Structure and Behavior of the Ni End-Member Schreibersite Ni 3 P under Compression to 50 GPa

: To better understand the potential presence of light element alloys of Fe and Ni in the Earth’s interior, the crystal structure and compressional behavior of the Ni-P binary compound, schreibersite (Ni 3 P), have been investigated using synchrotron X-ray di ﬀ raction experiments. Both powder and two single-crystal samples of synthetic Ni 3 P (in di ﬀ erent orientations with respect to the loading axis of the diamond anvil cell) were compressed up to approximately 50 GPa at ambient temperature. The compressional data obtained for Ni 3 P were ﬁtted with a 3rd order Birch–Murnaghan equation of state. All data indicated that the c / a ratio of unit cell parameters remained approximately constant up to about 30 GPa but then increased progressively with pressure, exhibiting a second slight discontinuity at approximately 40 GPa. The changes in unit cell parameters at ~30 GPa and ~40 GPa suggested discontinuous changes in magnetic ordering. Moreover, the threshold of these subtle discontinuities is sensitive to the stress state and orientation of the crystal in the diamond anvil cell. This study is the ﬁrst report on the compressional behavior of both powder and single-crystal schreibersite at high-pressure (up to 50 GPa). It o ﬀ ers insights into the e ﬀ ects of Ni 3 P components on the compressional behavior of the Earth’s core.


Introduction
Knowledge of the chemical composition and physical properties of the Earth's interior comes mostly from seismic observations, geophysical modeling, direct observation of surface rocks, and the study of meteorites [1][2][3]. Unfortunately, at present, Earth's deep interior cannot be directly sampled due to engineering limitations, as the deepest hole that has been drilled thus far reached only approximately 12 km [4]. Consequently, experimental investigations at high pressures and high temperatures have played an essential role in studying the Earth's interior. The Earth's core is believed to be comprised primarily of an iron-nickel (Fe-Ni) alloy. Still, a light element (sulfur, phosphorus, oxygen, etc.) component appears to be required as well, based upon current models and observations [1][2][3]5]. From seismic evidence, we know that the density of Earth's core is approximately 10% lower than that of pure Fe at the estimated core pressure and temperature [2,5,6]. The current interpretation of this density deficit involves the presence of a significant amount of nickel, along with small amounts (up to 10%) of one or more light elements such as sulfur, phosphorus, oxygen, silicon, hydrogen, carbon, and potassium [1,3,7]. In addition to reducing the density, the presence of light elements in Fe-Ni alloys also affects the elastic properties and acoustic wave velocities of the core. For example, alloying of Fe with silicon increases both the compressional and shear wave velocities, whereas adding Ni decreases the compressional and shear wave velocities [8]. To better

Single Crystal X-Ray Diffraction at Ambient Conditions
The Ni 3 P compound used in all our studies was synthesized by Dr. Nabil Boctor, at the Carnegie Institution for Science, from a stoichiometric mixture of elemental Ni and P in a molar ratio of 3:1, fused in a silica tube at 1000 • C and 1 atm in a high-temperature furnace. Ambient pressure measurements were conducted at the University of Hawai'i at Manoa X-ray Atlas Diffraction Laboratory, using a Bruker D8 Venture single crystal diffractometer equipped with a PHOTON-II CPAD detector and an Ag kα IµS microfocus source (0.56089 Å) Hawai'i. A synthetic single-crystal approximately 0.10 × 0.08 × 0.02 mm in size was mounted on a Kapton loop and then aligned with the center of the instrument using a goniometer head. The data collection was conducted using APEX3 software (Version 2018.1-0, Bruker AXS Inc., Madison, WI, USA) [40]. The atomic positions, bond lengths, and angles were determined with the SHELXL program (Version 2018, Göttingen, Germany) [41].

High-Pressure X-Ray Diffraction
High-pressure single-crystal X-ray diffraction experiments were conducted at beamline 13BM-C of Advanced Photon Source (APS), Argonne National Laboratory. Two separate experiments were performed on the synthetic Ni 3 P. Experiment 1 used synchrotron powder X-ray diffraction. Finely ground powder of Ni 3 P was loaded into the diamond anvil cell with 0.300 mm culet-size standard diamonds mounted on asymmetric backing plates (cubic boron nitride towards the X-ray source and tungsten carbide towards the detector). A piece of Re metal foil with an initial thickness of 0.255 mm was pre-indented to 0.039 mm. The sample chamber was made by drilling a 0.180 mm diameter, laser-cut hole in the pre-indented gasket. A piece of gold foil and a ruby sphere were placed in the sample chamber, next to the sample for pressure calibration [42][43][44]. The diamond anvil cell (DAC) was loaded to~0.5 GPa with neon as a pressure medium using the GSECARS/COMPRES gas loading system [45]. A monochromatic incident beam with a wavelength of 0.434 Å (28.6 keV) was used. The incident beam was focused to a spot of approximately 0.015 by 0.015 mm with a pair of Kirkpatrick-Baez mirrors. A MAR165 charge-coupled device (CCD, Rayonix L.L.C, Evanston, IL, USA) detector for recording the diffraction images was placed approximately 180 mm from the sample. Lanthanum hexaboride (LaB 6 ) powder was used to calibrate the distance and the tilting of the detector. The total angular opening of the DAC was ±12 • . The sample was kept motionless during the exposure, with a typical exposure time of 5 s. The data were integrated and converted to 1-dimensional diffraction patterns using the Dioptas program [46]. Experiment 2 employed the synchrotron single-crystal x-ray diffraction technique. Two synthetic single-crystals of Ni 3 P, C1, and C2, with approximate sizes of 0.040 × 0.025 × 0.005 mm and 0.020 × 0.020 × 0.005 mm, respectively, were loaded into the DAC with standard diamonds (0.300 mm cutlets). The diamond anvils were mounted on asymmetric backing plates (cubic boron nitride towards the X-ray source and tungsten carbide towards the detector). Crystal C1 was oriented with the (001) direction perpendicular to the diamond's cutlet, and C2 was oriented with the (001) parallel to the cutlet. The Re metal foil with an initial thickness of 0.255 mm was pre-indented to 0.045 mm, and the sample chamber was prepared by laser-cutting a 0.180 mm diameter hole in the pre-indented gasket using laser cutting. Gold foil and two ruby spheres were placed in the sample chamber, next to the samples for pressure calibration [42][43][44]. The DAC was loaded to~0.5 GPa with neon as a pressure medium using the GSECARS/COMPRES gas loading system [45]. The characteristics of the beam and the instrument in experiment 2 were the same as in experiment 1. The total angular range (ϕ ) covered during the scans ranged from 57 to 123 • (with a total angular opening of ±33 • ). A series of step and wide-step ϕ-exposures were collected.
Step scans involved 1 • angular increments, and wide-step scans used 9.8 • angular increments. The sample was rotated at a constant speed during the exposure, with a typical exposure time of 1s/deg. The single-crystal X-ray diffraction data were analyzed with GSE_ADA and Reciprocal Space Viewer (RSV), as described in Reference [47]. The refinement of the crystal structure was done using the program SHELXL [41].

Single Crystal X-Ray Diffraction at Ambient Conditions
The unit cell parameters of the Ni end-member schreibersite (Ni 3 P) measured in our single-crystal X-ray diffraction experiment at ambient pressure. The measurements were as follows: a = 8.9515(2) Å, c = 4.3859(1) Å, and V 0 = 351.44(8) Å 3 , consistent with the tetragonal structure with I-4 space group [48][49][50]. The fractional atomic coordinates and interatomic distances (bonding distances) in Ni 3 P at ambient pressure are summarized in Tables 1 and 2, respectively. The structure of Ni 3 P determined in this experiment is shown in Figure 1. The final figure of merit of the structure refinement, R1 obtained in this experiment, was 0.0239.

High-Pressure X-Ray Diffraction
The powder experiment was conducted in the pressure range of 0.5-46.0 GPa at ambient temperature. The unit cell parameters obtained from the powder data at the first pressure point are a = 8.945(1) Å, and c = 4.381(1) Å, consistent with the tetragonal structure. The crystal structure of Ni 3 P remained tetragonal on compression to 46.0 GPa ( Table 3). The ratio of the unit cell parameters

High-Pressure X-Ray Diffraction
The powder experiment was conducted in the pressure range of 0.5-46.0 GPa at ambient temperature. The unit cell parameters obtained from the powder data at the first pressure point are a = 8.945(1) Å, and c = 4.381(1) Å, consistent with the tetragonal structure. The crystal structure of Ni 3 P remained tetragonal on compression to 46.0 GPa ( Table 3). The ratio of the unit cell parameters (c/a) as a function of pressure remained constant with minor scatter around 0.4897(1) below 35.0 GPa. Above 35.0 GPa, the c/a ratio increased noticeably and approached 0.492(1) at 46.0 GPa ( Figure 2). The normalized lattice parameters (a/a 0 and c/c 0 ) showed a decrease at a continuous rate for both parameters up to 46 GPa. Meanwhile, the slope of c changed discontinuously at 35 GPa (Figure 2), resulting in a change in the c/a ratio.  (1) 8.480 (7) 4.165 (5) 299.5(7) 46.0 (2) 8.467 (7) 4.163 (7) 298.4 (8) The single crystal experiment was conducted over the pressure range 1.1-49.5 GPa at ambient temperature. Given the different orientation of the two sample crystals, the corresponding diffraction patterns were different, as shown in Figure 1. The unit cell parameters of the two samples are shown in Table 4. The unit cell parameters at 1.1 GPa confirmed that both single crystals were tetragonal, with a = 8.939(1) Å, and c = 4.378(2) Å for C1 and a = 8.936(1) Å, c = 4.375(1) Å for C2. Similar to the powder experiment, the c/a ratio was approximately constant at around 0.4899(3) below 30.0 GPa but started increasing significantly above that pressure, approaching 0.4928(4) at 49.5 GPa. For crystal C2, although the ratio of the cell parameter c/a below 25 GPa was constant at around 0.4897 (2), it started to increase substantially above that pressure and reaches 0.4931(6) at 49.5 GPa, as shown in Figure 2. Moreover, between 40 and 45 GPa, both single crystals exhibited a slight change in the c/a ratio, which remained approximately constant at 0.4924(4). The normalized lattice parameters (a/a 0 and c/c 0 ) for the single crystal experiment revealed that there was a slight decrease in the slope of the c-axis at 30 GPa for C1 and 25 GPa for C2. This contributed to the change in the c/a ratio in both crystals, as shown in Figure 2.  The changes in bulk modulus as a function of pressure can be represented in the form of normalized pressure (F = P(3f(1 + 2f) 5/2 ) − 1) versus a Eulerian strain (f = 0.5((V0/V) 2/3 − 1)) plot [52]. The F-f plot from all data indicates K' > 4 ( Figure 4). The linear character of all three F-f plots suggested that the second pressure derivative of the bulk modulus (K'') was negligible. EoS fit confidence ellipses are used for a visual assessment of the quality of the correlation between KT0 and K' ( Figure  5). The confidence ellipses from all our data on Ni 3 P are shown in Figure 5, drawn at a 95.4% confidence level (2σ), and it indicates that all calculated KT0 and K' values from this study are internally consistent.  The changes in bulk modulus as a function of pressure can be represented in the form of normalized pressure (F = P(3f(1 + 2f) 5/2 ) − 1) versus a Eulerian strain (f = 0.5((V 0 /V) 2/3 − 1)) plot [52]. The F-f plot from all data indicates K' > 4 ( Figure 4). The linear character of all three F-f plots suggested that the second pressure derivative of the bulk modulus (K") was negligible. EoS fit confidence ellipses are used for a visual assessment of the quality of the correlation between K T0 and K' (Figure 5). The confidence ellipses from all our data on Ni 3 P are shown in Figure 5, drawn at a 95.4% confidence level (2σ), and it indicates that all calculated K T0 and K' values from this study are internally consistent.

Crystal Structure at Ambient Condition.
The ambient unit cell parameters and interatomic distances of Ni 3 P determined in this study are in good agreement with previous reports [48][49][50]. The atomic coordinates of Ni 3 P determined in our single-crystal experiment represent the opposite absolute structure configuration of the mineral, which is a well-known phenomenon for molecules or crystals without a center of symmetry or mirror

Crystal Structure at Ambient Condition.
The ambient unit cell parameters and interatomic distances of Ni 3 P determined in this study are in good agreement with previous reports [48][49][50]. The atomic coordinates of Ni 3 P determined in our single-crystal experiment represent the opposite absolute structure configuration of the mineral, which is a well-known phenomenon for molecules or crystals without a center of symmetry or mirror plane [53]. The space group of Ni 3 P (I-4) does not include an inversion center (it is acentric). The fractional atomic coordinates from our experiments have been transformed to follow the convention used by previous studies [48][49][50]. However, despite differences in the absolute configuration, the structure of Ni 3 P in this experiment is in excellent agreement with previously reported results.

Crystal Structure Evolution on Compression to 50 GPa
At ambient conditions, the unit cell parameters and volume of Ni 3 P are slightly smaller than the ones of Fe 3 P [19,35,54]. This shows that the unit cell parameters are controlled mainly by the cation size, as the ionic radius of nickel (~1.24 Å) is smaller than that of iron (~1.26 Å) [55].
In the powder sample, the c/a ratio starts to increase at 40 GPa; the same behavior is observed in single-crystal at 30 GPa in single crystal 1 and single-crystal 2 at 25 GPa ( Figure 2). The experimental results indicate that the axial compressibility of Ni 3 P is almost identical up to the transition point, above which the c-axis becomes less compressible. Differences in the transition pressure observed in the three experiments (powder, C1, and C2) indicate that the stress state and the orientation of the uniaxial stress component have a controlling effect over the transition point.
The sensitivity of some phase changes to uniaxial stress has been reported in the scientific literature. For example, first-principles calculations were used to predict the formation of a previously unknown high-pressure phase of SiO 2 with five-coordinated silicon that forms in response to stress applied to α-quartz, along a specific crystal orientation [56]. In SiO 2 α-cristobalite, two-phase changes to cristobalite II and cristobalite X-I are either observed [57] or suppressed [58] depending on the degree of hydrostaticity and stress rate. CuGeO 3 is one of the best-known examples of a material that is sensitive to uniaxial stress, with the ambient pressure phase going through two different series of phase changes depending on the degree of non-hydrostaticity [59].
In the three comparative experiments conducted in this study, the pressure medium and stress fields were very similar (Ne). Neon is a good soft quasi-hydrostatic medium, but at pressures above 20 GPa, it starts displaying signs of uniaxial stress [60]. The three samples in our experiments were oriented in different ways in the stress field of the diamond anvil cell, which featured an enhanced uniaxial component aligned with the loading axis. The two single crystals had either the [100] or [001] directions exposed explicitly to the uniaxial stress. In contrast, in the powder samples, individual grains had all possible orientations to the uniaxial stress. We do not know the exact dependence of the phase change transition point on the direction of the uniaxial stress. It is hypothetically possible, for example, that the strongest effect would be associated with the [110] or [011] directions, rather than the principal directions [100] or [001]. The observed transition pressures for the two single crystals are both lower than the transition point observed for the powder sample. It is worth noting that the nature of the discontinuity in the single crystal and powder experiments was different. Single crystals seemed to transform through an immediate single-crystal to the single-crystal mechanism, with no evidence of two-phase coexistence. In the powder sample, there was most likely a two-phase coexistence with populations of differently oriented powder grains undergoing the phase change at different pressures, and relative phase fractions changing gradually. However, this effect was difficult to quantify, given the continuous nature of changes in the unit cell parameters.
Very similar effects observed in Fe 3 P and Fe 3 S have been attributed to changes in magnetic ordering [35,37,38]; therefore, we assume that the nature of the discontinuity in Ni 3 P is of magnetic origin. However, we did not directly measure magnetic properties to provide direct proof of this interpretation. We were also not able to conclusively verify the existence of the second transition due to the small number of pressure points collected above 40 GPa. Gu et al. [35] reported a magnetic collapse in Fe 3 P around 40 GPa corresponding to a change of symmetry from I-4 to P4/mnc, based on first-principle calculations. The discontinuities in lattice parameters and volume as a function of pressure observed in our experiments at approximately 30 GPa and 40 GPa might be related to displacive phase changes. The change in the trend of the c/a ratio of Ni 3 P in our experiments was also very similar to the magnetic transition and analogous c/a change observed in Cr 2 O 3 [61,62]. The decreasing compressibility of the c-axis, contributing to the discontinuity in the c/a ratio trend, suggests that there are differences in the magnetic structure of schreibersite below and above the transition point [54].
The bulk modulus (K T0 ) of Ni 3 P from this experiment was in good agreement with the results of the first-principles calculations [63]. Moreover, the values of K T0 and K' of Ni 3 P from our experiments were higher than values reported for isostructural compounds such as Fe 3 P [19,35], Fe 3 S [36][37][38][39], and Ni 3 S [64]. This outcome suggested that the compressibility was controlled mainly by the cation size. Interestingly, K T0 and K' of Fe 3 P and Fe 3 S have quite similar values within the uncertainty, whereas K T0 and K' of Ni 3 P are higher than Ni 3 S. This indicates that changing the anion has a small effect on the compressibility behavior between Fe 3 P and Fe 3 S. However, the effect on the compressibility between Ni 3 P and Ni 3 S is stronger. The cause of the difference is that the synthetic Ni 3 P in this paper was a stoichiometric compound, while Ni 3 S in the earlier studies was non-stoichiometric. Moreover, the studies on Ni 3 S were conducted only up to about 10 GPa, whereas we compressed our sample to approximately 50 GPa. If we focus only on the first 10 GPa of compressibility data, we also find that the trend of the c/a ratio of C1 is decreasing slightly over this range. Thus, to study the effect of the anion size between Ni 3 P and Ni 3 S, one might have to compress both samples to pressures higher than 10 GPa using samples as close to stoichiometric as possible.

Implications for Planetary Cores
To assess the effect the presence of Ni-rich schreibersite would have on the Earth's core, we compared the densities of pure iron, Fe 3 P, and Ni 3 P at pressures corresponding to the inner and outer core. It should be noted that these calculations were performed by extrapolating our results far beyond the range of conditions covered in our experiments based on a geothermal equation. The comparison showed that the density of Ni 3 P from this experiment and Fe 3 P from Gu et al. [35] was approximately 5% lower than the pure Fe at core pressure and ambient temperature. This result suggests that the presence of a significant amount of nickel and light elements such as phosphorus has the effect of lowering the density, consistent with the observed deficit in the density of the core as determined from seismic evidence [2,5,6]. Although our experiments did not include a study of the effects of high temperature on the unit cell parameter of Ni 3 P, to a very simplified first approximation, we can compare the cold compressibility curves.
Gu et al., [35] argued that the discontinuities observed around 17 and 40 GPa were not only consistent with the calculated magnetic transitions but also probably produced discontinuous changes in the coefficient of thermal expansion. The thermal expansion coefficient α(p) decreases with increasing pressure. By analogy, we can assume that the compressional discontinuities observed in our experiments for Ni 3 P at approximately 30 GPa and 40 GPa might also be related to discontinuities of thermal expansion and magnetic transitions. Thermal expansion decreases at high pressure, and with increasing bond energy, contributes to the high melting point. Therefore, at high pressure, most materials stay in the solid-state to much higher temperatures than at low pressure. At ambient pressure, Ni 3 P has a melting point (~960 • C) lower than Fe 3 P (~1100 • C) and pure iron (~1500 • C), which implies that addition of Ni 3 P to natural schreibersite lowers the melting point [65][66][67].
The presence of Ni leads to loss of ferromagnetic order in Fe 3 P because Ni causes a decrease of the magnetic moment [68,69]. Ni 3 P is less compressible than pure hcp-Fe or iron phosphide phase, including Fe 3 P [19,35]. Moreover, first-principles calculations on Ni 3 P, Fe 3 P, and pure hcp-Fe suggest that the shear modulus of Ni 3 P is lower than Fe 3 P and pure hcp-Fe by approximately 30% and 20%, respectively [63,70,71]. The higher incompressibility and lower shear modulus of Ni 3 P are consistent with the decrease of shear wave velocity of Fe under pressure when adding Ni to Fe-compounds [8].

Conclusions
The results of our diamond anvil cell experiments suggest that the volume and unit cell parameters of Ni 3 P experience two discontinuities, at approximately 30 GPa and 40 GPa, which may be associated with corresponding magnetic transitions. The results of this study also illustrate that the transition c-axis of Ni 3 P becomes less compressible than the a-axis. The discontinuity is sensitive to the stress state and orientation of the crystal in the diamond anvil cell. Moreover, the experiments suggest that substituting Ni into Fe-bearing compounds results in higher incompressibility of the mineral.
Further investigations of Fe-Ni alloys, including more direct measurements of their magnetic properties, are needed to explain the observed transitions fully more fully. Moreover, to reliably model core conditions, additional measurements will need to be conducted at a higher pressure and high temperature.