Excess heat capacity and entropy of mixing along the hydroxyapatite-chlorapatite and hydroxyapatite-fluorapatite binaries

The heat capacity, Cp, of synthetic hydroxyapatite [Ca5(PO4)3OH–OH-Ap], as well as of ten compositions along the OH-Ap-chlorapatite (Cl-Ap) join and 12 compositions along the OH-Ap-fluorapatite (F-Ap) 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 of 5–764 K. Apatites along the Cl-OH and F-OH joins were synthesized at 1100 °C and 300 MPa in an internally heated gas pressure vessel via an exchange process between synthetic fluorapatite or chlorapatite crystals (200–500 μm size) and a series of Ca(OH)2-H2O solutions with specific compositions and amounts relative to the starting apatite. The standard third-law entropy of OH-Ap, derived from the low-temperature heat capacity measurements, is S° = 386.3 ± 2.5 J mol−1 K−1, which is ~ 1% lower than that resulting from low-temperature adiabatic calorimetry data on OH-Ap from the 1950’s. The heat capacity of OH-Ap above 298.15 K shows a hump-shaped anomaly centred around 442 K. Based on published structural and calorimetric work, this feature is interpreted to result from a monoclinic to hexagonal phase transition. Super ambient Cp up to this transition can be represented by the polynomial: $$C_{p}^{{\text{OH - Ap}}} {}_{{298K - 442K}}\left( {{\text{J mol}}^{ - 1} {\text{K}}^{- 1}} \right) = {1013.7-13735.5T^{{ - 0.5}}} + 2.616718\,10^{7} T^{{ - 2}} - 3.551381\,10^{9} T^{{ - 3}} .$$ C p OH - Ap 298 K - 442 K J mol - 1 K - 1 = 1013.7 - 13735.5 T - 0.5 + 2.616718 10 7 T - 2 - 3.551381 10 9 T - 3 . . The DSC data above this transition were combined with heat capacities computed using density functional theory and can be given by the Cp polynomial: $$C_{p}^{{\text{OH - Ap}}} {}_{{ >\,442K}}\left( {{\text{J mol}}^{ - 1} {\text{K}}^{- 1}} \right) = {877.2-11393.7 T^{ - 0.5}} + {5.452030\,10^{7}} \,T^{- {2}} - {1.394125\,10^{10}} \,T^{- {3}}$$ C p OH - Ap > 442 K J mol - 1 K - 1 = 877.2 - 11393.7 T - 0.5 + 5.452030 10 7 T - 2 - 1.394125 10 10 T - 3 . Positive excess heat capacities of mixing, ∆Cpex, in the order of 1–2 J mol−1 K−1, occur in both solid solutions at around 70 K. They are significant at these conditions exceeding the 2σ-uncertainty of the data. This positive ∆Cpex is compensated by a negative ∆Cpex of the same order at around 250 K in both binaries. At higher temperatures (up to 1200 K), ∆Cpex is zero within error for all solid solution members. As a consequence, the calorimetric entropies, Scal, show no deviation from ideal mixing behaviour within a 2σ-uncertainty for both joins. Excess entropies of mixing, ∆Sex, are thus zero for the OH-Ap–F-Ap, as well as for the OH-Ap–Cl-Ap join. The Cp–T behaviour of the OH-Ap endmember is discussed in relation to that of the F- and Cl-endmembers.