Skip to main content
SpringerLink
Log in

Thermodynamics of mixing in diopside–jadeite, CaMgSi2O6–NaAlSi2O6, solid solution from static lattice energy calculations

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

Abstract

Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have been performed for a set of 800 different structures in a 2 × 2 × 4 supercell of C2/c diopside with compositions between diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273–2,023 K and to calculate a temperature–composition phase diagram. The simulations predict the order–disorder transition in omphacite at 1,150 ± 20°C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433–440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1–M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral 83:419–433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600°C.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Angel RJ, Carpenter MA, Finger LW (1990) Structural variation associated with compositional variation and order–disorder behavior in anorthite-rich feldspars. Am Mineral 75:150–162

    Google Scholar 

  • Bass JD (1995) Elasticity of minerals, glasses, and melts. In: Ahrens T (ed) Mineral physics and crystallography. A handbook of physical constants. (AGU Reference Shelf 2) American Geophysical Union, Washington, D.C., pp 45–63

    Google Scholar 

  • Becker U, Fernandez-Gonzalez A, Prieto M, Harrison R, Putnis A (2000) Direct calculation of thermodynamic mixing properties of the barite/celestite solid solution from molecular principles. Phys Chem Miner 27:291–300

    Article  Google Scholar 

  • Boffa Ballaran T, Carpenter MA, Domeneghetti MC, Tazzoli V (1998) Structural mechanisms of solid solution and cation ordering in augite–jadeite pyroxenes: I. A macroscopic perspective. Am Mineral 83:419–433

    Google Scholar 

  • Bosenick A, Dove MT, Myers ER, Palin EJ, Sainz-Diaz CI, Guiton BS, Warren MC, Craig MS (2001a) Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions. Mineral Mag 65:193–219

    Article  Google Scholar 

  • Bosenick A, Dove MT, Heine V, Geiger CA (2001b) Scaling of the thermodynamic mixing properties in garnet solid solutions. Phys Chem Miner 28:177–187

    Article  Google Scholar 

  • Brenker FE, Müller WF, Brey GP (2003) Variation of antiphase domain size in omphacite: a tool to determine the temperature–time history of eclogites revisited. Am Mineral 88:1300–1311

    Google Scholar 

  • Burton BP, Davidson PM (1988) Short-range order and frustration in omphacite: comparison of three CVM approximations. Phys Chem Miner 15:570–578

    Article  Google Scholar 

  • Cameron M, Sueno S, Prewitt CT, Papike JJ (1973) High-temperature crystal chemistry of acmite, diopside, hedenbergite, jadeite, spodumene, and ureyite. Am Mineral 58:594–618

    Google Scholar 

  • Carpenter MA (1981) Time–temperature–transformation (TTT) analysis of cation disordering in omphacite. Contrib Mineral Petrol 78:433–440

    Article  Google Scholar 

  • Carpenter MA, Dmeneghetti MC, Tazzolli V (1990) Application of Landau theory to cation ordering in omphacite I: equilibrium behaviour. Eur J Mineral 2:7–18

    Google Scholar 

  • Cohen RE, Burnham CW (1985) Energetics of ordering in aluminous pyroxenes. Am Mineral 70:559–567

    Google Scholar 

  • Connolly JWD, Williams AR (1983) Density-functional theory applied to phase transformations in transition-metall alloys. Phys Rev B 27:5169–5172

    Article  Google Scholar 

  • Dachs E, Geiger CA (2006) Heat capacities and entropies of mixing of pyrope–grossular (Mg3Al2Si3O12–Ca3Al2Si3O12) garnet solid solutions: a low-temperature calorimetric and a thermodynamic investigation. Am Mineral 91:894–906

    Article  Google Scholar 

  • Davidson PM, Burton BP (1987) Order–disorder in omphacitic pyroxenes; a model for coupled substitution in the point approximation. Am Mineral 72:337–344

    Google Scholar 

  • Dove MT (1993) Introduction to lattice dynamics. Cambridge topics in mineral physics. Cambridge University Press, Cambridge

    Google Scholar 

  • Ferreira LG, Mbaye AA, Zunger A (1988) Chemical and elastic effects on isostructural phase diagrams: the e-G approach. Phys Rev B 37:10547–10570

    Article  Google Scholar 

  • Gale JD (1996) Empirical derivation of interatomic potentials for ionic materials. Philos Mag B 73:3–19

    Article  Google Scholar 

  • Gale JD (1997) GULP—a computer program for the symmetry adapted simulation of solids. J Chem Soc Faraday Trans 93:629–637

    Article  Google Scholar 

  • Gale JD, Rohl AL (2003) The general utility lattice program (GULP). Mol Simul 29:291–341

    Article  Google Scholar 

  • Ganguly J (1973) Activity–composition relation of jadeite in omphacite pyroxene: theoretical deductions. Earth and Planet. Earth Planet Sci Lett 19:145–153

    Article  Google Scholar 

  • Gasparik T (1985) Experimentally determined compositions of diopside–jadeite pyroxene in equilibrium with albite and quartz at 1200–1350°C and 15–34 kbar. Geochim Cosmochim Acta 49:865–870

    Article  Google Scholar 

  • Harlow GE, Brown GE (1980) Low albite: an X-Ray and neutron diffraction study. Am Mineral 65:986–995

    Google Scholar 

  • Haselton HT Jr, Westrum EF Jr (1980) Low-temperature heat capacities of synthetic pyrope, grossular, and pyrope60grossular40. Geochim Cosmochim Acta 44:701–709

    Article  Google Scholar 

  • Hillert M (1998) Phase equilibria, phase diagrams and phase transformations. Cambridge University Press, Cambridge

    Google Scholar 

  • Holland TJB (1983) The experimental determination of activities in disordered and short-range ordered jadeitic pyroxenes. Contrib Miner Petrol 82:214–220

    Article  Google Scholar 

  • Holland TJB, Powell R (1996) Thermodynamics of order–disorder in minerals: II. Symmetric formalism applied to solid solutions. Am Mineral 81:1425–1437

    Google Scholar 

  • Kandelin J, Weidner DJ (1988) The single-crystal elastic properties of jadeite. Phys Earth Planet Int 50:251–260

    Article  Google Scholar 

  • Kushiro I (1969) Clinopyroxene solid solutions formed by reactions between diopside and plagioclase at high pressures. Mineral Soc Am Spec Pap 2:179–191

    Google Scholar 

  • Lavrentiev MY, van Westrenen W, Allan NL, Freeman CL, Purton JA (2006) Simulation of thermodynamic mixing properties of garnet solid solutions at high temperatures and pressures. Chem Geol 225:336–346

    Article  Google Scholar 

  • Levien L, Weidner DJ, Prewitt CT (1979) Elasticity of diopside. Phys Chem Miner 4:105–113

    Article  Google Scholar 

  • Metropolis NI, Rosenbluth AW, Rosenbluth MN, Teller AN, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  Google Scholar 

  • Myers ER, Heine V, Dove MT (1998) Some consequences of Al/Al avoidance in the ordering of Al/Si tetrahedral framework structures. Phys Chem Miner 25:457–464

    Article  Google Scholar 

  • Nakamura D, Banno S (1997) Thermodynamic modelling of sodic pyroxene solid-solution and its application in a garnet–omphacite–kyanite–coesite geothermobarometer for UHP metamorphic rocks. Contrib Mineral Petrol 130:93–102

    Article  Google Scholar 

  • Patel A, Price GD, Mendelsson MJ (1991) A computer-simulation approach to modeling the structure, thermodynamics and oxygen isotope equilibria of silicates. Phys Chem Miner 17:690–699

    Article  Google Scholar 

  • Rodehorst U, Geiger CA, Armbruster T (2002) The crystal structures of grossular and spessartine between 100 and 600 K and the crystal chemistry of grossular–spessartine solid solutions. Am Mineral 87:542–549

    Google Scholar 

  • Rossi G, Smith DC, Ungaretti L, Domeneghetti MC (1983) Crystal-chemistry and cation ordering in the system diopside–jadeite: a detailed study by crystal structure refinement. Contrib Mineral Petrol 83:247–258

    Article  Google Scholar 

  • Sainz-Diaz CI, Hernandez-Laguna A, Dove MT (2001) Modeling of dioctahedral 2:1 phyllosilicates by means of transferable empirical potentials. Phys Chem Miner 28:130–141

    Article  Google Scholar 

  • Sanchez JM, Ducastelle F, Gratias D (1984) Generalized cluster description of multicomponent systems. Physica 128A:334–350

    Google Scholar 

  • Sanders MJ, Leslie M, Catlow CR (1984) Interatomic potentials for SiO2. J Chem Soc Chem Commun 19:1271–1273

    Article  Google Scholar 

  • Swainson IP, Dove MT, Schmahl WW, Putnis A (1992) Neutron diffraction study of the akermanite–gehlenite solid solution series. Phys Chem Miner 19:185–195

    Article  Google Scholar 

  • Vinograd VL (2002a) Thermodynamics of mixing and ordering in the diopside–jadeite system: I. A CVM model. Mineral Mag 66:513–536

    Article  Google Scholar 

  • Vinograd VL (2002b) Thermodynamics of mixing and ordering in the diopside–jadeite system: II. A polynomial fit to the CVM results. Mineral Mag 66:537–545

    Article  Google Scholar 

  • Vinograd VL, Sluiter MHF (2006) Thermodynamics of mixing in pyrope–grossular, Mg3Al2Si3O12–Ca3Al2Si3O12, solid solution from lattice dynamics calculations and Monte Carlo simulations. Am Mineral 91:1815–1830

    Article  Google Scholar 

  • Vinograd VL, Sluiter MHF, Winkler B, Putnis A, Gale JD (2004) Thermodynamics of mixing and ordering in silicates and oxides from static lattice energy and ab initio calculations. In: Warren M, Oganov A, Winkler B (eds) First-principles simulations: perspectives and challenges in mineral sciences (Deutsche Gesellschaft für Kristallographie. Berichte aus Arbeitskreisen der DFK) 14, pp 143–151

  • Vinograd VL, Winkler B, Putnis A, Kroll H, Milman V, Gale JD, Fabrichnaya OB (2006) Thermodynamics of pyrope–majorite, Mg3Al2Si3O12–Mg4Si4O12, solid solution from atomistic model calculations. Mol Simul 32:85–99

    Article  Google Scholar 

  • Vinograd VL, Burton BP, Gale JD, Allan NL, Winkler B (2007a) Activity–composition relations in the system CaCO3–MgCO3 predicted from static structure energy calculations and Monte Carlo simulations. Geochim Cosmochim Acta 71:974–983

    Article  Google Scholar 

  • Vinograd VL, Perchuk LL, Gerya TV, Putnis A, Winkler B, Gale JD (2007b) Order/disorder phase transition in cordierite and its possible relationship to the development of symplectite reaction textures in granulites. Petrology 15(5):427–440

    Article  Google Scholar 

  • Warren MC, Dove MT, Myers ER, Bosenick A, Palin EJ, Sainz-Diaz CI, Guiton BS (2001) Monte Carlo methods for the study of cation ordering in minerals. Mineral Mag 65:221–248

    Article  Google Scholar 

  • Winkler B, Dove MT, Leslie M (1991) Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. Am Mineral 76:313–331

    Google Scholar 

  • Wood BJ, Holland TJB, Newton RC, Kleppa OJ (1980) Thermochemistry of jadeite–diopside pyroxenes. Geochim Cosmochim Acta 44:1363–1371

    Article  Google Scholar 

Download references

Acknowledgments

The support of the Deutsche Forschungsgemeinschaft (grant Wi 1232/27-1) is gratefully acknowledged. JDG thanks the Government of Western Australia for support through a Premier’s Research Fellowship.

Author information

Authors and Affiliations

  1. Institute of Geosciences, University of Frankfurt, Altenhöferallee 1, 60438, Frankfurt, Germany

    Victor L. Vinograd & Björn Winkler

  2. Nanochemistry Research Institute, Department of Applied Chemistry, Curtin University of Technology, PO Box U1987, Perth, 6845, WA, Australia

    Julian D. Gale

Authors
  1. Victor L. Vinograd
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julian D. Gale
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Björn Winkler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Victor L. Vinograd.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vinograd, V.L., Gale, J.D. & Winkler, B. Thermodynamics of mixing in diopside–jadeite, CaMgSi2O6–NaAlSi2O6, solid solution from static lattice energy calculations. Phys Chem Minerals 34, 713–725 (2007). https://doi.org/10.1007/s00269-007-0189-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00269-007-0189-z

Keywords

Search

Navigation