P2₁/c Postorthopyroxene γ-LiScGe₂O₆, a New Dense High-Pressure Polymorph and Its Direct Transformation from the Pbca Structure

Abstract

Orthorhombic β-LiScGe₂O₆ single crystals were compressed hydrostatically up to 10.35 GPa using a diamond anvil cell and investigated in situ by means of X-ray diffraction and Raman spectroscopy. Crystal-structure investigations at ambient conditions and at high pressure show a structural transition from an orthopyroxene-type Pbca structure (a ≈ 18.43 Å, b ≈ 8.85 Å, and c ≈ 5.34 Å at 8.6 ± 0.1 GPa) to a postorthopyroxene type P2₁/c structure of the new dense γ-LiScGe₂O₆ (a ≈ 18.62 Å, b ≈ 8.85 Å, c ≈ 5.20 Å, and β ≈ 93.1° at 9.5 ± 0.1 GPa). The structure refinements reveal displacive shifts of O atoms associated with a rotation of every other tetrahedral-chain unit from the O- to S-type position similar to the postorthopyroxene-type MgSiO₃. As a consequence of the oxygen displacement, the coordination number of Li atoms is changing from [5 + 1] to a proper 6-fold coordination. The transition around P_c = 9.0 ± 0.1 GPa is associated with a volume discontinuity of ΔV = −1.6%. This orthopyroxene (OEn-Pbca) to postorthopyroxene (pOEn-P2₁/c) transition is the second example of this type of transformation. Precise lattice parameters have been determined during isothermal compression. The fit of the unit-cell volumes of β-LiScGe₂O₆, using a third-order Birch–Murnaghan equation of state, yields V₀ = 943.63 ± 0.11 ų, K₀ = 89.8 ± 0.6 GPa, and dK/dP = 4.75 ± 0.18 as parameters. Evaluation of the data points beyond the critical transition pressure using a second-order Birch–Murnaghan equation suggests V₀ = 940.6 ± 4.4 ų and K₀ = 82.4 ± 4.8 GPa. A series of high-pressure Raman spectra confirm the symmetry-related structural transition, with band positions shifting in a noncontinuous manner, thus confirming the proposed first-order transition.

Short abstract

Synthetic lithium−scandium germanate crystals (space group Pbca at ambient conditions) were the subject of in situ high-pressure solid-state investigations (single-crystal X-ray diffraction, lattice parameter, and Raman spectra) in a diamond anvil cell up to 10 GPa. One phase transition, apparently of first order, is identified at 9.0 ± 0.1 GPa. The Birch−Murnaghan equations of state were fitted to the P−V data, and the obtained parameters are given. The transition is of the type orthoenstatite (Pbca) to postorthoenstatite (P2₁/c).

1. Introduction

Lithium homologues of the pyroxene structure family have recently come into the focus of interest in the search for novel multiferroic materials, especially because monoclinic LiMT₂O₆ and NaMT₂O₆ representatives (T = tetrahedral void occupied by, e.g., Si and Ge; M = octahedral void, occupied by, e.g., Sc, In, and Fe) exhibit orbital-assisted spin-Peierls transitions and magnetically driven ferroelectric properties.¹⁻⁷ Pyroxenes M1M2T₂O₆ occur in nature as rock-forming inosilicate minerals⁸ and are known for their wide crystallographic versatility, which includes the two major subgroups of orthorhombic orthopyroxenes and monoclinic clinopyroxenes. Considering the structural modularity and unit-cell twinning-based polytypism for observed crystallographic variations,⁹ structural diversifications have been explained based on variations within the infinite tetrahedral–octahedral–tetrahedral “I-beam” units and associated stacking sequences.^10,11 Essential features for distinguishing the structural variants are the TO₄-unit rotations in the T-chains (rotation of the S and O type) and the relative orientations of the octahedral M layers (M+ and M−).¹⁰⁻¹²

Because major parts of the Earth’s upper mantle consist of silicate pyroxenes, these isostructural compounds have been the subject of systematic studies of thermomechanical behavior and structure–property relationships, in particular with regard to temperature (T) and pressure (P) variations (cf. selected examples¹³⁻¹⁹). A rich polymorphism has been reported that includes the following four archetype phases, referred to as “enstatite” (En) based on the MgSiO₃ composition: high-clinoenstatite HCEn (C2/c), low-clinoenstatite LCEn (P2₁/c), orthoenstatite OEn (Pbca), and protoenstatite PEn (Pbcn).²⁰ The acentric structure variants, such as P2₁cn, are derived from a distorted PEn-Pbcn structure.²¹ Other exceptional symmetries, i.e. P2₁/n and P1̅, have so far only been found for individual representatives, such as LiAlGe₂O₆²² or NaTiSi₂O₆.^23,24 HCEn (C2/c) occurs in two variants, i.e., a unquenchable high-pressure (HP) form (HP-CEn^25,26) and a quenchable high-temperature phase (HT-CEn²⁷). A comparable distinction has to be made for the P2₁/c pyroxenes, where, in addition to the low-clinopyroxene form (LCEn-P2₁/c²⁸), HP variants (referred to as “HP-CEn2” or “HP-P2₁/c” in the literature) have recently been found for several representatives.²⁹⁻³²

Because of diverse polytypism, pyroxene structures were the subject of early studies on the course of phase transformation and the associated transformation mechanisms. Most prominent are the transitions between C2/c and P2₁/c, which are relevant for discontinuities in the seismic wave propagation within the Earth’s upper mantle.^33,34 LiAlSi₂O₆ (spodumene) represents one of the archetype structures (HT-CEn-C2/c), which was investigated for T and P variations. It shows a distinct displacive first-order phase transition from HT-CEn-C2/c to LCEn-P2₁/c.^16,35,36 The equivalent phase transition was reported for LiScSi₂O₆ and ZnSiO₃.³⁵ ZnSiO₃ was found to be one of the few examples showing a transition sequence upon isothermal compression at 298 K starting from HT-CEn-C2/c to LCEn-P2₁/c and continuing later to HP-CEn-C2/c. The second step corresponds to the well-known transformation reported for Mg₂Si₂O₆ and Fe₂Si₂O₆.^25,26,37 At considerably higher pressures, HP-CEn-C2/c structures undergo a further pressure-induced transition to the so-called “HP-P2₁/c” (here further referred to as HP-CEn2-P2₁/c), whereby part of the T cations transform to a 6-fold octahedral coordination.³⁰⁻³²

Germanate-analogue phases were already in focus early on because the larger Ge atoms were supposed to provide easier access to equivalent HP phases. Regardless of Si or Ge on the T sites, it is the relative size of the individual cations and their interplay at the T, M1, and M2 positions in the M2M1T₂O₆ compounds that control the structural stabilities and transformations (e.g., ref (38)). The exceptional P2₁/n germanate spodumene homologue, LiAlGe₂O₆, was found to transform to LCEn-P2₁/c.³⁹ Hydrostatic compression of the LCEn-P2₁/c spodumene analogue α-LiScGe₂O₆ shows no phase transition up to the hydrostatic limit of the pressure-transmitting medium at ∼10 GPa.⁴⁰ With regard to the ongoing systematic investigations on lithium pyroxene representatives, we have now conducted a compression study under comparable conditions on the β-LiScGe₂O₆ orthopyroxene of the OEn-Pbca type. The aim of this study was to understand the stability criteria from a structural point of view, any polymorphism, and the mechanisms of underlying transitions at nonambient pressure conditions.

2. Materials and Methods

Synthesis

Single-crystal synthesis of the orthorhombic form of β-LiScGe₂O₆ (β-LSG) was achieved using stoichiometric mixtures of Li₂CO₃, GeO₂, and Sc₂O₃. Crystallization was promoted by following a flux-growth method using a mixture of Li₂MoO₄ (8 parts) and LiVO₃ (2 parts) as the high-T solvent. The weight proportion between the stoichiometric nutrient materials and flux components was about 1:10. The mixtures of finely ground solid starting materials were placed in a platinum crucible and slowly heated to the target T of 1323 K at a rate of 3 K min^–1; going higher in the target temperature yields the formation of monoclinic α-LiScGe₂O₆.⁴⁰ After annealing for 24 h, the sample was cooled over 250 h at a rate of −0.03 K min^–1 to 873 K. After quenching to room temperature, the remnant flux was dissolved in hot distilled water. This synthesis route results in euhedral, idiomorphically shaped, colorless crystals of up to 2 mm in size (Figure S1). Selected crystals were checked by means of energy-dispersive X-ray spectroscopy for element substitutions from flux components. All investigated crystals reveal contents well below the detection limit and confirm the absence of any significant Mo and V substitution.

HP Sample Environment

Selected crystal fragments of suitable size and sufficient optical quality were loaded into ETH-type⁴¹ diamond anvil cells (DACs) using a conventional mixture of 4:1 methanol–ethanol as a pressure-transmitting medium. The pressure chamber, prepared in a stainless-steel gasket, had a starting diameter of 250 ± 5 μm and an initial thickness of around 98 ± 3 μm. The experiments were carried out using DACs with a culet-face diameter of 600 μm. Two to three small ruby spheres (∼12 μm) were used for P determination from their ruby R1 luminescence line.⁴²

Lattice Parameter and Isothermal Equation of State (EoS)

Precise pressures, as required for the EoS determination, were obtained from the volume data of an extra quartz standard crystal (40 × 40 × 20 μm³), applying the quartz gauge calibration data.⁴³ Thus, single-crystal X-ray diffraction (scXRD) used the 8-position centering technique.⁴⁴ The sample-crystal size was approximately 100 × 70 × 50 μm³. The setting angles of approximately 20 Bragg peaks were recorded using a Huber 5042 four-circle diffractometer with Mo Kα_1,2 radiation (λ ≈ 0.71 Å) from a conventional fine-focus sealed tube source. The software SINGLE(45) was used for controlling the diffractometer and to determine the lattice parameters and unit-cell volumes by applying refinements with symmetry-constraint vector least squares. The pressure for the individual data sets taken for this isothermal compression study ranges from ambient conditions up to around 10 GPa. Prior to fitting an EoS equation, f–F plots⁴⁶ were used to evaluate the influence of the pressure derivatives K′ and K″ on reproduction of the compressibility given by the P–V data points. Finally, the EoS parameters were determined by fitting a third-order Birch–Murnaghan (BM) equation⁴⁶ using the analytical software EoSFit7.^47,48

HP Crystal Structure

X-ray intensity data sets were recorded from a single-crystal sample mounted in a DAC with Boehler-Almax-type anvils.⁴⁹ Again, the sample-crystal size was about 100 × 70 × 50 μm³ (Figure S2). The scXRD data were collected using a Stoe StadiVari diffractometer, a molybdenum 50 W air-cooled Incoatec microfocus source, high-brilliance 2D-focusing Quazar multilayer optics, and a Dectris Pilatus 300 K pixel detector with a 450 μm Si layer. Data collection was achieved by ω scans with a 0.5° step width and 50, 70, and 90 s of exposure time per frame (for ambient pressure, 8.6 and 9.5 GPa, respectively). Further experimental details on the instrument settings, subsequent data reduction, and data resolution are summarized in Table 1. At ambient pressure, the reflection conditions were consistent with the orthorhombic space group Pbca, while at pressures higher than ∼9 GPa, they were consistent with the monoclinic space group P2₁/c. Careful inspection of the reconstructed reciprocal space suggests the existence of twinning of two monoclinic crystal domains for the P2₁/c structure (Figure 1). The measurements as well as the integration, scaling, and numerical absorption correction were performed by applying the X-AREA (Stoe & Cie GmbH) and Absorb7(50) software packages. The measurements at ambient pressure were carried out on the sample outside the DAC mounted on a glass fiber. All structure refinements were performed with SHELXL(51) and the graphical user interface ShelXle(52) based on the structure models reported earlier.^29,53 For twin refinement at 9.5 ± 0.1 GPa, both crystal domains were integrated into an hklf5 file and Mergehklf5(54) was used for merging the data sets. The resulting crystal structures were validated with checkCIF/Platon⁵⁵ for integrity and consistency.

Table 1. Crystal Data, Parameters of the scXRD Data Collection, and Results of the Structure Refinements.

	pressure (GPa)/temperature (K)
	10–4/298	8.6(1)/298	9.5(1)/298
space group (No.)	Pbca (61)	Pbca (61)	P21/c (14)
a (Å)	18.856(3)	18.428(2)	18.617(13)
b (Å)	9.125(1)	8.853(1)	8.849(1)
c (Å)	5.484(1)	5.342(1)	5.198(1)
β (deg)			93.13(5)
V (Å3)	943.6(3)	871.5(2)	855.1(2)
Z	8	8	8
measd reflns	52368	10947	15928a
unique reflns	3471	573	1078a
all/obsd reflns	3992	678	1218a
max 2θ	91.05	69.19	69.53
exposure time (s)	52	70	90
Rint	0.026	0.029	b
Rσ	0.011	0.014	0.015
R1(obs)c	0.013	0.029	0.031
R1(all)	0.018	0.037	0.037
wR2	0.024	0.070	0.083
GOF	1.014	1.122	1.060
refined parameter	101	66	90
weighting param (a/b)	0.013/0	0.039/2.64	0.052/2.78
max/min e– density (e Å–3)	0.49/–0.51	0.84/–0.56	1.42/–1.27

^ahklf5, two twin domains.

^bNot calculated, due to hklf5.

^cIntensity(obs) ≥ 3σ.

Figure 1.

Reconstructed h0l-plane sections of the reciprocal space as derived from the measured XRD image series collected at 8.6 ± 0.1 GPa (right) and 9.5 ± 0.1 GPa (left). Unit cells (dotted lines) with base vectors corresponding to the a* and c* reciprocal vector lengths are superimposed with the reconstructed sections in this projection down the [010] zone axis. While the reciprocal space at 8.6 GPa can be indexed based on an orthorhombic Pbca single-domain lattice, the pattern of reconstructed Bragg peaks at 9.5 GPa suggests the existence of two twinned lattices of monoclinic symmetry related to twin domains rotated by 180° around the former orthorhombic c axis.

HP Raman Spectroscopy

A LabRam HR800 spectrometer from Horiba Jobin Yvon with backscatter geometry and a Si-based Peltier-cooled CCD detector was used to monitor the P-induced band shifts of the R1 luminescence line of ruby, in order to monitor and adjust the pressure inside the pressure chamber. The calibration terms for the band shift reported by Chijioke et al.⁵⁶ were used to derive the pressure values. The same LabRam HR800 instrument was used for acquisition of the in situ Raman spectra of the sample. For both measurements, a grating with 1800 grooves mm^–1 was used in combination with a 532 nm Nd:YAG laser and an Olympus 50× objective with a 10.6-mm-long working distance. Wavenumber calibration was done using the laser Rayleigh line, and Raman-band fitting was done with PeakFit4 (Systat Software Inc.) by assuming mixed Lorentzian–Gaussian band shapes after subtraction of the background. The reported uncertainties for the ruby pressure values correspond to the standard deviation, as determined from different rubies within the DAC.

3. Results and Discussion

Evidence for Transformations in Raman Spectra

A series of HP Raman spectra were measured within the hydrostatic limit of the used pressure medium up to 9.94 ± 0.15 GPa, in two different orientations of the β-LSG crystals relative to the direction of laser-beam polarization. The two orientations of the randomly mounted idiomorphically shaped sample crystal were rotated by 90° and maintained throughout the whole series between 0.66 and 9.94 GPa. Two series of subsequent 20 spectra each were recorded within the spectral range of 40–1200 cm^–1 (Figures 2 and S3 and S4).

Figure 2.

Variation of the Raman spectra of LSG at hydrostatic HP conditions in a sequence of isothermal compression (T = 298 K) from 0.64(7) to 9.95(8) GPa in two orientations (a and b) with the laser polarization vector rotated by 90°. In both series, a distinct change at ∼9 GPa indicates the occurrence of a phase transition. Some small Raman bands between 800 and 1000 cm^–1 possibly originate from the 4:1 methanol–ethanol mixture showing a different linear behavior in the P-induced band-shift evolution.

A uniform development can be seen in both series of spectra, which is accompanied by a clearly recognizable change in the pressure interval between 8.92 ± 0.09 and 9.09 ± 0.08 GPa. The observed changes in the band positions, relative intensities, and number of bands clearly suggest a phase transformation with the corresponding structural changes. The recorded spectra are rich in vibrational modes especially after the phase transition, which can be attributed to symmetry breaking from orthorhombic to monoclinic lattice metrics if compared to other model pyroxenes.⁵⁷⁻⁵⁹ For orthorhombic Pbca pyroxenes, factor group analysis shows 120 Raman-active modes (30 A_g, 30 B_1g, 30 B_2g, and 30 B_3g); in the new HP monoclinic P2₁/c pyroxene, factor group analysis predicts also 120 Raman-active modes (60 A_g and 60 B_g); in contrast, the P2₁/c pyroxenes at room conditions have only 60 Raman-active modes (30 A_g and 30 B_g).^60,61 The most prominent bands are due to the vibrational modes of the tetrahedral GeO₄ units⁶² in the wavenumber range of 500–950 cm^–1. They are equivalent to the SiO₄ modes of related pyroxene-type silicates^62,63 but shifted to lower wavenumbers.

Pressure-dependent evolution of the Raman bands reveals clear changes with respect to the number and wavenumber positions of these bands (cf. Figures 2 and 3 as well as Figures S3 and S4). The apparent spectral changes suggest a first-order character of the transition and imply a change in symmetry from the orthorhombic (β-LSG) to probably monoclinic (γ-LSG). The Raman bands above and below the critical transition pressure undergo a smooth evolution with a typical blue shift toward higher energy due to the expected P-induced frequency increase of the vibrational modes. The investigated P-dependent Raman band positions show an apparently linear and smooth evolution of all bands with a typical dν/dP between +0.98(4) and +4.25(7) cm^–1/GPa. Some small Raman bands between 800 and 1000 cm^–1 possibly originate from the 4:1 methanol–ethanol mixture used as a pressure-transmitting medium and show a different linear behavior in the P-induced band-shift evolution. Furthermore, a new band seems to arise at 6 GPa around 870 cm^–1, which could be associated with a continuous coordination change of the Li cation mentioned in the crystal structure part below. It would be conceivable that the Li atom dynamically switches between two positions under standard conditions and, after a certain pressure, remains in a position where it has a higher coordination, for instance, [6] instead of [5 + 1]. This would change the number and intensity of the Raman bands, as observed, e.g., for dynamic disordered H₂O molecules and OH groups.⁶⁴

Figure 3.

Positional Raman shifts of selected representative bands of LSG as a function of the pressure upon isothermal compression. Shown are only intense, selected bands.

Isothermal Compressibilities and EoS

Symmetry-unconstrained vector least-squares fits to the corrected diffractometer setting angles were applied in a first step to prove the lattice metrics at individual pressure points. According to the findings, constrained refinements were applied to derive the values for the lattice parameters (Figure 4) listed in Table S1. Below 9 GPa, the refined values of α, β, and γ for β-LSG correspond to 90° within an uncertainty of less than ±0.01°. Beyond 9 GPa, the angle β spontaneously increases within a short interval to 93.0°, which further increases to 93.3° at a maximum pressure of 10.35 GPa. Discontinuous evolution, not only of the angle β but also for all lattice parameters and the unit-cell volume (Figures 4and S5), clearly confirms the nature of the β-to-γ phase transition as first-order in character. All lattice parameters, including the unit-cell volume, show clear discontinuities in the pressure evolution. The volume data reveal a spontaneous decrease in ΔV by about −1.6% and are comparable to many first-order transitions in pyroxene-type structures.^{16,23,25,26,35−37,39} The discontinuity can also be seen in the crystallographic axes, with a strong shortening of the lattice periodicity along the c axis (−2.6%), while in the a- and b-axis directions, changes across the transition point yield opposite signs (+1.0%∥a and +0.02%∥b). This behavior can be explained by changes to the tetrahedron chains and is proven for several other pyroxene transformations.^{16,23,25,26,35−37,39}

Figure 4.

Compression behavior of the normalized unit-cell volume and normalized lattice parameters a–c of the orthorhombic β-LSG and monoclinic γ-LSG. Uncertainties of the respective x/x₀ values and those for the experimentally determined pressure are smaller than the given symbol size. The values obtained from the EoS fits are listed in Table 2.

The pressure–volume (P–V) data were analyzed with respect to the volume compression properties. The corresponding isothermal EoS is usually parametrized in terms of the values of the bulk modulus (K) and its pressure derivatives K′ = dK/dP and K″ = dK′/dP. In a plot of normalized P(F) versus Eulerian strain (f_E) (Figure S6), the trend line follows a relationship in a linear fashion with a clearly positive slope, which indicates that K′ must be significantly larger than 4. Accordingly, a third-order BM EoS appears to be appropriate for the P–V data below 9 GPa for β-LSG. Weighted fits return reasonably small uncertainties for the calculated parameters V₀, K₀, and K′, as well as for x₀, M₀, and M′ describing the compressibilities of the individual crystallographic axes (Table 2). Any attempt to fit higher order, i.e., a fourth-order BM-EoS, only brings marginal deviations for K″ with respect to its implied uncertainty [K″ = −0.05(29)]. The bulk modulus of 89.8 ± 0.6 GPa, as obtained by the third-order BM-EoS, compares to equivalent orthopyroxene structures and follows the systematics of the Anderson–Anderson relationship.⁶⁵ The axial moduli (Table 2) are very similar (M₀ = 296 ± 8 GPa∥a, 266 ± 3 GPa∥b, and 248 ± 4 GPa∥c), even compared to those of monoclinic α-LSG (M₀ = 225 GPa∥a, 277 GPa∥b, and 226 GPa∥c⁴⁰), showing a nearly isotropic compression of β-LSG. The volume compression V/V₀ at 10 GPa is nearly the same as that observed for α-LSG. Compared to other ortho- and clinopyroxenes in a plot versus the unit-cell volume at ambient conditions (Figure S7), it possesses a relatively large volume compression, together with a large unit cell, and therewith it probably continues the trend observed by Hofer et al. (2015)⁴⁰ for clinopyroxenes, although the data for orthopyroxenes are still a bit sparse.

Table 2. Least-Squares-Fitted BM3-EoS Parameters of the Unit-Cell Volumes and Lattice Parameters for β-LSG and γ-LSG.

	orthorhombic LSG at 0–9 GPa			monoclinic LSG above 9 GPa
	X0/V0 [Å3]	M0/K0 [GPa]	M′/K′	X0/V0 [Å3]	M0/K0 [GPa]	M′/K′
V	943.63(11)	89.8(6)	4.75(18)	940.6(4.4)	82.4(4.8)	4 fixeda
a	18.856(3)	296(8)	20.7(2.3)	19.008(12)	403(13)	12 fixeda
b	9.1248(6)	266(3)	5.1(6)	9.113(27)	268(31)	12 fixeda
c	5.4843(4)	248(4)	21.1(1.1)	5.430(14)	168(13)	12 fixeda

^aBecause of a limited number of data points, a BM2-EoS is used here.

Attempts to fit the equivalent moduli for γ-LSG are much more difficult because of the short pressure interval between 9.0 and 10.35 GPa. Equivalent fits finally based on BM2-EoS (K′ and M′ fixed to 4 and 12; Table 2) yield K₀ = 82.4 ± 4.8 GPa, M₀ = 403 ± 13 GPa∥a, 268 ± 31 GPa∥b, and 168 ± 13 GPa∥c. The bulk modulus indicates higher compressibility above the critical transition pressure, although the monoclinic structure of γ-LSG is denser than that of the LP β-LSG. This can be attributed to elastic softening, as is typical for lithium pyroxenes.¹⁶ Moreover, it is remarkable that γ-LSG shows a more pronounced anisotropic compression behavior compared to both the orthorhombic β-LSG and monoclinic low-pressure α-LSG.

HP Crystal Structures

Structure refinements were carried out at 8.6 and 9.5 GPa, just below and above the critical transition pressure around 9.0 GPa, in addition to one refinement at ambient conditions (cf. Table 1). The observed systematic absences of the XRD intensities confirm space group Pbca for β-LSG at 1 bar and at 8.6 GPa, while they suggest P2₁/c at 9.5 GPa for monoclinic γ-LSG. Because of the restricted number of Fourier coefficients in the given crystal orientation, the HP refinements were carried out with anisotropic displacement parameters only for Sc and Ge atoms, while Li and O atoms were refined using an overall isotropic displacement parameter (cf. Table 3). In contrast, a model with anisotropic displacement parameters for all atoms was used for the refinements at 1 bar, with the crystal mounted on a glass fiber. For refinement of the P2₁/c structure of γ-LSG, a twin domain was additionally indexed, integrated, and refined according to the presence of a 2-fold rotation about the c axis, giving the twin law [−1 0 (2a cos β)/c 0 −1 0 0 0 1]⁶⁶ with (2a cos β)/c ≈ −0.39 for γ-LSG at 9.5 GPa. The relationships between the number of refined parameters, observed unique reflections, and resulting reliability indices are listed in Table 1. The obtained positional parameters and isotropic or equivalent displacement parameters are provided in Table 3. The anisotropic displacement parameters for the measurement at 1 bar are listed in Table S2. Selected interatomic distances, relevant bond angles, and octahedral distortion are summarized in Tables 4 and 5.

Table 3. Atomic Coordinates and Displacement Parameters of β-LSG at 10^–4 GPa (Ambient Pressure, aP) and 8.6 GPa as well as γ-LSG at 9.5 GPa.

aP
	x	y	z	Ueq		x	y	z	Ueq
GeA	0.47291(2)	0.66284(2)	0.28415(2)	0.00492(1)	O2	0.18260(2)	0.67104(5)	0.54917(7)	0.00622(5)
GeB	0.27526(2)	0.66067(2)	0.55489(2)	0.00501(1)	O3	0.43346(2)	0.50354(5)	0.18946(8)	0.00881(6)
Li	0.62453(9)	0.49241(19)	0.1268(3)	0.0211(3)	O4	0.44568(2)	0.80612(5)	0.08880(8)	0.00862(6)
Sc	0.37572(2)	0.35124(2)	0.37429(2)	0.00494(1)	O5	0.31030(2)	0.77947(5)	0.33580(8)	0.00990(6)
O1	0.56621(2)	0.66787(5)	0.29511(7)	0.00646(5)	O6	0.30869(2)	0.48649(5)	0.54397(9)	0.01051(6)

8.6 GPa
	x	y	z	Ueq/Uiso		x	y	z	Ueq/Uiso
GeA	0.47034(3)	0.66444(6)	0.28992(7)	0.0063(2)a	O2	0.1816(2)	0.6678(4)	0.5316(5)	0.0074(6)
GeB	0.27513(3)	0.65846(6)	0.54569(7)	0.0065(2)a	O3	0.4321(2)	0.5068(4)	0.1672(5)	0.0092(7)
Li	0.6222(6)	0.4853(12)	0.1480(14)	0.0153(18)	O4	0.4445(2)	0.8211(4)	0.1079(5)	0.0087(6)
Sc	0.37673(5)	0.35002(11)	0.36109(13)	0.0056(2)a	O5	0.3131(2)	0.7793(4)	0.3280(5)	0.0098(7)
O1	0.5646(2)	0.6661(4)	0.3038(5)	0.0072(6)	O6	0.3057(2)	0.4771(4)	0.5393(5)	0.0121(7)

9.5 GPa
	x	y	z	Ueq/Uiso		x	y	z	Ueq/Uiso
GeA1	0.47010(4)	0.66326(9)	0.29495(11)	0.0059(2)a	O2A	0.1832(3)	0.6665(5)	0.5438(7)	0.0074(7)
GeA2	0.02686(4)	0.33952(8)	0.79780(10)	0.0059(2)a	O2B	0.3174(3)	0.3334(6)	–0.0253(7)	0.0074(7)
GeB1	0.27566(5)	0.65945(8)	0.53983(11)	0.0063(2)a	O3A	0.4356(3)	0.5059(6)	0.1504(7)	0.0076(6)
GeB2	0.22466(5)	0.34114(8)	–0.04743(10)	0.0063(2)a	O3B	0.0643(3)	0.4972(6)	0.6754(7)	0.0076(6)
LiA	0.6176(8)	0.4854(17)	0.1779(19)	0.014(3)	O4A	0.4414(3)	0.8225(5)	0.1121(7)	0.0070(6)
LiB	0.8749(8)	0.5207(17)	0.6285(19)	0.016(3)	O4B	0.0558(3)	0.1804(6)	0.6255(7)	0.0070(6)
ScA	0.37605(7)	0.35114(15)	0.32029(18)	0.0050(2)a	O5A	0.3093(3)	0.8055(6)	0.3573(7)	0.0072(6)
ScB	0.12475(7)	0.64765(16)	0.87282(18)	0.0050(2)a	O5B	0.1923(3)	0.3103(6)	0.6330(7)	0.0072(6)
O1A	0.5633(3)	0.6684(5)	0.3315(7)	0.0068(6)	O6A	0.3123(3)	0.4877(6)	0.4883(7)	0.0099(7)
O1B	0.9337(3)	0.3331(5)	0.8003(7)	0.0068(6)	O6B	0.1893(3)	0.5028(6)	0.0694(7)	0.0099(7)

^aU_eq.

Table 4. Interatomic Distances of β-LSG at 10^–4 and 8.6 GPa and γ-LSG at 9.5 GPa.

	10–4 GPa	8.6(1) GPa	9.5(1) GPa		10–4 GPa	8.6(1) GPa	9.5(1) GPa
Li–O1	2.151(2)	2.093(11)	2.090(15)/2.155(15)a	Sc–O1	2.1252(5)	2.096(3)	2.088(4)/2.074(5)b
Li–O2	2.188(2)	2.175(11)	2.184(15)/2.147(15)a	Sc–O1	2.2049(5)	2.144(4)	2.147(5)/2.140(5)b
Li–O3	2.051(2)	1.960(9)	1.927(12)/1.999(13)a	Sc–O2	2.1047(5)	2.068(3)	2.057(4)/2.083(5)b
Li–O4	2.660(2)	2.307(10)	2.146(15)/2.262(14)a	Sc–O2	2.1984(5)	2.142(4)	2.145(5)/2.139(5)b
Li–O5	2.308(2)	2.183(11)	2.109(16)/2.337(14)a	Sc–O3	2.0357(5)	2.010(4)	1.998(5)/ 1.992(5)b
Li–O6	2.210(2)	2.160(10)	2.127(12)/2.035(13)a	Sc–O6	1.9966(5)	1.971(4)	1.935(5)/ 1.999(5)b

^aLiA–OXA/LiB–OXB.

^bScA–OXA/ScB–OXB.

Table 5. Characteristic Interatomic Distances (Å) and Angles (°) for the [Ge₂O₆]_n Chains of Orthorhombic and Monoclinic LSG^a.

	10–4 GPa	8.6(1) GPa	9.5(1) GPa
GeA–GeAb	3.1699(5)	3.0707(7)	3.018(1)/3.044(1)
GeB–GeBb	3.1902(5)	3.1243(7)	3.053(1)/3.059(1)
GeA–O4–GeAc	127.32(3)	121.0(2)	117.5(3)/118.9(3)
GeB–O5–GeBc	130.63(3)	127.8(2)	121.4(3)/120.8(3)
O3–O4–O3d	138.69(2)	128.6(2)	128.5(2)/126.4(2)
O6–O5–O6d	166.22(2)	166.1(2)	147.1(2)/133.6(2)
O4–O4–O4d	139.04(2)	129.53(12)	127.5(2)/129.3(2)
O5–O5–O5d	157.81(2)	158.02(14)	138.6(2)/135.4(2)

^aThe distances and angles are calculated according to the crystallographic data given in Table 3.

^bGeA1–GeA1, GeA2–GeA2 respectively GeB1–GeB1, GeB2–GeB2.

^cGeA1–O4A–GeA1, GeA2–O4B–GeA2 respectively GeB1–O5A–GeB1, GeB2–O5B–GeB2.

^dOXA–OXA–OXA, OXB–OXB–OXB.

At first glance, the stereochemistry and bonding relationships between the individual structure variants are not fundamentally different (Figure 5). The coordination geometries of the various building units are almost unchanged, with Ge atoms in tetrahedral coordination and Sc and Li atoms in more or less distorted octahedral arrangements. The bond distances for all Ge atoms (GeA and GeB sites in β-LSG; GeA1, GeA2, GeB1, and GeB2 sites in γ-LSG) and the Sc atoms on the M1 site are in agreement with the expected bond compression variations in the corresponding GeO₄ and ScO₆ units (Tables 4 and S3). The Li atoms, hosted at the M2 site (one Li position in β-LSG; two LiA and LiB positions in γ-LSG), reveal a significant shortening of the individual nonbonding M2–O distances, which only contribute at high P with appropriate bond strengths. The effective coordination number changes gradually from [4 + 1 + 1] to [5 + 1] in β-LSG up to 8.6 GPa and reveals a significant change to a proper 6-fold coordination for both Li sites in γ-LSG (Table 4). Simultaneously, the LiO₆ coordination polyhedra show decreasing polyhedral distortion with increasing P, mainly manifested by the shrinking Li–O4 distance from 2.660(2) Å at ambient conditions to 2.307(10) Å at 8.6 GPa and 2.146(15) Å at 9.5 GPa (cf. Table 4).

Figure 5.

Crystal structures of α-LSG at 9.5 GPa as well as β- and γ-LSG at HP conditions below (8.6 GPa) and above (9.5 GPa) the transition pressure at 9.0 GPa. The structures are shown at the top in a projection of two unit cells along the b axis, and below the GeO₄ tetrahedron, chain units can be seen in a view on the bc plane. The most significant changes concerning the O4–O4–O4 and O5–O5–O5 angles, which determine the S-rotated (yellow, GeA) and O-rotated (turquoise, GeB) chains (cf. Figure 6), are marked accordingly.

The most striking structural change concerns the relative position and orientation of the GeO₄ tetrahedra within the symmetrically individual [Ge₂O₆]_n chains (one type of chain in β-LSG, in contrast to two types in γ-LSG, i.e., the so-called A-chain and B-chain; cf. Figure 5). The symmetry decoupling associated with the transition from the P-centered orthorhombic lattice to a monoclinic P Bravais lattice is also evidenced by a change of the vibrational modes assigned to the GeO₄ tetrahedra themselves as well as modes originating from the vibration dynamics within the parent chain units. In both chain types, which are aligned parallel to the crystallographic c axis, the bridging O atoms (O4 and O5) are subjected to the largest positional shifts. It is not surprising that precisely these atoms show the aforementioned strong changes in the Li–O bond distances, being involved in the reported stereochemical changes around the Li atoms. In detail, the A-site T-chain in β-LSG splits into two T-chains with the O6–O5–O6 angle changing from 166.22 ± 0.02° (at ambient pressure) and 166.1 ± 0.2° (at 8.6 GPa) to 147.1 ± 0.2° and 133.6 ± 0.2° (at 9.5 GPa). The B-site T-chain in β-LSG undergoes a change in the O3–O4–O3 angle from 138.69 ± 0.02° (at ambient pressure) and 128.6 ± 0.2° (at 8.6 GPa) to 128.5 ± 0.2° and 126.4 ± 0.2°, which is comparable to that reported for the P2₁/c postorthopyroxene MgSiO₃ phase²⁹ (Figure S8). The large change of angle in the A-chain can be assigned to the splitting of the Raman doublet, whereas the change for the B-chain is so small that the associated peak splitting cannot be resolved, thus yielding only a triplet instead of the expected quadruplet. The atomic displacements involved are more pronounced in the A-chain along the a axis toward the center of the unit cell, while the largest displacement in the B-chain occurs within the (100) plane. According to the common nomenclature,¹⁰ the A-chain is S-rotated and the B-chain is O-rotated. Both chain types reveal internal folding, as expressed by all Ge–O4/5–Ge, O4–O4–O4, and O5–O5–O5 angles getting smaller with increasing pressure (Table 5). This corresponds to the compression mechanisms observed in several P2₁/c pyroxenes.¹⁵

Transformation Pathway of the β-to-γ Transition

Similar to the previous findings,²⁹ the structure of γ-LSG could not be assigned to any of the established archetypes, to neither orthopyroxene (OEn-Pbca), LP-clinopyroxene (LCEn-P2₁/c), high-temperature-clinopyroxene (HT-CEn-C2/c), nor HP clinopyroxene (HP-CEn-C2/c). Despite the same space group (P2₁/c), the structure determined for γ-LSG showed clear differences in the β angle or the periodicity length of a, which is evident in the direct comparison between LCEn-P2₁/c α-LSG⁴⁰ and γ-LSG (α-LSG, β = 102.9°, a = 9.69 Å; γ-LSG, β = 93.1°, a = 18.86 Å). Both the lattice-metric characteristic and the finding of the γ-LSG structure to be isostructural with the postorthopyroxene type MgSiO₃ confirm the existence of a comparable transformation between the orthorhombic OEn-Pbca-type β-LSG and the monoclinic postorthopyroxene pOEn-P2₁/c-type γ-LSG.

The transformation from OEn-Pbca orthopyroxene to the pOEn-P2₁/c postorthopyroxene structure has so far only been reported for MgSiO₃ (Zhang et al., 2012²⁹), with half of the tetrahedra in every second layer to change from the original O configuration to S-rotated chain units across the OEn–pOEn transition (Figure S5). As previously reported, the M+ M+ M– M– sequence of the octahedral layer alignment along the a-axis direction, typical for orthopyroxene topology,^10,11 is also retained here. This makes the pOEn-P2₁/c phase very different from a further HP clinopyroxene phase, which also crystallizes in P2₁/c but has the M+ M+ sequence typical for clinopyroxene phases and is confirmed by the HP-CEn2-P2₁/c structures of various silicate clinopyroxenes.³⁰⁻³²

The transition mechanism corresponds to previous predictions⁶⁷ and can be interpreted as an incomplete rotation from O- to S-chains within every second tetrahedral layer. According to the established nomenclature,¹¹ the local stacking sequence within one-fourth of the I-beams has to change from A^T(O-rot)B^MC^T(O)A to A^T(O)B^MC^T(S-rot)B. The corresponding O-monolayer stacking sequence thus changes from ABACBABC (pyroxene no. 10 = OEn-Pbca) to ABABCABC (pyroxene no. 8b = pOEn-P2₁/c). This can be achieved by a simple rotation of the basis triangle of the GeO₄ tetrahedra by about 30° (cf. Figure 6). The pure rotation would not be associated with a volume reduction, but only the simultaneous shortening of the Li–O distances (Table 4) by displacing the O atoms within the basic triangle of the GeO₄ tetrahedra enables the described reduction in the a-axis direction and in the volume, respectively.

Figure 6.

Individual octahedra–tetrahedra bilayer sheets in a polyhedral illustration according to the bilayer sequence along a [following the bilayer labels in the (001) projection on the left side]. The following structures are compared: (a) LCEn-P2₁/c, α-LSG⁴⁰ at 9.5 GPa; (b) OEn-Pbca, β-LSG at 8.6 GPa (this study); (c) pOEn-P2₁/c, γ-LSG at 9.5 GPa (this study; see a comparison with MgSiO₃ at 14.3 GPa²⁹ in Figure S8); (d) HP-CEn-C2/c, FeSiO₃ at 1.9 GPa;³⁷ (e) HP-CEn2-P2₁/c, FeSiO₃ at 35.9 GPa.³¹

4. Conclusions

The transformation into the crystallographically new postorthopyroxene structure type proves the existence of three different polymorphs of LiScGe₂O₆, i.e., α-LSG (=LCEn-P2₁/c clinopyroxene type), β-LSG (=OEn-Pbca orthopyroxene type), and γ-LSG (=pOEn-P2₁/c postorthopyroxene type). The molar volume, or the relative volume units per formula unit Z, at 1 bar indicate that α-LSG (V/Z = 117.35 ų) is the low-T form and β-LSG [V/(2*Z) = 117.95 ų] the corresponding high-T form. A comparison of all three phases at 9 GPa, the β-to-γ transformation point, shows from the V/Z volume fractions calculated from the EoS data (α-LSG, 108.13 ų; β-LSG, 108.68 ų; γ-LSG, 107.33 ų) that the new γ phase is the densest and can therefore be assigned as the HP phase in this system. Its density is even higher than that of the β phase at the same pressure conditions. The compressibility of the three phases is extremely similar because the structure topologies of the three phases are also very similar in comparison.

The β-to-γ transition for LSG reported here was predicted⁶⁷ and later reported only for MgSiO₃ in the pressure interval between 10 and 14.2 GPa.²⁹ The new dense γ-LSG structure is therefore the second example of this type of phase transition, which in both cases takes place through direct transformation from the OEn-Pbca orthopyroxene structure. Nevertheless, the terms used for the monoclinic HP phases are sometimes confusing because there are at least three different pyroxene structures with the same space group P2₁/c, including the new postorthopyroxene described here, the early-established “low-clinopyroxene” (=LCEn-P2₁/c), and the recently described HP-CEn2 structures.³⁰⁻³² The latter structure is the one that transforms exclusively from the C2/c-type HP forms of the clinopyroxenes (HP-CEn-C2/c), whereby every second tetrahedron layer is transformed into an octahedron in the course of a translation between the O monolayers. The former T-cations are thus coordinated octahedra in the sense of the formula AMT^[4]T^[6]O₆. In addition, this C2/c-to-P2₁/c transformation retains the typical M+ M+ sequence of the octahedral layer alignment along the a-axis direction, such that the completely different M+ M+ M– M– sequence is preserved for the structurally different Pbca-to-P2₁/c orthopyroxene–postorthopyroxene transition, which is reported here.

A schematic diagram in the sense of a P–T phase diagram (Figure 7) shows the single-phase regions of the relevant structures in which the separating lines do not correspond to the proper thermodynamic equilibrium boundaries but rather represent tie lines along which the structural transitions can be expected. The diagram again shows the three different P2₁/c phases (yellow, turquoise, and red) and which phases correspond to the three LSG polymorphs (yellow, green, and turquoise). The diagram also clarifies the confusion regarding the recently published HP forms of P2₁/c symmetry. Referring to the purely displacive character involving rotation of the TO₄ units, it is understandable that the OEn–pOEn transformation takes place at much lower pressures, and the second transition of the HP-CEn structures from C2/c to P2₁/c can only take place at significantly higher pressures because of the change in coordination. It is noteworthy that the HP-CEn-C2/c phase has not been observed yet as another phase during the compression of LSG, which should only be due to the fact that the pressure in previous studies was not high enough. Such a transformation into C2/c and further into the HP-CEn2-P2₁/c structure is therefore very likely.

Figure 7.

Schematic diagram showing the regions of occurring pyroxene phases in the P–T space. Abbreviations: PEn = protoenstatite (pink field); LCEn = low clinoenstatite (yellow field); HT-CEn = high-temperature clinoenstatite (pink field); HP-CEn = high-pressure clinoenstatite (orange field); HP-CEn2 = high-pressure clinoenstatite-II (red field); OEn = orthoenstatite (green field); pOEn = postorthoenstatite (turquoise field). The three polymorphs of LSG correspond to LCEn-P2₁/c (=α-LSG), OEn-Pbca (=β-LSG), and pOEn- P2₁/c (=γ-LSG).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.0c02284.

• Refined pressure-dependent monoclinic and orthorhombic lattice parameters and corresponding plots, observed bond lengths of the GeA and GeB tetrahedra, pressure-dependent Raman waterfall plots, and crystal pictures (PDF)

Accession Codes

CCDC 2020095–2020097 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

The authors declare no competing financial interest.