 compounds

1992 ◽  
Vol 70 (9) ◽  
pp. 745-751
Author(s):  
K. S. Viswanathan ◽  
J. C. Jeeja Ramani
Keyword(s):  
Elastic Constants ◽  
Fourth Order ◽  
Order Parameter ◽  
Zero Point ◽  
Stability Conditions ◽  
Point Energy ◽  
The Third ◽  
Limit Formula ◽  
The Stability ◽  
Elastic Anomalies

The anomalies of the second-, third-, and fourth-order elastic constants are considered for the phase transition of Hg2X2 type of compounds. Expressions are obtained for the equilibrium values of the order parameters in the ferroelastic phase from the stability conditions. The fluctuation in the order parameter is evaluated from the Landau–Khalatnikov equation. An expression is derived for the shift in the zero-point energy in the low-temperature ferroelastic phase and the specific heat anomaly. It is shown that these are proportional to (T − T)2 and (T − Tc), respectively. All the anomalies of the second-order elastic (SOE) constants are obtained from a single general formula, and relations among them are established. The temperature variation of the SOE constants in the limit [Formula: see text] is discussed. Similarly, expressions are derived for the anomalies of the third- and fourth-order elastic constants. In the limit [Formula: see text] it is shown that these constants diverge as [Formula: see text] and [Formula: see text], respectively.

STRUCTURAL, ELECTRONIC, AND OPTICAL PROPERTIES OF ZnxSy (x + y = 2 TO 4) NANOCLUSTERS: A B3LYP-DFT STUDY

2011 ◽  
Vol 10 (01n02) ◽  
pp. 341-344
Author(s):  
P. S. YADAV ◽  
D. K. PANDEY ◽  
S. AGRAWAL ◽  
B. K. AGRAWAL
Keyword(s):  
Optical Properties ◽  
Visible Region ◽  
Zero Point ◽  
Binding Energies ◽  
Ultraviolet Region ◽  
Point Energy ◽  
Electronic And Optical Properties ◽  
The Stability ◽  
The One ◽  
Homo Lumo

The stability, structural, electronic, and optical properties have been studied for most stable zinc sulfide nanoclusters Zn x S y (x + y = n = 2 to 4). A B3LYP-DFT/6-311G(3df) method is employed to optimize the geometries, and a TDDFT method is used for the study of the optical properties. The binding energies (BE), HOMO–LUMO gaps and the bond lengths have been obtained for all the clusters. We have considered also the zero point energy (ZPE) corrections ignored by the earlier workers. For a fixed value of n, we designate the most stable structure the one, which has maximum final binding energy per atom. The adiabatic and vertical ionization potentials (IP) and electron affinities (EA), charge on atoms, dipole moment, and optical properties have been investigated for the most stable structures. The nanoclusters containing large number of S atoms for each "n" are found to be most stable. Except for ZnS nanocluster, the HOMO–LUMO gap increases with the number of S atoms. Similarly, except for ZnS , IP and EA fluctuate with the cluster size but reveal downward trend. The optical absorption is quite weak in visible region but is strong in the ultraviolet region in most of the nanoclusters except a few. The growth of most stable nanoclusters may be possible in the experiments.

Ab-Initio Study of Structural and Electronic Properties of ZnxTey (x + y = 2 to 5) Nanoclusters

2020 ◽  
Vol 12 (7) ◽  
pp. 930-938
Author(s):  
D. K. Pandey ◽  
P. S. Yadav
Keyword(s):  
Ab Initio ◽  
Electronic Properties ◽  
Quantum Confinement Effect ◽  
Zero Point ◽  
Stable Structure ◽  
Ab Initio Study ◽  
Point Energy ◽  
Structural And Electronic Properties ◽  
The Stability ◽  
Homo Lumo

An ab initio study has been performed for the stability, structural and electronic properties of forty-four ZnxTey (x + y = p = 2 to 5) nanoclusters by employing B3LYP-DFT/LANL2DZ method. The zero-point energy correction is also considered in this study. For a particular configuration, the nanoclusters containing a large number of Te atoms are found the most stable structure in comparison with the other nanoclusters. The most stable nanoclusters have either linear or planer structures and, only Zn4Te configuration has no stable structure as the structures of this configuration have at least one imaginary vibrational frequency. The HOMO–LUMO gap of the most stable structure shows a zigzag variation with the increase in the number of atoms in the nanocluster. The observed enhancement trend of the HOMO–LUMO gap with a decrease in the size of the nanocluster confirms to the quantum-confinement effect. The ionization potential (IP) shows decreasing behavior with an increase in the number of atoms in nanoclusters and the variation of electron affinity (EA) with nanocluster size shows zig-zag behavior.

scholarly journals On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

2021 ◽  
Author(s):  
Xue Zhong ◽  
Jie Zhao ◽  
Kaiping Yu ◽  
Minqiang Xu
Keyword(s):  
Periodic Solutions ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Elliptical Orbit ◽  
Periodic Motions ◽  
Nonlinear Stability Analysis ◽  
The Third ◽  
The Stability ◽  
Lyapunov Instability

Abstract This paper deals with periodic motions and their stability of a flexible connected two-body system with respect to its center of mass in a central Newtonian gravitational field on an elliptical orbit. Equations of motion are derived in a Hamiltonian form and two periodic solutions as well as the necessary conditions for their existence are acquired. By analyzing linearized equations of perturbed motions, Lyapunov instability domains and domains of stability in the first approximation are obtained. In addition, the third and fourth order resonances are investigated in linear stability domains. A constructive algorithm based on a symplectic map is used to calculate the coeffcients of the normalized Hamiltonian. Then a nonlinear stability analysis for two periodic solutions is performed in the third and fourth order resonance cases as well as in the nonresonance case.

scholarly journals Extraction of Zero-Point Energy from the Vacuum: Assessment of Stochastic Electrodynamics-Based Approach as Compared to Other Methods

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 51 ◽  
Author(s):  
Garret Moddel ◽  
Olga Dmitriyeva
Keyword(s):  
Detailed Balance ◽  
Zero Point ◽  
Zero Point Energy ◽  
Stochastic Electrodynamics ◽  
Point Energy ◽  
The Third ◽  
Point Field ◽  
Nonlinear Processing ◽  
Mechanical Extraction ◽  
Energy From The Vacuum

In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, and conservation laws are presented for zero-point energy extraction. The proposed methods are separated into three classes: nonlinear processing of the zero-point field, mechanical extraction using Casimir cavities, and the pumping of atoms through Casimir cavities. The first two approaches are shown to violate thermodynamics principles, and therefore appear not to be feasible, no matter how innovative their execution. The third approach, based upon stochastic electrodynamics, does not appear to violate these principles, but may face other obstacles. Initial experimental results are tantalizing but, given the lower than expected power output, inconclusive.

Structural and Electronic Properties of ZnO NANOCLUSTERs: A B3LYP DFT Study

2013 ◽  
Vol 650 ◽  
pp. 29-33 ◽  
Author(s):  
D.K. Pandey ◽  
P.S. Yadav ◽  
S. Agrawal ◽  
B.K. Agrawal
Keyword(s):  
Electronic Properties ◽  
Three Dimensional ◽  
Zero Point ◽  
Point Energy ◽  
Stable Clusters ◽  
Structural And Electronic Properties ◽  
Zno Nanoclusters ◽  
The Stability ◽  
Homo Lumo ◽  
Zero Point Energy Correction

An ab initio B3LYP-DFT/6-311G(3df) study has been performed for the stability, structural and electronic properties of forty ZnmOn(m + n = p = 2 to 4) nanoclusters. We also consider the zero point energy correction. The nanoclusters containing large number of strongly electronegative O atoms for p = 3 and 4 are found to be most stable as compared to the other nanoclusters of the same configuration. The most stable clusters have linear or planer structures and not the three dimensional ones. The observed trend of decrease of the HOMO-LUMO gap with the size of the nanocluster is in conformity with the quantum confined behavior.

Higher order elastic tensors of crystal structure under non-linear deformation

2019 ◽  
Vol 04 (04) ◽  
pp. 1950007 ◽  
Author(s):  
B. Xiao ◽  
J. Feng
Keyword(s):  
Crystal Structure ◽  
Mechanical Properties ◽  
Sound Velocity ◽  
Elastic Constants ◽  
Fourth Order ◽  
High Pressures ◽  
Higher Order ◽  
Linear Deformation ◽  
The Third ◽  
Non Linear

The higher-order elastic tensors can be used to characterize the linear and non-linear mechanical properties of crystals at ultra-high pressures. Besides the widely studied second-order elastic constants, the third- and fourth-order elastic constants are sixth and eighth tensors, respectively. The independent tensor components of them are completely determined by the symmetry of the crystal. Using the relations between elastic constants and sound velocity in solid, the independent elastic constants can be measured experimentally. The anisotropy in elasticity of crystal structures is directly determined by the independent elastic constants.

Stability of a Simply Supported or Clamped Silo Wall Subjected to Frictional Tangential Follower Loads

1978 ◽  
Vol 5 (2) ◽  
pp. 69-78
Author(s):  
H.H.E. Leipholz ◽  
K.D. Bhalla
Keyword(s):  
Boundary Value Problem ◽  
Direct Method ◽  
Specific Form ◽  
Turn Of The Century ◽  
Stability Conditions ◽  
Simply Supported ◽  
The Third ◽  
The Stability ◽  
Complete Investigation ◽  
Liapunov's Direct Method

In this paper, the stability of a silo wall has been investigated without considering the edge effect caused by adjacent walls. The silo wall is assumed to be subjected to tangential, compressive, exponentially varying following loads. Janssen, in his publications, justified using such loads. Hence, since the turn of the century loading of such a type has been widely used for silo design. The direct method of Liapunov is used for the stability investigation. Following this method, one determines the stability conditions without solving explicitly the boundary value problem of the system’s motion. Since no specific form for the solution is assumed when working with Liapunov’s approach, one does not know whether the structure will fail by buckling or by flutter. However, one does obtain the critical load beyond which the safety of the structure is endangered. The results are obtained in the form of three stability conditions. Two of these conditions may be used to determine the dimensions of the silo. The third condition then prescribes the required material damping. The paper may be considered as a first attempt into the investigation of silo stability with Liapunov’s direct method. A complete investigation has to include edge effects and may be left for further research.

Singularities in Landau-Devonshire Potentials for Ferroelectric Phase-Transitions

2010 ◽  
Author(s):  
Fabrizio Davi´
Keyword(s):  
Phase Transitions ◽  
Fourth Order ◽  
Ferroelectric Phase ◽  
Phase Interface ◽  
Reference Configuration ◽  
Complex Nature ◽  
Stability Conditions ◽  
The Stability ◽  
Ferroelectric Phase Transitions

Ferroelectrics phase transitions are studied in terms of fourth-order Landau potentials: a clever choice of the reference configuration allows for a complete description of all the possible transitions. The study of the stability conditions at the phase interface helps to explain the fairly complex nature of the observed twins.

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