scholarly journals Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

2019 ◽  
Vol 97 (1) ◽  
pp. 114-116 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Boundary Condition ◽  
Fourth Order ◽  
Fundamental Theorem ◽  
High Pressures ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Gruneisen Parameter ◽  
The Third ◽  
Properties Of Materials ◽  
Derivatives Of

Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.

scholarly journals Higher order derivatives of bulk modulus of materials at infinite pressure

2016 ◽  
Vol 94 (8) ◽  
pp. 748-750 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Bulk Modulus ◽  
Higher Order ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Pressure Derivative ◽  
Basic Principles ◽  
Gruneisen Parameter ◽  
The Third ◽  
The Status ◽  
Derivatives Of

Pressure derivatives of bulk modulus of materials at infinite pressure or extreme compression have been studied using some basic principles of calculus. Expressions for higher order pressure derivatives at infinite pressure are obtained that are found to have the status of identities. A generalized formula is derived for the nth-order pressure derivative of bulk modulus in terms of the third-order Grüneisen parameter at infinite pressure.

Formulation of the third-order Grüneisen parameter at extreme compression

2012 ◽  
Vol 407 (12) ◽  
pp. 2082-2083 ◽  
Author(s):  
J. Shanker ◽  
K. Sunil ◽  
B.S. Sharma
Keyword(s):  
Grüneisen Parameter ◽  
Third Order ◽  
Gruneisen Parameter ◽  
The Third

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

scholarly journals Third derivatives of the integrable part of an asteroid Hamiltonian

2007 ◽  
pp. 53-60 ◽  
Author(s):  
R. Pavlovic
Keyword(s):  
Third Order ◽  
Geometrical Condition ◽  
The Third ◽  
Derivatives Of ◽  
Quasi Convexity ◽  
Explicit Expressions

To apply the theorem of Nekhoroshev (1977) to asteroids, one first has to check whether a necessary geometrical condition is fulfilled: either convexity, or quasi-convexity, or only a 3-jet non-degeneracy. This requires computation of the derivatives of the integrable part of the corresponding Hamiltonian up to the third order over actions and a thorough analysis of their properties. In this paper we describe in detail the procedure of derivation and we give explicit expressions for the obtained derivatives. .

scholarly journals Asymptotic formulae for linear equations

1972 ◽  
Vol 13 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Don B. Hinton
Keyword(s):  
Asymptotic Behaviour ◽  
Fourth Order ◽  
Linear Equations ◽  
Order Equation ◽  
Third Order ◽  
Fourth Order Equation ◽  
The Third ◽  
Asymptotic Formulae ◽  
Image Position

Numerous formulae have been given which exhibit the asymptotic behaviour as t → ∞solutions ofwhere F(t) is essentially positive and Several of these results have been unified by a theorem of F. V. Atkinson [1]. It is the purpose of this paper to establish results, analogous to the theorem of Atkinson, for the third order equationand for the fourth order equation

Grüneisen parameter of quartz, quartzite, and fluorite at high pressures

1979 ◽  
Vol 84 (B7) ◽  
pp. 3527-3531 ◽  
Author(s):  
R. Boehler ◽  
A. Skoropanov ◽  
D. O'Mara ◽  
G. C. Kennedy
Keyword(s):  
High Pressures ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter

scholarly journals Elastic Behaviour of Terbium Metaphosphate Glasses Under High Pressures

1994 ◽  
Vol 47 (6) ◽  
pp. 795 ◽  
Author(s):  
HB Senin ◽  
HAA Sidek ◽  
GA Saunders
Keyword(s):  
Hydrostatic Pressure ◽  
High Pressures ◽  
Uniaxial Stress ◽  
Elastic Stiffness ◽  
Acoustic Mode ◽  
Elastic Behaviour ◽  
Third Order ◽  
Long Wavelength ◽  
Two Level Systems ◽  
Derivatives Of

The elastic and nonlinear acoustic vibrational properties of terbium metaphosphate glasses (Tb2O3)x(P2O5)1?x with x = 0�226,0�247,0�263 and 0�271 (x is the mole fraction) have been determined from measurements of the effects of temperature, hydrostatic pressure, and uniaxial stress on' ultrasonic wave velocity. At temperatures below about 140 K, the elastic stiffness of' (Tb2O3)x(P2O5)1?x glasses becomes anomalously dependent upon temperature, a behaviour usually associated with interactions between acoustic phonons and two-level systems. Except for the (Tb2O3)0�271(P205)0�729 glass, the hydrostatic pressure derivatives of the elastic stiffness and also of the bulk modulus BS of terbium metaphosphate glasses are small and negative. The third-order elastic stiffness tensor components CIJK of the (Tb2O3)0�247(P2O5)0�753 glass between 77 K and 400 K have also been determined. At room temperature, C112, C123 and C144 are positive while C111, C155 and C456 are negative. Both longitudinal and shear acoustic mode Gr�neisen parameters are small and negative: the application of pressure softens the long-wavelength acoustic phonon mode frequencies. The mode softening is enhanced as the temperature is reduced.

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