Crystal Chemistry of Synthetic Mg(Si_1−xGe_x)O₃ Pyroxenes: A Single-Crystal X-ray Diffraction Study

Abstract

Germanate-pyroxenes often are used as model systems to study the stability and phase relationships of analog silicate systems. Based on such analyses, it is assumed that silicates and germanates behave ideally in terms of mixing. A systematic study was performed to monitor in detail the changes introduced by a Si⁴⁺ through Ge⁴⁺ replacement in the important rock-forming pyroxene enstatite MgSiO₃. Well-shaped, idiomorphic singe crystals of a MgSi_1−xGe_xO₃ pyroxene solid solution were grown at ambient pressure from a high-temperature flux-assisted synthesis. Structural analysis using single-crystal X-ray diffraction methods revealed orthorhombic symmetry, Pbca, Z = 8, for the complete solid-solution series. Long-term storage over a period of 8 years at ambient conditions or annealing at 525 °C over a period of 10 weeks did not change the symmetry of the proposed thermodynamically stable monoclinic polymorph. Within the solid-solution series, lattice parameters increased almost linearly with increasing Si⁴⁺ by Ge⁴⁺ substitution. The main changes occurred on the tetrahedral sites, which showed an almost linear increase in individual and average bond lengths but also in distortion parameters. The refined site occupancy of Si⁴⁺ and Ge⁴⁺ showed a distinct preference of Ge⁴⁺ for the TB site. The altered topology and kinking state in the tetrahedral chains also imposed significant changes to the bonding topology and geometry of the neighboring M1 and M2 sites.

1. Introduction

Pyroxenes are very abundant and important rock-forming silicates and, thus, are widely studied in geoscience. Pyroxenes of the (Mg,Fe)SiO₃ series make up approximately 40% of the Earth’s upper mantle [1,2]. An understanding of the phase relationships and physical properties under the geological conditions of these phases is thus of general interest in geoscience. However, there is also a vivid interest in pyroxenes in crystal structure research because of their rich crystal chemistry with triclinic ($P\overline{1}$), monoclinic (high-temperature and high-pressure C2/c structures, namely, P2₁/c, P2₁/n and P2/n) and orthorhombic (Pbca) polymorphs as a function of temperature (T), pressure (P) and chemical composition (X). The crystal structures of these polymorphs are closely related to each other. The main characteristics of the pyroxene structure are infinite zig-zag chains of octahedrally coordinated M1 sites with laterally attached five- to eight-fold coordinated M2 sites. Both sites form bands parallel to the c-axis, which themselves are stacked along the a-axis alternately with layer-like units built up by infinite single chains of tetrahedral sites. The tetrahedral chains are kinked to maintain the connection between M1 and octahedral sites and also run parallel to the c-axis. The stacking and orientation of the M1 site octahedra with respect to the silicate chain along the a-axis and the topology of the tetrahedral chains (one equivalent T or two symmetry non-equivalent TA and TB chains) yield different polymorphs with different space group symmetries. A detailed review of pyroxene topology and chemistry with the introduction of the often-used I-beam scheme was carried out by Cameron and Papike [2], and more information on the behavior of pyroxenes at high T and P levels can be found in [3]. Generalized phase relationships in the P-T field were proposed by Angel and Arlt [4]. The rarely found $P\overline{1}$ polymorph is the low-temperature form of synthetic NaTiSi₂O₆ [5], while the unusual P2₁/n structure is found so far only in synthetic LiAlGe₂O₆ [6].

Enstatite MgSiO₃ is a typical example of a pyroxene, showing both monoclinic and orthorhombic polymorphs depending on formation (synthesis) conditions, with a total of five different polymorphs. In its low-temperature, low-pressure form, MgSiO₃ adopts a monoclinic P2₁/c structure (clino-enstatite). At elevated temperatures, it transforms to the orthorhombic Pbca structure, while increasing pressure stabilizes the high-pressure C2/c structure for P > 6 GPa [7,8,9]. A similar effect was found by Ulmer and Stalder from Raman spectroscopic data on quenched samples [10]. Extrapolating the phase boundary between P2₁/c clino- and Pbca orthopyroxene to atmospheric pressure gives a transition temperature of ~550 °C [10]. At a high temperature of 1170 °C, ortho-enstatite transforms to proto-enstatite (high-temperature orthopyroxene) [11,12]. This high-temperature orthorhombic phase is non-quenchable and is only observable in in situ experiments. The equation of state and the phase relationships of the MgSiO₃ pyroxene system at pressures up to 12 GPa were recently summarized by Sokolova et al. [13], confirming the generally accepted P-T phase diagram, with P2₁/c clino-enstatite being the thermodynamically stable phase at ambient pressure and temperature conditions.

Several studies, however, have shown that during single-crystal growth of MgSiO₃ and using solvent-assisted synthesis with a lithiumvanadomolybdate as flux at ambient pressures, Pbca ortho-enstatite is the phase obtained instead of clino-enstatite, as would be expected from the phase relationships [9,11,14]. This indicates that the Pbca phase is quenchable and preserved during the (rapid) cooling from high temperatures after synthesis. Using this synthesis method, large, euhedral single crystals up to several millimeters in size were grown [9].

Many studies have also been performed on MgGeO₃, as can be seen in a low-pressure model of the (Mg,Fe)SiO₃ Earth crust- and mantle-forming system [15,16]. Like in MgSiO₃, MgGeO₃ pyroxene-type structures transform to ilmenite, to perovskite, and to post-perovskite structures but at lower and thus more accessible pressures [15]. Several studies were performed to determine the phase stability of different pyroxene modifications of MgGeO₃ at pressures < 8 GPa [14,17,18], yielding partially contradicting results. Recently Hunt et al. [15] reinvestigated the phase relationships and confirmed the results of [17], with orthorhombic MgGeO₃ being the stable phase at ambient pressures up to at least 1200 °C. Applying low pressures < 1 GPa, however, quickly stabilizes the clinopyroxene structure. This contradicts some findings of [19] that state that the stable, low-temperature form of MgGeO₃ at ambient pressure is also monoclinic: space group C2/c. Their monoclinic MgGeO₃ material was synthesized from flux-assisted crystal growth, quenched from 800 °C. Ozima and Akimoto [14] observed dominating orthopyroxene in their flux growth experiments but also, simultaneously, some monoclinic-phase MgGeO₃ in a single run. Their cut-off temperature of synthesis was 650 °C. Welch and Pawley [20] performed synthesis of MgGeO₃ using hydrothermal techniques at 650 °C and low pressures of 0.2 GPa, also yielding monoclinic C2/c clinopyroxenes.

Many silicate pyroxenes can only be synthesized by applying non-ambient pressures (>1 kbar), which makes experimental set-up more advanced. For such synthesis techniques, special equipment (hydrothermal synthesis in cold-sealed autoclaves or piston–cylinder apparatus for pressures < 4 kbar) is needed. Besides more sophisticated synthesis techniques, an additional disadvantage is the often very limited sample amount. This may hinder analyses requiring sample masses in the gram range, such as neutron diffraction, or multi-methodical approaches. Alternatively, it has been shown that Ge analogs of silicate-based minerals can often be used as good model systems to understand the mechanisms of structural phase transitions in minerals as a function of T and P [20,21,22,23,24]. As summarized in [20], the main assumption in investigations of Si⁴⁺ with Ge⁴⁺ substituted synthetic minerals is that they are thermodynamically and structurally representatives of their silicate counterparts. This holds true in the general sense and adds some additional benefits: (i) the synthesis of Ge analogs often can be performed at ambient pressures and (ii) phase transitions are shifted to experimentally more accessible (lower) temperature and pressure regions [25,26,27,28]. Studying binary Si-Ge series can offer reliable information on the ideality or non-ideality of such substitutions. This can finally prove the utility of Ge analogs as model systems for silicate mineral behavior.

Herein, the geoscientific, important solid-solution series MgSiO₃-MgGeO₃ was investigated structurally at room temperature to clarify the ideal (linear) or non-ideal behavior of mixing. Further aims are mainly the question of symmetry of the MgSiO₃ end-member, how the substitution of the larger Ge⁴⁺ cation in place of Si⁴⁺ alters the structure and if there is random distribution of Ge⁴⁺ onto the two possible tetrahedral positions.

2. Materials and Methods

2.1. Synthesis

Single crystals of MgSi_1−xGe_xO₃ with 0.0 ≤ x ≤ 1.0 were synthesized using a high-temperature, flux-assisted growth technique, which was first applied by Ito [9] for the synthesis of ortho-enstatite MgSiO₃ and later by Ozima [14] for the orthopyroxene MgGeO₃. In the first step, reagent-grade MgO (98%, Merck, Darmstadt, Germany), quartz SiO₂ (99.8%, Merck, Darmstadt, Germany) and GeO₂ (99.998% metal basis, Aldrich, St.Louise, MO, USA) were weighed to the stoichiometry of the desired solid-solution composition and carefully mixed by grinding them in an agate mortar under alcohol for at least 20 min. The flux was the same as used by [9] and consisted of a mixture of 34.9 weight % MoO₃ (99.5%, Sigma-Aldrich), 6.3 weight % V₂O₅ (>99.6%, Aldrich) and 21.9 weight % Li₂CO₃ (99.9%, Merck). The flux was also mixed carefully by grinding for 20 min. One large batch of flux was prepared and the same flux was used for all experiments. For the synthesis itself, the flux-to-nutrient ratio was 14:1 by weight. The mixture was put into a platinum crucible, covered with a platinum lid, heated to 960 °C at a rate of 5°/minute in a chamber furnace under ambient conditions (air, atmospheric pressure) and maintained at this temperature for 7 d for soaking. Then, the melt was cooled to 700 °C at a rate of 0.03°/min. After reaching the final temperature, the furnace was shut down and the synthesis batch furnace cooled.

After synthesis, the melt cake had a yellowish color. The flux was removed completely by soaking the synthesis batch in hot distilled water for several hours with intermediate washing cycles until only small, transparent, colorless pyroxene crystals were recovered. The final product was filtered, air dried and stored for further analysis.

2.2. Single-Crystal X-ray Diffraction (SCXRD)

For single-crystal X-ray diffraction, suitable crystals, selected on the basis of their optical properties (regular shape and homogeneity in color), were glued on top of glass capillaries (0.1 mm Ø). Single-crystal X-ray diffraction data were collected on a Bruker SMART APEX CCD-diffractometer. Intensity data were collected with graphite-monochromatized Mo K_α X-radiation (50 kV, 20 mA); the crystal-to-detector distance was 60 mm and the detector was positioned at −30° and −50° 2Θ using an ω-scan mode strategy at four different ϕ positions (0°, 90°, 180° and 270°) for each 2Θ position. In total, 630 frames with Δω = 0.3° were acquired for each run.

Three-dimensional data were integrated and corrected for Lorentz, polarization and background effects using the APEX3 software [29]. Structure solution (using direct methods) and subsequent weighted full-matrix least-squares refinements on F² were performed with SHELX-2012 [30] as implemented in the program suite WinGX 2023.1 [31]. Structural drawings and calculations of polyhedral volume and distortion parameters were carried out using VESTA [32]. The definition of the distortion parameters can be found in Appendix A.

3. Results and Discussion

3.1. Synthesis and Morphology

It was possible to synthesize well-shaped, colorless crystals, partly reaching up several mm in size for all compositions. This especially holds true for Si-rich compositions. The obtained crystals are highly transparent without obvious defects inside, except for some cracks. Optical microscopic photographs of typical crystals of MgSiO₃ and MgGeO₃ crystals are displayed in Figure 1. For MgSiO₃, the crystals are needle-like, columnar and they are elongated along the c-axis with well-developed faces. The largest needles reach up 5 mm in length, while most of the crystals are shorter and prismatic with sizes up to 0.5 mm. The crystals have an octagonal cross-section with well-developed {1 0 0}, {0 1 0} and {2 1 0} faces, and these columns are capped by {1 1 1} and {2 1 1} faces. Some large platelet-shaped crystals were also observed (up to 3 × 5 × 0.5 mm), with {1 0 0} and {0 1 0} faces dominating. In MgGeO₃, crystals tend to be smaller and exhibit less perfect idiomorphic shapes; however, the habit is exactly the same as for the MgSiO₃ end-member described above. No obvious coloring of the crystals was observed.

3.2. Single-Crystal X-ray Diffraction

A total of 26 datasets for crystals with 11 different nominal compositions were collected. Most of the data recordings were conducted directly after the synthesis experiments in early 2016. Additionally, some new datasets were collected recently for the Si and Ge end-member compositions to check for any changes in symmetry due to long storage times at ambient pressure and temperature over a period of ~8 years. Analysis of systematic absences of observed Bragg peaks and intensity statistics yields orthorhombic symmetry with space group Pbca for all crystals along the solid solution and for those in long-term storage. No change to the proposed thermodynamic stable monoclinic P2₁/c polymorphs was observed with time and the orthorhombic forms remained metastable when exposed to ambient pressure/temperature conditions.

Single crystals of pure MgSiO₃ and MgGeO₃ were also annealed at 400 °C over a period of 14 days. Quick data collections to check the unit cell parameters and symmetry of these annealed crystals showed them to have retained their original structure. Lattice parameters are identical within standard deviations to full data collections. In addition, the same material was further annealed at 525 °C for another 56 days and no change from orthorhombic to monoclinic symmetry was observed; diffraction peaks remained remarkably sharp with no indication of streaks or any hints of transformation.

Details on data collection and structure refinement for selected crystals are given in

Table 1. Experimental details and refinement results of X-ray diffraction data of selected flux-grown MgSi_1−xGe_xO₃ single crystals. Experiments were carried out with Mo Kα-radiation, λ = 0.71073 Å, using a Bruker Smart Apex 3-circle diffractometer. Full-matrix least-squares refinement of F² crystal system is orthorhombic; space group is Pbca with Z = 8 for all data given.

Composition Sample ID	MgSiO3 MgGe00_1	MgSi0.83Ge0.17O3 MgGe20_1	MgSi0.63Ge0.37O3 MgGe40_1	MgSi0.41Ge0.59O3 MgGe60_1	MgSi0.22Ge0.78O3 MgGe80_1	MgGeO3 MgGe100_1
Crystal Data
a (Å)	18.2399(12)	18.3324(3)	18.4792(15)	18.6067(5)	18.7076(3)	18.8189(7)
b (Å)	8.8207(6)	8.84471(15)	8.8717(7)	8.8974(3)	8.92245(14)	8.9516(3)
c (Å)	5.1843(4)	5.21380(9)	5.2519(4)	5.2863(2)	5.31456(8)	5.3470(2)
V (Å3)	834.10(10)	845.39(2)	861.01(12)	875.15(5)	887.09(2)	900.75(6)
Density mg/m3	3.198	3.395	3.603	3.841	4.037	4.274
μ (mm−1)	1.098	3.380	5.899	8.634	10.890	13.575
Crystal Size (mm)	0.12	0.14	0.11	0.13	0.12	0.14
	0.07	0.08	0.10	0.11	0.10	0.11
	0.07	0.08	0.08	0.09	0.09	0.10
Data Collection
${\left(sin\theta /\lambda \right)}_{max}$ (Å−1)	0.698	0.694	0.687	0.694	0.691	0.689
Reflections coll.	10,420	21,158	9929	21,907	18,421	11,566
Independ. Refl.	1150	1185	1182	1222	1240	1250
Index Ranges: h	−25 … 25	−25 … 25	−25 … 25	−25 … 25	−25 … 25	−25 … 25
k	−12 … 11	−12 … 12	−12 … 11	−12 … 12	−12 … 12	−12 … 12
l	−6 … 7	−7 … 7	−6 … 7	−7 … 7	−7 … 7	−7 … 7
Completeness %	99.7	99.7	99.6	99.6	99.8	99.8
Rint	0.018	0.020	0.021	0.0307	0.0302	0.0216
Refinement
Data	1150	1185	1182	1222	1240	1250
Restrains	0	2	2	2	2	0
Parameters	92	96	96	96	96	92
R1 (all data)	1.86	1.78	2.32	1.63	1.60	1.52
wR2 (all data)	6.11	4.92	4.59	3.84	3.49	3.93
Goodness of Fit	1.156	1.217	1.136	1.185	1.119	1.188
$\mathsf{\Delta }{\rho }_{max},\mathsf{\Delta }{\rho }_{min}$ (e/Å)	0.461/−0.378	0.392/−0.300	0.351/−0.382	0.460/−0.275	0.505/−0.309	0.366/−0.572

. Fractional atomic coordinates and equivalent isotropic atomic displacement parameters are given in

Table 2. Atomic coordinates and equivalent isotropic displacement parameters for selected single crystals of the MgSi_1−xGe_xO₃ solid-solution series. U (eq) is defined as one-third of the trace of the orthogonalized U_ij tensor.

ID	Wykoff Site	x	y	z	s.o.f.	U (eq)
MgGe00_1
Mg(1)	8c	0.3758(1)	0.6537(1)	0.8661(1)	1	0.00507(13)
Mg(2)	8c	0.3768(1)	0.4869(1)	0.3589(1)	1	0.00814(13)
SiA	8c	0.2717(1)	0.3416(1)	0.0504(1)	1	0.00406(11)
SiB	8c	0.4736(1)	0.3374(1)	0.7983(1)	1	0.00375(11)
O(1A)	8c	0.1834(1)	0.3400(1)	0.0351(2)	1	0.0058(19)
O(2A)	8c	0.3109(1)	0.5026(1)	0.0433(2)	1	0.00699(1)
O(3A)	8c	0.3032(1)	0.2227(1)	−0.1685(2)	1	0.00671(1)
O(1B)	8c	0.5625(1)	0.3402(1)	0.8000(2)	1	0.00603(19)
O(2B)	8c	0.4328(1)	0.4832(1)	0.6892(2)	1	0.00712(19)
O(3B)	8c	0.4476(1)	0.1950(1)	0.6036(2)	1	0.00654(18)
MgGe20_1
Mg(1)	8c	0.3754(1)	0.6539(1)	0.8624(1)	1	0.00563(13)
Mg(2)	8c	0.3767(1)	0.4871(1)	0.3548(1)	1	0.00872(14)
SiA	8c	0.2715(1)	0.3420(1)	0.0471(1)	0.901(2)	0.00414(12)
GeA	8c	0.2715(1)	0.3420(1)	0.0471(1)	0.099(2)	0.00414(12)
SiB	8c	0.4732(1)	0.3385(1)	0.8019(1)	0.756(3)	0.00430(10)
GeB	8c	0.4732(1)	0.3385(1)	0.8019(1)	0.244(3)	0.00430(10)
O(1A)	8c	0.1832(1)	0.3401(1)	0.0315(2)	1	0.0070(2)
O(2A)	8c	0.3109(1)	0.5035(1)	0.0407(2)	1	0.0082(2)
O(3A)	8c	0.3034(1)	0.2219(1)	−0.1707(2)	1	0.0082(2)
O(1B)	8c	0.5632(1)	0.3398(1)	0.8045(2)	1	0.0067(2)
O(2B)	8c	0.4321(1)	0.4844(1)	0.6842(2)	1	0.0085(2)
O(3B)	8c	0.4467(1)	0.1908(1)	0.6108(2)	1	0.0092(2)
MgGe40_1
Mg(1)	8c	0.3752(1)	0.6545(1)	0.8582(1)	1	0.00758(16)
Mg(2)	8c	0.3767(1)	0.4875(1)	0.3505(1)	1	0.00965(16)
SiA	8c	0.2713(1)	0.3425(1)	0.438(1)	0.763(3)	0.00547(12)
GeA	8c	0.2713(1)	0.3425(1)	0.0438(1)	0.237(3)	0.00547(12)
SiB	8c	0.4730(1)	0.3393(1)	0.8039(1)	0.502(3)	0.00565(10)
GeB	8c	0.4730(1)	0.3393(1)	0.8039(1)	0.498(3)	0.00565(10)
O(1A)	8c	0.1827(1)	0.3402(1)	0.0275(3)	1	0.0087(3)
O(2A)	8c	0.3111(1)	0.5050(2)	0.0375(3)	1	0.0101(3)
O(3A)	8c	0.3037(1)	0.2200(2)	−0.1717(3)	1	0.0109(3)
O(1B)	8c	0.5640(1)	0.3395(1)	0.8080(2)	1	0.0083(3)
O(2B)	8c	0.4313(1)	0.4858(2)	0.6791(3)	1	0.0103(3)
O(3B)	8c	0.4459(1)	0.1862(2)	0.6178(3)	1	0.0112(3)
MgGe60_1
Mg(1)	8c	0.3753(1)	0.6550(1)	0.8551(1)	1	0.00596(14)
Mg(2)	8c	0.3768(1)	0.4879(1)	0.3472(1)	1	0.00833(15)
SiA	8c	0.2712(1)	0.3432(1)	0.0420(1)	0.542(2)	0.00368(9)
GeA	8c	0.2712(1)	0.3432(1)	0.0420(1)	0.458(3)	0.00368(9)
SiB	8c	0.4727(1)	0.3397(1)	0.8047(1)	0.284(3)	0.00349(8)
GeB	8c	0.4727(1)	0.3397(1)	0.8047(1)	0.716(3)	0.00349(8)
O(1A)	8c	0.1818(1)	0.3402(1)	0.0248(2)	1	0.0075(2)
O(2A)	8c	0.3115(1)	0.5080(1)	0.0361(2)	1	0.0092(3)
O(3A)	8c	0.3046(1)	0.2174(1)	−0.1703(2)	1	0.0100(3)
O(1B)	8c	0.5646(1)	0.3390(1)	0.8114(2)	1	0.0068(2)
O(2B)	8c	0.4308(1)	0.4872(1)	0.6746(2)	1	0.0087(2)
O(3B)	8c	0.4451(1)	0.1828(1)	0.6226(2)	1	0.0088(3)
MgGe80_1
Mg(1)	8c	0.3760(1)	0.6557(1)	0.8531(1)	1	0.00674(14)
Mg(2)	8c	0.3773(1)	0.4884(1)	0.3454(1)	1	0.00840(14)
SiA	8c	0.2710(1)	0.3441(1)	0.0416(1)	0.298(3)	0.00445(8)
GeA	8c	0.2710(1)	0.3441(1)	0.0416(1)	0.702(3)	0.00445(8)
SiB	8c	0.4724(1)	0.3397(1)	0.8052(1)	0.156(3)	0.00423(7)
GeB	8c	0.4724(1)	0.3397(1)	0.8052(1)	0.844(3)	0.00423(7)
O(1A)	8c	0.1806(1)	0.3403(1)	0.0233(2)	1	0.0080(2)
O(2A)	8c	0.3120(1)	0.5115(1)	0.0360(2)	1	0.0097(3)
O(3A)	8c	0.3058(1)	0.2142(1)	−0.1669(2)	1	0.0101(3)
O(1B)	8c	0.5646(1)	0.3387(1)	0.8134(2)	1	0.0074(2)
O(2B)	8c	0.4306(1)	0.4878(1)	0.6724(2)	1	0.0089(2)
O(3B)	8c	0.4447(1)	0.1810(1)	0.6248(2)	1	0.0085(3)
MgGe100_1
Mg(1)	8c	0.3765(1)	0.6561(1)	0.8516(1)	1	0.00316(13)
Mg(2)	8c	0.3778(1)	0.4887(1)	0.3437(1)	1	0.00705(14)
GeA	8c	0.2710(1)	0.3450(1)	0.0413(1)	1	0.00365(7)
GeB	8c	0.4722(1)	0.3396(1)	0.8053(1)	1	0.00332(7)
O(1A)	8c	0.1794(1)	0.3399(2)	0.0219(3)	1	0.0048(3)
O(2A)	8c	0.3124(1)	0.5148(2)	0.0352(3)	1	0.0073(3)
O(3A)	8c	0.3070(1)	0.2110(2)	−0.1639(2)	1	0.0063(3)
O(1B)	8c	0.5646(1)	0.3379(1)	0.8149(3)	1	0.0050(3)
O(2B)	8c	0.4305(1)	0.4886(2)	0.6710(2)	1	0.0069(3)
O(3B)	8c	0.4444(1)	0.1798(2)	0.6262(3)	1	0.0056(3)

.

Table 3. Selected bond length and distortion parameters for single crystals along the MgSi_1−xGe_xO₃ solid-solution series.

Composition Sample ID	MgSiO3 MgGe00_1	MgSi0.83Ge0.17O3 MgGe20_1	MgSi0.63Ge0.37O3 MgGe40_1	MgSi0.41Ge0.59O3 MgGe60_1	MgSi0.23Ge0.77O3 MgGe80_1	MgGeO3 MgGe100_1
M1 site
Mg1-O2Aviii (Å)	2.0049(9)	2.0086(12)	2.0121(15)	2.0095(13)	2.0082(13)	2.0052(13)
Mg1-O1Aiv (Å)	2.0282(10)	2.0329(12)	2.0407(15)	2.0450(13)	2.0484(13)	2.0533(14)
Mg1-O2B (Å)	2.0454(10)	2.0470(12)	2.0502(14)	2.0507(13)	2.0520(13)	2.0524(13)
Mg1-O1Bvii (Å)	2.0656(9)	2.0700(12)	2.0829(14)	2.0883(13)	2.0924(13)	2.0995(13)
Mg1-O1Avi (Å)	2.1526(9)	2.1547(11)	2.1530(14)	2.1566(13)	2.1565(13)	2.1547(13)
Mg1-O1Bv (Å)	2.1717(9)	2.1742(11)	2.1719(14)	2.1686(12)	2.1646(13)	2.1598(13)
<Mg1-O> (Å)	2.0781	2.0812	2.0851	2.0865	2.0870	2.0875
Volume (Å3)	11.824	11.867	11.930	11.924	11.915	11.912
Dist. Index (a)	0.0270	0.0267	0.0250	0.0247	0.0244	0.0242
OQE (b)	1.0089	1.0095	1.0101	1.0112	1.0122	1.0133
OAV (c)	26.72	28.86	31.27	35.21	39.01	42.94
M2 site
Mg2-O2B (Å)	1.9944(10)	1.9955(12)	2.0001(15)	2.0019(13)	2.0036(13)	2.0111(13)
Mg2-O2A (Å)	2.0344(9)	2.0388(12)	2.0481(15)	2.0526(13)	2.0586(13)	2.0712(13)
Mg2-O1Biii (Å)	2.0570(9)	2.0607(11)	2.0619(14)	2.0650(13)	2.0671(13)	2.0744(13)
Mg2-O1Aiv (Å)	2.0910(10)	2.0951(12)	2.0994(15)	2.1010(13)	2.0987(13)	2.1019(13)
Mg2-O3Ai (Å)	2.2892(9)	2.2895(12)	2.2838(15)	2.2690(13)	2.2492(13)	2.2299(13)
Mg2-O3Bii (Å)	2.4484(10)	2.3961(12)	2.3456(15)	2.3087(13)	2.2909(13)	2.2804(13)
<Mg2-O> (Å)	2.1524	2.1460	2.1398	2.1329	2.1280	2.1281
Volume (Å3)	12.479	12.392	12.323	12.243	12.195	12.244
Dist. Index (a)	0.0670	0.0612	0.0545	0.0488	0.0445	0.0398
OQE (b)	1.0491	1.0466	1.0434	1.0405	1.0379	1.0359
OAV (c)	140.95	137.523	131.849	126.098	120.083	116.143
Tetrahedral A-site
GeA-O2A (Å)	1.5909(9)	1.6005(11)	1.6188(14)	1.6472(13)	1.6782(12)	1.7085(12)
GeA-O1A (Å)	1.6124(10)	1.6218(11)	1.6395(14)	1.6656(13)	1.6944(12)	1.7281(13)
GeA-O3A (Å)	1.6484(9)	1.6612(11)	1.6795(14)	1.7032(13)	1.7307(12)	1.7615(12)
GeA-O3Ai (Å)	1.6655(9)	1.6808(11)	1.7022(14)	1.7292(12)	1.7589(12)	1.7876(12)
<GeA-O> (Å)	1.6293	1.6411	1.6600	1.6863	1.7156	1.7464
Volume (Å3)	2.189	2.234	2.307	2.410	2.527	2.658
Dis. Index (a)	0.0170	0.0183	0.0186	0.0177	0.0171	0.0161
TQE (d)	1.0098	1.0106	1.0101	1.0142	1.0172	1.0202
TAV (e)	39.222	42.591	48.002	56.471	67.851	78.566
O3A-O3A-O3A (°)	158.96(8)	158.39(9)	157.05(9)	155.22(8)	152.94(9)	150.74(8)
Tetrahedral B site
GeB-O2B (Å)	1.5892(9)	1.6154(11)	1.6436(15)	1.6741(12)	1.6907(12)	1.7060(12)
GeA-O1B (Å)	1.6223(9)	1.6503(11)	1.6827(13)	1.7099(12)	1.7253(12)	1.7405(14)
GeA-O3B (Å)	1.6771(9)	1.7131(12)	1.7470(14)	1.7718(12)	1.7871(12)	1.7985(12)
GeA-O3Bi (Å)	1.6793(9)	1.7017(11)	1.7375(14)	1.7686(12)	1.7857(12)	1.8022(12)
<GeA-O> (Å)	1.6420	1.6701	1.7027	1.7311	1.7472	1.7618
Volume (Å3)	2.2559	2.3726	2.516	2.6404	2.715	2.787
Dis. Index (a)	0.0220	0.0223	0.0228	0.0226	0.0224	0.0219
TQE (d)	1.0052	1.0056	1.0059	1.0061	1.0061	1.0063
TAV (e)	19.572	21.390	22.874	24.062	24.399	25.177
O3A-O3A-O3A (°)	138.98(8)	136.21(9)	133.33(10)	131.30(9)	130.26(8)	129.68

(a) Distortion index, (b) OQE = octahedral quadratic elongation, (c) OAV = octahedral angle variance, (d) TQE = tetrahedral quadratic elongation, (e) TAV = tetrahedral angle variance. All values calculated with VESTA [32]. For definition of parameters, see Appendix A.

reports selected bond lengths for the refinements given in Table 1. The full data for 10 representative compositions in this study, including anisotropic atomic displacement parameters, were deposited as a CIF (crystallographic information file) to the Cambridge Crystallographic Data Centre and can be retrieved under CSD Numbers # 2371508–# 2371517.

Data for pure enstatite MgSiO₃ were used for model building. Structure solution and subsequent refinements yield a model with two positions for Mg and Si each and six positions for the oxygen atoms in agreement with published data. All atoms reside on general position 8c with site symmetry 1, so there are no symmetry-equivalent coordinating anions to the cations, nor are there symmetry-equivalent bonds. In the final model, fractional atomic coordinates were listed in accordance with the established convention [33,34,35]. Test refinements on end-member compositions with unconstrained site occupation factors for the M1, M2, TA and TB sites with the site occupation of the oxygen atoms were fixed to l (full occupation) yield values of ~1, indicating that all the sites show full occupation. Thus, in subsequent refinements on end-member and solid-solution compounds, the occupation of the tetrahedral sites TA and TB was constrained to a value of Si + Ge = 1, but the fraction and distribution of Si + Ge over the two T sites was allowed to refine freely. The scattering contrast is significantly different between these two elements (14 e⁻ vs. 32 e⁻), so a refinement of the chemical composition of the investigated crystals is enabled from the structure refinement. During these refinements, the occupation factors of the M1 and M2 sites were kept unconstrained and refined to values between 0.97 and 0.99, indicating full occupation of M sites. To reduce refinement parameters, in the final refinements the site occupation of M1 and M2 was also fixed to 1.

Exceptions to these observations were crystals from the first batch of compositions with x Ge = 0.5. Modeling the electron density at the M1 and M2 sites, respectively, with Mg only, it turned out that the M1 site showed site occupations larger than 1, i.e., heavier elements than Mg were present to some extent. At the M2 site, however, the reverse was observed with occupation factors of ~0.8 only, meaning that some lighter elements were present. As the flux contained Li, Mo and V, the M1 site finally was modeled with a mixed occupation of M1 = Mo + Mg = 1. For the M2 site, Li was also assumed to be present here for the charge balance and M2 = Li + Mg = 1. With this model, charge-balanced structural formulas were almost obtained, yielding Mg_0.84Mo_0.05Li_0.12Si_0.56Ge_0.44O₃ as the chemical composition from SCXRD. A second crystal gave Mg_0.85Mo_0.03Li_0.12Si_0.60Ge_0.40O₃. The incorporation of Mo³⁺ into the structure of orthopyroxene was facilitated by the coupled substitution Mg_1−3yMo³⁺_yLi⁺_3y(Si_1−xGe_x)O₃. More experiments would be necessary to clarify the maximum solubility of Mo³⁺ and Li⁺ in the pyroxene and the effect of Ge⁴⁺ by Si⁴⁺ substitution on it. The reason for the exceptional behavior of this run is unknown. It may be speculated that some problems occurred during furnace cooling as, in total, the number of single crystals in this run was low.

Because of the above behavior, new syntheses were performed with compositions of x = 0.50 to check for any unusual effects at the intermediate states of the solid-solution series. The obtained single crystals here fit perfectly to trends observed for all other compositions with no Li⁺ and Mo³⁺ incorporation.

3.2.1. Unit Cell Parameters

The variation in unit cell parameters and unit cell volume as a function of the Ge⁴⁺ content (x Ge) is shown in Figure 2. Data from the literature are included for comparison. It is evident that the increase in lattice parameters is smooth and follows a slightly non-linear trend for all three main axes. The substitution of the smaller Si⁴⁺ (Shannon ionic radius 0.26 Å) with the larger Ge⁴⁺ (Shannon radius = 0.40 Å) expands the a and c unit-cell dimension by ~3%, while the expansion along the b-axis is ~½ the value (Figure 2d). This smaller value can be related to changes in the kinking state of the tetrahedral chains, which mainly affects the b-axis.

3.2.2. Crystal Structure of MgSiO₃-MgGeO₃ Compounds

As mentioned in the Introduction, the structure of the orthopyroxenes is built up by three main building blocks: (i) octahedrally coordinated M1, (ii) octahedral M2 sites and (iii) two symmetrically distinct tetrahedral sites, TA and TB. A representative drawing of the structure of MgSiO₃, based on data from this study, is given in Figure 3. The M1 octahedra share two common edges with neighboring M1 sites, forming the infinite zig-zag chain parallel to the c-axis (Figure 3c). The M2 sites are alternatively attached left and right of the M1 chain forming M-site bands within the (1 0 0)/b–c plane. The orientation of the triangular faces of the M1 site with respect to the a-axis is of special interest. The tetrahedral sites share two common corners with each other (the O3 bridging oxygen atom O3_br), forming a distinctly kinked chain running parallel the c-axis (Figure 3b). These tetrahedral chains also form layer-like units within the (1 0 0) plane. These M-site and T-site “layers” alternate along the a-axis. It is to be noted that these—of course—are not classical layers as individual chains are not interconnected with each other.

In the monoclinic polymorphs, the orientation of the M1 sites along the a-axis (expressed by the orientation of the triangular faces of the octahedra) is the same throughout the whole structure, while in the orthorhombic form, a stagging with different orientations (expressed as + and − signs) is found as displayed in Figure 3a. This doubles the a unit-cell parameter with respect to the monoclinic polymorphs and also allows the choice of an orthogonal cell. The infinite tetrahedral zig-zag chains TA and TB also alternate in their stagging along the a-axis (Figure 3a).

As can be seen from Figure 4, the cations exhibit small and almost isotropic atomic displacement parameters. The smallest values are found for the atoms at the tetrahedral site, indicating strong bonding here. Within the solid-solution series, there is no evident increase in the atomic displacement parameters, which indicates some positional disorder at the TA and TB sites. For the cations, the largest atomic displacement is found for the Mg2 site with its more distant and highly distorted oxygen atom environment. Chemical bonding is obviously slightly weaker here than for the Mg1 and TA and TB sites. Oxygen atoms are generally larger and also display partly more anisotropic atomic displacement parameters. The O1A and O1B oxygen atoms bonded to the M1 and the tetrahedral sites (via the apex of the tetrahedron) exhibit the smallest values among the O sites, while the O3A and O3B exhibit largest atomic displacements. The latter are more anisotropic with the longest elongation perpendicular to the O3-O3-O3 bonds within the tetrahedral chains.

Looking at bond valences, the Mg1 cation in both MgSiO₃ and MgGeO₃ is over-bonded with valence sums of 2.149(2) and 2.099(4) charges, respectively, while the Mg2 cation is under-bonded with 1.885(3) and 1.919(2) charges, respectively. For the tetrahedral sites, the TA appears to be close to the ideal value of 4, while the TB site is distinctly under-bonded with 3.831(5) and 3.877(7) charges for MgSiO₃ and MgGeO₃, respectively. Generally, it can be observed that bond valences in MgGeO₃ are closer to the ideal value than in the Si⁴⁺ end-member. This also is expressed by a smaller global instability index GII in MgGeO₃.

3.2.3. The M1 Site

The Mg²⁺ ion at the M1 site in MgSiO₃ is six-fold coordinated to the O1A^iv,vi, the O1B^v,vii and the O2A^viii and the O2B oxygen atom, there is no link to the O3 tetrahedral bridging oxygen atoms (Figure 4). Individual M1 sites are connected to each other via the common O1A-O1B edges. The M1 site appears to be regular with Mg-O bond lengths in the range from 2.0049(9) to 2.1717(9) Å with an average value of <Mg1-O> = 2.0781 Å. Even if there is no change in chemistry at the M1 site, increasing Ge⁴⁺ substitution affects the M1 site as there is a direct connection of tetrahedral chains with the octahedral ones via common oxygen atoms O1A and O1B (apex oxygen atoms of the tetrahedral chain). The average <Mg1-O> bond length increases non-linearly by ~0.45% with the main increase at Si⁴⁺-rich compositions, while above x ~0.5 <Mg-O> remains almost constant. Data from the literature [20,35] are included for comparison and show the very same trend as that observed in this study; however, the trend is supported by more data with less scatter. The non-linear variation in <Mg1-O> is mainly due to the distinct anisotropic and also non-linear variation in individual M1-O bond lengths with increasing Ge⁴⁺ content (Table 3).

The changes in the bonds involving the O1A and O1B oxygen atoms can be directly related to the increasing kinking of the tetrahedral chains. Also, the O1A^iv-O1A^vi and the O1B^v-O1B^vii octahedral edge become stretched (Figure 5b). The oxygen atoms involved here are not only bonded to the M1 site but also are the apex oxygen atoms of the two opposing tetrahedral chains TA and TB.

The bonds from Mg1 to the O2 oxygen atoms remain constant within 0.3%. These bonds involve the connection of the M1 sites with the tetrahedral sites within the b,c plane and appear to be less affected by the Si⁴⁺ with Ge⁴⁺ replacement on the neighboring tetrahedral sites. The volume of the M1 site increases slightly towards intermediate compositions and remains constant afterwards. The M1 site in pure MgSiO₃ is remarkably regular, expressed by small numbers of the octahedral quadratic elongation (OQE) and octahedral angle variance (OAV). The Si⁴⁺ with Ge⁴⁺ substitution introduces increasing distortion both in the OQE as well as in the OAV, which increases by more than 60%.

3.2.4. The M2 site

The Mg2 cation in MgSiO₃ is six-fold coordinated to the O1A^iv, O1Bⁱⁱⁱ, O2A, O2B, O3Aⁱ and O3Bⁱⁱ oxygen atoms; the resulting octahedral site, however, is highly distorted, especially in the MgSiO₃ end-member. Four Mg-O bond lengths lie within 1.9952(8) and 2.0912(7) Å, while the bonds to the O3 bridging oxygen atoms O3Aⁱ and O3Bⁱⁱ of the tetrahedral chain are distinctly stretched with 2.2876(8) and 2.4218(8) Å, respectively. The large distortion of the M2 site is mainly due to the bonding to these two oxygen atoms. With increasing substitution of Si⁴⁺ by Ge⁴⁺, marked changes can be observed especially for the Mg2-O3Aⁱ and Mg2-O3Bⁱⁱ bond lengths, which distinctly decrease non-linearly (Figure 6a) by −2.6 and as much as −6.9%, respectively. The average M2-O bond length in sum decreases almost linearly up to x ~0.6 and then starts to flatten out (Figure 6b). Generally, <Mg2-O> is distinctly longer than <Mg1-O> by ~0.08 Å in pure MgSiO₃. This difference is halved towards MgGeO₃, but still amounts to ~0.04 Å.

The volume of the M2 octahedron decreases by ~2% toward MgGeO₃ and approaches the value of the M1 octahedron. Due to the more regular bond length distribution, all distortion parameters decrease and the M2 site in MgGeO₃ is much more regular than that in MgSiO₃ (Figure 6c,d). It is worth recalling that the OAV increases by 60% for the M1 site, while it decreases by 17% with increasing Ge⁴⁺ content for the M2 site. Still, the M2 octahedron is also distinctly more distorted than the corresponding M1 octahedron in MgGeO₃. Similar is observed for the other distortion parameters like the distortion index or the quadratic octahedral elongation. The observations of more regular M2 sites and a closer similarity between M1 and M2 octahedra in MgGeO₃ is also depicted by the more ideal bond valence sums and smaller global instability index (GII) values as reported in Section 3.2.2.

3.2.5. The Tetrahedral Sites

Pyroxenes with primitive unit cells (P2₁/c, Pbca) show two symmetrically distinct tetrahedral chains, TA and TB, also allowing different kinking states. This is the main difference to C-centered pyroxenes, where the two chains become symmetric-equivalent. The tetrahedral cation is four-fold coordinated to the O1A, O2A, O3A and O3Aⁱ oxygen atoms for the TA and to O1B, O2B, O3B and O3Bⁱ for the TB site. In MgSiO₃, the SiA-O bond lengths vary between 1.5909(9) Å and 1.6655(9) Å; the average bond length is <SiA-O> = 1.6293(9) Å. Generally, the distances to the bridging oxygen atoms, O3, are longer than those to O1 and O2. This is related to the stronger covalent character of the T-O3 bridging bond [35]. The difference between bridging <SiA-O_br> and non-bridging <SiA-O_nbr> bond lengths amounts to 0.055 Å.

The SiB-O bonds in MgSiO₃ vary between 1.5892(9) Å and 1.6793(10) Å, with an average value of <SiB-O> = 1.6420(10) Å. The difference between SiB-O_br and SiB-O_nbr is 0.075 Å and thus larger than for the A-chain. Because of the larger distribution of Si-O bonds, the distortion index is somewhat larger for the SiB tetrahedron, while in terms of the bond angle variance and the tetrahedral quadratic elongation, the SiB tetrahedron is more regular. The SiB tetrahedron exhibits a somewhat larger volume (2.19 ų and 2.26 ų for SiA and SiB, respectively). The A-chain is more stretched than the B-chain, expressed by larger ∠ O3A-O3A-O3A = 158.96(6)°. For the B-chain, the ∠ O3B-O3B-O3B = 138.98(7)°, showing this chain to be distinctly more kinked.

An important finding of this study is how Ge⁴⁺ distributes over the two possible sites, TA and TB. The high-quality data of this study allow for the refinement of Si⁴⁺ and Ge⁴⁺ distribution over the two possible TA and TB sites. In agreement with results of Welch and Pawley [20], there is a distinct ordering of the Ge⁴⁺ onto the TB site, as displayed in Figure 7a. Data from this study and those from [20] perfectly plot onto each other. For low overall Ge⁴⁺ concentrations, almost three times more Ge⁴⁺ enters the B site than the A site. With increasing overall Ge⁴⁺ content, the ratio between Ge⁴⁺ on TA/TB sites approaches a value of 1:2 for ~MgSi_0.65Ge_0.35O₃ and a ratio 1:1.5 for intermediate compositions. The TA/TB ratio becomes close to equal distribution only for very high overall Ge⁴⁺ contents. The variation in the Ge⁴⁺ distribution on TA and TB sites is non-linear. Due to different concentrations of Ge⁴⁺ on the two possible tetrahedral sites, considerations of variations in structural parameters are performed as a function of the Ge⁴⁺ content on the specific site.

Increasing the replacement of Si⁴⁺ by Ge⁴⁺ yields almost linear variations in average bond length with the Ge⁴⁺ content at the specific site. They increase by ~7.3% on average from MgSiO₃ to MgGeO₃ (Figure 7b). The difference between T-O_br and T-O_nbr bonds is unaffected by the Ge⁴⁺ substitution at the A-chain, while for the B-chain it increases slightly. This can be interpreted as an increasing covalency of the bonding within the bridging bonds towards the MgGeO₃ end-member in the B-chain. The volume of the TA and TB tetrahedra increases linearly with the Ge⁴⁺ content (Figure 7c) by 21.5% and 23.3%, respectively. There is a somewhat steeper increase in the volume of the B-chain tetrahedron, so the volume difference between the two tetrahedral sites also increases towards the MgGeO₃ end-member.

The substitution of Ge⁴⁺ influences the geometry and the distortion state of the tetrahedra (Figure 7d). The distortion of the A-chain tetrahedra thereby increases in a more pronounced manner as compared to the B-chain ones. For the B-chain, the tetrahedral angle variance (TAV) as well as the tetrahedral quadratic elongation (TQE) increase by 26% and 0.1%, respectively. This is distinctly smaller than the changes in TAV and TQE for the A-chain tetrahedra, with an increase in TAV of 102% and in TQE of 1.1% from MgSiO₃ to MgGeO₃. It is to be noted that the slopes and variations in TAV and TQE are almost identical; thus, only the TAV is shown in Figure 7d. For the distortion index, which is based on the deviations in individual bond length from their mean value, the situation is reversed. It slightly decreases for the A-chain tetrahedra, while it tends to increase for the B-chain. This means that even if the T-O bonds at the A-tetrahedron become more similar, the bond angles deviate more from their ideal value towards MgGeO₃.

As the size of the tetrahedra increases in course of the Si⁴⁺ by Ge⁴⁺ replacement (bond lengths increase by ~7%, volume increase by ~23%), however, the size of the M1 and M2 sites exhibit only small changes in the range of 1%; some effective mechanisms need to be at work to maintain connection, especially between the tetrahedral chains and the M1 octahedral zig-zag chains, which is sandwiched between a TA and TB chain. This mechanism is found in a rotation of the tetrahedra within the tetrahedral chains. With increasing Ge⁴⁺ content, the ∠ O3-O3-O3 bridging angles, which are the indicators for tetrahedral rotation in the pyroxenes, decrease for both sites, reflecting an increase in the tetrahedral kinking (Figure 8a). Different to [20], a somewhat non-parallel variation in angle reduction with increasing Ge⁴⁺ content is observed. Recalling the distinct changes in the Mg2-O3A and Mg2-O3B bond lengths, they can be explained as a direct consequence of this tetrahedral rotation. The smaller change in the Mg2-O3A bond lengths correlates with the smaller decrease in kinking of the A-chain. Also, the smaller change in the O1A^iv-O1A^vi octahedral edge compared to the O1B^v-O1B^vii edge is related to the smaller rotation of the A-chain with Ge⁴⁺.

It is pointed out by [20] that the reduced kinking of the A-chain is due to a constraining effect of the O2A-O3A edge, which is shared by the TA and the M2 polyhedra. When looking at the variations in tetrahedral O-O edge lengths with the Ge⁴⁺ content, it becomes evident that by far the shortest among all the tetrahedral edges is indeed the shared O2A-O3A edge (Figure 8b). Also, the rate of lengthening with increasing Ge⁴⁺ content is smallest and amounts to 3.7% only, followed by 4.8% for the O3-O3ⁱ edge. Also, for this edge, some constraining effects of the sharing of the O3 oxygen atoms with the M2 site are observed. The remaining four edges of the TA tetrahedron expand by 7.9%–8.7% with increasing Ge⁴⁺ content. The TB tetrahedron shares only corners with the neighboring Mg2 polyhedron and no obvious hindering effects on edge length expansion is found.

4. Conclusions

In this study, the structural variations within a series of synthetic MgSi_1−xGe_xO₃ pyroxenes have been studied. Different to [20], where the synthesis was performed under low-pressure conditions and the orthorhombic structure was found only for 0.2 ≤ x ≤ 0.65, the orthorhombic Pbca symmetry is observed throughout the whole solid-solution series in this study. Even long storage times of crystals and annealing at 525 °C preserves orthorhombic symmetry. Most structural parameters vary linearly as a function of Si⁴⁺ with Ge⁴⁺ substitution. This especially accounts for the unit cell parameters and the bond lengths on the tetrahedral sites. So, the exchange of Si⁴⁺ with Ge⁴⁺ seems to be ideal and using the Ge analog of silicates is a justified approach to study phase relations and phase transitions. The changed topology of the tetrahedral sites also introduces distinct changes at the M1 and M2 sites, respectively. In particular, the highly distorted Mg2 is subjected to distinct changes in bond lengths to the O3 oxygen atoms. These changes are a direct consequence of the rotation of the tetrahedral chains to maintain connection between octahedral M1 and tetrahedral chains.

The preferential ordering of Ge⁴⁺ onto the TB tetrahedron can be explained by the fact that the A-chain shares a polyhedral edge with the distorted M2 octahedron. This edge forces a significant limitation in the expansion of the tetrahedral TA site. In contrast, there is only corner sharing of the TB tetrahedron with the M2 octahedron and thus can accommodate the expansion of the tetrahedron in due course of Si⁴⁺ simple with Ge⁴⁺ substitution by a rotation of the base plane of the tetrahedron within the infinite chain. What is more, the TB site is already somewhat larger in MgSiO₃ and probably is more favorable for chemical substitution.