Lattice dynamics of magnesium oxide
TL;DR: In this paper, measurements of the inelastic neutron scattering by longitudinal optic phonons in MgO are reported and used in an investigation of various lattice dynamical models, including shell and breathing shell models.
Abstract: Measurements of the inelastic neutron scattering by longitudinal optic phonons in MgO are reported. These results and those previously obtained for other branches are used in an investigation of various lattice dynamical models, including shell and breathing shell models. It is shown that the agreement with the measured data is improved by the inclusion of breathing effects.
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TL;DR: In this article, the authors present a systematic approach to the derivation of empirical potential parameters for binary oxides; they also consider their modification for use in mixed oxide systems, and discuss successful applications of the potentials to the calculation of perfect lattice properties.
Abstract: The authors present a systematic approach to the derivation of empirical potential parameters for binary oxides; they also consider their modification for use in mixed oxide systems. Shell-model potentials are used but, unlike the case of the alkali halides within which polarisability and short-range interaction parameters can be transferred, modifications must be introduced when transferring potential parameters between different oxides. The anion polarisability varies with structure and with the nature of the host cation, and changes in cation coordination are reflected in the short-range repulsive cation-anion interaction. Parameters are derived for a range of oxides, and trends in these parameters are discussed. They discuss successful applications of the potentials to the calculation of perfect lattice properties. Equal success is enjoyed when defect and surface properties are considered; in particular the models correctly predict the activation energies for dopant diffusion in NiO, and to a large extent model the surface rumpling of MgO.
1,035 citations
TL;DR: In this article, the authors studied the thermal conductivity of non-metallic crystals at temperatures comparable to or higher than the Debye temperature, where the dominant carriers of thermal energy are phonons and the dominant scattering mechanism is the intrinsic phonon-phonon scattering.
Abstract: Publisher Summary This chapter reviews the thermal conductivity of nonmetallic crystals at temperatures comparable to or higher than the Debye temperature. It deals with the intrinsic behavior of such pure crystals at high temperatures. In such crystals, the dominant carriers of thermal energy are phonons and the dominant scattering mechanism to be considered is the intrinsic phonon–phonon scattering. This is a small section of the much larger problem of the thermal conductivity of nonmetallic solids and clearly it neglects possible heat transport by photons, charge carriers, polarons, and magnons. It also neglects other possible phonon scattering mechanisms such as isotopes, impurities, vacancies, charge carriers, dislocations, grain boundaries, and crystal boundaries. It presents the absolute value of the thermal conductivity, K, as determined by phonon–phonon scattering, the temperature dependence of K, the volume dependence of K, the change in K upon melting, and the minimum value of K. The chapter discusses a composite curve for the thermal conductivity versus temperature of pure KCl measured at a constant pressure of, say, one atmosphere.
734 citations
TL;DR: The program phon calculates force constant matrices and phonon frequencies in crystals and from the frequencies it also calculates various thermodynamic quantities, like the Helmholtz free energy, the entropy, the specific heat and the internal energy of the harmonic crystal.
643 citations
TL;DR: In this paper, the authors present a survey of interionic potential models for alkali halides, including the rigid ion potentials of Fumi and Tosi, and a major part of the section is devoted to deriving a new set of polarizable ion potential, which incorporate the ideas behind the lattice dynamical shell model.
Abstract: After an outline of work on rare-gas systems, which serves as a target for parallel work on alkali halides, and an initial brief survey of those parts of this parallel work for which results have been obtained, interionic potential models for alkali halides are considered in some detail. The rigid ion potentials of Fumi and Tosi are discussed and then a major part of the section is devoted to deriving a new set of polarizable ion potentials, which incorporate the ideas behind the lattice dynamical shell model. Extensions which include many-body terms in the potentials are considered briefly and finally the information which can be obtained from alkali halide diatomic molecules is discussed. In the third section methods of computer simulation for ionic liquids are outlined, concentrating on the molecular dynamics method, and some of the properties which can be obtained by analysing the ion trajectories are listed. Results from simulations, including some new work on LiF, NaCl and RbI, are reviewed.
551 citations
TL;DR: The theory of lattice dynamics has some claim to being the oldest branch of solid state physics as discussed by the authors, and it has been used to account for the thermal and other properties of crystals.
Abstract: Lattice dynamics has some claim to being the oldest branch of solid state physics. Planck's Theory of Radiation and the Theory of Specific Heat was published by Einstein in 1907, On Vibrations in Space Lattices by Born and von Karman in 1912, and On the Theory of Specific Heat by Debye in the same year. Other early papers on lattice dynamics included those by Debye and by Waller on the effect of temperature op the scattering of x-rays by a crystal. In the 1920's Peierls made fundamental contributions to the theory of thermal conductivity and of electrical conductivity involving lattice dynamics, and in the 1930's Blackman brought to an end the acceptance of the complete validity of the Debye theory of specific heat and also contributed the first papers on anharmonic effects in the absorption of infrared radiation by ionic crystals. The work we have mentioned used the formal theory of lattice dynamics to account for the thermal and other properties of crystals. It was not until 1940 that Kellerman...
287 citations
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TL;DR: In this paper, a theory of the lattice dynamics of ionic halides is given based on replacement of a polarizable ion by a model in which a rigid shell of electrons (taken to have zero mass) can move with respect to the massive ionic core.
Abstract: The paper comprises theoretical and experimental studies of the lattice dynamics of alkali halides. A theory of the lattice dynamics of ionic crystals is given based on replacement of a polarizable ion by a model in which a rigid shell of electrons (taken to have zero mass) can move with respect to the massive ionic core. The dipolar approximation then makes the model exactly equivalent to a Born-von K\'arm\'an crystal in which there are two "atoms" of differing charge at each lattice point, one of the "atoms" having zero mass. The model has been specialized to the case of an alkali halide in which only one atom is polarizable, and computations of dispersion curves have been carried out for sodium iodide. We have determined the dispersion $\ensuremath{
u}(\mathrm{q})$ relation of the lattice vibrations in the symmetric [001], [110], and [111] directions of sodium iodide at 110\ifmmode^\circ\else\textdegree\fi{}K by the methods of neutron spectrometry. The transverse acoustic, longitudinal acoustic, and transverse optic branches were determined completely with a probable error of about 3%. The dispersion relation for the longitudinal optic (LO) branch was determined for the [001] directions with less accuracy. Frequencies of some important phonons with their errors (units ${10}^{12}$ cps) are: TA[0,0,1]1.22\ifmmode\pm\else\textpm\fi{}0.04, LA[0,0,1] 1.82\ifmmode\pm\else\textpm\fi{}0.06, TA[\textonehalf{},\textonehalf{},\textonehalf{}]1.52\ifmmode\pm\else\textpm\fi{}0.05, LA[\textonehalf{},\textonehalf{},\textonehalf{}]2.32\ifmmode\pm\else\textpm\fi{}0.06, TO[0,0,0] ${3.6}_{0}$\ifmmode\pm\else\textpm\fi{}0.1, TO[0,0,1]${3.8}_{0}$\ifmmode\pm\else\textpm\fi{}0.1, TO[\textonehalf{},\textonehalf{},\textonehalf{}]${3.5}_{0}$\ifmmode\pm\else\textpm\fi{}0.1. The agreement between the experimental results and the calculations based on the shell model, while not complete, is quite satisfactory. The neutron groups corresponding to phonons of the LO branch were anomalously energy broadened, especially for phonons of long wavelength, suggesting a remarkably short lifetime for the phonons of this branch.
393 citations
TL;DR: In this article, the authors generalized the model for the lattice dynamics of alkali halides to include the case in which both ions are polarizable, and derived Dispersion curves and density of states for LiF and NaCl at 0 and 300 °K.
Abstract: The model for the lattice dynamics of alkali halides as given in a previous paper is generalized to include the case in which both ions are polarizable. Dispersion curves and density of states are calculated for LiF and NaCl at 0 °K. The Debye characteristic temperatures ΘD(T) for 0 °K and 300 °K are computed for these crystals, and good agreement with experimental values is obtained.
In einer vorhergehenden Arbeit wurde ein neues Modell fur die Gitterdynamik der Alkalihalogenide vorgeschlagen. Dieses Modell wird verallgemeinert fur den Fall, das beide Ionen polarisierbar sind. Anschliesend werden die Dispersionskurven und Zustandsdichten fur NaCl und LiF bei 0 °K angegeben. Die ebenfalls berechneten Debye-Temperaturen ΘD(T) dieser Kristalle fur 0 und 300 °K stimmen gut mit experimentellen Ergebnissen uberein.
148 citations
TL;DR: The heat capacity of single crystals of magnesium oxide has been measured in the temperature range 3 to 270 $^{o}$K with estimated accuracies of $\pm $0$\cdot $5% for 10 20 $€ o}$k as mentioned in this paper.
Abstract: The heat capacity of single crystals of magnesium oxide has been measured in the temperature range 3 to 270 $^{o}$K with estimated accuracies of $\pm $0$\cdot $5% for 10 20 $^{o}$K. Reliable results were not obtained below 10 $^{o}$K because of desorption of helium exchange gas in the calorimeter vessel. With the assumption that the effect of anharmonicity of the lattice vibrations may be neglected for T < $\frac{1}{3}\Theta \_{D}$, the experimental results have been analyzed to obtain a number of properties of an effective harmonic frequency spectrum of magnesium oxide. In particular, several negative moments, three even positive moments, and the coefficients of the first three terms in the low-frequency expansion have been calculated. From the low-frequency expansion the apparent Debye characteristic temperature at 0 degrees K ($\Theta \_{0}$) is calculated to be 946 $\pm $ 4 degrees K, in good agreement with the measured elastic constants ($\Theta $ (elastic) = 949 $^{o}$K). The zero-point energy is found to be 3455 $\pm $ 25 cal mole$^{-1}$ deg$^{-1}$; it is pointed out that zero-point energy will cause some anharmonic effects even at the lowest temperatures. A comparison with the heat capacities and elastic constants of the alkali halides suggests that the interatomic forces in magnesium oxide may be rather similar to those in lithium fluoride. The difference between the present heat capacity results and earlier results of Giauque & Archibald (1937) for small particles of magnesium oxide is much larger than that predicted by theoretical estimates of the effect of particle size on the heat capacity of solids. A simple theoretical approximation is derived for the change of $\Theta _{\infty}$ with particle size; here again the experimental change is found to be much larger.
98 citations
01 Mar 1967
TL;DR: Inelastic neutron scattering from magnesium oxide at room temperature has been measured and the frequencies of 656 phonons with wave vectors in mirror planes deduced in this paper, in good agreement with dispersion relations calculated on the basis of a shell model, the parameters of which were obtained from independent measurements of the elastic constants, dielectric constants and infra-red dispersion frequency.
Abstract: Inelastic neutron scattering from magnesium oxide at room temperature has been measured and the frequencies of 656 phonons with wave vectors in mirror planes deduced. The results are shown to be in good agreement with dispersion relations calculated on the basis of a shell model, the parameters of which were obtained from independent measurements of the elastic constants, dielectric constants and infra-red dispersion frequency.
94 citations
TL;DR: In this article, the equations of motion in the dipole approximation for the normal modes of vibration of a crystal with polarizable ions are expanded by the method of long waves and separation of the macroscopic electric field.
Abstract: The equations of motion, in the dipole approximation, for the normal modes of vibration of a crystal with polarizable ions, are expanded by the method of long waves and separation of the macroscopic electric field. The elastic and dielectric constants are then obtained in terms of the interactions between the ions and the electronic dipole moments. The formulae are simplified for diagonally cubic crystals and explicit expressions deduced for the elastic constants of crystals having the sodium chloride, caesium chloride, and zinc blende structures. The theory is then extended to include the quadrupole moments of the electronic charge distribution and the elastic and dielectric constants obtained.
67 citations