P21/c-C2/c phase transition and mixing properties of the (Li, Na)FeGe2O6 solid solution: A calorimetric and thermodynamic study. (May 2018)

• Record Type: Journal Article
• Authors: Dachs, Edgar; Benisek, Artur; Redhammer, Günther
• Is Part Of: Journal of chemical thermodynamics. Volume 120(2018)
• Page Start: 123
• Page End: 140
• Publication Date: 2018-05
• Subjects: Calorimetry -- Heat capacity -- Standard state entropy and enthalpy of formation from the elements -- P21/c↔C2/c phase transition properties -- (Li, Na)FeGe2O6 -- Thermodynamic mixing properties; Thermodynamics -- Periodicals; Thermochemistry -- Periodicals; Thermodynamique -- Périodiques; Thermochimie -- Périodiques; Thermochemistry; Thermodynamics; Periodicals; 541.369
• DOI: 10.1016/j.jct.2018.01.019
• Languages: English
• ISSNs: 0021-9614

Abstract

Graphical abstract: Highlights: A calorimetric study of the (Li, Na)FeGe2 O6 pyroxene solid solution was undertaken.. The enthalpy and entropy changes due to P 21 /c– C 2/c phase transitions were determined. Heat capacities were separated into vibrational and magnetic contributions. Positive excess magnetic entropies of mixing were observed. Thermodynamic endmember and mixing properties are provided. Abstract: A calorimetric and thermodynamic study of the (Li1- x Na x )FeGe2 O6 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 P 21 / c ↔ C 2/ c phase transitions at higher temperatures were observed that decrease in temperature with increasing Na/(Na + Li). The P 21 / c ↔ C 2/ c transition showed a considerable temperature hysteresis that is largest for LiFeGe2 O6 (∼30 K) and decreases with increasing Na/(Na + Li) in the pyroxene. The molar enthalpy and entropy changes associated with the P 21 / c ↔ C 2/ c phase transitions, Δ H tr, m and Δ S tr, m, were determined. They can be described by quadratic and linear functions across the solid solution. A linear correlation between Δ H tr, m and the square of the volume strain at the transition temperature was established. The P 21 / c ↔ C 2/ c phase transition of LiFeGe2 O6 is compared to that of α-β quartz, whose Cp, m was also measured. The molar enthalpy of order, Δ H ord, m, was calculated from the calorimetric data. It has a maximum of Δ H ord, m = (−11.6 ± 1.5)kJ·mol −1 for the P 21 / c ↔ C 2/ c phase transition of LiFeGe2 O6, which is in reasonable agreement with a maximum Δ H ord, m = −9.9 kJ·mol −1 calculated using density functional theory. Δ H ord, 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 P 21 / c ↔ C 2/ c phase transition in LiFeGe2 O6 can be calculated using this value. The Cp, m behavior at T < 300 K for each pyroxene composition was decomposed into molar vibrational ( C vib, m ) and molar magnetic ( C mag, m ) contributions by applying a single-parameter phonon dispersion model. The molar vibrational entropy at 298.15 K, S vib, m 298.15, and the molar magnetic entropy, S mag, m, were also calculated. Both quantities, together, give the molar calorimetric entropy at 298.15 K, S cal, 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, S o m ). The behavior of S mag, m, S vib, m 298.15 and S cal, m 298.15 as function of Na/(Na + Li) in the pyroxene was described by applying Darkens' quadratic formalism (DQF) and a Margules model. S vib, m 298.15 as function of composition is ideal within error, whereas S mag, 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) > 0.4 have the P 21 / c ↔ C 2/ c phase transition below 298.15 K, this results in a discontinuity in S cal, 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)FeGe2 O6 solid solution at 298.15 K is characterized by positive excess molar magnetic entropies of mixing onto which entropy changes due to the structural P 21 / c ↔ C 2/ c phase transitions are superimposed in the Na-rich part of the binary system. Excess volumes of mixing for the (Li, Na)FeGe2 O6 solid solution were calculated from published data and DQF parameters were derived that allow volume as function of temperature and composition to be calculated. The molar third law entropies at T = 298.15 K are S o m = (188.3 ± 2)J·K −1 ·mol −1 and S o m = (203.1 ± 2)J·K −1 ·mol −1 and the molar enthalpies of formation from the elements at T = 298.15 K are Δf H o m = (−1817.2 ± 9)kJ·mol −1 and Δf H o m = (−1834.0 ± 9)kJ·mol −1 for the end members LiFeGe2 O6 and NaFeGe2 O6, respectively. Δf H o m was calculated using density functional theory (DFT). Values for Δf H o m, S o m, and molar volume, for the coefficients of Cp, m polynomials, for thermal expansion and for the bulk modulus of the end members were compiled and can be used, in combination with the derived volumetric and entropic mixing properties, for phase diagram calculations involving the (Li, Na)FeGe2 O6 solid solution.