Origin of pressure-induced insulator-to-metal transition in the van der Waals compound FePS3 from first-principles calculations
OOrigin of pressure-induced insulator-to-metal transitionin the van der Waals compound FePS fromfirst-principles calculations Robert A. Evarestov ∗ and Alexei Kuzmin † February 25, 2020
Abstract
Pressure-induced insulator-to-metal transition has been studied in the van derWaals compound iron thiophosphate (FePS ) using first-principles calculations withinthe periodic linear combination of atomic orbitals (LCAO) method with hybrid Hartree-Fock-DFT B3LYP functional. Our calculations reproduce correctly the insulator-to-metal transition (IMT) at ∼
15 GPa, which is accompanied by a reduction of the unitcell volume and of the vdW gap. We found from the detailed analysis of the projecteddensity of states that the 3p states of phosphorus atoms contribute significantly at thebottom of the conduction band. As a result, the collapse of the band gap occurs dueto changes in the electronic structure of FePS induced by relative displacements ofphosphorus or sulfur atoms along the c -axis direction under pressure. Keywords:
FePS , layered compound, high pressure, insulator-to-metal transition, firstprinciples calculations. ∗ Department of Quantum Chemistry, Saint Petersburg State University, 7/9 Universitetskaya Naberezh-naya, St. Petersburg 199034, Russian Federation; E-mail: [email protected] † Institute of Solid State Physics, University of Latvia, Kengaraga street 8, LV-1063, Riga, Latvia; E-mail:a.kuzmin@cfi.lu.lv a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b FePS B a nd g a p ( e V ) Pressure (GPa)
C2/mLP C2/mHP-I P-31mHP-II
Pressure-induced phase transitions in iron thiophosphate (FePS ) at ∼ ∼
15 GPawere studied using first-principles calculations. The calculations reproduce the insulator-to-metal transition (IMT) at ∼
15 GPa, accompanied by a reduction of the unit cell volumeand of the van der Waals gap. The origin of the IMT is attributed to the pressure-inducedchanges in the FePS electronic structure caused by the relative displacement of phosphorusor sulfur atoms along the c -axis direction. 2 NTRODUCTION
Iron thiophosphate (FePS ) belongs to a family of van der Waals (vdW) layered materialsand attracted recently much attention due to its remarkable physicochemical and magneticproperties . FePS is a magnetic semiconductor with the band gap of 0.5-1.6 eV andintrinsic antiferromagnetism below the N´eel temperature of about 120 K . Besides, it canbe exfoliated into single and few-layer sheets having enhanced catalytic activity .At low (ambient) pressure , the crystallographic structure of FePS (Fig. 1) is composedof 2D layers extended parallel to the ab -plane and separated by the vdW gaps along the c -axis . Each layer contains Fe atoms octahedrally coordinated by six S atoms andP atoms tetrahedrally coordinated by three S atoms and one P atom, forming a [P S ] − unit . The vdW gap (defined as the shortest distance between the adjacent S layers) isabout 2.8 ˚A.In low-pressure (LP) phase , FePS has monoclinic lattice with space group C /m (No.12) and two FePS formula units in the primitive unit cell, but four formula units in thecrystallographic unit cell. The atoms occupy the following Wyckoff positions: Fe 4g(0,y,0),P 4i(x,0,z), S1 4i(x,0,z), S2 8j(x,y,z). The antiferromagnetic ordering in FePS is controlledby in-plane interactions between the high-spin ( S = 2) Fe ions arranged on a honeycomblattice . They are coupled ferromagnetically to the two nearest Fe neighbours andantiferromagnetically to the third one. As a result, iron moments form in the ab -planesferromagnetic chains coupled antiferromagnetically to each other . The weak vdWinteraction between layers results in an Ising-type antiferromagnetic ordering which remainspreserved down to the monolayer limit .According to recent pressure-dependent X-ray diffraction experiments , FePS ex-hibits two phase transitions upon increasing pressure. At about 4 GPa, it transforms tointermediate-pressure phase (HP-I) with monoclinic ( C /m (No. 12)) symmetry. The prin-cipal difference between LP and HP-I phases is a displacement of the unit cell along the a -axis in the latter, so that iron ions in the adjacent layers become located on top of eachother along the c -axis, and the β angle between the a and c axes reduces from 107.34 ◦ to89.33 ◦ (Fig. 1 and Table 1). The antiferromagnetic ordering survives in the HP-I phase .3n the high-pressure (HP-II) phase above ∼
14 GPa, FePS crystal belongs to the spacegroup P ¯31 m (No. 162) with the hexagonal lattice and two formula units in the primitiveunit cell. The atoms occupy the following Wyckoff positions: Fe 2c(1/3,2/3,0), P 2e(0,0,z),S 6k(x,0,z). The transition to the HP-II phase is accompanied by 10.6% volume collapse(due to a significant reduction of the b and c lattice parameters), abrupt spin-crossovertransition from magnetic high-spin ( S = 2) to non-magnetic low-spin ( S = 0) state, andinsulator-to-metal transition (IMT) . It was also found that the in-plane metallizationmakes most contribution to the IMT phenomenon . Note also that the resistivity of FePS shows stronger dependence on pressure than on temperature .To understand the mechanism of the pressure-driven IMT transition in FePS , first-principles calculations based on the plane-wave density functional theory (DFT) were re-cently performed in the range from 0 to 35 GPa in Ref. . The two structural phase tran-sitions were correctly reproduced to occur at about 5 and 17 GPa. The calculations alsoshowed that the LP and HP-I phases posses antiferromagnetic ordering in agreement withthe experiment. The band gap of about 1.31 eV was found in the LP phase. It decreases to1.00 eV at 10 GPa in the HP-I phase, and, finally, down to zero in the metallic HP-II phase.The analysis of the orbital projected density of states allowed the authors to determine theorigin of the electronic states above and below the Fermi level. It was concluded that in bothLP and HP-I phases, the bottom of the conduction band is formed mainly by the 3d(Fe)and 3p(S) states, whereas the valence band originates mainly from the 3d(Fe) states . Inthe HP-II phase, the states near the Fermi level are mainly of the 3d(Fe) origin .In the present study, we concentrate on the detailed understanding of the origin ofpressure-induced IMT in FePS . We demonstrate that opposite to previous work , theIMT is determined by the significant contribution of 3p(P) states into conduction band bot-tom, which can be tuned by the relative displacement of phosphorus or sulfur atoms alongthe c -axis. We show that metallic conductivity could occur in any of LP, HP-I, and HP-IIphases when P and S atoms are located within one plane upon displacement.4 ETHODOLOGY
Pressure-dependent properties of FePS have been studied using the first-principle linearcombination of atomic orbitals (LCAO) calculations as implemented in the CRYSTAL17code . All-electron triple-zeta valence (TZV) basis sets augmented by one set of polarizationfunctions (pob-TZVP) have been employed for Fe, P, and S atoms.The accuracy in evaluating the Coulomb series and the exchange series was controlled bya set of tolerances, which were taken to be (10 − , 10 − , 10 − , 10 − , 10 − ). The Monkhorst-Pack scheme for an 8 × × k -point mesh in the Brillouin zone was applied. The SCFcalculations were performed for several hybrid DFT-HF functionals with a 10 − toleranceon change in the total energy. The best agreement with the experimental structural data and the band gap value for the low-pressure ( P =0 GPa) phase was obtained for Becke’s3-parameter functional (B3LYP-13%) , which was used in all reported simulations. Thepercentage (13%) defines the Hartree-Fock admixture in the exchange part of DFT func-tional. All calculations were performed using a restricted closed-shell hamiltonian, i.e. fornon-magnetic structures. We believe that such approximation is consistent with the exper-imental temperature dependence of the electrical resistance (see Figs. 4 and 5 in Ref. andFig. 3 in Ref. ), which demonstrates the IMT in FePS in a wide range of temperatures upto 300 K, i.e. far above its N´eel temperature of T N = 120 K .The lattice parameters and atomic fractional coordinates were optimized for each selectedpressure in the range of 0–30 GPa for three phases (Figs. 2 and 3): low-pressure (LP)monoclinic (space group C /m ) phase, high-pressure (HP-I) monoclinic (space group C /m )phase, and high-pressure (HP-II) trigonal (space group P ¯31 m ) phase. The starting structuralparameters were taken from the experimental data . The structure optimization at requiredpressure was performed using the approach developed in Ref. .The phonon frequencies were computed at the center of the Brillouin zone (the Γ-point)within the harmonic approximation using the direct (frozen-phonon) method for eachFePS phase. The primitive cell of FePS in all phases includes 10 atoms (2 Fe, 2 P, and6 S), so that 30 phonon modes are expected and are classified as the Raman-active (R),infrared-active (IR), and silent (S) modes. 5ccording to group theoretical analysis for space group C /m in LP and HP-I phases,there are the 7B g and 8A g Raman-active even modes, whereas the 9B u and 6A u odd modesare infrared-active (three of them (2B u and 1A u ) are acoustic modes with zero frequency atthe Γ-point).In HP-II phase with space group P ¯31 m , the 5E g and 3A g even modes are Raman-active,whereas the 5E u and 4A u odd modes are infrared-active (two of them (1E u and 1A u ) areacoustic modes with zero frequency at the Γ-point). There are also three silent modes (1A u and 2A g ) in HP-II phase.The obtained structural parameters such as lattice parameters ( a , b , c , β ) and atomicfractional coordinates ( x , y , z ) as well as the values of the band gap E g are reported in Table1. The phonon frequencies calculated at P =0, 10, and 18 GPa are given in Table 2. Thepressure dependence of the van der Waals (vdW) gap defined as the distance between twoplanes containing lowest and highest sulfur atoms in the two neighbouring layers (Fig. 1) isreported in Fig. 3. Calculated band structures and total/projected density of states for theLP, HP-I, and HP-II FePS phases are shown in Figs. 4, 5 and 6.Finally, we have performed the calculations of the electronic structure of FePS for artifi-cial situations with P atoms displaced along the c -axis. The crystal structures were fixed atthe ones optimized for LP (0 GPa), HP-I (10 GPa), and HP-II (18 GPa) phases, while thedisplacement of P atoms ∆ z was varying between − E g are shown in Fig. 7. RESULTS AND DISCUSSION
The structural properties of FePS from our LCAO calculations, which correspond to thelowest temperature limit ( T =0 K), agree with the experimental findings from Ref. (Table 1).The comparison for the phonon frequencies is possible only for the LP phase, for which theexperimental infrared and Raman spectra measured at room temperature are available .The calculated values of phonon modes at the Γ-point (Table 2) are in qualitative agreementwith the experimental data, however the low-frequency modes are slightly overestimated.Our calculations reproduce correctly the transition to metallic state at ∼
15 GPa (Fig. 3),6hich is accompanied by a reduction of the unit cell volume by ∼
7% (Fig. 2) and of thevdW gap by ∼
13% (Fig. 3).Pressure dependence of the band gap E g in LP, HP-I, and HP-II phases was evaluatedfrom the band structure calculations performed for optimized crystal lattice geometry (latticeparameters and atomic fractional coordinates) and is reported in Fig. 3. The results suggestthat low-pressure monoclinic C /m lattice is very stable against the compression, showingno transition to metallic state up to 30 GPa. The monoclinic C /m lattice of the HP-Iphase is more pliable, however the collapse of the band gap was only observed for pressuresstarting from 30 GPa and above. Much softer behaviour was found for trigonal P ¯31 m lattice,in which the band gap drops from ∼ was performed (Fig. 4). The calculated band gap for theFePS LP phase at P =0 GPa is 1.84 eV, i.e. the material is an insulator. Upon increasingpressure to 3 GPa, the band gap reduces monotonically to 1.75 eV. The transition to theHP-I phase occurs at ∼ xz,yz,xy (Fe), 3p z (P) and 3p x (S) states. Note thatin the recent work not enough attention has been paid to the contribution of the 3p(P)states to the conduction band.A pressure-dependent variation of the calculated electronic structure of FePS is due toseveral effects that complicate its analysis. These include the reduction of the vdW gap, acompression of the 2D layers in the ab -plane and changes in atomic fractional coordinates.To simplify the task, we considered three artificial models based on the optimized crystal-lographic structures for the LP (0 GPa), HP-I (10 GPa), and HP-II (18 GPa) phases. Inthese models, the position of P atoms was varying along the c -axis direction relative to the7ptimized one (Figs. 7 and 8). We found that the displacement of P atoms in the directionof the plane formed by sulfur atoms in the LP and HP-I phases (Fig. 1) leads to a decreaseof the band gap up to the transition to the metallic state.In the HP-II phase at 18 GPa, P atoms have 3-fold triangular coordination by sulfuratoms, thus they are already located within the S atom plane (Fig. 1). Therefore, thedisplacement of P atoms along the c -axis direction moves them away from the plane formedby sulfur atoms that results in the opposite effect (Fig. 7), i.e. opening of the band gap whenthe displacement is large enough (∆ z (P) > . Under increasing pressure, the relativedisplacement of the P atoms leads to the broadening of both valence and conduction bandsthat results in the band gap collapse, i.e. insulator-to-metal transition. The control over therelative displacements of P atoms can be used to tune the transition. CONCLUSIONS
First-principles LCAO calculations using hybrid DFT-HF B3LYP functional have been per-formed to understand the insulator-to-metal transition in FePS . The calculated insulator-to-metal transition occurs at ∼
15 GPa and is accompanied by the unit cell volume and vander Waals gap reduction and the space group change from monoclinic C /m to trigonal P ¯31 m . The obtained results are in agreement with the available experimental data andrecent calculations .The origin of the insulator-to-metal transition is attributed by us to the pressure-inducedbroadening of valence and conduction bands in the FePS electronic structure caused bythe relative displacement of phosphorus or sulfur atoms along the c -axis direction. Thisdisplacement leads to the P and S atoms arrangement within one plane. Our calculationsshow (Fig. 7) that even in the absence of the vdW gap and lattice parameter reduction due tocompression, a sufficiently large displacement of P atoms could lead to metallic conductivityin both LH and HP-I phases, whereas could produce opposite effect, i.e. opening of the bandgap, in the HP-II phase. Such behaviour is explained by the significant contribution of the8p(P) states in the conduction band bottom (Figs. 5 and 7). ACKNOWLEDGMENTS
The authors acknowledge the assistance of the University Computer Center of Saint-PetersburgState University in the accomplishment of high-performance computations. A.K. is gratefulto the Latvian Council of Science project no. lzp-2018/2-0353 for financial support.9 eferences
1. C. C. Mayorga-Martinez, Z. Sofer, D. Sedmidubsk´y, ˇS. Huber, A. Y. S. Eng, andM. Pumera, ACS Appl. Mater. Interfaces , 12563 (2017).2. F. Wang, T. A. Shifa, P. Yu, P. He, Y. Liu, F. Wang, Z. Wang, X. Zhan, X. Lou, F. Xia,et al., Adv. Func. Mater. , 1802151 (2018).3. K. Burch, D. Mandrus, and J. Park, Nature , 47 (2018).4. H. Li, S. Ruan, and Y.-J. Zeng, Adv. Mater. , 1900065 (2019).5. C. Gong and X. Zhang, Science , eaav4450 (2019).6. R. Brec, D. M. Schleich, G. Ouvrard, A. Louisy, and J. Rouxel, Inorg. Chem. , 1814(1979).7. P. Foot, J. Suradi, and P. Lee, Mater. Res. Bulletin , 189 (1980).8. C. R. S. Haines, M. J. Coak, A. R. Wildes, G. I. Lampronti, C. Liu, P. Nahai-Williamson,H. Hamidov, D. Daisenberger, and S. S. Saxena, Phys. Rev. Lett. , 266801 (2018).9. G. Le Flem, R. Brec, G. Ouvard, A. Louisy, and P. Segransan, J. Phys. Chem. Solids , 455 (1982).10. K. Kurosawa, S. Saito, and Y. Yamaguchi, J. Phys. Soc. Jap. , 3919 (1983).11. P. A. Joy and S. Vasudevan, Phys. Rev. B , 5425 (1992).12. K. C. Rule, G. J. McIntyre, S. J. Kennedy, and T. J. Hicks, Phys. Rev. B , 134402(2007).13. Z. Cheng, T. A. Shifa, F. Wang, Y. Gao, P. He, K. Zhang, C. Jiang, Q. Liu, and J. He,Adv. Mater. , 1707433 (2018).14. W. Zhu, W. Gan, Z. Muhammad, C. Wang, C. Wu, H. Liu, D. Liu, K. Zhang, Q. He,H. Jiang, et al., Chem. Commun. , 4481 (2018).105. G. Ouvrard, R. Brec, and J. Rouxel, Mater. Res. Bulletin , 1181 (1985).16. D. Lan¸con, H. C. Walker, E. Ressouche, B. Ouladdiaf, K. C. Rule, G. J. McIntyre, T. J.Hicks, H. M. Rønnow, and A. R. Wildes, Phys. Rev. B , 214407 (2016).17. J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J.-G. Park, andH. Cheong, Nano Lett. , 7433 (2016).18. Y. Wang, J. Ying, Z. Zhou, J. Sun, T. Wen, Y. Zhou, N. Li, Q. Zhang, F. Han, Y. Xiao,et al., Nature Commun. , 1914 (2018).19. Y. Zheng, X.-x. Jiang, X.-x. Xue, J. Dai, and Y. Feng, Phys. Rev. B , 174102 (2019).20. R. Dovesi, A. Erba, R. Orlando, C. M. Zicovich-Wilson, B. Civalleri, L. Maschio,M. Rrat, S. Casassa, J. Baima, S. Salustro, et al., WIREs Comput. Mol. Sci. , e1360(2018).21. M. F. Peintinger, D. V. Oliveira, and T. Bredow, J. Comput. Chem. , 451 (2013).22. H. J. Monkhorst and J. D. Pack, Phys. Rev. B , 5188 (1976).23. A. D. Becke, J. Chem. Phys. , 5648 (1993).24. A. J. Jackson, J. M. Skelton, C. H. Hendon, K. T. Butler, and A. Walsh, J. Chem. Phys. , 184101 (2015).25. F. Pascale, C. M. Zicovich-Wilson, F. L´opez Gejo, B. Civalleri, R. Orlando, andR. Dovesi, J. Comput. Chem. , 888 (2004).26. M. Bernasconi, G. L. Marra, G. Benedek, L. Miglio, M. Jouanne, C. Julien, M. Scagliotti,and M. Balkanski, Phys. Rev. B , 12089 (1988).27. X. Wang, K. Du, Y. Y. F. Liu, P. Hu, J. Zhang, Q. Zhang, M. H. S. Owen, X. Lu, C. K.Gan, P. Sengupta, et al., 2D Materials , 031009 (2016).28. K. Momma and F. Izumi, J. Appl. Crystallogr. , 1272 (2011).11igure 1: Crystallographic structure of FePS in the low-pressure ( P =0 & 30 GPa) mono-clinic (space group C /m ) phase, intermediate pressure ( P =10 & 30 GPa) monoclinic (spacegroup C /m ) phase and high-pressure ( P =18 & 30 GPa) trigonal (space group P ¯31 m )phase. The van der Waals (vdW) gaps are indicated. The illustrations were created usingthe VESTA software .Figure 2: Pressure dependence of the calculated lattice parameters and primitive cell volumein FePS .Figure 3: Pressure dependence of the calculated band gap E g and the van der Waals (vdW)gap in FePS .Figure 4: Band structure diagram for the LP, HP-I, and HP-II FePS phases. The energyzero is set at the top of the valence band (Fermi energy position).Figure 5: Total and projected density of states (DOS) for the LP, HP-I, and HP-II FePS phases. The energy zero is set at the top of the valence band (Fermi energy position).Figure 6: Total and projected onto the set of atomic orbitals density of states (DOS) for theLP, HP-I, and HP-II FePS phases. The energy zero is set at the top of the valence band(Fermi energy position).Figure 7: Dependence of the band gap E g in LP, HP-I, and HP-II FePS phases on thedisplacement of phosphorus atoms ∆ z (P) along the c -axis.Figure 8: Total and projected density of states (DOS) for the LP ( C /m ) FePS phase as afunction of phosphorus atoms displacement ∆ z (P) along the c -axis. The energy zero is setat the top of the valence band (Fermi energy position).12 vdW gap vdW gap C2/m, HP-I (P=10 GPa)P-31m, HP-II (P=18 GPa) vdW gap
FePP S C2/m, LP (P=30 GPa) vdW gapvdW gap
C2/m, HP-I (P=30 GPa)P-31m, HP-II (P=30 GPa) vdW gap
FePS
Figure 1R. A. Evarestov, A. KuzminJ. Comput. Chem. ca=bcb FePS L a tt i ce p a r a m e t e r s ( Å ) Pressure (GPa) a bca
C2/mLP
FePS Experiment Calculation P r i m i t i ve ce ll v o l u m e ( Å ) Pressure (GPa)
Figure 2R. A. Evarestov, A. KuzminJ. Comput. Chem. C2/m, LP
C2/m, HP-I
P-31m, HP-II
FePS B a nd g a p ( e V ) Pressure (GPa)
FePS v d W g a p ( Å ) Pressure (GPa)
Figure 3R. A. Evarestov, A. KuzminJ. Comput. Chem. P-31m, HP-II (P=18 GPa) E n e r g y ( e V ) Figure 4R. A. Evarestov, A. KuzminJ. Comput. Chem. P-31m, HP-II (P=18 GPa)
Energy (eV) Energy (eV) Energy (eV)
Total DOS Total DOS Total DOSFe Fe FeP P PS2 S1 SS1 S2 D e n s i t y o f S t a t e s ( a . u . ) Figure 5R. A. Evarestov, A. KuzminJ. Comput. Chem. xz, yz, xy (Fe)d (Fe) p x (Fe)p y (Fe)p z (Fe) s(S)p x (S)p y (S)p z (S)Total DOSs(P)p y (P)p x (P)p z (P)Total DOS Energy (eV) Energy (eV) Energy (eV) D e n s i t y o f S t a t e s ( a . u . ) C2/m, LP (P=0 GPa)d xz, yz, xy (Fe)d (Fe) p x (Fe)p y (Fe)p z (Fe) s(S)p x (S)p y (S)p z (S)Total DOSs(P)p y (P)p x (P)p z (P)Total DOS Energy (eV) Energy (eV) Energy (eV) D e n s i t y o f S t a t e s ( a . u . ) C2/m, HP-I (P=10 GPa)d xz, yz, xy (Fe)d (Fe) p x (Fe)p y (Fe)p z (Fe) s(S)p x (S)p y (S)p z (S)Total DOSs(P)p y (P)p x (P)p z (P) Total DOS Energy (eV) Energy (eV) Energy (eV) D e n s i t y o f S t a t e s ( a . u . ) P-31m, HP-II (P=18 GPa)
Figure 6R. A. Evarestov, A. KuzminJ. Comput. Chem. C2/m, LP (0 GPa)
C2/m, HP-I (10 GPa)
P-31m, HP-II (18 GPa)
FePS B a nd g a p ( e V ) D z(P) (Å) Figure 7R. A. Evarestov, A. KuzminJ. Comput. Chem. nergy (eV) Energy (eV) Energy (eV) C2/m, LP (P=0 GPa) D z(P)=0 C2/m, LP (P=0 GPa) D z(P)=0.2 C2/m, LP (P=0 GPa) D z(P)=0.5 D e n s i t y o f S t a t e s ( a . u . ) Total DOS Total DOS Total DOSFe Fe FeP P PS2 S1 S2S1 S2 S1
Figure 8R. A. Evarestov, A. KuzminJ. Comput. Chem. at 0, 10, and 18 GPa.Experimental data are taken from Refs. . Space group C /m (12) Space group C /m (12) Space group P ¯31 m (162)LP ( P =0 GPa) HP-I ( P =10 GPa) HP-II ( P =18 GPa)Experiment LCAO Experiment LCAO Experiment LCAOa (˚A) 5.9428 5.816 5.7620 5.666 5.699 5.791b (˚A) 10.299 10.047 9.988 9.813c (˚A) 6.7160 6.600 5.803 5.652 4.818 4.786 β ( ◦ ) 107.34 108.05 89.33 90.01y(Fe) 0.3320 0.3332 0.3225 0.3333x(P) 0.0860 0.0619 0.0 0.0z(P) 0.1670 0.1716 0.184 0.1868 -0.206 -0.2603x(S1) 0.7600 0.7251 0.638 0.6375 0.3241 0.3686z(S1) 0.2860 0.2332 0.259 0.2529 -0.195 -0.2632x(S2) 0.2690 0.2610 0.127 0.1813y(S2) 0.1745 0.1797 0.1624 0.1813z(S2) 0.2470 0.2308 0.299 0.2529 E g (eV) 1.5 − ) at the Γ-point for FePS at P =0, 10, and18 GPa. Raman active (R), infrared active (IR), and silent (S) modes are indicated. Theacoustic modes with zero frequency are not given. The experimental infrared and Ramanfrequencies (exp.) measured at room temperature are also reported for comparison. Space group C /m (12) Space group C /m (12) Space group P ¯31 m (162)LP ( P =0 GPa) HP-I ( P =10 GPa) HP-II ( P =18 GPa)Mode Frequency Frequency (exp.) Activity Mode Frequency Activity Mode Frequency ActivityB g
151 101 R B g
133 R A u
168 IRB u
174 151 IR B u
160 IR A g
217 SA g
185 R A g
204 R E g
259 RB g
185 R B g
204 RB u
207 IR A u
233 IR E u
266 IRA u
215 IR B u
233 IRB g
239 153 R B g
241 R E g
276 RA g
240 R A g
241 RB u
241 185 IR B u
267 IR E u
301 IRB u
242 IR A u
267 IRA u
245 IR B u
278 IR A u
334 IRA g
267 220 R A g
312 R A g
334 RA u
270 IR A g
312 R E g
352 RB g
272 R B g
313 RA g
276 244 R A u
313 IR E g
380 RB g
281 277 R B g
323 R A u
380 IRB g
314 R A g
344 RA g
315 R B g
344 R A g
381 RA u
318 258 IR A u
360 IR A u
386 SB u
321 295 IR B u
360 IR A g
397 SA g
363 378 R A g
398 R E u
401 IRB u
413 445 IR B u
432 IRA g
506 R B g
539 R A g
416 RB g
508 R A g
539 R E g
486 RB u
526 IR A u
565 IRA u
530 578 IR B u
565 IR E u
532 IRA g
574 573 R A g
613 R613 R