We have studied the thermal expansion of 15 synthetic and two natural F-Cl apatite solid solutions through the calculation of unit-cell dimensions at elevated temperatures based on X-ray powder diffraction data collected from room temperature to ~900 °C at 50 to 100 °C intervals. Coefficients of thermal expansion for the a and c unit-cell axes show sensitivity to composition, with αa increasing by about 50% and αc decreasing by a third from chlorapatite to fluorapatite. Despite the relationships observed for a and c, the thermal expansion coefficient for unit-cell volume shows little sensitivity to composition, which can be explained only by a mutually compensating structural adjustment along the latter axes as temperature rises. Results of this study also imply that the thermodynamically ideal volumes of mixing for F-Cl apatite solid solutions observed at ambient conditions continue to at least 900 °C.


Apatite, A5(XO4)3Z, is a common mineral that occurs in igneous, metamorphic, and sedimentary rocks. Additionally, it is an important component of planetary materials (Piccoli and Candela 2002; Spear and Pyle 2002; Knudsen and Gunter 2002; Patiño Douce and Roden 2006; Jones et al. 2014), having been used to estimate H2O abundances in the interiors of the Moon and Mars (McCubbin et al. 2010a, 2010b, 2011, 2012; Gross et al. 2013). Apatite is the main hard part of the human anatomy, the source of phosphorous in fertilizer, and an important potential material for the storage of nuclear waste (Ewing and Wang 2002). Understanding fundamental properties of the apatite mineral group is of significant interest, therefore, to the fields of geology, biology, medicine, planetary science, and materials science.

Numerous chemical substitutions occur in this complex mineral system. Although the primary occupants of the A and X sites are Ca2+ and P5+, respectively, natural specimens can display substitutions of REE3+, Sr2+, and Na+ in A; S6+, Si4+, and C4+ in X; and F, Cl, (OH), O2−, (CO3)2−, and S2− in Z (Pan and Fleet 2002; Hovis and Harlov 2010; Boyce et al. 2010; Gross and Berndt 2002).

Despite the importance of apatite as an Earth material, basic thermodynamic data are nonexistent for much of the system, especially for compositions between end-members. In our initial studies of apatite thermodynamics, the goal has been to investigate behavior of the main anion substitutions in Ca(PO4)3Z apatite, namely F, Cl, and OH, noting that fluorapatite is the most commonly occurring member of this mineral group in rocks. In this regard, Hovis and Harlov (2010) reported on the enthalpy-of-mixing behavior for F-Cl binary apatites. This was followed by investigation of F-OH apatite enthalpies and volumes of mixing (Hovis et al. 2014a). The third contribution to this work concerned thermal expansion data for the F-OH apatite system (Hovis et al. 2014b). In the current paper, we report on thermal expansion properties of the synthetic F-Cl apatite specimens studied by Hovis and Harlov (2010), as well as natural samples of the F, Cl, and OH end-members.


Sample synthesis

Synthesis of F-Cl apatite crystalline solutions took place at the GeoForschungs-Zentrum-Potsdam (GFZ) using the slow-cooled, molten flux method described by Cherniak (2000) and Prener (1967). As described by Hovis and Harlov (2010) and Schettler et al. (2011), the flux consisted of molar amounts of thoroughly mixed, fine powders of CaF2 and CaCl2 in variable proportions such that they summed to 0.1 mol × CaF2 + (1 – x)CaCl2 or about 10 to 11 g total. A fine Ca3(PO4)2 powder (0.03 mol or 9.305 g) was then mechanically dry mixed into the flux. Because F strongly partitions into apatite, for all intermediate compositions the flux consisted principally of CaCl2 with minor amounts of CaF2. Either pure CaCl2 or CaF2 was utilized as a flux for end-member chlorapatite or fluorapatite, respectively. The dry mix was packed into a 30 mL volume Pt crucible and pressed down using the pestle. The Pt crucible, with a loose fitting Pt cover, was then placed in a programmable high-temperature oven and the temperature ramped to 1375 °C over a period of 4 h. The melt was allowed to equilibrate or “soak” at 1375 °C for 15 h, then slowly cooled to 1220 °C at a rate of 3 °C/h during which fluor-chlorapatite crystals nucleated and grew in the melt. After 1 to 20 h at 1220 °C, the crucible was removed from the oven and quenched in air for about 30 min until it was cool enough to extract the flux-crystal mass as a solid lump. The fluor-chlorapatite crystals were separated from the flux by boiling the quenched product in distilled water in a 2 L beaker. If the flux contained more than a few percent by weight CaF2, the flux + crystals were boiled in an aqueous 20% solution of Al(NO3)3·9H2O to dissolve the residual CaF2. The resulting transparent, inclusion-free, light blue-green, euhedral–semi-euhedral fluor-chlorapatite crystals ranged in length from 100 μm up to 6–7 mm in length and from 20 μm to 3–4 mm in diameter.

The compositions of each of the fluor-chlorapatite samples synthesized for the original study were carefully determined by wet chemical means as discussed in detail by Schettler et al. (2011). In general, the principal differences in composition among the various apatite samples are their F:Cl ratios. However, compositions for the Cl-rich third of the compositional range contain nontrivial amounts of oxyapatite [Ca5(PO4)3O0.5] (ibid). Indeed, natural F-Cl apatites containing an oxyapatite component have been described by Young and Munson (1966).

In addition to the samples synthesized at GFZ-Potsdam, thermal expansion measurements have been made on three natural apatite samples: chlorapatite, American Museum of Natural History specimen AMNH 23101 from Kragerø, Norway; fluorapatite, National Museum of Natural History specimen NMNH 144954-3, from Durango, Mexico; and hydroxylapatite, National Museum of Natural History specimen NMNH R9498, from Holly Springs, Georgia, U.S.A. The chlorapatite composition, (Ca4.88Fe0.01Na0.08Ce0.01)(P3.01O12)(F0.09Cl0.91), given by Hughes et al. (1989) is based on electron microprobe and INAA analyses. The fluorapatite analysis, (Ca4.97Na0.04Ce0.02)(P2.98Si0.01S0.02O12)(F0.92Cl0.06OH0.03), was performed by Francis McCubbin at the University of New Mexico using continuous flow mass spectrometry for H2O determination and specialized electron-probe microanalysis for fluorine, as described in Hovis et al. (2014a). [Also see the composition of Young et al. (1969) on a different (but related) sample of Durango fluorapatite.] That for NMNH R9498, [Ca5.00(P3.00O12.00)(F0.09Cl 0.04(OH)0.89)], also analyzed by McCubbin, is given in Table 1 of Hovis et al. (2014b).

Thermal expansion data for the natural fluorapatite and hydroxylapatite samples were given previously in Hovis et al. (2014b), but those for chlorapatite AMNH 23101 are given here for the first time.

High-temperature X-ray powder diffraction measurements

The thermal expansion research involved subjecting powdered apatite samples to CuKα X-radiation at a series of temperatures, then using the diffraction data to calculate unit-cell dimensions of the samples at each temperature. The research extended over a several-year period. Initial measurements were made during several short-term visits to the University of Cambridge, U.K., on a Bruker D8 θ-θ system having high-temperature capability; digital data were brought back to Lafayette College for analysis using IGOR spectral-analysis software. More recent work on natural chlorapatite, fluorapatite, and hydroxylapatite specimens were made at Lafayette College on a newly-acquired PANalytical Empyrean θ-θ X-ray diffractometer equipped with a PIXEL 3D detector and an Anton Parr HTK 1200N furnace. In the transitional year between the Cambridge- and Lafayette-based work, high-temperature measurements were made at Specialty Minerals Inc. (Easton, Pennsylvania) on a Rigaku Ultima θ-θ system. X-ray data from both the Rigaku and PANalytical systems consisted of direct output produced by system software and did not require IGOR analysis. Note that the measurement site and XRD unit utilized for each sample are included in Tables 11 and 2.

For measurements made in Cambridge, temperature calibration of the Bruker system was limited by the short-term nature of our visits. Temperatures were checked via the high/low quartz transition and generally found to be within ~20–30 °C of the set temperature. However, having no basis for temperature corrections at additional temperatures, no temperature corrections have been made to the Cambridge data. As documented below, duplicate experiments made on systems that were better-calibrated for temperature have allowed us to confirm the temperature integrity of the earlier data.

For the Rigaku-based measurements made at Specialty Minerals Inc., sample temperatures were checked through a set of experiments that utilized reversible phase transformations for KNO3, KClO4, K2SO4, K2CrO4, BaCO3, and SrCO3, collectively resulting in temperature calibration from ~115 to 930 °C. Based on the latter, it is estimated that the set-point temperatures for the Rigaku-based XRD measurements are correct to ±15 °C.

X-ray measurements made at Lafayette College with the PANalytical system were calibrated for temperature utilizing the same methodology as for the Rigaku system using KNO3, KClO4, K2SO4, and BaCO3, resulting in calibration measurements taken between ~115 and 800 °C. Based on the latter, it was determined that actual temperatures were approximately 25 to 30 °C higher than the set-point values; results in the data tables and figures of this paper reflect the corrected temperatures.

Apatite peak positions were corrected through use of National Institute of Standards and Technology (NIST) sample SRM 640a silicon (with a stated unit-cell dimension of 5.430825 Å), which was mixed with each sample. High-temperature Si peak positions were based on the Si thermal expansion data of Parrish (1953). Unit-cell dimension calculations for all data utilized the software of Holland and Redfern (1997). The indexing of apatite peaks at elevated temperatures simply involved tracking known peaks at room temperature to higher temperatures utilizing data for both F and Cl apatite end-members.


Unit-cell results for all samples are reported in Table 11. This table also records the X-ray unit on which each data set was collected (Cambridge University/Bruker D8, Specialty Minerals/Rigaku Ultima, Lafayette College/PANalytical Empyrean). Note that duplicate experiments were conducted on samples APS21, APS25, APS26, APS27, and APS36 to check early Cambridge-based unit-cell parameters against later results based on temperature calibrations that were more thorough. Figure 1 demonstrates good internal consistency among the data.

For the most part, apatite-group minerals display hexagonal symmetry. However, the powder diffraction methods used here did not allow distinction between hexagonal and monoclinic symmetry for Cl-rich samples (e.g., Mackie et al. 1972). Even when present, monoclinic symmetry for the latter is reflected by only a minute departure (≤0.06°) from a γ interaxial angle of 120° (e.g., note the data of Hounslow and Chao 1970).

Figures 2 to 4 show plots of unit-cell volume (V), a, and c, respectively, against temperature. For the sake of clarity, we have chosen not to plot all data that were collected, but rather representative data for 10 (of the 15 different) series at more-or-less regular compositional intervals. The parameters for both linear and quadratic fits to V, a, and c as a function of temperature, along with R2 for each, are given for all series in Table 2. It is evident that quadratic fits to V, a, and c as a function of temperature are statistically justified in many cases. Nevertheless, the linear fits for V and a shown in Figures 2 and 3 do well in fitting the data. Relationships for the c dimension (Fig. 4), on the other hand, are generally more curved and better fit by quadratic relationships.

For a general comparison of samples in terms of the degree to which they expand, it is useful to compare either the slopes of linear least-squares fits to the data on the various graphs or the coefficients of thermal expansion, which are calculated for volume as



where ΔVT is the slope of the fit and V0°C is the intercept of the same fit at 0 °C. The latter are included in Table 2.

It is instructive to plot the thermal expansion coefficients for V, a, and c (the latter two calculated in a manner comparable to that for V) against composition (Figs. 5 through 7). Figure 5 demonstrates that the thermal expansion coefficient for volume is affected little, if at all, by F:Cl ratio; this is reflected as well by the parallelism of V-T data for the various samples on Figure 2. Figures 6 and 7, on the other hand, show clearly that thermal expansion coefficients for the individual unit-cell axes a and c are a function of composition, αa increasing and αc decreasing as fluorine content rises. The systematic behavior of ΔcT relations with composition also is readily evident from relationships in Figure 4, where values of c among all series display greater convergence at high than at low temperature. Thus, volume, which is itself a function of the a and c unit-cell lengths, behaves differently than the axes themselves.

In Figures 5 to 7, we have included data for the thermal expansion coefficients of F-OH apatite solid solutions based on the recent results of Hovis et al. (2014b). Note that although values of αV for F-OH apatites may generally fall slightly below those of F-Cl solutions (Fig. 5), there is general overlap and a lack of compositional variability among data for both the F-Cl and F-OH series. The same is not true, however, for the thermal expansion coefficients related to a and c (Figs. 6 and 7), at least for F-Cl apatite solutions.


Generally, Figure 5 demonstrates that there is little sensitivity of volume expansion to composition shown by F, Cl, and OH apatite end-members, nor by intermediate members of the F-Cl and F-OH apatite series. This means that the ideal thermodynamic mixing behavior related to volume for F-Cl (Fig. 8) and F-OH (Hovis et al. 2014b, their Fig. 3) apatite series extends from room temperature to at least 900 °C, although admittedly there is some uncertainty in interpretation of F-Cl apatite volumes due to the presence of an oxyapatite component in Cl-rich samples.

One can surmise that the insensitivity of volume expansion to F:Cl:OH ratio is related to the seemingly insignificant role of the anion in the apatite structure, as the latter constitutes just one of six ions that coordinate the so-designated Ca(2) position in the structure (Hughes et al. 1989; also see Hughes and Rakovan 2002, for multiple additional references), the remaining five being O2−. From Figures 6 and 7, however, it is clear that the anion does indeed make a difference to expansion along the individual unit-cell axes, where αa increases by about 50% from the Cl- to the F-end of the apatite series as αc decreases by about a third over the same range.

One is tempted to ascribe the observed sensitivity of αa, seen mainly in the Cl-rich third of the compositional range (Fig. 6), to the oxyapatite substitution described by Schettler et al. (2011) for Cl-rich samples. We reject such interpretation, however, for several reasons. One is that the amount of oxyapatite substitution varies considerably among Cl-rich samples (ibid), whereas related variability in αa data is not evident. Another is that data for natural chlorapatite AMNH 23101 and hydroxylapatite NMNH R9498 fit well with those of synthetic Cl-rich and OH-rich samples, respectively. And, finally, compositional variability for αc is seen over the entire compositional range (Fig. 7), not just for Cl-rich samples. It seems clear, then, that thermal expansion along a and c must involve a cooperative and inverse structural relationship that depends mainly upon F:Cl ratio.

Hughes et al. (2014) recently have discussed in detail the anion arrangements of F and Cl in fluor-chlorapatite solid solutions. Based on structure, it seems that there are at least two possible explanations for the cooperative relationship between a and c during thermal expansion. One is that thermal ellipsoids of the anions, and perhaps other ions as well, change with heating. A second possibility is that the positioning (and/or arrangement) of anions in the apatite anion column changes with temperature. Unfortunately, however, we know of no single-crystal work on apatite-group minerals at elevated temperatures that might help clarify the observed relationships.

Finally, one can ask why the F:Cl-dependent relationship between αa and αc for the fluor-chlorapatite system is not observed as much, or at all, in F-OH apatite solid solutions. It seems likely that this is related to anion size differences, where OH and F are approximately the same size, but Cl is considerably larger than either of the latter. On the other hand, size arguments relative to anions in the apatite structure can be misleading, as Cl-bearing chlorapatite displays a smaller c dimension than F-bearing fluorapatite (Fig. 4), despite parallelism of the anion column to the c axis.


It is our hope that full thermodynamic characterization of apatite-group minerals will lead to the successful use of these minerals as petrogenetic indicators. Further work, however, remains on the thermodynamic characterization of solid solutions in this complex system. Hopefully, binary Cl-OH and ternary F-Cl-OH apatite solid solutions can be synthesized so as to allow completion of work relative to the primary monovalent anion substitutions. Our laboratory is anxious to contribute to this endeavor when such samples become available.


G.L.H. thanks the National Science Foundation for grant EAR-1028953, which funded purchase of the PANalytical Empyrean X-ray powder diffraction system at Lafayette College. Sincere thanks to NSF also for grant EAR-1019809 and the EXCEL Program of Lafayette College, which together funded undergraduate student research. John Wilson of the Department of Geology and Environmental Geosciences at Lafayette College provided valuable assistance in setup of our new X-ray system. We greatly appreciate provision of X-ray facilities by the Earth Sciences Department of Cambridge University, as well as generous other help that facilitated our visits over the years. Thanks to Specialty Minerals Inc., Easton, Pennsylvania, where a portion of the X-ray measurements were made. Thank you to Jeff Post, Mike Wise, and Paul Powhat of the National Museum of Natural History for providing apatite samples NMNH 144954-3 and R9498. Thank you to George Harlow of the American Museum of Natural History for providing AMNH 23101 chlorapatite. We thank Matthias Gottschalk and Georg Schettler of the GFZ-Potsdam for sharing chemical and structural data on the synthetic F-Cl apatite samples. G.L.H. appreciates valuable discussions regarding apatite structure with John Hughes (University of Vermont), and also his work as AE for this manuscript. Our sincere thanks go to Hanna Nekvasil (Stony Brook University) and Francis McCubbin (University of New Mexico) for constructive criticisms during the review of this paper.

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