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.

scholarly journals Acoustic Vibrational Properties and Fractal Bond Connectivity of Praseodymium Doped Glasses

2000 ◽  
Vol 53 (6) ◽  
pp. 805
Author(s):  
H. B. Senin ◽  
H. A. A. Sidek ◽  
G. A. Saunders
Keyword(s):  
Hydrostatic Pressure ◽  
Bulk Modulus ◽  
Ultrasonic Wave ◽  
Mole Fraction ◽  
Wave Attenuation ◽  
Elastic Stiffness ◽  
Ultrasonic Waves ◽  
Elastic Behaviour ◽  
Doped Glasses ◽  
Two Level Systems

The velocities of longitudinal and shear ultrasonic waves propagated in the (Pr2O3)x(P2O5)1-x glass system, where x is the mole fraction of Pr2O3 and (1 - x) is the mole fraction of P2O5, have been measured as functions of temperature and hydrostatic pressure. The temperature dependencies of the second order elastic stiffness tensor components (SOEC) CS IJ , which have been determined from the velocitydata between 10 and 300 K, show no evidence of phonon mode softening throughout the whole temperature range. The elastic stiffnesses increased monotonically, the usual behaviour associated with the effect of the phonon anharmonicityof atomic vibration. At low temperatures, strong phonon interactions with two-level systems have been observed. The ultrasonic wave attenuation of longitudinal and shear waves is dominated bya broad acoustic loss peak whose height and peak position are frequencydependent. This behaviour is consistent with the presence of thermally activated structural relaxation of the two-level systems in these glasses. The fractal bond connectivity of these glasses, obtained from the elastic stiffnesses determined from ultrasonic wave velocities, has a value between 2.32 to 2.55, indicating that their connectivitytends towards having a threedimensional character. The hydrostatic pressure dependencies of longitudinal ultrasonic waves show a slight increase with pressure. As a consequence, the hydrostatic pressure derivatives ( CS11/ P)P=0 of the elastic stiffness CS11/ and (BS/P)P=0 of the bulk modulus BS of (Pr2O3)x(P2O5)1-x glasses are positive. The bulk modulus increases with pressure, and thus these glasses stiffen under pressure, which is associated with the normal elastic behaviour. The GrÜneisen parameter approach has been used to quantifythe vibrational anharmonicityof the long-wavelength acoustic phonons in these glasses.

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.

Hydrostatic pressure and uniaxial stress derivatives of the Fermi surface of rhenium

1983 ◽  
Vol 61 (10) ◽  
pp. 1428-1433 ◽  
Author(s):  
J. R. Anderson ◽  
F. W. Holroyd ◽  
J. M. Perz ◽  
J. E. Schirber ◽  
I. M. Templeton
Keyword(s):  
Transition Temperature ◽  
Hydrostatic Pressure ◽  
Fermi Surface ◽  
Cross Sections ◽  
Solid Helium ◽  
Uniaxial Stress ◽  
Superconducting Transition ◽  
Cross Sectional ◽  
Effective Masses ◽  
Derivatives Of

Derivatives with respect to hydrostatic pressure of extremal cross-sectional areas normal to [Formula: see text] of all closed sheets of the Fermi surface of rhenium have been determined by both fluid–helium and solid–helium phase shift techniques. Precise values of de Haas–van Alphen frequencies and effective masses have also been measured for these cross sections. In addition, uniaxial stress derivatives of the zone seven cross sections have been deduced from quantum oseillations in magnetostriction and torque. Previously observed anomalies in the pressure dependence of the superconducting transition temperature are interpreted in terms of the present results.

Influence of Stress on Thermoelectric Properties of Antimony Telluride

2003 ◽  
Vol 793 ◽  
Author(s):  
Gerald D. Mahan ◽  
Gun Sang Jeon ◽  
T. Thonhauser
Keyword(s):  
Hydrostatic Pressure ◽  
Power Factor ◽  
First Principles ◽  
High Pressures ◽  
Uniaxial Stress ◽  
Antisite Defect ◽  
First Principles Calculation ◽  
Antimony Telluride ◽  
Stress Dependent ◽  
Induced Defects

ABSTRACTWe present first-principles calculation for the behavior of antimony telluride under stress. We focus on the calculation of transport properties for pure Sb2Te3 and the investigation of stress-induced defects. Our transport calculations were done within first-principles using the linearized-augmented plane-wave method, where we first calculated the transport distribution for several stress conditions. Next, using these stress dependent transport distributions, we derived the stress dependence of the electrical conductivity, the Seebeck coefficient, and the power factor. Our calculations for the stress-induced defects were done utilizing a pseu-dopotential method and confining ourselves to the antisite defect. In all cases, our results are in good agreement with experimentally obtained data. Furthermore, we found that hydrostatic pressure does not improve the power factor, while, on the other hand, a large increase under uniaxial stress can be observed. Also, both hydrostatic pressure and uniaxial stress are found to lower the formation energies of the antisite defects, suggesting a structural transition at high pressures.

High temperature elastic anharmonicity in lanthanum mono-chalcogenides

2011 ◽  
Vol 89 (7) ◽  
pp. 817-824 ◽  
Author(s):  
Krishna Murti Raju
Keyword(s):  
Elastic Constants ◽  
Short Range ◽  
Elevated Temperatures ◽  
Theoretical Data ◽  
Elastic Behaviour ◽  
Physical Parameters ◽  
Nearest Neighbour ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Derivatives Of

The elastic behaviour of lanthanum mono-chalcogenides is investigated at elevated temperatures. This study includes second- and third-order elastic constants of compound semiconductors LaS, LaSe, and LaTe, starting from primary physical parameters, that is, nearest neighbour distance and hardness parameters, assuming long- and short-range potentials. The variations of elastic constants with temperature follow a systematic trend identical to that observed in other chalcogenides in the NaCl-type structure family. The present approach can also succeed in predicting the pressure derivatives of the elastic constants. The obtained results are compared with available theoretical data and are found to be in satisfactory agreement with present values.

The elastic behaviour of orthorhombic sulphur under pressure

1986 ◽  
Vol 407 (1833) ◽  
pp. 325-342 ◽  
Keyword(s):  
Molecular Crystal ◽  
Room Temperature ◽  
Acoustic Mode ◽  
Elastic Behaviour ◽  
Grüneisen Parameter ◽  
Phonon Modes ◽  
Gruneisen Parameter ◽  
Long Wavelength ◽  
Wave Velocities ◽  
Vibrational Anharmonicity

Orthorhombic, α -sulphur comprises S 8 rings strongly bound by covalent, intramolecular forces but held together by much weaker intermolecular bonds. To examine the vibrational anharmonicity of the long-wavelength acoustic modes in a molecular crystal of this type, the effects of hydrostatic and uniaxial pressures upon the velocities of ultrasonic modes propagated in a single crystal of orthorhombic sulphur have been measured. From the experimental results at room temperature 19 of 20 third-order elastic constants and also the hydrostatic pressure derivatives of the 9 second-order elastic constants have been obtained. The elastic stiffnesses and their hydrostatic pressure derivatives have also been calculated from an intermolecular potential of the 6-exp variety. Good agreement between the results obtained from this lattice dynamical calculation and the ultrasonic experiments establishes that the potential model provides a reasonable description of the elastic behaviour of this molecular crystal. The compression estimated from the Murnaghan equation of state agrees well with that estimated theoretically from the lattice dynamic calculations. The Debye temperature determined from the ultrasonic-wave velocities is 187.5 ± 2 K. Ultrasonic-wave velocities are linear up to about 100°C; the crystals do not undergo the transition to a monoclinic (β) phase which can take place at 95°C. There is no indication of softening of the long-wavelength acoustic phonon modes. Vibrational anharmonicity is discussed in terms of the long-wavelength acoustic-mode Grüneisen parameters obtained from the generalized Grüneisen theory in the quasiharmonic approximation. The mean high-temperature long-wavelength acoustic-mode Grüneisen parameter γ̄ el H (= 2.72) is much larger than the room-temperature thermal Grüneisen parameter γ th (=0.54). In this molecular crystal the intermolecular volume is much more compressible than the intramolecular volume; the mode Grüneisen parameters for purely internal vibrational modes are small, whereas those for the external modes are large. At room temper­ature all phonon modes contribute so that γ th is made small by the small internal-mode contributions. In contrast, the weak, strongly pressure dependent intermolecular forces dominate the zone-centre acoustic modes and lead to a large mean Grüneisen parameter γ̄ el H .

scholarly journals Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Lithium Niobate

2006 ◽  
Vol 3 (3) ◽  
pp. 122-133 ◽  
Author(s):  
Thresiamma Philip ◽  
C. S. Menon ◽  
K. Indulekha
Keyword(s):  
Energy Density ◽  
Lithium Niobate ◽  
Elastic Constants ◽  
Elastic Stiffness ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Gruneisen Parameters ◽  
Derivatives Of

The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3(lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO3are obtained in the present work. The second and third-order elastic constants are compared with available experimental values. The second-order elastic constant C11which corresponds to the elastic stiffness along the basal plane of the crystal is less than C33which corresponds to the elastic stiffness tensor component along thec-axis of the crystal. The pressure derivatives, dC'ij/dp obtained in the present work, indicate that trigonal LiNbO3is compressible. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in LiNbO3. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

Poly(methyl-phenylsilylene) Derivatives as Photoconductors

1993 ◽  
Vol 58 (10) ◽  
pp. 2337-2348 ◽  
Author(s):  
Ivan Kmínek ◽  
Stanislav Nešpůrek ◽  
Eduard Brynda ◽  
Jiří Pfleger ◽  
Věra Cimrová ◽  
...  
Keyword(s):  
Spectral Properties ◽  
Long Wavelength ◽  
Langmuir Blodgett ◽  
Ultrathin Layers ◽  
Polar Derivatives ◽  
Derivatives Of

The attachment of long wavelength absorbing π-conjugated chromophores to poly(methyl-phenylsilylene) (PMPSi) via reactions of its formylated derivative is described. Some of the obtained polymers exhibit improved photostability in comparison with the parent polymer. Their spectral properties and photoconductivity are discussed. Ultrathin layers and multilayers were prepared from polar derivatives of PMPSi by the Langmuir-Blodgett technique and their photoconductive behaviour was studied.

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. .

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