Skip to main content
SpringerLink
Log in

Pressure and temperature dependence of the single crystal elastic moduli of the cubic perovskite KMgF3

  • Published:
Physics and Chemistry of Minerals Aims and scope Submit manuscript

Abstract

The elastic moduli (c) of single crystal KMgF3 have been determined by the ultrasonic pulse superposition technique as a function of temperature from T=298−550 K, and as a function of pressure from P=1 bar−2.5 kbar. Room temperature values of the elastic moduli and their temperature derivatives are consistent with Reshchikova's (1969) values. Comparison with the data for SrTiO3 indicates that, for most of the moduli, 1/c(∂c/∂T) P and (∂c/∂P) T are very similar for the fluoride-oxide analogue pair, KMgF3-SrTiO3. Values of (∂c/∂P) T for KMgF3 are calculated from a simple central force model using parameters determined for KF and are in good agreement with the measured values. The bulk sound velocity-mean atomic weight relationship, v ф M 1/2=constant, is well obeyed by the fluoroperovskites; comparison with the perovskite oxide data on a log-log plot of v ф versus M leads to a value of 70% for the relative effective charge of the oxides with respect to the fluorides.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. New York: Dover Publications 1965

    Google Scholar 

  • Aleksandrov, K.S., Reshchikova, L.M., Beznosikov, B.V.: Behaviour of the elastic constants of KMnF3 single crystals near the transition of puckering. Phys. Status. Solidi 18, K17-K20 (1966)

    Google Scholar 

  • Anderson, D.L.: A seismic equation of state. Geophys. J. Roy. Astron. Soc. 13, 9–30 (1967)

    Google Scholar 

  • Anderson, D.L., Anderson, O.L.: The bulk modulus-volume relationship for oxides. J. Geophys. Res. 75, 3494–3500 (1970)

    Google Scholar 

  • Anderson, O.L.: Patterns in elastic constants of minerals important to geophysics. In: The Nature of the Solid Earth, Robertson, E.C. (ed.). New York: McGraw-Hill 1972, Chapt. 21, pp. 575–613

    Google Scholar 

  • Anderson, O.L., Liebermann, R.C.: Equations for the elastic constants and their pressure derivatives for three cubic lattices and some geophysical applications. Phys. Earth Planet. Inter. 3, 61–85 (1970)

    Google Scholar 

  • Anderson, O.L., Nafe, J.E.: The bulk modulus-volume relationship for oxide compounds and related geophysical problems. J. Geophys. Res. 70, 3951–3963 (1965)

    Google Scholar 

  • Anderson, O.L., Soga, N.: A restriction to the law of corresponding states. J. Geophys. Res. 72, 5754–5757 (1967)

    Google Scholar 

  • Beattie, A.G., Samara, G.A.: Pressure dependence of the elastic constants of SrTiO3. J. Appl. Phys. 42, 2376–2381 (1971)

    Google Scholar 

  • Beckman, O., Knox, K.: Magnetic properties of KMnF3. I Crystallographic Studies. Phys. Rev. 121, 376–380 (1961)

    Google Scholar 

  • Bell, R.O., Rupprecht, G.: Elastic constants of strontium titanate. Phys. Rev. 129, 90–94 (1963)

    Google Scholar 

  • Bevington, P.R.: Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill 1969

    Google Scholar 

  • Cohen, A.J., Gordon, R.G.: Theory of the lattice energy, equilibrium structure, elastic constants, and pressure-induced phase transitions in alkali-halide crystals. Phys. Rev. 12B, 3228–3241 (1975)

    Google Scholar 

  • Cook, R.K.: Variation of elastic constants and static strains with hydrostatic pressure: a method for calculation from ultrasonic measurements. J. Acoust. Soc. Am. 29, 445–449 (1957)

    Google Scholar 

  • Cowley, R.A.: Lattice dynamics and phase transitions of strontium titanate. Phys. Rev. 134A, 981–997 (1964)

    Google Scholar 

  • Davies, G.F.: The estimation of elastic properties from analogue compounds. Geophys. J. Roy. Astron. Soc. 44, 625–647 (1976)

    Google Scholar 

  • Davies, G.F., O'Connell, R.J.: Transducer and bond phase shifts in ultrasonics, and their effects on measured pressure derivatives of elastic moduli. In: High Pressure Research: Applications in Geophysics, Manghnani, M.H. and Akimoto, S. (eds.). New York: Academic Press 1977, pp. 533–562

    Google Scholar 

  • Fischer, M., Perrin, B., Rousseau, M., Zarembowitch, A.: Unusual non-linear elastic behaviour of some ionic crystals. International Conference on Lattice Dynamics, Paris: Flammarion Médecine Sciences 1978

    Google Scholar 

  • Frisillo, A.L., Barsch, G.R.: Measurement of single-crystal elastic constants of bronzite as a function of pressure and temperature. J. Geophys. Res. 77, 6360–6384 (1972)

    Google Scholar 

  • Gesland, J.Y., Binois, M., Nouet, J.: Constantes elastiques de la fluoperovskite KZnF3. C.R. Acad. Sci. (B) (Paris) 275, 551–552 (1972)

    Google Scholar 

  • Goldschmidt, V.M.: Geochemische Verteilungsgesetze der Elemente VIII. Untersuchungen über Bau und Eigenschaften von Krystallen. Skr. Nor. Vidensk.-Akad. Oslo, I, Math.-Naturvidensk. Klasse 2(8), 1–156 (1927)

    Google Scholar 

  • Ito, E.: The absence of oxide mixture in high-pressure phases of Mg-silicates. Geophys. Res. Lett. 4, 72–74 (1977)

    Google Scholar 

  • Johnson, Q.C., Templeton, P.H.: Madelung constants for several structures. J. Chem. Phys. 34, 2004–2007 (1961)

    Google Scholar 

  • Jones, L.E.A.: High temperature elasticity of fluoride and oxide analogues. Ph. D. thesis, A.N.U., Canberra, Australia (1976a)

    Google Scholar 

  • Jones, L.E.A.: High temperature behaviour of the elastic moduli of LiF and NaF: Comparison with MgO and CaO. Phys. Earth Planet. Inter. 13, 105–118 (1976b)

    Google Scholar 

  • Jones, L.E.A.: High temperature elasticity of rutile-structure MgF2. Phys. Chem. Minerals 1, 179–197 (1977a)

    Google Scholar 

  • Jones, L.E.A.: High temperature elasticity of the fluorite-structure compounds CaF2, SrF2 and BaF2. Phys. Earth Planet. Inter. 15, 77–89 (1977b)

    Google Scholar 

  • Jones, L.E.A., Liebermann, R.C.: Elastic and thermal properties of fluoride and oxide analogues in the rocksalt, fluorite, rutile and perovskite structures. Phys. Earth Planet. Inter. 9, 101–107 (1974)

    Google Scholar 

  • Julliard, J., Nouet, J.: Analyse radiocristallographique de la distorsion magnetostrictive dans les antiferromagnetiques KCoF3, RbCoF3 et TlCoF3. Rev. Phys. Appl. 10, 325–329 (1975)

    Google Scholar 

  • Liebermann, R.C.: Elasticity of pyroxene-garnet and pyroxene-ilmenite phase transformations in germanates. Phys. Earth Planet. Inter. 8, 361–374 (1974)

    Google Scholar 

  • Liebermann, R.C.: Elasticity of olivine (α), beta (β) and spinel (γ) polymorphs of germanates and silicates. Geophys. J. Roy. Astron. Soc. 42, 899–929 (1975)

    Google Scholar 

  • Liebermann, R.C., Jones, L.E.A., Ringwood, A.E.: Elasticity of aluminate, titanate, stannate and germanate compounds with the perovskite structure. Phys. Earth Planet. Inter. 14, 165–178 (1977)

    Google Scholar 

  • Liu, L.G.: Silicate perovskite from phase transformations of pyrope-garnet at high pressure and temperature. Geophys. Res. Lett. 1, 277–280 (1974)

    Google Scholar 

  • Liu, L.G.: Post-oxide phases of forsterite and enstatite. Geophys. Res. Lett. 2, 417–419 (1975a)

    Google Scholar 

  • Liu, L.G.: Post-oxide phases of olivine and pyroxene and mineralogy of the mantle. Nature (London) 258, 510–512 (1975b)

    Google Scholar 

  • Liu, L.G.: Orthorhombic perovskite phases observed in olivine, pyroxene and garnet at high pressures and temperatures. Phys. Earth Planet. Inter. 11, 289–298 (1976)

    Google Scholar 

  • Lytle, F.W.: X-ray diffractometry of low-temperature phase transformations in strontium titanate. J. Appl. Phys. 35, 2212–2215 (1964)

    Google Scholar 

  • McSkimin, H.J.: Pulse superposition method for measuring ultrasonic wave velocities in solids. J. Acoust. Soc. Am. 33, 12–16 (1961)

    Google Scholar 

  • Melcher, R.L., Bolef, D.I.: Ultrasonic propagation in RbMnF3. I Elastic properties. Phys. Rev. 178, 864–873 (1969)

    Google Scholar 

  • Mitskevich, V.V.: Temperature coefficients of elastic constants of alkali halide crystals. Sov. Phys. Solid State 6, 2404–2409 (1965)

    Google Scholar 

  • Naimon, E.R.: Elastic constants of the perovskite RbMnF3 using a Born model. Phys. Rev. B9, 737–740 (1974)

    Google Scholar 

  • Naimon, E.R., Granato, A.V.: Third-order elastic constants of RbMnF3. Phys. Rev. B7, 2091–2094 (1973)

    Google Scholar 

  • Nouet, J., Plicque, F.: Propagation d'ondes ultrasonores au voisinage de la temperature de Neel dans la perovskite antiferromagnetique RbCoF3. International Congress on Acoustics, Budapest, Vol. 4, 173–174 (1971)

  • Reshchikova, L.M.: Elastic properties of a KMgF3 single crystal. Sov. Phys. Solid State 10, 2019–2020 (1969)

    Google Scholar 

  • Ringwood, A.E.: Mineralogical constitution of the deep mantle. J. Geophys. Res. 67, 4005–4010 (1962)

    Google Scholar 

  • Ringwood, A.E.: Composition and Petrology of the Earth's Mantle. New York: McGraw-Hill 1975

    Google Scholar 

  • Roberts, R.W., Smith, C.S.: Ultrasonic parameters in the Born model of the sodium and potassium halides. J. Phys. Chem. Solids 31, 619–634 (1970a)

    Google Scholar 

  • Roberts, R.W., Smith, C.S.: Ultrasonic parameters in the Born model of the rubidium halides. J. Phys. Chem. Solids 31, 2397–2400 (1970b)

    Google Scholar 

  • Rosenberg, H.M., Wigmore, J.K.: The elastic constants of potassium magnesium fluoride. Phys. Lett. 24A, 317 (1967)

    Google Scholar 

  • Rousseau, M., Gesland, J.Y., Julliard, J., Nouet, J., Zarembowitch, J., Zarembowitch, A.: Crystallographic, elastic, and Raman scattering investigations of structural phase transitions in RbCdF3 and TlCdF3. Phys. Rev. B12, 1579–1590 (1975)

    Google Scholar 

  • Rousseau, M., Nouet, J., Zarembowitch, A.: Interatomic force constants studies of AMF3 perovskite-type crystals. J. Phys. Chem. Solids 35, 921–926 (1974)

    Google Scholar 

  • Shankland, T.J.: Velocity-density systematics: Derivation from Debye theory and the effect of ionic size. J. Geophys. Res. 77, 3750–3758 (1972)

    Google Scholar 

  • Shannon, R.D., Prewitt, C.T.: Effective ionic radii in oxides and fluorides. Acta Cryst. B25, 925–946 (1969)

    Google Scholar 

  • Shannon, R.D., Prewitt, C.T.: Revised values of effective ionic radii. Acta Cryst. B26, 1046–1048 (1970)

    Google Scholar 

  • Smith, C.S., Cain, L.S.: Born model repulsive interactions in the alkali halides determined from ultrasonic data. J. Phys. Chem. Solids 36, 205–209 (1975)

    Google Scholar 

  • Stirling, W.G., Cowley, R.A.: The lattice dynamics of strontium titanate. J. Phys. (Paris), Colloq. C2 33, 135–137 (1972)

    Google Scholar 

  • Teaney, D.T., Moruzzi, V.L., Argyle, B.E.: Critical point of the cubic antiferromagnet RbMnF3. J. Appl. Phys. 37, 1122–1123 (1966)

    Google Scholar 

  • Waterman, P.C.: Orientation dependence of elastic waves in signle crystals. Phys. Rev. 113, 1240–1253 (1959)

    Google Scholar 

  • Wyckoff, R.W.G.: Crystal Structures (2nd edition), Vol. 2, New York: Interscience 1963

    Google Scholar 

Download references

Author information

Author notes

  1. Leonie E. A. Jones

    Present address: Department of Geology and Geophysics, University of Wisconsin, 53706, Madison, WI, U.S.A.

Authors and Affiliations

  1. Research School of Earth Sciences, The Australian National University, 2600, Canberra, Australia

    Leonie E. A. Jones

Authors
  1. Leonie E. A. Jones
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jones, L.E.A. Pressure and temperature dependence of the single crystal elastic moduli of the cubic perovskite KMgF3 . Phys Chem Minerals 4, 23–42 (1979). https://doi.org/10.1007/BF00308357

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00308357

Keywords

Search

Navigation