Uncovering the Effects of Non-Hydrostaticity on Pressure-Induced Phase Transformation in Xenotime-Structured TbPO₄

Abstract

The pressure-induced phase transformations of rare earth orthophosphates (REPO₄s) have become increasingly relevant in ceramic matrix composite (CMC) research; however, understanding of the shear-dependence of these transformations remains limited. This study employs diamond anvil cell experiments with three pressure media (neon, KCl, sample itself/no medium) to systematically assess the effect of shear on the phase transformations of TbPO₄. Results show a lowering of the TbPO₄ transformation onset pressure (P_onset) as well as an extension of the xenotime–monazite phase coexistence range under non-hydrostatic conditions. The TbPO₄ P_onset under no medium (4.4(3) GPa) is the lowest REPO₄ P_onset reported to date and represents a ~50% drop from the hydrostatic P_onset. Enthalpic differences likely account for lower P_onset values in TbPO₄ compared to DyPO₄. Experiments also show scheelite may be the post-monazite phase of TbPO₄; this phase is consistent with observed and predicted REPO₄ transformation pathways.

1. Introduction

The deformation mechanisms of rare earth orthophosphates (REPO₄s) under complex stress states are highly pertinent to several research fields including geoscience and structural ceramics. In shocked xenotime and monazite minerals, REPO₄ deformation microstructures can provide insight into the extreme conditions generated during impact events [1,2,3]. In addition, the pressure-induced xenotime–monazite phase transformation of certain REPO₄ compositions offers the possibility of enhanced toughness and plasticity in ceramic matrix composites (CMCs) for aerospace components subject to extreme conditions [4,5]. When tested as CMC fiber coatings, transforming compositions have been shown to deflect or arrest cracks and facilitate fiber sliding at lower stresses than non-transforming compositions [5].

Identifying REPO₄ compositions that undergo the pressure-induced xenotime–monazite phase transformation requires understanding the compositional phase boundary in the middle of the lanthanide series. In equilibrium at 1 atm (10⁻⁴ GPa), compositions with smaller RE³⁺ ionic radii (RE = Tb-–Lu, Sc, Y) adopt the xenotime (tetragonal, I4₁/amd) structure while those with larger RE³⁺ ionic radii (RE = La-Gd) adopt the monazite (monoclinic, P2₁/n) structure [6]. Under high hydrostatic pressure, xenotime-structured compositions are known to transform into either the monazite structure or the scheelite (tetragonal, I4₁/a) structure, with the latter being more favorable in xenotime compositions with the smallest RE³⁺ ionic radii [7]. The three aforementioned crystal structures are illustrated in Figure 1.

The xenotime, monazite, and scheelite structures all contain chains of alternating RE-O polyhedra and PO₄ tetrahedra and have RE-O coordination numbers of 8, 9, and 8, respectively [8]. Figure 1 shows the compaction of the REPO₄ structure from xenotime to monazite to scheelite due to the increasing rotations and translations of the RE-O polyhedra and PO₄ tetrahedra [8]. Such rotations and translations can be induced using hydrostatic pressure, and they can be prematurely induced in the presence of non-hydrostatic stress, which disrupts stable bonding symmetries more dramatically than pure hydrostatic stress [5,9]. An intermediate structure, anhydrite (orthorhombic, Amma), has also been reported in xenotime compositions that are extremely close to the xenotime–monazite phase boundary (e.g., Gd₀.₅Tb₀.₅PO₄) or subjected to high deviatoric stresses at low hydrostatic pressures (e.g., Gd_xDy_1−xPO₄, TbPO₄) [5,10,11].

While the pressure-induced phase transformations of REPO₄s have been extensively characterized in (quasi-)hydrostatic environments via in situ diamond anvil cell (DAC) X-ray diffraction (XRD) and Raman spectroscopy (RS), studies which systematically evaluate the influence of non-hydrostaticity are extremely limited [7]. Such studies typically vary the pressure-transmitting medium (PTM) in the DAC in order to vary the hydrostaticity of the stress state experienced by the sample. For example, Santamaria-Perez et al. studied orthorhombic BaSO₄ using three different fluid PTMs (helium, silicone oil, and 4:1 methanol–ethanol), finding a decreasing hydrostatic limit led to lower transformation onset pressures (P_onset) and wider pressure ranges of phase coexistence [12]. In REPO₄ literature specifically, Lacomba-Perales et al.’s in situ DAC XRD study notes that shear promotes earlier xenotime–monazite transformation in YPO₄, but this conclusion is based on a cursory comparison of their findings to a prior YPO₄ study carried out by others [13]. Our recent in situ DAC XRD study probed the effect of shear on the xenotime–monazite transformation of DyPO₄ by systematically varying the PTM [9]. We found neon and 16:3:1 methanol–ethanol–water (MEW) PTM yield similar P_onset values of 9.1(1) GPa and 9.3 GPa, respectively, while KCl PTM yields a much lower P_onset of 7.0 GPa (a ~22% drop). Even though neon crystallizes at 4.7 GPa, neon and MEW both remain (quasi-)hydrostatic at P_onset; therefore, employing only one of these two PTMs is sufficient (assuming other conditions are held constant) [14]. The significant P_onset reduction under KCl is likely attributable to a higher shear stress state given the fact that KCl is never hydrostatic, and its ambient pressure bulk modulus (B₀) is ~20 times that of neon [15,16,17]. We note that B₀ does not reflect the DAC conditions at P_onset since a material’s bulk modulus (B) generally increases with pressure. However, materials whose B₀ values differ by orders of magnitude do not attain similar B values at the high pressures of interest. At a given DAC pressure, an increase in the B value of a PTM results in less PTM compression, which is expected to generate greater contact stresses and friction at PTM–sample interfaces. Given the non-uniform magnitude and direction of the contact stresses and friction, greater shear stress is expected to be induced in the sample. While the quantification of stress transfer and shear stress generation by solid PTMs has not been detailed in the literature, results from prior DAC experiments on α-Ti support the expectation that solid PTMs with higher B₀ impart more shear stress on the sample than PTMs with lower B₀ [18]. Because DyPO₄ was not tested under any solid PTM (solid at 1 atm) other than KCl, another high-shear state was not evaluated. Beyond our DyPO₄ study, the effect of shear on phase transformations has yet to be reported for any other REPO₄ [9]. In addition, the high-pressure, post-monazite phase of TbPO₄ has yet to be experimentally observed.

This study employs in situ DAC synchrotron XRD to probe the pressure-induced phase transformations of xenotime TbPO₄ under variable hydrostaticity. The experiments performed in this study involve three PTMs: neon, KCl, and “none” (i.e., cell packed with sample and no PTM material). In the “none” PTM condition, the sample is effectively the PTM. Xenotime DyPO₄ is also tested in the “none” condition to build on our prior study [9]. DyPO₄ and TbPO₄ have B₀ values of 144 GPa and 134 GPa, respectively, which are an order of magnitude higher than the B₀ of KCl [9,19]. Our TbPO₄ experiment using neon PTM shows a xenotime–monazite P_onset of 8.7(6) GPa, which is lower than other reported XRD-based hydrostatic P_onset values of 9.8 GPa and 9.9 GPa [19]. In addition, TbPO₄ experiments in this study show a systematic lowering of the xenotime–monazite P_onset when changing the PTM from neon to KCl to “none” (i.e., as PTM bulk modulus increases). Lastly, our TbPO₄ experiment with no medium shows an almost 50% drop in P_onset (reaching the lowest value reported for any REPO₄ to date), provides evidence for scheelite as the post-monazite phase, and corroborates Hay et al.’s ex situ observation of monazite in indented xenotime TbPO₄.

2. Materials and Methods

Xenotime TbPO₄ and DyPO₄ powders were synthesized via precipitation reactions and subsequent calcination. Details of these synthesis steps are provided in the Supplementary Materials. The sample powder consisted of grains ranging from sub-micrometer to a few micrometers in size; these grains exhibited the anisotropic, elongated crystal habit expected of tetragonal materials (see Figure S1). In situ DAC XRD was conducted at room temperature at Beamline 12.2.2 of the Advanced Light Source at Berkeley National Laboratory. For experiments involving neon PTM, DACs were loaded with neon using the University of Chicago Gas Loader in the high-pressure lab at Beamline 12.2.2. Two-dimensional diffraction patterns were collected with a PILATUS 3S 1M detector at an X-ray wavelength of 0.4947 Å and an exposure time of 20 s. All DACs used were of the symmetric Princeton design and were compressed using a membrane driven by a Druck PACE 6000 pressure controller. Additional experiment details are shown in

Table 1. Details of the XRD experiments performed at Beamline 12.2.2 at the Advanced Light Source.

Experiment Name	Sample	PTM	Culet Diameter (μm)	Spot Size (μm)	Gasket Material	Gasket Indented Thickness, Hole Diameter (μm)	Pmax (GPa)
Tb-neon	TbPO4	neon	500	30	301 stainless steel	60–80, 260	14.0(10)
Tb-KCl	TbPO4	KCl	500	20	301 stainless steel	60–80, 260	11.9(8)
Tb-none	TbPO4	none	300	10	rhenium	50, 160	19.3(14)
Dy-none	DyPO4	none	300	30	rhenium	50, 160	10.4(7)

. In the table and elsewhere in the manuscript, values within parentheses following a pressure represent the standard deviation of the last digit of the pressure.

For pressure marking during initial membrane engagement, ruby was used (R1 fluorescence calibration) [20], while gold was used during diffraction data collection (using a 3rd order Birch–Murnaghan equation of state) [21]. Data collection began at pressures higher than 0 GPa due to some initial compression required to confirm membrane engagement. There are no reported TbPO₄ or DyPO₄ phase transitions below these starting pressures (as corroborated by prior work); therefore, the initial jump does not preclude any material insight [7,9,19]. The maximum pressure in each experiment (P_max) was limited by the performance of the gasket. Experiments were concluded when the gasket hole collapsed, approached the edge of the culets, or was otherwise unable to maintain a proper seal.

XRD pattern integration, masking, and background subtraction were performed using Dioptas [22]. Pattern fitting was then performed using X’Pert HighScore Plus 3.0 [23]. This software fits monazite using the P2₁/c cell setting as a default. Though both the P2₁/c and P2₁/n cell settings are valid descriptions of monazite (space group No. 14), fitted lattice parameters were converted to the P2₁/n cell setting to facilitate comparison to the literature. The LeBail fitting approach was used instead of traditional Rietveld structural refinement to accommodate the significant preferred orientation present in all scans [24]. This apparent preferred orientation appears due to the small spot size of the beam with respect to the grain size of the sample (effectively sampling a finite number of grains), rather than any systematic preferred orientation of the sample grains. P_onset is determined by visual inspection of individual XRD patterns and fit residuals, not by judging color in the contour plots shown in the next section. Visual inspection involves plotting the square root of intensity against Q to ensure emerging peaks are not overlooked due to their extremely low intensity. The following reference structures were used in this study: xenotime TbPO₄ from Lopez-Solano et al. [19], xenotime DyPO₄ from Milligan et al. [25], monazite TbPO₄ and DyPO₄ from Heuser et al. [26], anhydrite TbPO₄ from Losch et al. [27], gold from Couderc et al. [28], ruby from Jephcoat et al. [29], and calculated scheelite TbPO₄ from López-Solano et al. [19]. In the XRD patterns, the peaks of the ruby, anhydrite TbPO₄, and scheelite TbPO₄ structures are extremely weak or obscured by stronger peaks; as a result, LeBail fits incorporating these phases did not converge. Thus, the peaks of these three phases were only used in peak position comparison and were not employed in LeBail fitting. Traces of the anhydrite phase of TbPO₄ appear at the beginning of the Tb-neon experiment and may have arisen inadvertently from grinding during sample preparation or DAC loading. This phase does not appear in every scan (or even in every experiment), as the particular set of sample grains under X-ray illumination varies. For computation involving derived data (e.g., unit cell volume, gold-based pressure, cell setting conversion), the uncertainties Python package was used to propagate error [30].

3. Results and Discussion

Across all experiments, increasing pressure causes XRD peaks to drift to higher Q and broaden due to uniform and non-uniform strain, respectively. In addition, XRD signal quality deteriorates under increasingly non-hydrostatic PTMs (i.e., going from neon to KCl to none); this trend has been previously reported in hydrostaticity studies of other materials [12,18]. Given these effects, the XRD patterns analyzed in the current study are limited to pressures at which key peaks are sufficiently distinguishable for phase identification and LeBail fitting.

For the Tb-neon experiment, Figure 2a shows XRD pattern evolution throughout the entire experiment, while Figure 2b shows LeBail fit quality at P_initial (1.6(1) GPa), P_onset (8.7(6) GPa), the transformation end pressure (P_end, 13.7(10) GPa), and P_max (14.0(10) GPa). The first scan in this experiment features xenotime, anhydrite, and gold (upward triangle symbol) peaks. At ~5 GPa, the neon PTM crystallizes, and conditions shift from hydrostatic (in liquid neon) to quasi-hydrostatic (in solid neon) [31]. Solid neon adopts an FCC structure and is still extremely compressible with a bulk modulus of ~1 GPa [32]. Neon remains the most compressible material in the DAC, as evidenced by neon peaks shifting much more dramatically with increasing pressure than the other materials’ peaks in Figure 2a. The first discernible monazite peaks emerge at 8.7(6) GPa and are located at Q = 1.58 Å⁻¹, 1.59 Å⁻¹, 1.98 Å⁻¹, 2.13 Å⁻¹, and 2.29 Å⁻¹ (as denoted by stars in Figure 2); these are the (110), (10$\overline{2}$), (002), (02$\overline{1}$), and (21$\overline{2}$) reflections, respectively. Figure 2 also shows these peaks grow with pressure. In the P_onset scan in Figure 2b, the refined monazite lattice parameters are a = 6.175(1) Å, b = 6.699(1) Å, c = 6.483(1) Å, and β = 100.67(1)°. This P_onset value is higher than neon’s crystallization pressure and lower than neon’s hydrostatic limit, meaning the stress state is quasi-hydrostatic at P_onset. With increasing pressure, monazite peaks grow while xenotime peaks diminish. At 13.7(10) GPa, there are no longer any clearly discernible peaks that are attributable to xenotime. Therefore, 13.7(10) GPa is P_end and yields a xenotime–monazite phase coexistence range of 5.0(10) GPa. In the final scan at 14.0(10) GPa, monazite, gold, and neon are the only phases present.

A key result from the Tb-neon experiment is the P_onset of 8.7(6) GPa, which is the lowest P_onset value for TbPO₄ in neon PTM reported to date. Lopez-Solano et al. reported a higher value of 9.9 GPa based on XRD experiments also conducted with neon PTM [19]. Our experiment shows monazite peaks are clear at 9.9 GPa and at pressures leading up to this value (see Figure 2a). Figure 3 provides a closer look at our dataset, showing how including the monazite structure improves the fit of the XRD pattern collected at 8.7(6) GPa.

When monazite is excluded from the fit, there are regions of increased residual intensity (denoted by stars) that align with monazite peak positions. Although some ruby peaks are also quite close to the starred regions, ruby peaks do not align with all of these regions. Furthermore, the ruby signal is not expected to intensify with pressure, while the intensity in those starred regions does (as shown in Figure 2).

Further consideration of thermodynamic data between neighboring REPO₄ compounds gives additional support to a lower P_onset than the one reported by Lopez-Solano et al. [19]. Thermodynamic data (i.e., calculated enthalpy differences between xenotime and monazite phases as well as experimental calcination temperatures required to convert monazite to xenotime) show the monazite phase is more favorable in TbPO₄ than in DyPO₄ [33,34,35,36]. As a result, TbPO₄ is expected to have a lower xenotime–monazite P_onset than DyPO₄, but Lopez-Solano et al.’s TbPO₄ P_onset is higher than the previously reported DyPO₄ P_onset of 9.1(1) GPa (also in neon PTM) [9]. The lower TbPO₄ P_onset reported in the present study is consistent with thermodynamic expectations. Nevertheless, the P_end of 13.7(10) GPa determined in this study is consistent with Lopez-Solano et al.’s P_end of 13.8 GPa.

For the Tb-KCl experiment, Figure 4a shows XRD pattern evolution throughout the entire experiment, while Figure 4b shows LeBail fit quality at P_initial (2.2(2) GPa), P_onset (5.6(4) GPa), and P_max (11.9(8) GPa). The first scan in this experiment contains peaks belonging to xenotime, gold (upward triangle symbol), and B1-KCl (left-pointing triangle symbol). B1-KCl is the ambient pressure phase of KCl with a NaCl-type structure, and it begins transforming into the CsCl-type B2-KCl structure (right-pointing triangle symbol) at 2.3(1) GPa. Similar to neon in the Tb-neon experiment, KCl in this experiment is the most compressible material in the DAC, causing its peaks to shift in Q more than the sample’s peaks [37]. KCl peaks do not shift as dramatically as neon’s peaks in the Tb-neon experiment because KCl has a higher bulk modulus than neon.

At 5.6(4) GPa, monazite peaks emerge at Q = 1.55 Å⁻¹, 2.1 Å⁻¹, and 2.58 Å⁻¹ (as denoted by stars in Figure 4); these are the (110), (02$\overline{1}$), and (211) reflections, respectively. In the P_onset scan, the refined monazite lattice parameters are a = 6.239(1) Å, b = 6.832(3) Å, c = 6.793(1) Å, and β = 99.06(1)°. Both the xenotime and monazite phases persist through the end of the experiment at 11.9(8) GPa, so the phase coexistence range is at least 6.3(8) GPa. In the final scan at 11.9(8) GPa, xenotime, monazite, gold, and B2-KCl are the only phases present.

For the Tb-none experiment, Figure 5a shows XRD pattern evolution throughout the entire experiment, while Figure 5b shows LeBail fit quality at P_initial (1.9(1) GPa), the xenotime–monazite P_onset (4.4(3) GPa), the potential scheelite P_onset (10.2(7) GPa), and P_max (19.3(14) GPa). The first scan in this experiment shows xenotime, gold (upward triangle symbol), and possibly weak ruby (circle symbol) peaks. At 4.4(3) GPa, monazite peaks emerge at Q = 1.55 Å⁻¹, 2.10 Å⁻¹, and 2.58 Å⁻¹ (as denoted by stars in Figure 5); these are the (110), (02$\overline{1}$), and (211) reflections, respectively. In the P_onset scan, the refined monazite lattice parameters are a = 6.134(1) Å, b = 6.870(1) Å, c = 6.187(2) Å, and β = 99.83(2)°.

At 10.2(7) GPa, new peaks emerge at Q = 1.43 Å⁻¹, 3.05 Å⁻¹, 3.89 Å⁻¹, and 4.29 Å⁻¹ (denoted by diamond symbols in Figure 5), and these peaks grow as pressure continues to increase. The phase giving rise to these peaks is likely scheelite-structured TbPO₄, as Lopez-Solano et al. and Bose et al. both predicted scheelite would be the post-monazite phase of TbPO₄, and scheelite has been experimentally observed in YPO₄, TmPO₄, YbPO₄, LuPO₄, and ScPO₄ [19,38,39,40]. Figure 5 also shows ‘S*’ ticks, which represent the peak positions of a scheelite TbPO₄ structure simulated at 20.5 GPa, as reported by Lopez-Solano et al. [19]. The diamond symbols are not perfectly aligned with the S* ticks; however, this slight misalignment is expected given the differences in conditions between this experimental study and Lopez-Solano et al.’s simulation (e.g., pressure, stress state, temperature, and the confounding effects of these factors on individual peak positions). Therefore, the emergence of new peaks (diamond symbols) and their proximity to the ‘S*’ ticks suggests the presence of scheelite is plausible and requires confirmation via further XRD experiments. If confirmed, 10.2(7) GPa would be the lowest pressure at which any scheelite structure has been reported in REPO₄s to date.

The final scan in this experiment contains xenotime, monazite, gold, and potentially scheelite. Therefore, this experiment yields a xenotime–monazite phase coexistence range of at least 14.9(14) GPa and a potential xenotime–monazite–scheelite phase coexistence range of at least 9.1(14) GPa.

A Dy-none experiment was also performed to build on our prior DyPO₄ study, in which KCl was the only PTM tested that was solid at 1 atm [9]. Figure 6a shows XRD pattern evolution throughout the entire experiment, while Figure 6b shows LeBail fit quality at P_initial (3.1(2) GPa), at the xenotime–monazite P_onset (6.9(5) GPa), and at P_max (10.4(7) GPa). The first scan in this experiment shows xenotime, gold (upward triangle symbol), and ruby (circle symbol) peaks. At 6.9(5) GPa, monazite peaks emerge at Q = 1.59 Å⁻¹, 2.10 Å⁻¹, and 2.57 Å⁻¹ (as denoted by stars in Figure 5); these are the (110), (02$\overline{1}$), and (211) reflections, respectively. In the P_onset scan, the refined monazite lattice parameters are a = 6.187(3) Å, b = 6.603(2) Å, c = 6.783(5) Å, and β = 102.40(4)°. The final scan at 10.4(7) GPa contains xenotime, monazite, and gold. Consequently, the DyPO₄ xenotime–monazite phase coexistence range is found to be at least 3.5(7) GPa.

Figure 7 summarizes the DyPO₄ and TbPO₄ phase behavior transformation data reported in this study as well as in two prior DyPO₄ studies [7,9]. In the DyPO₄ section, phase data from an experiment using the MEW PTM (Dy-MEW [7]) are shown, since a prior experiment using neon (Dy-neon [9]) did not reach pressures high enough to gauge the xenotime–monazite phase coexistence range. MEW has a hydrostatic limit of 10.5(5) GPa and is therefore hydrostatic at the xenotime–monazite P_onset, like neon. The P_onset from the Dy-neon experiment (9.1(1) GPa) is shown as an orange dashed line in Figure 7 and is within the error bar of the P_onset from the Dy-MEW experiment (9.6(7) GPa).

Figure 7 shows DyPO₄ and TbPO₄ both exhibit xenotime–monazite P_onset reductions with non-hydrostatic PTMs. Shear can facilitate the plastic deformation involved in phase transformation (i.e., polyhedral rotations and translations) and thereby reduce the hydrostatic pressure required to induce phase transformation. In fact, non-hydrostatic conditions have been suggested to lower the pressure required to induce mechanical instability in other REPO₄ and REVO₄ materials [41,42]. High-pressure dynamical instability (i.e., the softening of Raman-active and silent phonon modes) has also been observed in these materials, but it has less influence on P_onset than mechanical instability does [36,41,42]. In addition, the TbPO₄ P_onset values are marginally (KCl) or significantly (none) lower than those of DyPO₄ in the same PTM. TbPO₄ P_onset values being lower likely stems from the monazite phase being more thermodynamically favorable in TbPO₄ than in DyPO₄ regardless of the kinetic barriers involved [33,34,35,36].

Figure 7 also shows the onset of the scheelite phase at 13.9(10) GPa in the Dy-MEW experiment and at 10.2(7) GPa in the Tb-none experiment. This difference in scheelite P_onset values is likely a convolution of compositional and shear effects. Because the Tb-none experiment is less hydrostatic than the Dy-MEW experiment, the onset pressure of the scheelite phase in the former experiment is expected to be lower. This expectation is consistent with observations from the other experiments. However, the effect of composition on the onset of the scheelite phase remains unclear. Moreover, the lack of scheelite (green bars) in the other four experiments shown in Figure 7 may simply be a consequence of those four experiments not reaching sufficiently high pressures. Considering strictly the DyPO₄ experiments, we expect the scheelite P_onset to be lower in Dy-KCl and Dy-none than in Dy-MEW (as MEW is the most hydrostatic medium of the three) based on a hypothesis of shear-induced lowering of transformation pressure. Unfortunately, the Dy-KCl and Dy-none experiments terminated at pressures significantly lower than the scheelite P_onset of Dy-MEW, leaving significant untested pressure ranges in which the onset of scheelite is still plausible. Considering the TbPO₄ experiments, the emergence of scheelite in Tb-none evidently shows a shear-induced lowering of P_onset because scheelite is not observed at the same pressure in lower shear experiments (i.e., Tb-neon, Tb-KCl). These lower shear experiments are expected to yield higher scheelite P_onset values than Tb-none, so the lack of scheelite observation may be attributable to an insufficient P_max. In order to clarify the presence of scheelite, additional Dy-KCl, Dy-none, Tb-neon, and Tb-KCl experiments going to higher pressures are merited.

Next, the effect of shear on xenotime–monazite phase coexistence is considered. All experiments shown in Figure 7 show significant phase coexistence ranges of at least 3 GPa, further supporting the notion that REPO₄ phase transformations are diffusional rather than martensitic. Consistent with our prior DyPO₄ studies, the coexistence of multiple REPO₄ phases at certain pressures defies Gibbs’ phase rule and further shows the sluggish nature of pressure-induced phase transformation in these materials [7,9]. Furthermore, the TbPO₄ experiments show that while shear induces earlier onset of transformation, it does not induce earlier completion of transformation. While the xenotime–monazite coexistence range is 5.0(10) GPa in the Tb-neon experiment, this range extends to at least 6.3(8) GPa and at least 14.9(14) GPa in the Tb-KCl and Tb-none experiments, respectively. This range extension has also been reported in BaSO₄ and α-Ti when these materials are compressed using non-hydrostatic PTMs [18,19]. At a fundamental level, extended phase coexistence under shear may be attributable to non-uniform stress fields causing varying degrees of transformation progression in a given volume of material. Conclusions regarding coexistence trends cannot be drawn from the DyPO₄ experiments, as the Dy-KCl and Dy-none experiments do not go to sufficiently high pressures. For completeness, plots showing the pressure-dependence of TbPO₄ and DyPO₄ monazite and xenotime lattice parameters as well as a table of axial compressibilities are provided in the Supplementary Materials.

The findings in this study provide key insights for understanding REPO₄s under complex stress states and inform potential structural applications, including CMC fiber coatings. This work provides in situ evidence to corroborate ex situ observations of phase transformation of TbPO₄ under shear from other types of experiments (e.g., indentation, fiber pull-out) [4,5]. In addition, this study shows a high-shear environment can lower the P_onset to pressures below the xenotime REPO₄′s hardness, suggesting transformation-related strain-hardening affects measured hardness values [4,43]. Moreover, this work suggests REPO₄ compositions further from the xenotime–monazite phase boundary (i.e., with higher hydrostatic P_onset values) may be considered for CMC fiber coating applications if P_onset is proven to drop as dramatically under shear as it does in TbPO₄. The benefits of REPO₄ phase transformation (i.e., enhanced CMC plasticity and toughening) may be accessible at lower pressures and over a wider range of pressures than previously understood.

4. Conclusions

This study systematically probes the effect of non-hydrostaticity on the pressure-induced phase transformations of xenotime TbPO₄ using in situ DAC XRD. Our prior DyPO₄ study found non-hydrostatic KCl PTM induces the xenotime–monazite phase transformation at a pressure ~22% lower than in hydrostatic media (e.g., neon, 16:3:1 MEW) [9]. In this work, our experiments with three PTMs (neon, KCl, and none) show a lowering of the TbPO₄ xenotime–monazite P_onset from 8.7(6) GPa to 5.6(4) GPa to 4.4(3) GPa, respectively. The P_onset value for TbPO₄ with no PTM is the lowest value reported to date for any REPO₄ and represents an almost 50% P_onset reduction in a high-shear stress state relevant to potential CMC applications. When comparing DyPO₄ and TbPO₄, the latter’s P_onset values are consistently lower; this fact is likely due to the monazite phase being more thermodynamically favorable in TbPO₄ than in DyPO₄. Lastly, our TbPO₄ experiment with no PTM provides preliminary proof of scheelite as the high-pressure, post-monazite phase.