On the nature of the excess heat capacity of mixing |
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| Authors: | Artur Benisek Edgar Dachs |
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| Institution: | 1.Materialforschung und Physik,Universit?t Salzburg,Salzburg,Austria |
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| Abstract: | The excess vibrational entropy (ΔS
vibex) of several silicate solid solutions are found to be linearly correlated with the differences in end-member volumes (ΔV
i
) and end-member bulk moduli (Δκ
i
). If a substitution produces both, larger and elastically stiffer polyhedra, then the substituted ion will find itself in
a strong enlarged structure. The frequency of its vibration is decreased because of the increase in bond lengths. Lowering
of frequencies produces larger heat capacities, which give rise to positive excess vibrational entropies. If a substitution
produces larger but elastically softer polyhedra, then increase and decrease of mean bond lengths may be similar in magnitude
and their effect on the vibrational entropy tends to be compensated. The empirical relationship between ΔS
vibex, ΔV
i
and Δκ
i
, as described by ΔS
vibex = (ΔV
i
+ mΔκ
i
)f, was calibrated on six silicate solid solutions (analbite–sanidine, pyrope–grossular, forsterite–fayalite, analbite–anorthite,
anorthite–sanidine, CaTs–diopside) yielding m = 0.0246 and f = 2.926. It allows the prediction of ΔS
vibex behaviour of a solid solution based on its volume and bulk moduli end-member data. |
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| Keywords: | |
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