Browsing by Author "B. Dayal"

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A revision of Kellermann's calculations of the specific heats of sodium chloride
(1961) B. Dayal; B.B. Tripathi
In the well-known work on the lattice vibrations and the specific heats of sodium chloride, Kellermann has not assigned a correct statistical weight to several frequencies and has, further, omitted one point of the Brillouin zone. His results have, therefore, been revised to take these factors into account.
An Electron Gas Model for the Lattice Dynamics of Beryllium
(1965) R.P. Gupta; B. Dayal
The model originally proposed by Slutsky and Garland for the lattice dynamics of the hexagonal close‐packed structure is modified by introducing the contributions of the electron gas. The latter are computed from the Cauchy discrepancy by following Sharma and Joshi's work on cubic metals. The force constants for beryllium are calculated, using this new model, from the experimental data and one observed vibration frequency. The dispersion curves for the [0001] and [0110] directions are the computed and found to be in satisfactory agreement with the results of neutron scattering in beryllium. Copyright © 1965 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Bradburn-Fürth equation of state and thermal expansion of face-centered metals
(De Gruyter, 2021) H.D. Pandey; B. Dayal
The relative changes of lattice constants due to thermal expansion are calculated for seven metals, viz., Al, Ag, Cu, Au, Ni, Pt, and Pd, by means of the Bradburn-Furth equation of state. The theoretical results at high temperatures, where this equation of state is valid, are found to be in very good agreement with experimental data. © 1964, The authors.
Correct enumeration of vibration frequencies in the Brillouin zone
(1960) B. Dayal; S.P. Singh
In order to calculate the vibration frequencies by Born's method the Brillouin zone is sub-divided into a number of points. The actual number of frequencies used by the workers for the calculation of Cv is, however, different from the number of points of the zone, resulting in a non-uniform distribution of points. It has been shown that this results in an incorrect value of the specific heat. As an example Hsieh's theoretical results have been used to recalculate the specific heat of silicon with a proper number of frequencies. The difference between these revised results and Hsieh's original calculations is found to be large.
Crystal Vibrations of Silicon by the Use of Valence Force Potentials
(1970) B.D. Singh; B. Dayal
The dispersion curves for silicon in the symmetry directions [ζ, 0, 0], [ζ, ζ, 0] and [ζ, ζ, ζ] are calculated using valence force potentials. Two different models have been used, the one with three valence force constants and the other with six valence force constants. The initial set of three valence force constants have been derived by incorporating Lippincott potential in the general valence force field for silicon. The force constants have been refined using a manual method and further by a least square fitting program with some known neutron scattering frequencies. The results with the six adjusted valence force constants potential model are in good agreement with the experimental results. The Debye characteristic temperatures have been calculated and they are in good agreement with the experimental values. Copyright © 1970 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Effect of zero‐point energy on the specific heats of solidified neon and xenon
(1966) N.P. Gupta; B. Dayal
The specific heats of neon and xenon are calculated from a study of their lattice vibrations. The effect of zero‐point energy is included by an iterative method and a Buckingham exponential potential is used. The calculated and experimental values of Cv agree well for xenon but not so well for neon. It is suggested that the interatomic forces in neon are similar to those in helium and that a Buckingham potential, which is applicable to solids formed from heavy rare gases, is inapplicable to solid neon. Copyright © 1966 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Equation of state and the thermal expansion of KCl and KI
(1975) Manikarnika Lagu; B. Dayal
The equation of state and the thermal expansion of KCl and KI have been studied by evaluating the vibration spectra at different volumes with the help of the simple shell model. An exponential form of the potential energy of the crystal lattice has been used in the investigation. Isotherms have been drawn and the coefficients of thermal expansion have been evaluated for different temperatures in the range 0-1000°K. Unlike the results of early workers, the present calculations show that the melting-point isotherm cuts the zero-pressure axis and does not have a minimum. It has also been shown, in agreement with experiments, that the thermal expansion at the melting point has a finite value. Our results show a good agreement with the experimental data right up to the melting point. © 1975 The American Physical Society.
Equation of State of LiF
(1964) M.P. Verma; B. Dayal
The equation of state of LiF is studied by the method discussed in the authors' earlier paper on sodium chloride. The agreement between the calculated and the experimental values for thermal expansion becomes poor at high temperatures. Various possibilities for improving this agreement are discussed. Copyright © 1964 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Equation of State of Solid Argon and Krypton
(1967) N.P. Gupta; B. Dayal
The equation of state, thermal expansion, and isothermal compressibilities of solidified argon and krypton are studied in the harmonic approximation. An exponential interatomic potential is used, and zero‐point quantum effects are included. There is good agreement between the calculated and the observed values. Copyright © 1967 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Equation of state of solids [8]
(1956) B. Dayal; C. Purhothaman
[No abstract available]
Evaluation of Specific Heats of Titanium, Zirconium, and Hafnium
(1966) R.P. Gupta; B. Dayal
The electron gas model, described by the authors in an earlier paper, is extended to the three transition metals titanium, zirconium, and hafnium. The theoretic θ − T curves agree to within 3 to 5% with experimental values. Copyright © 1966 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Fuchs's Relations in Alkali Halides and Their Application to the Lattice Dynamics of Lithium Fluoride
(1966) M.P. Verma; B. Dayal
A discussion is given of the work of Lowdin and Lundqvist in which the failure of Cauchy relations in ionic crystals is attributed to the existence of a many‐body potential arising from the overlap of atomic wave functions. It is shown that this many‐body interaction may be represented by a volume force which satisfies Fuchs's relations. A simple model is developed incorporating volume forces phenomenologically. In addition to this, the three‐body interaction introduces an effective charge in to the Coulomb term of the point‐ion model. The model is applied to lithium fluoride and good agreement is obtained between the theoretical and observed values of cv. Copyright © 1966 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Inter-atomic force law and equation of state of solids
(1955) B. Dayal; R.S. Sharma
The pressure of a solid has been divided into two terms p1 and p2, of which the first is the static part due to a non-vibrating lattice at T = 0, and the second arises from the thermal vibrations. For all volumes measured at zero pressure the two are equal and opposite to each other. The static pressures of eight solid elements, aluminium, copper, silver, gold, lead, platinum, tungsten and molybdenum, have been obtained from their thermal pressures γE/V by the use of the above condition. The average Gruneisen constant γ has been calculated in the usual way from the thermal expansion and the specific heat data. These static pressures have been compared with the derivatives of the potential energy as derived from the inter-atomic potential used earlier by Furth, and a very close agreement has been observed between them.
Krebs's model for noble metals and the screening parameter
(1965) M.M. Shukla; B. Dayal
The specific heats of silver have been calculated on Krebs's model. These results have been discussed along with the earlier calculations on copper and gold published by one of us. It is found that Krebs's model is able to reproduce the experimental values remarkably well provided we consider the screening parameter as an adjustable constant. In the case of copper its numerical value is given by the theory of Bohm and Pines and for gold by that of Thomas and Fermi. For silver it lies between the two theories. © 1965.
Krebs's Model for the Alkali Metals and the Screening Parameter
(1965) P.S. Mahesh; B. Dayal
The specific heats of sodium, potassium, rubidium, and caesium are calculated on the basis of Krebs's model (1). It is found that the theoretical θ−T curves agree with experiment if the screening parameter is taken as an adjustable constant. The deduced values of this parameter show a gradual change from the Bohm‐Pines to the Thomas‐Fermi form during the transition from sodium to caesium. The model, however, fails to give agreement in the case of lithium. Since the measured elastic constants of this metal do not give the correct value of θ0, the discrepancy for this case may be due to the errors in measurement. Copyright © 1965 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Lattice constants and thermal expansion of AgCl up to 878 °C by x-ray method
(De Gruyter, 2021) B.N. Dutta; B. Dayal
The thermal expansion of AgCl has been studied over the temperature range 25 to 878 °C by the X-ray powder technique. The experimental coefficients can be represented by the interpolation formula αt = 30 × 10-6 + 1.5 × 10-8 t - 0.9 × 10-10 t2 + 0.6499 × 10-12 t3. The presence of Frenkel defects has been discussed. © 1964, The authors.
Lattice Constants and Thermal Expansion of Gold up to 878 °C by X‐Ray Method
(1963) B.N. Dutta; B. Dayal
The thermal expansion of gold has been studied over the temperature range 25° to 878 °C by the X‐ray powder technique. The experimental coefficients can be represented by the interpolation formula αt = 13.99 × 10−8 + 0.491 × 10−3 t. The work of LAWSON, and MITRA and MITRA is discussed, and it is shown that in this temperature range it is not necessary to postulate the existence of any anomalous expansion arising from lattic defects. Copyright © 1963 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Lattice Constants and Thermal Expansion of Palladium and Tungsten up to 878 °C by X‐Ray Method
(1963) B.N. Dutta; B. Dayal
The lattice parameters, and coefficients of thermal expansion, of palladium and tungsten are measured by means of a high temperature X‐ray powder camera. The lattice constants of palladium are expressed by an analytical formula at = 3.8890 × 10− + 4.5 × 10−13 t + 1.37 × 10−16 t2 and those of tungsten by at = 3.1646 × 10−8 + 1.4398 × 10−13 t + 0.3164 × 10−16 t2. It is found that the thermal expansion coefficients can not be satisfactorily explained by Grüneisen's theory. Copyright © 1963 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Lattice dynamics and specific heats of some transition metals on krebs's model
(1966) P.S. Mahesh; B. Dayal
Krebs's model for the lattice dynamics of cubic metals has been extended by including the third-nearest-neighbor ionic interactions. The cases of three transition metals, viz., α-iron, molybdenum and tungsten, are discussed in this paper. The force constants appearing in the secular equations for the lattice frequencies are estimated from experimental elastic constants and one observed vibration frequency. The phonon dispersion curves for the three major symmetry directions show a good agreement with the results for neutron scattering. The frequency distributions are computed. The theoretical specific heats and Debye parameters also exhibit a good agreement with the experimental data. © 1966 The American Physical Society.
Lattice Dynamics of MgO
(1967) M.P. Verma; B. Dayal
A phenomenological model developed by the author in an earlier paper [1] is applied to the case of MgO. The two‐phonon combined density of states (C.D.S.) is computed from the calculated frequencies. The C.D.S. peaks show good agreement with the subsidiary maxima in the infrared absorption spectrum of the solid. The calculated dispersion curves agree with Pekham's measurements except for the large wave‐vector region, and the specific heats agree with the experimental observations of Barron et al. Copyright © 1967 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim