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Kinetic rate laws derived from order parameter theory IV: Kinetics of Al,Si disordering in Na-feldspars


The kinetic rate laws of Al-Si disordering under dry conditions (T = 1353K, 1253 K, 1223 K, 1183 K) and in the presence of water (p = 1 kbar, T = 1023 K, 1073 K, 1103 K) were studied both experimentally and theoretically. A gradual change of the degree of order was found under dry conditions. For intermediate degrees of order broad distributions of the order parameter Q od occur. The variations of Q od are correlated with structural modulations as observed in the transmission electron microscope. The time evolution of the mean value of Q od can be well described by the rate law:

$$\frac{{dQ_{od} }}{{dt}} = - \frac{\gamma }{{RT}}\exp \sum\limits_{i = 1}^n {X_i^2 } \left[ {\frac{{ - (G_a^0 + \varepsilon (\Delta Q_{od} )^2 )}}{{RT}}} \right]\frac{{dG}}{{dQ_{od} }}$$

with the excess Gibbs energy G and G a 0 = 433.8 kJ/mol, ɛ= -27.4 kJ/mol, γ = 1.687 · 1014 h −1.

Under wet conditions, two processes were found which occur simultaneously. Firstly, some material renucleated with the equilibrium degree of order. Secondly, the bulk of the material transformed following the same rate law as under dry conditions but with the reduced activation energy G a 0 = 332.0 kJ/mol and ɛ = -43.0 kJ/ mol, γ = 1.047 · 1013 h−1. The applicability of the kinetic theory is discussed and some ideas for the analysis of geological observations are evolved.

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  1. Bernotat-Wulf H, Bertelmann D, Wondratschek H (1988) The annealing behaviour of Eifel sanidine (Volkesfeld) III. The influence of the sample surface and sample size on the order-disorder transformation rate. N Jb. Miner. Mh 11:503–515

  2. Carpenter MA, Domenighetti MC, Tazzoli V (1990) Application of Landau theory to cation ordering in omphacite II: kinetic behaviour. Eur J Mineral 2:19–28

  3. Carpenter MA, Salje E (1989) Time-dependent Landau theory for order/disorder processes in minerals. Mineral Mag 53:483–504

  4. Güttler B, Salje E, Putnis A (1989) Structural states of Mg cordierite III: Infrared spectroscopy and the nature of the hexagonal-modulated transition. Phys Chem Minerals 16:365–375

  5. Harris MJ, Salje EKH, Güttler BK, Carpenter MA (1989) Structural states of natural potassium feldspar: an infrared spectroscopic study. Phys Chem Minerals 16:649–658

  6. McKie D, McConnell JDC (1963) The kinetics of the low-high transformation in albite under dry conditions. Mineral Mag 33:581–588

  7. Müller G (1970) Der Ordnungs-Unordnungs-Übergang in getemperten Mikroklinen und Albiten. Z Kristallogr 132:212–227

  8. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical recipies. Cambridge University Press, Cambridge

  9. Rachinger WA (1948) as quoted by A. Guinier (1963) X-Ray Diffraction, Freeman, San Francisco

  10. Salje E (1988) Kinetic rate laws as derived from order parameter theory I: theoretical concepts. Phys Chem Minerals 15:336–348

  11. Salje E (1989) Towards a better understanding of time-dependent geological processes: kinetics of structural transformations in minerals. Terra Nova 1:35–44

  12. Salje E (1990) Phase transitions in ferroelastic and co-elastic crystals. Cambridge University Press, Cambridge

  13. Salje E, Güttler B, Ormerod C (1989) Determination of the degree of Al,Si order in kinetically disordered albite using hard mode infrared spectroscopy. Phys Chem Minerals 16:576–581

  14. Salje E, Kroll H (1991) Kinetic rate laws derived from order parameter theory III: Al,Si ordering in sanidine. Phys Chem Minerals 17:563–568

  15. 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

  16. Salje E, Wruck B (1988) Kinetic rate laws derived from order parameter theory II: Interpretation of experimental data by Laplace transformation, the relaxation spectrum, and the kinetic gradient coupling between two order parameters. Phys Chem Minerals 16:140–147

  17. Schneider TR (1957) Röntgenographische und optische Untersuchung der Umwandlung Albit-Analbit-Monalbit. Z Kristallogr 109:245–271

  18. Yund Ra, Tullis J (1980) The effect of water, pressure, and strain on Al,Si order-disorder kinetics in feldspars. Contrib Mineral Petrol 72:297–302

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Wruck, B., Salje, E.K.H. & Graeme-Barber, A. Kinetic rate laws derived from order parameter theory IV: Kinetics of Al,Si disordering in Na-feldspars. Phys Chem Minerals 17, 700–710 (1991).

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  • Transmission Electron Microscope
  • Activation Energy
  • Gibbs Energy
  • Mineral Resource
  • Material Processing