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Thermodynamics of plagioclase II: Temperature evolution of the spontaneous strain at the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition in anorthite

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Abstract

The temperature dependence of the lattice parameters of pure anorthite with high Al/Si order reveals the predicted tricritical behaviour of the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition at T *c =510 K. The spontaneous strain couples to the order parameter Q° as x iS ixQ 2 with S 1xQ =4.166×10−3, S 2xQ =0.771×10−3, S 3xQ =−7.223×10−3 for the diagonal elements. The temperature dependence of Q° is

$$Q^{\text{o}} = \left( {1 - \frac{T}{{510}}} \right)^\beta ,{\text{ }}\beta = \tfrac{{\text{1}}}{{\text{4}}}$$

A strong dependence of T *c , S ixQ and β is predicted for Al/Si disordered anorthite.

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References

  • Adlhart W, Frey F, Jagodzinski H (1980) X-ray and neutron investigations of the \(P\bar 1 - I\bar 1\) transition in pure anorthite. Acta Crystallogr A 36:450–460

    Google Scholar 

  • Aizu K (1970) Determination of the state parameters and formulation of spontaneous strain for ferroelastics. J Phys Soc Japan 28:706–716

    Google Scholar 

  • Bhagavantam S (1966) Crystal symmetry and physical properties. Academic Press, London

    Google Scholar 

  • Borg IY, Smith DK (1969) Calculated X-ray powder patterns for silicate minerals. Geol Soc Amer Mem 122, 896 pp

    Google Scholar 

  • Brown WL, Hoffman W, Laves F (1963) Über kontinuierliche und reversible Transformation des Anorthits (CaAl2Si2O8) zwischen 25 und 350 °C. Naturwissenschaften 50:221

    Article  Google Scholar 

  • Carpenter MA, Ferry JM (1984) Constraints on the thermodynamic mixing properties of plagioclase feldspars. Contrib Mineral Petrol 87:138–148

    Google Scholar 

  • Carpenter MA, McConnell JDC, Navrotsky A (1985) Enthalpies of ordering in the plagioclase feldspar solid solution. Geochim Cosmochim Acta 49:947–966

    Article  Google Scholar 

  • Czank M (1973) Strukturuntersuchungen von Anorthit im Temperaturbereich von 20 °C bis 1,430 °C. Dissertation ETH Zürich

    Google Scholar 

  • Frey F, Jagodzinski H, Prandl W, Yelon WB (1977) Dynamic character of the primitive to body-centered phase transition in anorthite. Phys Chem Minerals 1:227–231

    Article  Google Scholar 

  • Kalus C (1978) Dissertation. Univ. München

  • Kempster CJE, Megaw HD, Radoslovich EW (1962) The structure of anorthite, CaAl2Si2O8. I. Structure analysis. Acta Crystallogr 15:1005–1017

    Article  Google Scholar 

  • Laves F, Czank M, Schulz H (1970) The temperature dependence of the reflection intensities of anorthite (CaAl2Si2O8) and the corresponding formation of domains. Schweiz Mineral Petrogr Mitt 50:519–525

    Google Scholar 

  • Laves F, Goldsmith JR (1954) Long-range-short-range order in calcic phagioclases as a continuous and reversible function of temperature. Acta Crystallogr 7:465–472

    Google Scholar 

  • Nye JF (1957) Physical properties of crystals. Oxford University Press, London

    Google Scholar 

  • Ralston A, Wilf HS (1960) Mathematical methods for digital computers, vol 1. Wiley, New York

    Google Scholar 

  • Salje E (1985) Thermodynamics of sodium feldspar I: Order parameter treatment and strain induced coupling effects. Phys Chem Minerals 12:93–98

    Google Scholar 

  • Salje E (1987) Thermodynamics of plagioclase I: Theory of the \(I\bar 1 - P\bar 1\) phase transition in anorthite and calcium rich plagioclases. Phys Chem Minerals 14:181–188

    Article  Google Scholar 

  • Salje E, Kuscholke B, Wruck B, Kroll H (1985) Thermodynamics of sodium feldspar II: Experimental results and numerical calculations. Phys Chem Minerals 12:99–107

    Google Scholar 

  • Schlenker JL, Gibbs GV, Boisen MB (1978) Strain-tensor components expressed in terms of lattice parameters. Acta Crystallogr. A 34:52–54

    Article  Google Scholar 

  • Staehli JL, Brinkmann D (1974) A nuclear magnetic resonance study of the phase transition in anorthite CaAl2Si2O8. Z Kristallogr 140:360–373

    Google Scholar 

  • Tolédano JC, Tolédano P (1980) Order parameter symmetries and free-energy expansions of purely ferroelastic transitions. Phys Rev B 21:1139–1172

    Article  Google Scholar 

  • Wruck B (1986) Einfluß des Na-Gehaltes und der Al, Si-Fehlordnung auf das thermodynamische Verhalten der Phasenumwandlung \(P\bar 1 - I\bar 1\) in Anorthit. Dissertation Univ Hannover

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Redfern, S.A.T., Salje, E. Thermodynamics of plagioclase II: Temperature evolution of the spontaneous strain at the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition in anorthite. Phys Chem Minerals 14, 189–195 (1987). https://doi.org/10.1007/BF00308224

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