Pressure-induced structural phase transition in iron phosphide

Computational Materials Science 107 (2015) 204–209

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Pressure-induced structural phase transition in iron phosphide Haiyan Yan ⇑ College of Chemistry and Chemical Engineering, Shaanxi Key Laboratory for Phytochemistry, Baoji University of Arts and Sciences, Baoji 721013, China

a r t i c l e

i n f o

Article history: Received 11 March 2015 Received in revised form 9 May 2015 Accepted 28 May 2015

Keywords: First-principles calculations Iron phosphide Pressure-induced phase transition

a b s t r a c t The high-pressure structural stability of FeP is systematically explored up to 150 GPa by using first-principles calculations combined with crystal structure prediction techniques. We firstly predicted that FeP undergoes a structural phase transition from the low-pressure MnP-type phase to a simple cubic FeSi-type phase at high pressure of 87.5 GPa with a volume drop of 4.3%. The occurrence of this high-pressure FeSi-type phase follows the increased distortions of FeP6 polyhedron in MnP-type phase and the coordination of Fe atoms increased from 6 to 7. Phonon calculations indicated that this FeSi-type structure is dynamically stable under high pressure as well as ambient pressure. The variations of elastic parameters (including elastic constants, elastic moduli, and sound velocities) of these two structures for FeP under pressure are also investigated for the first time. Further electronic structure calculations showed that FeSi-type structure exhibits a much weaker metallic character compared to the low-pressure MnP-type phase, originating from the increased Fe-d–P-p orbital hybridization under high pressure. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction In the field of Earth sciences, the composition of the Earth’s core is still a hot topic which is significant to understand the structure and dynamics of the Earth’s interiors. In the past many years, it has been suggested that the Earth’s core is dominantly iron and nickel, alloyed with a certain amount of light elements including sulfur (S), silicon (Si), oxygen (O), hydrogen (H), and carbon (C) according to cosmochemical and geophysical arguments [1–3]. A great deal of experimental and theoretical works thus have been carried out to determine phase diagrams of iron compounds with light elements under extreme conditions (high pressure and high temperature) relevant to the core’s formation [4–9]. Besides, phosphide (P) has been recognized as another important components presented in the Earth’s core by the reaction between molten iron and phosphorus. Moreover, the previous studies have demonstrated that the phosphorus possesses a much higher solubility in the melting iron than that of sulfur and the phase diagram of Fe–P compound is similar to that of Fe–S, a typical composition in Earth’s interiors [10–12]. Therefore, the structural stability and properties of Fe–P compounds under high pressure are also important to the planetary cores. In the Fe–P binary phase diagram, the structural stabilities of iron phosphides under high pressure have been performed on ⇑ Tel./fax: +86 917 3364589. E-mail address: [email protected] http://dx.doi.org/10.1016/j.commatsci.2015.05.031 0927-0256/Ó 2015 Elsevier B.V. All rights reserved.

Fe3P, Fe2P, and FeP. Fe3P was first thought to present a phase transition from ambient-pressure structure to AuCu3-type structure at 30 GPa and below 1000 K [13], but later argued to adopt an orthorhombic structure in a quenched sample from 21 GPa and 2100 K [14]. Subsequently, by using synchrotron X-ray diffraction and laser-heating diamond anvil cell techniques at 64 GPa and 1650 K, Gu et al. proposed [15] that Fe3P undergo a structural transformation from ambient I-4 structure to a tetragonal P4/mnc structure which was further confirmed by the first principles calculations. However, the high-pressure structure of Fe2P is the subject of continuing debate because of its diverse magnetic properties at high pressure, and different candidates such as Pnma, P4/nmm, and P-3m phases have been proposed for Fe2P [14,16,17]. Compared to Fe3P and Fe2P, the experimental and theoretical investigations on the high-pressure behaviors of FeP are rarely studied, and there is lack of confirmed reports on the existence of pressure-induced structural phase transitions. A more recent experimental work [18] has proposed that no crystal structure and electronic structure changes of FeP occur up to 15.6 GPa and 1800 ± 200 K by combined in situ powder X-ray diffraction and Mössbauer spectroscopy. Therefore, the peculiarity and the absence of characterized high-pressure phase of FeP prompted our endeavor to investigate its structural stability behavior at higher pressure. Furthermore, the exploration of phase transition behavior of FeP would provide more insights into the pressure effect on other iron and light elements compounds. In order to address these points, we here presented extensive structure searches to explore the structural

H. Yan / Computational Materials Science 107 (2015) 204–209

evolution of FeP and the chemical nature of their bonding with neighboring atoms up to 150 GPa using an unbiased structure searching method in combination with ab initio calculations. A FeSi-type high-pressure phase of FeP was uncovered above 87.5 GPa, thereby demonstrating the pressure-induced increase in the coordination of Fe atoms from 6 to 7. Further calculations are performed to investigate the lattice parameters, equation of state, electronic properties as well as transition pressures between these two phases, provided valuable insights into the high pressure behaviors of FeP. 2. Computational methods The variable-cell high-pressure structure predictions with simulation cells containing up to four formula units (f.u.) were performed in the range of 0–150 GPa by using Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) code [19,20], designed to search for the structure possessing the lowest free energy at given pressure conditions. The effectiveness of this method has been demonstrated by recent successes in predicting high-pressure structures of various systems, ranging from elements to binary and ternary compounds [21–27]. The underlying ab initio structural relaxations and electronic calculations were performed using density functional theory within the Perdew–Bu rke–Ernzerh (PBE) of parameterization of the generalized gradient approximation (GGA) [28,29], as implemented in the VASP code [30]. The electronic wave functions are expanded in a plane-wave basis set with a cutoff energy of 450 eV, and all-electron projector-augmented wave (PAW) method [31] was utilized to describe the electron-ion interactions. Integration over the Brillouin zone was calculated using a Monkhorst–Pack grid [32], with the k meshes of 8  14  7 for MnP-type phase and 10  10  10 for FeSi-type phase. The Methfessel–Paxton electronic smearing method [33], with the smearing width of 0.2 eV, was used to improve convergence of the energies/forces in structural optimization. During the geometrical optimization, all forces on atoms were converged to less than 0.001 eV/Å and the total stress tensor was reduced to the order of 0.01 GPa. The phonon calculations were carried out by using a finite displacement approach through the PHONOPY program [34]. 3. Results and discussion According to the structural search results, at pressure points of 0, 25, and 50 GPa, FeP keeps the experimental MnP-type phase with space group Pnma (Z = 4, Fig. 1a), validating our method adopted here. In this structure, iron atoms locate at the center of distorted octahedra consisted of six phosphorus atoms and this structure can be described as closely packed FeP6 edge- and face-sharing octahedra, the same to the post-troilite FeS. At ambient pressure, the calculated lattice parameters of MnP-type phase are a = 5.128 Å, b = 3.036 Å, and c = 5.763 Å in a unit cell which are in good agreement with available experimental data (a = 5.1826(6) Å, b = 3.0976(3) Å, and c = 5.7838(7) Å; a = 5.193(1) Å, b = 3.099(1) Å, and c = 5.792(1) Å) [18,35]. In the FeP6 polyhedron presented in Fig. 1c, the Fe–P bond distances are calculated to be 2.246 (2) Å, 2.237 (2) Å, 2.225 Å, and 2.310 Å. In order to investigate the high-pressure behaviors of MnP-type phase according to Ref. [18], the pressure dependences of the unit-cell volume and lattice constants are plotted in Fig. 2b and c, along with the recent experimental data [18]. Strikingly, the calculated results are in agreement with these experimental results, indicating the reliability of our calculations. In addition, the obtained bulk modulus B0 and its pressure derivative B00 of MnP-type phase are 210 GPa and 4.4, which also agree

205

well with the experimental results of 205(7) and 4.0 [18]. For higher pressures of 90, 100 and 150 GPa, a simple cubic FeSi-type phase (space group P213, Z = 4, Fig. 1b) was uncovered for FeP. This FeSi-type structure contains four FeP f.u. in a unit cell (a = b = c = 4.045 Å at 100 GPa), in which two inequivalent atom Fe and P occupies the Wyckoff 4a (0.409, 0.409, 0.409) and 4a (0.092, 0.092, 0.092) sites, respectively. Compared to the ambient MnP-type structure, the coordination number of Fe ions in high-pressure FeSi-type structure increased up to 7, formed a FeP7 polyhedron building block shown in Fig. 1d. Additionally, the Fe–P bond lengths in the FeSi-type structure are also listed in the Fig. 1d. Our computational approach is based on constant pressure static quantum mechanical calculations at T = 0 K, so the Gibbs free energy (G = U + PV  TS) is reduced to enthalpy (H = U + PV). To determine the phase transition pressure point, we have plotted out the enthalpy differences curves of the predicted FeSi-type phase relative to the ambient-pressure MnP-type phase in Fig. 2a. In more detail, we have optimized these two structures at much more pressure points up to 180 GPa with certain pressure intervals. Due to the MnP–FeP phase is isostructural with FeS VI phase which has been recently predicted to transform to an orthorhombic Pmmn phase at 135 GPa [4]. So this Pmmn phase was also considered in Fig. 2a for comparison. From Fig. 2a, it is confirmed that the predicted FeSi-type phase becomes more stable than the MnP-type phase above 87.5 GPa. However, the Pmmn-FeP possesses larger enthalpy values compared to those of FeSi-type phase in the whole studied pressure range, and thus can be ruled out as existing high-pressure candidate. The corresponding volume drop at the phase transition boundary was also calculated and shown in the inset of Fig. 2b, and the obtained results suggest that MnP-type ? FeSi-type phase transition is first-order with volume drop of 4.3% which can be easily detected in further experiments. Meanwhile, both the variations of lattice parameters and Fe–P bond lengths of MnP-type and FeSi-type phases under high pressures are also presented in Fig. 2c and d. From Fig. 2d, the Fe–P bond length in MnP-type phase shows a nearly linear decrease with pressure and one can see that the trend of d2 > d4 at ambient pressure changes to d2 < d4 above 60 GPa, suggesting an increased distortion of FeP6 polyhedron under increasing pressures. The dynamical stability of a crystalline structure requires the eigen frequencies of its lattice vibrations be real for all wavevectors in the whole Brillouin zone. We need to check the dynamical stability of the proposed FeSi-type phase. Fig. 3 shows the phonon dispersion curves of the FeSi-type phase at 150 and 0 GPa, respectively. The absence of imaginary frequency suggests that the predicted FeSi-type phase is dynamically stable at both high and ambient pressures, which further supports the validity of this new structure. To explore the elastic behaviors of FeP at high pressure, we have computed the single elastic constants of MnP-type and FeSi-type phases from stress–strain relations by applying both positive and negative strains on the order of maximum 1.0%. The elastic stabilities, incompressibility, and rigidity of these two structures are thus determined based on the calculated elastic constants and derived Hill elastic moduli [36]. No experimental data for single-crystal elastic constants of MnP–FeP are presently available for any ambient and elevated pressures. Our calculated elastic constants and derived Hill elastic moduli at high pressures (up to 150 GPa) are shown in Table 1 and Fig. 4a. In Table 1, one can see that the calculated elastic parameters for MnP-type phase are in a good accordant with the previous theoretical results [37,38] at ambient conditions, and the agreement of MnP-type phase supports the reliability of the elastic calculations for this new FeSi-type phase although there are no available results for comparison. From Fig. 4a and b, the elastic constants

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H. Yan / Computational Materials Science 107 (2015) 204–209

Fig. 1. Crystal structure of low-pressure MnP–FeP (a), high-pressure FeSi-FeP (b), FeP6 polyhedron in MnP-type phase (c), and FeP7 polyhedron in FeSi-type phase (d). The grey and black spheres represent Fe and P atoms, respectively.

Fig. 2. Enthalpies differences of FeSi-type phase (P213) relative to ambient-pressure MnP-type phase (Pnma) as a function of pressure (a), the calculated volumes (b), lattice parameters (b), and bond lengths (c) as a function of pressure for MnP-type and FeSi-type phases.

and derived Hill elastic moduli of both MnP-type and FeSi-type phases increase monotonically with pressure. For MnP-type structure, the obtained results showed that the elastic constants possess the trend C11 > C33 > C22 in the whole studied pressures. The implication of this trend is that the b-axis is the most compressible compared to other two crystal axes which accords well with results presented in Fig. 2c. However, the elastic constants associated with shear strains (such as C44, C55, C66) changed with pressure differently. And the values of C44 become smaller than

those of C55 and C66 above 25 GPa, indicating that the shear along the (1 0 0) plane becomes easy relative to the shear along (0 1 0) and (0 0 1) planes. Although the phosphorus content in the cores of planets is uncertain, it is important to understand the high-pressure behaviors of possible core materials. At inner core conditions, the solids must have appropriate sound velocities. We calculate next the isotropic compressional (VP) and shear (VS) sound velocities for a polycrystalline aggregate of FeP at different pressures as follows:

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H. Yan / Computational Materials Science 107 (2015) 204–209

Fig. 3. Phonon dispersion curves of FeSi-type phase at 150 GPa (a) and 0 GPa (b).

Table 1 Calculated elastic constants Cij (in GPa), derived Hill bulk modulus B, shear modulus G, and Young’s modulus E in unit of GPa for MnP-type and FeSi-type phases at 0 GPa. Also shown is G/B ratio. Phases

References

C11

C22

C33

C44

C55

C66

C12

C13

C23

B

G

E

G/B

MnP-type

This work Ref. [37] Ref. [38]

445 505

284 286

431 467

175 171

148 154

154 165

141 151

137 135

162 182

224 238 216

139 144

345 360

0.62 0.61

FeSi-type

This work

364

226

109

283

0.48

114

157

Fig. 4. Pressure dependences of elastic constants Cij (a) and elastic moduli and velocities (b) for MnP-type and FeSi-type phases.

VP ¼

VS ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B þ 4G=3

q sffiffiffiffi G

q

ð1Þ

ð2Þ

where q is the density, B and G are Hill bulk and shear modulus which can be calculated from the elastic constants according to

Voigt–Reuss–Hill approximations [36]. The variations of VP and VS of these two phases in their stable pressure ranges are plotted in Fig. 4b, along with preliminary earth reference model (PREM) values [39] as well as the VP of experimental data of hcp-Fe [40] for comparisons. The calculated values of both MnP-type and FeSi-type phases are all lower than the PREM values by about 2.0–2.5 km/s for VP and by about 1.2–1.7 km/s for VS. Compared to the experimental data of VP of pure Fe presented in Fig. 4b, the alloying effects of P in Fe (both MnP-type and FeSi-type phases)

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H. Yan / Computational Materials Science 107 (2015) 204–209

Fig. 5. Band structure, total, and site projected density of states (DOS) of MnP-type phase at 0 GPa (a) and FeSi-type phase at 100 GPa (b).

Fig. 6. Charge density distributions in (0 1 0) planes in both MnP-type (a) and FeSi-type phases (b).

have resulted in reduced density and increased velocity as other Fe– L alloys (FeO, FeSi, etc.) at high pressures [40]. Comparisons of sound velocity vs. pressure (P) between MnP-type and FeSi-type phases illustrate VP–P and VS–P discontinuities through the MnP-type ? FeSi-type structural transition, which can be attributed to the density jump of approximately 4% through this structural phase transition.

Atomic displacements are always accompanied by a striking change of properties, especially electronic properties. Therefore, the total and site projected electronic densities of states (DOS) of MnP-type and FeSi-type phases were calculated at ambient pressure and 100 GPa. As expected in Fig. 5a, the MnP–FeP exhibits clear metallic behavior by evidence of the finite electronic DOS at the Fermi level, which agrees well with previous experimental

H. Yan / Computational Materials Science 107 (2015) 204–209

works [41]. From inspection of its partial DOS curves, the major orbital occupancy near Fermi level stems from Fe-3d electrons which are the principal cause for the metallicity. The significant hybridized Fe-d–P-p bonding can be concluded from the partial DOS profiles in the energy range from 7.5 eV to 2.5 eV, which is also in agreement with the experimental XPS valence band spectra of FeP [41]. Compared to the MnP–FeP, however, the high-pressure FeSi-type phase shows much weaker metallic character due to smaller electronic DOS at the Fermi level (Fig. 5b), originating from the increased hybridization of Fe-d–P-p in a larger energy range from 12.5 eV to 2.5 eV. It has been suggested that this increased hybridization effect might separate the bonding state from the antibonding states, leading to a lower electronic density of state at Fermi level. Apart from the covalent bonding feature, the ionic bonding nature of Fe and P atoms in these two structures is also demonstrated by the corresponding charge density distribution in (0 1 0) planes in both MnP-type and FeSi-type phases, as shown in Fig. 6. 4. Conclusions In conclusion, the structural stability of FeP has been investigated under high pressure up to 150 GPa by performing a swarm structure search combining first-principles calculations. The results demonstrated that the pressure-induced phase transition from the ambient MnP-type phase to a high-pressure FeSi-type phase occurs at about 87.5 GPa which extends the high-pressure structures of FeP. During this structural phase transition, compression induced the coordination of Fe atoms increased from 6 to 7, accompanied by the distortions of FeP6 polyhedron in MnP-type phase. The pressure dependences of elastic constants, elastic moduli as well as sound velocities of theses two phases have also been obtained. The analysis of the electronic structure reveals that the high-pressure FeSi-type phase possesses a much weaker metallic nature compared to the low-high MnP-type phase, originating from the increased Fe-d–P-p orbital hybridization under high pressure. These results should motivate further studies to investigate the high-pressure phase transitions of other Fe–L compounds. Acknowledgment This work was financially supported by the Natural Science Foundation of China (No. 11204007) and Natural Science Basic Research plan in Shaanxi Province of China (grant No. 2012JQ1005).

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References [1] J.P. Poirier, Phys. Earth Planet. Inter. 85 (1994) 319. [2] L. Stixrude, J. Geophys. Res. 102 (1997) 14835. [3] A. Dewaele, P. Loubeyre, F. Occelli, M. Mezouar, P.I. Dorogokupets, M. Torrent, Phys. Rev. Lett. 97 (2006) 215504. [4] S. Ono, A.R. Oganov, J.P. Brodholt, L. Vocˇadlo, I.G. Wood, A. Lyakhov, C.W. Glass, A.S. Côté, G.D. Price, Earth Planet. Sci. Lett. 272 (2008) 481. [5] H. Ohfuji, N. Sata, H. Kobayashi, Y. Ohishi, K. Hirose, T. Irifune, Phys. Chem. Miner. 34 (2007) 335. [6] N. Sata, K. Hirose, G. Shen, Y. Nakajima, Y. Ohishi, N. Hirao, J. Geophys. Res. 115 (2010) B09204. [7] L. Dubrovinsky, N. Dubrovinskaia, F. Langenhorst, D. Dobson, D. Rubie, C. Gessmann, I.A. Abrikosov, B. Johansson, V.I. Baykov, L. Vitos, T. Le Bihan, W.A. Crichton, V. Dmitriev, H.P. Weber, Nature 422 (2003) 58. [8] R. Jeanloz, T. Lay, Sci. Am. 268 (1993) 48. [9] E. Knittle, R. Jeanloz, Science 251 (1991) 1438. [10] I. Fleischer, C. Schroder, G. Klingelhofer, R. Gellert, Meteorit. Planet. Sci. 44 (2009) A70. [11] W.F. McDonough, S.S. Sun, Chem. Geol. 120 (1995) 223. [12] A.J. Stewart, M.W. Schmidt, Geophy. Res. Lett. 34 (2007) L13201. [13] H.P. Scott, S. Huggins, M.R. Frank, S.J. Maglio, C.D. Martin, Y. Meng, J. Santillán, Q. Williams, Geophys. Res. Lett. 34 (2007) L06302. [14] H.P. Scott, B. Kiefer, C.D. Martin, N. Boateng, M. Frank, Y. Meng, High Press. Res. 28 (2008) 375. [15] T.T. Gu, Y.W. Fei, X. Wu, S. Qin, Earth Planet. Sci. Lett. 390 (2014) 296. [16] P. Dera, B. Lavina, L.A. Borkowski, V.B. Prakapenka, S.R. Sutton, M.L. Rivers, R.T. Downs, N.Z. Boctor, T. Prewitt, Geophys. Res. Lett. 35 (2008) L10301. [17] X. Wu, S. Qin, J. Phys: Conf. Ser. 215 (2010) 012110. [18] T.T. Gu, X. Wu, S. Qin, L. Dubrovinsky, Phys. Earth Planet In. 184 (2011) 154. [19] Y.C. Wang, J. Lv, L. Zhu, Y.M. Ma, Phys. Rev. B 82 (2010) 094116. [20] Y.C. Wang, J. Lv, L. Zhu, Y.M. Ma, Comput. Phys. Commun. 183 (2012) 2063. [21] J. Lv, Y.C. Wang, L. Zhu, Y.M. Ma, Phys. Rev. Lett. 106 (2011) 015503. [22] L. Zhu, H. Wang, Y.C. Wang, J. Lv, Y.M. Ma, Q.L. Cui, Y.M. Ma, G.T. Zou, Phys. Rev. Lett. 106 (2011) 145501. [23] D.N. Hamane, M.G. Zhang, T. Yagi, Y.M. Ma, Am. Mineral. 97 (2012) 568. [24] Y.C. Wang, H.Y. Liu, J. Lv, L. Zhu, H. Wang, M.Y. Ma, Nature Commun. 2 (2011) 563. [25] L. Zhu, H.Y. Liu, C.J. Pickard, G.T. Zou, Y.M. Ma, Nature Chem. 6 (2014) 644. [26] Q. Li, D. Zhou, W.T. Zheng, Y.M. Ma, C.F. Chen, Phys. Rev. Lett. 110 (2013) 136403. [27] M. Zhang, H.Y. Liu, Q. Li, B. Gao, Y.C. Wang, H.D. Li, C.F. Chen, Y.M. Ma, Phys. Rev. Lett. 114 (2015) 015502. [28] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. [29] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [30] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [31] G. Kresse, D. Joubert, Phys. Rev. B 59 (17) (1999) 58. [32] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [33] M. Methfessel, A.T. Paxton, Phys. Rev. B 40 (1989) 3616. [34] A. Togo, F. Oba, I. Tanaka, Phys. Rev. B 78 (2008) 134106. [35] H. Fjellvag, A. Kjekshus, A.F. Andresen, Acta Chem. Scand. A40 (1986) 227. [36] R. Hill, Proc. Phys. Soc. London A 65 (1952) 349. [37] J.Y. Li, Appl. Mech. Mater. 321–324 (2013) 1761. [38] M. Cerny, J. Pokluda, Mater. Sci. Forum 482 (2005) 135. [39] A. Dziewonski, D.L. Anderson, Phys. Earth Planet. Inter. 25 (1981) 297. [40] Z. Mao, J.F. Lin, J. Liu, A. Alatas, L. Gao, J. Zhao, H.K. Mao, Proc. Natl. Acad. Sci. U.S.A. 109 (2012) 10239. [41] I.N. Shabanova, V.I. Kormilets, N.S. Terebova, J. Electron Spectrosc. 114–116 (2001) 609.