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54ª Reunião Anual da SBPC – Goiânia, GO – Julho/2002

GEOCIÊNCIAS

CORRELATIONS OFCHEMICAL COMPOSITION AND REFRACTIVE INDICES IN THE GARNET SOLID-SOLUTION SERIES

Joachim Werner Zang¹ (joachim.zang@t-online.de), Warde A. da Fonseca-Zang¹, Regina C. Bueno da Fonseca²
1 – Área de Química, CEFET-GO, Rua 75, 46, Setor Central, 74055-110, Goiânia, GO
2 – Departamento de Matemática, CEFET-GO, Rua 75, 46, Setor Central, 74055-110, Goiânia, GO

Fig. 1: Part of the garnet structure (Grossular) projected on (331), two of eight formula units per unit cell (Z=8)

INTRODUCTION:
The minerals of the garnet group are described with the crystal-chemical formula:
X^[8]₃ Y^[6]₂ [Z^[4]O₄]₃
With:   X = Ca²⁺, Mg²⁺, Fe²⁺, Mn²⁺ etc.
            Y = Al³⁺, Fe³⁺, Cr³⁺, Ti⁴⁺, Mn³⁺, V³⁺, Zr³⁺  etc.
            Z = Si⁴⁺ (also Al³⁺, Fe³⁺ or substitution of [ZO₄] by [OH]₄)
Due to extensive solid-solution, the composition of garnets is described by end-member components. The most important solid-solution groups, with complete miscibility within the groups and limited miscibility between them, are:
Pyralspite group: Pyrope Mg₃Al₂[SiO₄]₃, Almandine Fe²⁺₃Al₂[SiO₄]₃, Spessartine Mn²⁺₃Al₂[SiO₄]₃
Ugrandite group: Uwarowite Ca₃Cr₂[SiO₄]₃, Grossular Ca₃Al₂[SiO₄]₃, Andradite Ca₃Fe³⁺₂[SiO₄]₃

Without chemical analysis it is quite difficult for geoscientists to get information about the proportion of the end member components of a garnet sample. One of the aims of this work was to find out a possibility to estimate the chemical composition of garnets from refractive indices, which are much easier to obtain than chemical analyses.

METHODS:
To get the correlations between chemical composition and refractive indices, 87 garnets have been analyzed with an electron microprobe CAMECA CAMEBAX with 15 kV excitation voltage and 10 nA beam current. As calibration standards were used: Ca, Fe, Si – andradite, K – orthoclase, Al – corundum, V – pure element standard, Cr – chromite, Mn, Ti – alloy of Mn and Ti, Mg – MgO. The refractive indices were determined with a total reflection refractometer (TOPCON) with a yellow filter (maximum transmission at 589 nm), that has been calibrated with an oriented cut of a quartz crystal. The crystal-chemical formulae of these samples as well as 152 data sets of different garnets from literature have been calculated after Deer et al. (1992). The sum of the mass of the cations  (MC) have been determined from these crystal-chemical formulas.

 RESULTS:
The statistical examination show a tendency of raising refractive indices (n) with raising sum of the mass of the cations (MC ) due to the smaller speed of light caused by the higher electron density of the heavier atoms. The two solid solution series of the Pyralspites and the Ugrandites show a different correlation between the two variablesn and MC. In the Pyralspite group the n-values increase much slower with higher MC-values caused by the substitution of the lighter by heavier elements in the eight folded coordinated X-site than in the Ugrandite group, where the substitution is taking place mainly at the octahedral Y-site.

The resulting equations are as follows:
Pyralspite:       MC = 1580.80 n – 2267.53        with a correlation coefficient R² = 0.86
Ugrandite:       MC = 654.63 n – 613.21           with a correlation coefficient R²= 0.86 

CONCLUSIONS:
If the solid solution series (Pyralspite or Ugrandite) is known from appearance and/or geological back-ground information, the composition of the samples could be estimated with these formulas and a X-Y-plot (n : MC), where the data of the ideal en-members and the line of correlation and the line of correlation of the particular group are displayed.

AGÊNCIA FINANCIADORA: CNPq