Abstract
The heat capacities of Al, Si ordered alkali feldspars of different Na, K compositions were calculated using the density functional theory. The effect of the Na, K distribution, if random, ordered or clustered, on the resulting heat capacity was investigated on different cells with Ab50Or50 composition. For all compositions and distributions studied, the excess heat capacity of mixing is positive at low temperatures with a maximum at ~60 K. This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K. The amount of the excess heat capacity of Ab50Or50, however, depends on the Na, K distribution. Best agreement with measured excess heat capacities is achieved, if the distribution of Na and K is either ordered or clustered. The positive excess heat capacities can be attributed to a strong softening of the acoustic and the lowest optical modes related to a strong increase of Na–O bond lengths in samples with intermediate compositions. The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data. Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes.Electronic supplementary materialThe online version of this article (doi:10.1007/s00269-014-0715-8) contains supplementary material, which is available to authorized users.
Highlights
The heat capacity of solid solutions when plotted as a function of composition often deviates from linear behaviour at low temperatures
If the non-lattice contributions are not present or can be neglected, as it is the case with the alkali feldspars, only excess vibrational entropies are produced by the excess heat capacities
Excess vibrational entropies may be in the order of the configurational entropy and may have large effects on phase stability calculations
Summary
The heat capacity of solid solutions when plotted as a function of composition often deviates from linear behaviour at low temperatures. Bond softening increases the vibrational entropy because frequencies of lattice vibrations are shifted to lower values causing an increase in heat capacity and entropy, whereas bond stiffening has the opposite effect (Van de Walle and Ceder 2002). Mutual substitution of atoms of different size generally results in an increase in bond lengths around the smaller atom (bond softening) and a corresponding decrease around the larger atom (bond stiffening) compared to the bond lengths of the respective end-member structures. One of the both effects, may dominate
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