Thermal expansion of fluorapatite-hydroxylapatite crystalline solutions^†

Apatite, A₅(XO₄)₃Z, is a common mineral in igneous, metamorphic, and sedimentary rocks. It can be found in planetary materials as well (Piccoli and Candela 2002; Spear and Pyle 2002; Knudsen and Gunter 2002; Patiño Douce and Roden 2006; Jones et al. 2014), and in fact has been used to estimate abundances of H₂O in the interiors of the Moon and Mars (McCubbin et al. 2010a, 2012; Gross et al. 2013). Apatite is also a significant component in many fertilizers, an important material for nuclear waste storage (Hughes and Rakovan 2002; Ewing and Wang 2002), and the primary mineral composing solid parts of the human anatomy (Gross and Berndt 2002). As such, it has the potential to yield valuable information to the geological, biological, medical, planetary, and materials-science communities. Despite the broad range of its application, surprisingly little is known regarding the thermodynamics of apatite-group minerals. Consequently, it is of interest to characterize the thermodynamic behavior of minerals in the greater apatite system, as well as its individual subsystems.

For naturally occurring apatites, the primary occupants of the A and X sites are Ca²⁺ and P⁵⁺, respectively. However, the mineral varies widely in composition with continuous substitutions of F⁻, Cl⁻, and (OH)⁻ in the Z site, as well as limited substitutions of REE³⁺, Sr²⁺, Na⁺ (among others) for Ca²⁺ in A, and (CO₃)²⁻, S²⁻, or simply O²⁻ in Z (Pan and Fleet 2002; Hovis and Harlov 2010; Boyce et al. 2010). There also are many minor substitutions such as S⁶⁺, Si⁴⁺, and C⁴⁺ for P⁵⁺ in X. Initial work on thermodynamic characterization focused on F-Cl apatites (Hovis and Harlov 2010). More recently, Hovis et al. (2014) supplemented the latter with a study of the enthalpy and volume characteristics of a newly synthesized F-OH apatite series. Investigation of this series continues in the present work.

Synthesis of the present samples has been described in the previous paper on these minerals (Hovis et al. 2014) and builds upon ion-exchange techniques utilized in previous work on other mineral systems such as feldspars (e.g., Hovis 1988; Hovis and Roux 2008) and feldspathoids (e.g., Hovis and Roux 1993; Hovis et al. 2003, 2006). To summarize briefly, NIST special reference material 2910a hydroxylapatite was utilized as the base material to make a series of F-OH apatite solid solutions. The NIST hydroxylapatite was synthesized via solution reaction of calcium hydroxide and phosphoric acid at atmospheric pressure and a temperature near 100 °C; details in the certificate of analysis refer to the synthesis procedure of McDowell et al. (1977). Fluorapatite was made at Lafayette College by tamping down a thin layer of 2910a hydroxylapatite powder on a 50 mm diameter disk of optical-grade fluorite, then holding the disk in air at 750 °C for three days. The resulting F-rich apatite powder then was applied to a fresh fluorite surface and held at the same temperature for an additional three days. This double exchange resulted in a fluorapatite specimen containing ~85 mol% fluorapatite component. Successful ion exchange in the experiments was gauged through examination of the run products using X-ray powder diffraction, which showed well-defined changes in peak position from hydroxylapatite to fluorapatite; the resulting X-ray data also matched that of fluorapatite in the database of the International Center for Diffraction Data (ICDD). Subsequently, intermediate F-OH apatite compositions were synthesized by combining in various proportions 2910a hydroxylapatite and the newly synthesized fluorapatite powders, annealing these for three days at 750 °C, with daily mixing of each powder. Detailed synthesis conditions for all samples are summarized in Table 1 of Hovis et al. (2014).

Chemical characterization of all synthetic F-OH apatite specimens was done by Francis McCubbin at the University of New Mexico using continuous flow mass spectrometry for H₂O determination and electron probe microanalysis for fluorine. The latter utilized special techniques applicable to fine powders, as described in detail and reported in Table 2 of the previous paper (ibid; related references include Stormer et al. 1993; Goldoff et al. 2012; McCubbin et al. 2010b, 2011).

In addition to the synthetic F-OH apatite samples, two natural apatite specimens were obtained from the National Museum of Natural History (Smithsonian Institution) for this investigation, fluorapatite NMNH 144954-3 from Durango (Mexico) with composition (Ca_4.90Na_0.04Ce_0.02)(P_2.98Si_0.02S_0.02O₁₂)(F_0.92Cl_0.06OH_0.03) (Table 2 of Hovis et al. 2014; Young et al. 1969) and hydroxylapatite NMNH R9498 from Holly Springs, Georgia, of composition (Ca_5.00)(P_3.00O₁₂)(F_0.09Cl_0.04OH_0.89) (Table 1, this study; Hughes et al. 1989). As natural samples, each of the latter strays somewhat from the F-OH apatite binary system.

Initial room-temperature X-ray examination of the samples was done on a Scintag PAD V X-ray powder diffractometer. Scans using Cu radiation typically were run from 15 to 72° 2Θ at a rate of 0.25°/min. NIST 640a silicon, with a stated unit-cell dimension of 5.430825 Å, was used as an internal standard. Analysis of the hydroxylapatite X-ray diffraction pattern was aided by comparison with XRD data given in the NIST certificate of analysis. There also are multiple additional sources of XRD data for fluorapatite and hydroxylapatite, such as the ICDD database. Additionally, it was possible to track peaks from the OH to the F end of the ion-exchange series, and vica versa; this was helpful especially for peak indexing at mid-compositions where XRD data are sparse. Calculations of unit-cell dimensions utilized the unit-cell software of Holland and Redfern (1997).

High-temperature X-ray powder diffraction measurements on the synthetic F-OH apatite samples were made at Specialty Minerals, Inc., Easton, Pennsylvania, utilizing a Rigaku Ultima Theta-Theta diffractometer in conjunction with a high-temperature stage. Sample temperatures were evaluated in a separate set of experiments using reversible phase transformations for KNO₃, KClO₄, K₂SO₄, K₂CrO₄, BaCO₃, and SrCO₃; collectively, this resulted in temperature calibration from 130 to 930 °C. Based on these experiments, it is estimated that the set-point temperatures for the XRD measurements are known to ±15 °C.

High-temperature X-ray measurements on the two natural apatite specimens were made at Lafayette College utilizing a newly received PANalytical Empyrean Theta-Theta XRD system, with PIXEL3D detector and an Anton-Parr HTK 1200N high-temperature stage that enabled sample height adjustment. Temperatures for this stage too were calibrated using the methodology described above for samples of KNO₃, KClO₄, K₂SO₄, and BaCO₃; actual temperatures are thought to be within 20 °C of the stated values.

Unit-cell dimension calculations (again utilizing the software of Holland and Redfern 1997) based on both Rigaku and PANalytical data utilized NIST SRM 640a silicon as an internal standard, as well as the high-temperature Si data of Parrish (1953). X-ray peak positions at room temperature were easily tracked for scans at elevated temperatures.

Generally, apatite is a hexagonal mineral with P6₃/m space group symmetry. Various hydroxylapatite samples, however, have been found to display either the latter or monoclinic P2₁/b symmetry (Mackie et al. 1972; Elliott et al. 1973). In single-crystal work, Hughes et al. (1989) found NMNH R9498 hydroxylapatite, used in the present study, to display true hexagonal symmetry. There is no guarantee, however, that synthetic NIST 2910a hydroxylapatite has equivalent symmetry, even though the X-ray powder diffraction pattern indicates this to be the case. Because the β interaxial angle in monoclinic hydroxylapatite is extremely close to 120° (beyond resolution of the determined unit-cell parameters), distinction between the two symmetries can be impossible using X-ray powder diffraction techniques. For purposes here, it has been assumed that NIST 2910a sample is hexagonal, understanding that this is an uncertainty that cannot be resolved with techniques used in the present work.

Unit-cell dimensions a and c, as well as unit-cell volume, are presented for all specimens and temperatures in Tables 2a and 2b and plotted in Figures 1 to 3. Compositions (mole fractions F) for all synthetic samples are included in Table 3; the bulk composition of hydroxylapatite NMNH R9498 was given earlier in Table 1.

In Figure 1, one sees impressive parallelism of the a dimension with temperature among all synthetic F-OH apatite specimens. Data for both of the natural apatite samples fit well with those for the synthetic materials. Note that near-end-member Durango fluorapatite data occur among mid-compositional members of the F-OH synthetic series; offset of data from other F-rich apatites can be attributed to non-binary chemical components. Although some series exhibit slightly curved relationships between a and T, comparison of linear fits to all data produces closely grouped thermal expansion coefficients for a (α_a) (calculated similarly to those for volume given by Eq. 1 below) that average 13.6 ± 0.5 (1σ) × 10⁻⁶ deg⁻¹, reflecting a very small spread in the data. The parallelism of data in Figure 2 is the first hint that the Z-site anion makes little difference in the expansion behavior of these minerals.

The c unit-cell dimension is little affected by F:OH ratio (Hovis et al. 2014), as values across the F-OH series at room temperature are within 0.01 Å of one another, which explains the bunching of data in Figure 2. Data for NMNH R9498 Holly Springs hydroxylapatite falls slightly below other data, again the result of non-binary constituents. The latter do not seem to have affected Δc/ΔT slopes, however, and thermal coefficients for the c axis based on linear fits to c-T data average 13.2 ± 0.7 (1σ) × 10⁻⁶ deg⁻¹, again showing only a small range in the data. Overall, then, the fractional changes of a and c with temperature are the same, as reflected by the respective thermal expansion coefficients.

Unit-cell volume data are plotted in Figure 3. Statistics presented in Table 3 illustrate that in some cases linear and quadratic fits to V-T relations are statistically equivalent, whereas in others quadratic fits are slightly better. For all nine series, linear least-squares fits to the data give R² values ≥0.996. For series where quadratic fits are statistically justified, concave-up relationships are prevalent. Equations for both linear and quadratic relationships are included in Table 3.

To obtain a general picture of the effect of temperature on volume for F-OH apatite, one can focus on linear fits to the V-T data (Table 3). Thermal expansion coefficients for volume (α_V) have been calculated as

where ΔV/ΔT (ų/°C) are the slopes of the least-squares-fitted V-T lines and V_0°C (ų) values are the intercepts of those lines at 0 °C. Thermal expansion coefficients for volume average 41.0 ± 1.4 (1σ) × 10⁻⁶ deg⁻¹ (Table 3, Fig. 4) among all series. This reflects the general parallelism of data in Figure 3.

Thermal expansion coefficients for end-member F- and OH-apatite have been measured previously by Trombe (1973) and also Brunet et al. (1999). Trombe (1973) presents data in graphical (not tabular) form, so comparison with present data is difficult. Brunet et al. (1999) calculated values of α_V from Trombe’s data and determined quantities of 40 and 42 ×10⁻⁶ deg⁻¹ for fluroapatite and hydroxylapatite end-members, respectively; these agree well with present data. Brunet et al. (1999) give quadratic, not linear, relationships for their volume data (again in graphical, not tabular, form), which appear to be similar to ours. We have not attempted to reinterpret their data as linear relationships.

The object of this study was to determine whether the Z-site anions, in this case F⁻ vs. (OH)⁻, make a difference in the degree to which apatite expands when it is heated. The plot in Figure 3 and the resulting thermal expansion coefficients (Table 3, Fig. 4) indicate that it does not. In thinking about possible explanations for this, one must consider the nature of the anion (F, OH, Cl) position(s) in the apatite structure. In fact, the latter constitutes one of six ions that coordinate the so-designated Ca(2) position in the apatite structure (Hughes et al. 1989; also see Hughes and Rakovan 2002, for multiple additional references), the remaining five ions being O²⁻. The lower charge of (F/OH/Cl)⁻ ions compared with O²⁻ should result in a relatively weaker bond with Ca²⁺. One might expect a (F/OH/Cl)⁻ ion, therefore, to have a relatively large degree of vibrational freedom, regardless of which anion occupies this position. When one considers that F⁻ and (OH)⁻ have essentially the same radius [reflected by room-temperature apatite volumes, where the substitution of (OH)⁻ by F⁻ reduces unit-cell volume by only ~1%; Hovis et al. 2014], the similar thermal behavior of the two entities seems all the more reasonable. Even if two anions were different in size, however, the relatively weak Ca²⁺-anion bond could perhaps accommodate the size difference through vibrational flexibility.

Study of the thermal expansion behavior of F-OH apatite adds to the thermodynamic database for apatite solid solutions. For room temperature, Hovis et al. (2014) concluded from the linear relationship of unit-cell volume with composition for these same samples (their Fig. 3) that volumes of F-OH mixing (V_ex) are nonexistent. That thermal expansion coefficients are essentially the same across the fluorapatite-hydroxylapatite series now extends the V_ex = 0 relationship to temperatures above 900 °C and also makes the calculation of high-temperature volumes for any F-OH apatite solid solution quite easy.

Present data on F-OH apatite along with recent data on F-Cl apatite (Hovis and Harlov 2010) add significantly to the thermodynamic database for the apatite system, but there still is much work to do. The apatite Cl-OH binary and F-Cl-OH ternary systems remain thermodynamically uncharacterized. Thermodynamic quantification of substitutions such as (CO₃)²⁻ and O²⁻ in the anion sites, Na⁺ and Sr²⁺ for Ca²⁺ in the cation sites, and structural H₂O molecules (Mason et al. 2009; Yoder et al. 2012) remain on the “to do” list for this system. Given the widespread occurrence of apatite in igneous and metamorphic rocks and its potential to contribute substantially to the interpretation of rock petrogenesis, further thermodynamic characterization of this complex system seems likely to produce highly valuable data. When samples become available, our laboratory will be pleased to contribute further to this endeavor.

G.L.H. thanks the Earth Sciences Division of the U.S. National Science Foundation for support of this research through Earth Science Instruments and Facilities grant EAR-1028953, which was responsible for purchase of our PANalytical Empyrean XRD unit, with heating stage, and also research grant EAR-1019809, which included support for student research on these minerals. G.L.H. is grateful not only for support of present projects, but also for the support of undergraduate research over many years; indeed, several undergraduates are coauthors of this work. F.M.M. acknowledges support from NASA’s Cosmochemistry program through grant NNX11AG76G.