Thermodynamics Research Center / ThermoML | Journal of Chemical Thermodynamics

ABSTRACT

A calorimetric and thermodynamic study of the (Li1-xNax)FeGe2O6 solid solution with the pyroxene structure was undertaken. The molar heat capacity at constant pressure (Cp,m) for compositions with x = (0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) was measured using a Physical Properties Measurement System at temperatures from 2 K to 300 K and by differential scanning calorimetry between 282 and 870 K (these measurements were performed upon heating as well as upon cooling). Magnetic transitions below 20 K and structural P21/c MC2/c phase transitions at higher temperatures were observed that decrease in temperature with increasing Na/(Na + Li). The P21/cM C2/c transition showed a considerable temperature hysteresis that is largest for LiFeGe2O6 ( 30 K) and decreases with increasing Na/(Na + Li) in the pyroxene. The molar enthalpy and entropy changes associated with the P21/c M C2/c phase transitions, DHtr,m and DStr,m, were determined. They can be described by quadratic and linear functions across the solid solution. A linear correlation between DHtr,m and the square of the volume strain at the transition temperature was established. The P21/c MC2/c phase transition of LiFeGe2O6 is compared to that of a-b quartz, whose Cp,m was also measured. The molar enthalpy of order, DHord,m, was calculated from the calorimetric data. It has a maximum of DHord,m = ( 11.6 +- 1.5)kJ mol 1 for the P21/c MC2/c phase transition of LiFeGe2O6, which is in reasonable agreement with a maximum DHord,m = 9.9 kJ mol 1 calculated using density functional theory. DHord,m vs. T behavior was described using a tricritical Landau model with an a parameter of a = (41.8 +- 1.0)J K 1 mol 1. All properties associated with the P21/c MC2/c phase transition in LiFeGe2O6 can be calculated using this value. The Cp,m behavior at T less than 300 K for each pyroxene composition was decomposed into molar vibrational (Cvib,m) and molar magnetic (Cmag,m) contributions by applying a single-parameter phonon dispersion model. The molar vibrational entropy at 298.15 K, Svib,m 298.15, and the molar magnetic entropy, Smag,m, were also calculated. Both quantities, together, give the molar calorimetric entropy at 298.15 K, Scal,m 298.15. The term calorimetric means that configurational contributions that are non-zero for solid solution compositions are excluded (for the endmember pyroxenes this corresponds to the molar third law entropy, So m). The behavior of Smag,m, Svib,m 298.15 and Scal,m 298.15 as function of Na/(Na + Li) in the pyroxene was described by applying Darkens quadratic formalism (DQF) and a Margules model. Svib,m 298.15 as function of composition is ideal within error, whereas Smag,m shows significant positive deviations from a linear combination of the end members. This leads to positive excess molar magnetic entropies of mixing that can be described by a symmetrical Margules parameter smag,m = (3.7 +- 1.3)J K 1 mol 1. Because solid solutions with Na/(Na + Li) greater than 0.4 have the P21/c MC2/c phase transition below 298.15 K, this results in a discontinuity in Scal,m 298.15 behavior as function of composition at Na/(Na + Li) = 0.5. DQF was applied to model this behavior and the corresponding parameters were retrieved. The entropy of mixing behavior of the (Li,Na)FeGe2O6 solid solution at 298.15 K is characterized by positive excess molar magnetic entropies of mixing onto which entropy changes due to the structural P21/c MC2/c phase transitions are superimposed in the Na-rich part of the binary system. Excess volumes of mixing for the (Li,Na)FeGe2O6 solid solution were calculated from published data and DQF parameters were derived that allow volume as function of temperature and composition to be calculated.