Pressure Dependence of Elastic Constants and Crystal Stability of Alkali Halides: NaI and KI†

The single crystal elastic constants and their first and second pressure derivatives have been measured ultrasonically at 298 °K for NaI and KI. Fair agreement with lattice theoretical data calculated from an interaction potential composed of Coulomb, van der Waals and first and second nearest neighbor repulsive forces is found. On the basis of this model it is possible to explain semi-quantitatively that the first pressure derivatives of the elastic constants of all alkali halides depend almost exclusively on the cation. The convergence of the Taylor expansion of the elastic constants with respect to pressure is investigated theoretically. On the basis of Born's stability criteria the relations between the pressure dependence of the shear moduli c44 and cS to the B1-B2 transition and the melting curve are investigated. Die elastischen Konstanten sowie ihre ersten und zweiten Druckkoeffizienten wurden fur NaI- und KI-Einkristalle mittels Ultraschallverfahren bei 298 °K gemessen. Die Uberein-stimmung mit theoretischen Werten, die unter der Annahme von Coulomb-, van der Waals-und Abstosungskraften zwischen nachsten und ubernachsten Nachbarn berechnet wurden, ist befriedigend. Auf der Grundlage dieses Modells last sich qualitativ gut erklaren, das fur alle Alkalihalogenide die ersten Druckkoeffizienten der elastischen Konstanten praktisch nur vom Kation abhangen. Die Konvergenz der Reihenentwicklung der elastischen Konstanten bezuglich des Drucks wird theoretisch untersucht. Auf der Grundlage der Bornschen Stabilitatskriterien werden die Beziehungen zwischen der Druckabhangigkeit der beiden Schubmoduln c44 und cS und der B1-B2 Phasenumwandlung, sowie der Schmelzpunktkurve untersucht.

[1]  Z. Chang,et al.  Nonlinear Pressure Dependence of Elastic Constants and Fourth-Order Elastic Constants of Cesium Halides , 1967 .

[2]  C. Pistorius.  Effect of Pressure on the Melting Points of the Sodium Halides , 1966 .

[3]  Z. Chang,et al.  Pressure Dependence of Elastic Constants of Cesium Halides , 1967, October 1.

[4]  M. Figeac.  XXIII. Account of a new species of insect of the genus corynetes of Fabricius, observed in an Egyptian mummy at Grenoble , 1814 .

[5]  C. Pistorius.  Polymorphic transitions of the alkali bromides and iodides at high pressures to 200°C , 1965 .

[6]  M. Blackman.  On negative volume expansion coefficients , 1958 .

[7]  R. W. Roberts.  Ultrasonic parameters in the born model of the sodium and potassium halides , 1969 .

[8]  J. Fontanella,et al.  Low temperature grüneisen parameter of RbI from elasticity data , 1970 .

[9]  R. A. Miller,et al.  Pressure derivatives of the elastic constants of LiF and NaF , 1964 .

[10]  G. Barsch.  Adiabatic, Isothermal, and Intermediate Pressure Derivatives of the Elastic Constants for Cubic Symmetry. I. Basic Formulae , 1967 .

[11]  J. G. Collins,et al.  Thermal expansion of solids , 1964 .

[12]  O. Anderson,et al.  Equations for the elastic constants and their pressure derivatives for three cubic lattices and some geophysical applications , 1970 .

[13]  Percy Williams Bridgman,et al.  The physics of high pressure , 1931 .

[14]  H. Mao,et al.  Pressure‐Induced Phase Transformation in NaCl , 1968 .

[15]  S. Haussühl.  Thermo-elastische Konstanten der Alkalihalogenide vom NaCl-Typ , 1960 .

[16]  J. Thompson.  XV. Instability and melting of the alkali halides , 1953 .

[17]  E. H. Bogardus.  Third‐Order Elastic Constants of Ge, MgO, and Fused SiO2 , 1965 .

[18]  P. W. Bridgman.  The Compression of 46 Substances to 50,000 kg/cm , 1940 .

[19]  D. Schuele,et al.  Pressure derivatives of the elastic constants of NaCl and KCl at 295°K and 195°K , 1965 .

[20]  M. P. Tosi,et al.  Ionic sizes and born repulsive parameters in the NaCl-type alkali halides—II: The generalized Huggins-Mayer form☆ , 1964 .

[21]  M. Born.  Thermodynamics of Crystals and Melting , 1939 .

[22]  G. White.  The thermal expansion of alkali halides at low temperatures , 1965, Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences.

[23]  M. P. Tosi,et al.  Cohesion of Ionic Solids in the Born Model , 1964 .

[24]  H. J. Mcskimin,et al.  Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in Solids , 1961 .

[25]  B. Yates,et al.  Thermal Expansion of Alkali Halides at Low Temperatures , 1962 .

[26]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[27]  P. Meincke,et al.  The thermal expansion of alkali halides , 1965 .

[28]  C. Pistorius.  Melting curves of the potassium halides at high pressures , 1965 .

[29]  Max Born,et al.  Zur Gittertheorie der Ionenkristalle , 1932 .

[30]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[31]  S. Clark.  Effect of Pressure on the Melting Points of Eight Alkali Halides , 1959 .

[32]  K. S. Krishnan,et al.  The frequencies and the anharmonicities of the normal modes of oscillation of alkali halide crystals - II. Low-frequency acoustic modes , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[33]  L. Pauling.  XXIV. The sizes of ions and their influence on the properties of salt-like compounds , 1928 .

[34]  E. Kellermann.  Theory of the vibrations of the sodium chloride lattice , 1940, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[35]  A. Ruoff,et al.  Pressure Derivatives of the Elastic Constants of NaBr and KF , 1967 .

[36]  H. J. Mcskimin.  Notes and References for the Measurement of Elastic Moduli by Means of Ultrasonic Waves , 1961 .