Excess heat capacity and entropy of mixing along the chlorapatite–fluorapatite binary join

Abstract

The heat capacity at constant pressure, C p, of chlorapatite [Ca5(PO4)3Cl – ClAp], and fluorapatite [Ca5(PO4)3F – FAp], as well as of 12 compositions along the chlorapatite–fluorapatite join have been measured using relaxation calorimetry [heat capacity option of the physical properties measurement system (PPMS)] and differential scanning calorimetry (DSC) in the temperature range 5–764 K. The chlor-fluorapatites were synthesized at 1,375–1,220°C from Ca3(PO4)2 using the CaF2–CaCl2 flux method. Most of the chlor-fluorapatite compositions could be measured directly as single crystals using the PPMS such that they were attached to the sample platform of the calorimeter by a crystal face. However, the crystals were too small for the crystal face to be polished. In such cases, where the sample coupling was not optimal, an empirical procedure was developed to smoothly connect the PPMS to the DSC heat capacities around ambient T. The heat capacity of the end-members above 298 K can be represented by the polynomials: C p ClAp = 613.21 − 2,313.90T −0.5 − 1.87964 × 107 T −2 + 2.79925 × 109 T −3 and C p FAp = 681.24 − 4,621.73 × T −0.5 − 6.38134 × 106 T −2 + 7.38088 × 108 T −3 (units, J mol−1 K−1). Their standard third-law entropy, derived from the low-temperature heat capacity measurements, is S° = 400.6 ± 1.6 J mol−1 K−1 for chlorapatite and S° = 383.2 ± 1.5 J mol−1 K−1 for fluorapatite. Positive excess heat capacities of mixing, ΔC p ex , occur in the chlorapatite–fluorapatite solid solution around 80 K (and to a lesser degree at 200 K) and are asymmetrically distributed over the join reaching a maximum of 1.3 ± 0.3 J mol−1 K−1 for F-rich compositions. They are significant at these conditions exceeding the 2σ-uncertainty of the data. The excess entropy of mixing, ΔS ex, at 298 K reaches positive values of 3–4 J mol−1 K−1 in the F-rich portion of the binary, is, however, not significantly different from zero across the join within its 2σ-uncertainty.