Are the thermodynamic properties of natural and synthetic Mg₂SiO₄-Fe₂SiO₄ olivines the same?

Samples

Two natural olivine samples with different compositions, including a nearly end-member fayalite and a forsterite (Fo_0.904Fa_0.096), were selected for study. They are described in Table 1. Their compositions are given in Table 2. A fayalite-rich rock chip (Rockport, Massachusetts) roughly two centimeters in size was crushed to a sand size and clear olivine grains were carefully hand-picked under a binocular to obtain a clean separate. The forsterite-rich olivine (Pyaung-gaung Mine, Myanmar) was prepared as a doubly polished platelet, about 3.3 × 4.3 × 1.0 mm, as taken from a larger single crystal.

X‑ray powder diffraction, ⁵⁷Fe Mössbauer spectroscopy, and low-temperature C_P measurements

Sample purity was checked via X‑ray powder diffraction (XRPD) using a Bruker D8 Advance with DaVinci-Design diffractometer (Bruker AXS, Karlsruhe, Germany). Splits from both samples were ground, mounted on a single-crystal silicon holder and measured using CuKα radiation (40 kV, 40 mA) in continuous mode between 5° ≤ 2θ ≤ 95° with a step size of 0.015° and 0.15 s/step. The diffractometer has a Bragg-Brentano beam geometry with a fixed 0.3° divergence slit, primary and secondary side 2.5° Soller slits, a 4.0° antiscatter slit, and an energy-dispersive Lynxeye detector (opening angle 2.934°). Silicon powder NBS SRM 640b was used as an external calibration standard. Data were plotted using DIFFRAC.EVA (ver. 5.0.0.22, 2019, Bruker AXS Inc., Wisconsin, U.S.A.).

The experimental ⁵⁷Fe Mössbauer spectroscopic setup has been described before (Palke et al. 2015). In brief, ⁵⁷Fe Mössbauer transmission spectra were recorded in a horizontal arrangement using a ⁵⁷Co/Rh single-line source with constant acceleration and a symmetric sawtooth velocity shape. The absorption data were collected in a multi-channel analyzer having 1024 channels and the velocity calibration was made using a 30 μm thick α-Fe foil. The FWHM associated with the ⁵⁷Co source is 0.243 ± 0.015. A powdered sample was contained in a plastic disk held a Cu-ring of 10 mm inner diameter, covered with high-purity Al-foil on the backside. The folded spectrum was evaluated by using Lorentzian-shaped doublets using the program RECOIL.

C_P(T) was measured three times at 60 different temperature increments from 300 down to 2 K. The mass of the polycrystalline fayalite sample was 15.47 mg. The mass of the forsterite crystal platelet was 30.57 mg. The Quantum Design relaxation calorimeter and the experimental setup used to measure C_P have been described before (Dachs and Bertoldi 2005; Geiger and Dachs 2018) and are not repeated here. Measurements on standard Al₂O₃ and/or MgO single crystals (Geiger and Dachs 2018) are made on a regular basis to check the experimental accuracy.

Natural vs. synthetic crystals

Olivine can be synthesized in the laboratory without the use of a flux and from high-purity component oxides. The experiment involves relatively short sintering times at high temperature (e.g., T > 1000 °C). For Fe²⁺-bearing crystals the f_O2 conditions must be controlled. The resulting crystals are typically fine grained, roughly 1 to 100 μm in size. In nature, on the other hand, crystals can grow at lower temperatures (e.g., metamorphic regimes), and they do so over geologic time periods. They can be coarse grained ranging up to centimeters in size (of course, natural crystals can have varying modes of origin). Consequently, differences in the structural state, that is Fe²⁺-Mg order-disorder over the M1 and M2 sites, between synthetic and natural olivines can occur because of the different crystallization processes. Natural crystals from metamorphic or plutonic settings can, in general, be more ordered in terms of atomic structure compared to their synthetic analogues. Ordered crystals typically have stronger chemical bonding than disordered ones of the same composition. It follows that C _P(T) and S ° values for the former should be smaller than the latter. Heat capacity and entropy effects related to long-range cation order-disorder in Fe²⁺-Mg olivine solid solutions have not been investigated in a quantitative manner.

Natural olivine is expected to generally contain higher concentrations of minor or trace elements compared to synthetic crystals prepared from high purity reactants. Finally, there is also the issue of defect chemistry and point defects to consider and, here, there could also possibly be differences between synthetic and natural crystals. Some natural olivines may contain a little Fe³⁺ (Ejima et al. 2012), and minor structural OH^– can be present as well (Miller et al. 1987). What do the results of our X‑ray, ⁵⁷Fe Mössbauer and C _P measurements show?

X‑ray diffraction and ⁵⁷Fe Mössbauer spectroscopic interpretation

The X‑ray results indicate that both olivine samples are nearly pure. Only small amounts (about <1%) of other phases could be identified. The olivine powder diffraction peaks are intense and narrow in width indicating good crystallinity (Online Material^[1] Fig. OM1). The ⁵⁷Fe Mössbauer spectra can be fit well with two Fe²⁺ quadrupole-split doublets (Bancroft et al. 1967; Dyar et al. 2009). The amount of Fe³⁺ in both samples is very minor based on the minimal to nil absorption between about 0.0 and 1.0 mm/s (Fig. 1).

In terms of high-spin Fe²⁺ in olivine and for a first-order analysis, the magnitude of the quadrupole splitting gives a measure of the asymmetry of the charge distribution around the Fe nucleus (i.e., octahedral M-site distortion). It consists of valence and lattice terms, whereby the latter decreases with increasing distortion. The isomer shift measures the s electron contact density at the Fe nucleus (i.e., is a function of the ligand coordination). Single-crystal diffraction results on olivine indicate that M1 is smaller in volume and more distorted than M2 at room temperature (Princivalle 1990). The assignments of the two Fe²⁺ doublets in Table 3 follow this reasoning. The areas of the two doublets for both samples are similar. For the fayalite, the areas should be similar (assuming that the small amount of Mn²⁺ in the olivine is not located largely at either M1 or M2). The spectrum of the forsterite sample may show a slight tendency for Fe²⁺ to favor M2, but the difference in doublet areas is within experimental error. The hyperfine parameters of both natural olivines (Table 3) are in good agreement with those obtained on synthetic samples of similar composition (Dyar et al. 2007), except possibly for the quadrupole split value for doublet 2 for our fayalite (i.e., 2.71 mm/s) vs. that of an end-member composition synthetic fayalite (i.e., 2.76 mm/s).

A possible systematic difference between the spectra of natural and synthetic olivines may lie in the values of the absorption line widths (i.e., FWHM). For the two natural crystals they are the same with values of 0.24 mm/s, whereas synthetics give values of about 0.29 mm/s for Fa₁₀₀ and 0.27 mm/s for Fo₉₀Fa₁₀ (Dyar et al. 2009) A precise crystal-chemical interpretation of the line widths is difficult to make, but larger widths may reflect more nearest or next-nearest neighbor atomic disorder (i.e., structural heterogeneity).

C_P(T) and S° behavior

The C _P(2–300 K) behavior of natural fayalite and synthetic Fa₁₀₀ is in excellent agreement. Even C _P arising from magnon contributions and the Schottky anomaly is the same for the two crystal types. This agreement is a notable result, we think, considering the very different origins of the two olivine samples. There is a slight difference of about 2 K between the T_N values (~65 K for synthetic samples vs. 63 K for the natural crystal). In the case of “end-member composition” silicate garnets, small variations in T_N can arise from minor concentrations of “impurity” cations occurring in solid solution (Geiger et al. 2019). This is possibly the case here as well because the natural fayalite contains some Mn²⁺ substituting for Fe²⁺. Because Mn²⁺ and Fe²⁺ have similar masses (54.94 and 55.85 amu, respectively) and ionic radii in sixfold coordination (83 pm vs. 78 pm), their vibrational (phonon) behavior in olivine should be similar. There is excellent agreement among the S ° values for synthetic fayalite of 151.0 ± 0.2 J/(mol·K) (Robie et al. 1982b) and 151.4 ± 0.1 J/(mol·K) (Dachs et al. 2007) and for the natural fayalite [151.6 ± 1.1 J/(mol·K)].

The C _P(T) behavior of the natural forsterite Fo_0.894Fa_0.106 and the synthetic Fo₉₀Fa₁₀ sample (Dachs et al. 2007) are in excellent agreement between about 7 and 300 K. It would appear that any phonon difference arising from possible variations in Fe²⁺-Mg order-disorder are minimal to nil. The only observable differences in C _P behavior lies at T < 7 K. The natural crystal does not show Debye T³ behavior but instead a quasi-plateauing of C _P values between about 2 and 7 K (Fig. 2b).

A physical interpretation for this result is difficult to make. There is very little research, of any type, on silicates at such low temperatures. Many older adiabatic calorimetry investigations were only made down to roughly 8 K. However, one could speculate that the plateauing is due to an “impurity” atom such as Fe³⁺. Gmelin (1969) undertook very low C _P measurements down to 0.5 K on MgO and proposed that 340 ppm Fe³⁺ gives rise to an anomaly centered at roughly 1–2 K. Such concentrations of Fe³⁺ in natural olivine are possible, but more work is required to fully explain the nature of this C _P anomaly. This very low-temperature behavior is not of great significance for chemical thermodynamic calculations but rather for its thermal physical nature. The S° of the crystal is 99.1 ± 0.7 J/(mol·K) and, thus, the same as that measured for synthetic Fo_0.90Fa_0.10 having a value of 99.5 ± 0.1 J/(mol·K) (Dachs et al. 2007).