Browsing by Author "K.S. Dubey"

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A Modification of the Generalized Callaway Thermal Conductivity Equation to Allow for Phonon Dispersion
(1974) K.S. Dubey
[No abstract available]
Entropy catastrophe and superheating of crystals
(1988) S. Lele; P. Ramachandra Rao; K.S. Dubey
Kauzmann1 has pointed out that at a temperature (Tk) far below the melting temperature (Tm) of a crystal, the entropies of an undercooled liquid and its corresponding equilibrium crystal tend to become equal. At temperatures below Tk, the crystal would have a greater entropy than its liquid. Such a catastrophe is avoided through a glass transition of the liquid above Tk. Fecht and Johnson have shown that such a transition should occur for aluminium at 0.23 Tm. A similar entropy catastrophe can also arise at a temperature, TiS, above Tm . Above TiS, the crystalline solid is once again expected to have an entropy greater than that of the liquid. Cahn3 has considered the implications of this idea with respect to the superheating of a solid. Here we present an alternative evaluation of the two temperatures of instability, Tk and TiS, from experimentally measurable parameters. Results for alkali metals show that the Kauzmann-type entropy catastrophe occurs at about half the absolute melting temperature, whereas we find that the entropy catastrophe as described by Fecht and Johnson2 occurs at twice the absolute melting temperature. For most solids, vaporization will probably intervene before the entropy catastrophe temperature above the melting temperature is reached. © 1988 Nature Publishing Group.
Estimation of the free energy of undercooled oxide melts
(1989) K.S. Dubey; P. Ramachandrarao; S. Lele
The difference in free energy between a liquid and a solid phase (ΔG) is an important parameter in nucleation theory. We show that a novel expression derived by a Taylor series expansion of ΔG around its value at the melting temperature describes accurately the ΔG of oxide melts as a function of degree of undercooling. This is demonstrated for a number of pure (SiO2, GeO2, and B2O3) and compound oxides.
Estimation of the heat of fusion of a eutectic mixture from phase diagram data
(1992) P. Ramachandrarao; K.S. Dubey; Mamta Saroch
Simple methods are presented for the estimation of the heat of fusion of a eutectic mixture from the entropy of formation of constituent phases with the aid of data obtainable from the binary phase diagrams. The suggested methods do not require any thermodynamic information concerning the terminal solid solutions if any one of them has negligible solid solubility. In such cases the present methods also do not require thermodynamic information concerning the liquid phase. The procedures are tested with respect to a number of eutectic systems based on simple metals and intermetallic compounds. Results obtained are in excellent agreement with values obtained from direct experiments.
EVALUATION OF THE IDEAL GLASS TRANSITION TEMPERATURE AND OTHER THERMODYNAMIC PROPERTIES OF GLASS FORMING LIQUIDS.
(1986) S.P. Pandey; K.S. Dubey; P. Ramachandrarao
An earlier hole theoretical model of the liquid state developed by the authors is modified to reduce the number of parameters required to describe the thermodynamic properties. It has been shown that good agreement can be achieved between observed and calculated Gibb's free energy change accompanying freezing at large undercooling for a variety of substances. Estimates of the Kauzmann glass transition temperatures of these substances also agree well with those extrapolated from relaxation and thermodynamic data. The present analysis simplifies the procedures for obtaining the viscous behavior and time-temperature transformation diagrams for glass forming substances.
Free energies of undercooled phases
(1989) P. Ramachandrarao; K.S. Dubey; S. Lele
A novel approach for the estimation of the free energies of metastable liquid and allotropie phases has been presented. The method is based on the Taylor series expansion of the free energy différence between stable and metastable phases. The procedure has been applied to arrive at allotropie transformation temperatures in iron and also the isentropic temperature for any two coexisting phases. Results obtained strongly validate the expressions derived which involve only the use of equilibrium heat capacity and entropy data. © 1989.
Lattice thermal conductivity due to impurities
(1973) K.S. Dubey
Phonon conductivity of NaF has been calculated using non-linear theory of heat transfer in solid given by Kazakov and Nagaev and shows good agreement with the measurements of Jackson and Walker in the temperature range 2-10°K. © 1973.
Lattice thermal conductivity of Mg2Ge in the temperature range 4-800°K
(1976) K.S. Dubey
The Sharma-Dubey-Verma model of two-mode conduction, similar to the Holland model, has been applied to explain the phonon conductivity data of Mg2Ge in the temperature range 4-800°K. The temperature exponents m(T) for the three-phonon scattering relaxation rates have been calculated for both class-I and class-II events following Guthrie. Excellent agreement has been found between theoretical and experimental values of the phonon conductivity of Mg2Ge over a wide range of temperature. Separate percentage contributions of transverse and longitudinal phonons have also been calculated in the temperature range of investigation. © 1976 The American Physical Society.
Lattice thermal conductivity of NaF in the temperature range (2-100) °k
(1973) K.S. Dubey
The separate contributions of longitudinal and transverse phonons towards the lattice thermal conductivity of NaF have been calculated in the entire temperature range (2-100) °K using the relation τ3ph-1g(ω)Tme-θαT for the three-phonon-scattering relaxation rate. Following Verma et al., an improved dispersion relation q→=(ωv→)(1+γω2) has been used to calculate νgνp2 in the conductivity integrals. The effect of point-defect scattering on lattice thermal conductivity has been studied in the temperature range (2-100) °K. © 1973 The American Physical Society.
Lattice thermal conductivity of p-type GaSb in the temperature range 2-20°K
(1972) K.S. Dubey; G.S. Verma
In the present paper the resonance-scattering relaxation rate for the electron-phonon interaction as given by Kumar et al. is used in the calculation of the resonance scattering of phonons by bound holes in p-type GaSb in the temperature range 2-20°K. The present calculations show that with the simplified expressions of Kumar et al. for resonance scattering of phonons by bound electrons for ω>ωr and ω<ωr, one can explain the anomalous resonance dip in the phonon-conductivity-vs-temperature curves of p-doped GaSb. An excellent agreement between theoretical and experimental values of phonon conductivity is obtained for the entire temperature range 2-20°K on the basis of Callaway's model of phonon conductivity, provided one incorporates separate conductivity integrals for 0<ω<ωr and ωr<ω<ωD, where ωr is the resonance frequency and ωD is the Debye frequency. © 1972 The American Physical Society.
Lattice Thermal Conductivity of Sapphire in the Temperature Range 0.4 to 4.0 °K
(1972) K.S. Dubey
[No abstract available]
Lattice thermal conductivity of Si in the temperature range (2-1400) °k
(1973) K.S. Dubey; G.S. Verma
In the present paper we have determined the temperature dependence of the three-phonon relaxation rate, which is valid for the entire temperature range (2-1400)°K for Si and is expressed as τ3ph-1Tm(T)e-θαT The exponent m, which depends upon temperature, is determined with the help of Guthrie's expression as given in the Sharma-Dubey-Verma model. Using the SDV model we have calculated the lattice thermal conductivity of Si in the temperature range (2-1400)°K and found excellent agreement between experimental and calculated results. © 1973 The American Physical Society.
Nonlinear Heat Transfer in a Lattice Containing Impurities
(1973) K.S. Dubey
Nonlinear heat transfer in a lattice has been studied considering two scattering mechanisms, isotopic scattering and dislocation scattering as impurity scattering process. A sufficiently good agreement is observed between the experimental conductivity of NaF in the entire temperature range 2 to 10 °K. Copyright © 1973 WILEY‐VCH Verlag GmbH & Co. KGaA
On the composition dependence of faceting behaviour of primary phases during solidification
(1993) Mamta Saroch; K.S. Dubey; P. Ramachandrarao
The entropy of solution of the primary aluminium-rich phase in the aluminium-tin melts has been evaluated as a function of temperature using available thermodynamic and phase equilibria data with a view to understand the faceting behaviour of this phase. It was noticed that the range of compositions in which alloys of aluminium and tin yield a faceted primary phase is correlated with the domain of compositions over which the entropy of solution shows a strong temperature dependence. It is demonstrated that both a high value of the entropy of solution and a strong temperature dependence of it are essential for providing faceting. A strong temperature dependence of the entropy of solution is in turn a consequence of negligible liquidus slope and existence of retrograde solubility. The AgBi and AgPb systems have similar features. © 1993.
On the composition dependence of undercooling in binary alloy melts
(1990) P. Ramachandrarao; K.S. Dubey
The driving free energy for nucleation of a primary solid phase from an undercooled liquid solution is an important parameter in the theory of nucleation. In the present study an expression for the driving free energy has been obtained in a form that can be directly related to slopes of liquidus and solidus lines in a phase diagram. The expression has been used for an examination of the composition dependence of the maximum undercooling in alloy droplets of the eutectic systems silver-copper and lead-tin. It has been demonstrated that undercooling of an alloy melt is terminated by the nucleation of a primary phase when the driving force attains a composition-independent critical value. These critical values have been found to vary from experiment to experiment and possibly depend on the nature of the surface coating in the droplet emulsion samples as demonstrated by the results on the lead-tin alloys. © 1990 Taylor & Francis Ltd.
Phase diagram features and glass forming ability of liquid - quenched binary alloys
(1990) K.S. Dubey; P. Ramachandrarao
The tendency to/glass formation has been discussed in the light of the driving force for nucleation in a binary alloy melt. The relationship between phase diagram features such as slopes of liquidus and solidus lines, extent of solid solubility, existence of intermetallic phases etc., and observed composition ranges of glass formation is highlighted. It is shown that glass forming compositions will be symmetric with respect to the eutectic composition only in the case of pure metal eutectics with normal entropies of solution of the solid phase in the eutectic liquid. In most other cases the glass-forming composition range is shown to be asymmetric with respect to the eutectic.
Phonon conductivity of Ge in the temperature range 2-1000 °K
(1971) P.C. Sharma; K.S. Dubey; G.S. Verma
The contributions of transverse and longitudinal phonons toward thermal conductivity of undoped Ge have been investigated, both in high- as well as low-temperature regions. Four-phonon processes are also included in the determination of the combined relaxation time τc and hence the phonon conductivity. The group velocity of respective phonons in the conductivity integral is obtained on the basis of q→=(ωv→)(1+αω2) , where the parameter α is determined from the experimentally obtained dispersion curves for the different acoustic branches in the region 0-12qmax and 12qmax-qmax. It is observed that the transverse phonons in general make a major contribution toward thermal conductivity in the entire temperature range. © 1971 The American Physical Society.
Phonon conductivity of InSb and GaAs in the temperature range 2-300°K
(1971) K.S. Dubey; G.S. Verma
The recent modification of Holland's model of two-mode conduction, as proposed by us, has been applied to explain the phonon conductivity of InSb and GaAs. This model, Known as the Sharma-Dubey-Verma model, makes use of Guthrie's classification of three-phonon scattering events. In this model, the exponent m of the temperature, i.e., Tm(T) is a continuous function of temperature and approaches unity in the high-temperature region for both the longitudinal phonons as well as transverse phonons. The dispersion of acoustic branches is taken into account in replacing vgvp2 in the conductivity integrals and this forms the basis of the division of the conductivity integrals for the different polarization branches. The present model gives excellent agreement between the theoretical and experimental values of phonon conductivity except near the maximum where the scattering of phonons by point defects dominates over phonon-phonon scattering as well as boundary scattering of phonons. © 1971 The American Physical Society.
RATE OF ENTROPY LOSS WITH TEMPERATURE IN LIQUIDS AND ITS RELATION TO GLASS FORMING ABILITY OF MATERIALS.
(1984) K.S. Dubey; P. Ramachandrarao
The present paper deals with the evaluation of the ideal glass transition temperature from a knowledge of the ratio of the heat capacity and entropy differences between the liquid and solid phases at the equilibrium melting temperature of a material. This ratio is known to be a measure of the rate of entropy loss with temperature for the liquid phase. It has been shown that a correlation exists between the critical cooling rate for glass formation and the magnitude of the ratio of the heat capacity and the entropy of fusion.
Role of entropy of solution in
(Springer-Verlag, 1992) P. Ramachandrarao; K.S. Dubey
[No abstract available]