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A computational study of structural transitions in NpAs and NpTe induced by pressure
Journal of Alloys and Compounds 274 (1998) 18–22
L
A computational study of structural transitions in NpAs and NpTe induced by pressure Ch.U.M. Trinadh, M. Rajagopalan*, S. Natarajan Department of Physics, Anna University, Chennai 600 025, India Received 16 January 1998
Abstract Spin-polarized electronic structure calculations, by the tight binding linear muffin tin orbital (TBLMTO) method within the atomic sphere approximation (ASA), for neptunium compounds NpAs and NpTe at ambient pressure and high pressure are reported. The self-consistently calculated total energies at various cell volumes were fitted to Birch equation of state (EOS) in order to obtain the transition pressure from the B1 to the B2 phase and the volume collapse for each compound. The results indicate good agreement with high pressure X-ray diffraction (HPXRD) experiments. The role of interatomic distances in the transition is also examined. 1998 Elsevier Science S.A. Keywords: Electronic structure ; Interatomic distance; Neptunium compounds; Pressure induced transition
1. Introduction The pressure induced structural phase transition in binary compounds of lanthanides and actinides has received considerable attention recently [1]. Computational physics is an important area which can provide insight into the mechanism of these transitions via electronic structure studies. The element Np, with the 5f 4 valence configuration, is an actinide element (An). The 5f states are considered to be intermediate in localisation between the rare-earth 4f and transition metal 3d electrons. Hill [2] has shown that there is a critical interatomic distance between the lanthanide or actinide atoms below which the compound is non-magnetic and above which the compound is magnetic. On the other hand, in some of these compounds, the phase transition does not seem to have any link to the 5f electrons. The interest in these compounds lies in the following observations: (i) experimental X-ray diffraction (XRD) studies under high pressure (HP) have been reported for these compounds [3,4]; (ii) both compounds are known to possess 5f electrons in a localised state at ambient pressure from X-ray absorption studies [5]; (iii) there have been no reports of calculations of the electronic structure of NpAs and NpTe by band theory, even at ambient pressure. *Corresponding author. 0925-8388 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 98 )00550-7
The outline of this paper is as follows. Section 2 gives details of the calculations. The results are presented in Section 3 and Section 4. Section 5 presents the conclusions. At ambient pressure, neptunium monoarsenide (NpAs) is in the NaCl-type structure (B1 phase). NpAs is an anti-ferromagnetic (AFM) compound with an ordered moment of 2.5 m B [6]. Dabos et al. [3] carried out XRD experiments on NpAs under HP using a diamond anvil cell (DAC) and reported that the compound undergoes a sluggish structural transition to the CsCl structure (B2 phase) which starts at around 26 GPa. Dabos et al. [7] observed that the Np–Np distance decreases by 54 pm and the Np–As distance increases by 14 pm across the transition. Photoemission spectra (PES) and electronic structure calculations of NpAs have not been reported. Neptunium monotelluride (NpTe) crystallises in the B1 phase at ambient pressure with a lattice constant of ˚ Dabos et al. [4] carried out HPXRD studies 6.2021 A. using DAC on single crystals of NpTe and reported a B1 to B2 transition in the range 12–20 GPa with a 7% decrease in cell volume. It is also observed that the Np–Np distance decreases by 55 pm and the Np–Te distance increases by ¨ 19 pm during the transition. Mossbauer spectroscopy on NpTe [8] suggested a trivalent state for Np. At ambient pressure, NpTe shows AFM ordering with an ordered moment of 2 m B . There have been no photoemission
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22
spectroscopic (PES) results nor calculations of the electronic structure reported for NpTe in the literature.
2. Method of spin-polarized calculations on NpAs and NpTe Since these compounds are magnetic, spin-polarized calculations were carried out using the TBLMTO-ASA method [9] for different cell volumes in both the B1 and B2 phases, similar to our earlier studies an Fe 3 Pt [10]. The tetrahedron method [11] was employed to obtain the density of states (DOS). The exchange-correlation scheme employed was that due to von Barth and Hedin [12]. All relativistic corrections except that due to the spin–orbit coupling were included. Two empty spheres are positioned along the body diagonal in the B1 phase for closer packing. The radii of the spheres were chosen according to the electro-negativity criterion. Self-consistent band calculations were carried out for 512 k-points in the entire Brillouin zone (BZ). The valence configurations 7s 2 7p 0 5d 1 5f 4 for Np, 4s 2 4p 3 for As and 5s 2 5p 4 for Te were used.
3. Electronic structure and equation of state studies for NpAs The ‘‘spin-down’’ electron bands for the B1 phase of NpAs at ambient pressure are plotted in Fig. 1. The bands for the ‘‘spin-up’’ case will be similar and are not shown here. As is typical for monopnictides of f-block elements, the lowest-lying bands arise from the 4s states of pnictogen As and the bands in the valence region just below EF are due to the 4p states of As. One of the 5f bands crosses EF , indicating the metallicity of NpAs. The 6d states of Np are in the conduction band region and hybridise with the 5f states of Np. There are no previous calculations of the
Fig. 1. ‘‘Spin-up’’ electron dispersion curves for NpAs in the B1 phase at ambient pressure.
19
electronic structure of NpAs in the literature. However, a comparative study with other neptunium monopnictides can be made. Davis [13] performed ambient band structure calculations for a higher monopnictide, namely NpSb, in various Np valence configurations using the Kohn–Korringa–Rostoker (KKR) method. Of these, the case stated as NpSb1 by Davis [13] corresponds to the electron configuration (f 4 d 1 s 2 for Np) used in the present calculations. Although the calculations of Davis [13] are non-spin polarized and Sb has a higher atomic number than As, there is good agreement in the overall profile of the electronic structure for NpAs plotted in Fig. 1. Brooks [14] calculated the paramagnetic band structure for the lower monopnictide NpN using the non-relativistic as well as the relativistic LMTO method. The results of Brooks [14] show the partial f-occupation number of Np in NpN to be 3.8, which is close to the f-configuration that was used in the present calculations for NpAs and NpTe. The electronic structure calculations for ThAs were performed by the present authors and are reported elsewhere [15]. The resulting band structure for ThAs at ambient pressure is shown in Fig. 2. It can be seen that Th has the 5f 0 configuration. A comparison of Figs. 1 and 2 shows that the overall bandwidth increases as the actinide becomes heavier, as reported by Davis [13]. A histogram of the total density of states (DOS) is shown for NpAs in the B1 phase at ambient pressure in Fig. 3. PES studies on NpAs are not available in the literature for comparison. However, the DOS histogram depicts the following features: (i) a small feature due to the 4s of As around 20.8 Ry; (ii) a small peaked structure appearing from 20.4 to 20.1 Ry; (iii) a sharp peak due to 5f (Np) at 0.1 Ry in the valence region; and (iv) a broad feature due to 6d from about 10.2 Ry and extending over the length of the plot. The overall profile of the total DOS of NpAs qualitatively resembles that of NpN [14]. The total energies calculated for different cell volumes in the B1 and B2 phases of NpAs were fitted to the Birch equation of state (EOS). The total energy as a function of cell volume, and enthalpy as a function of pressure, are
Fig. 2. Band structure of ThAs in the B1 phase at ambient pressure.
20
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22 Table 1 Results for the B1 to B2 transition in NpAs induced by pressure
Fig. 3. Total DOS in the B1 phase of NpAs at ambient pressure.
plotted in Figs. 4 and 5, respectively. The results of EOS studies are given in Table 1. The error in the calculation of a 0 for NpAs was found to be 2.29%. The interatomic distance (d) plays a significant role in
Fig. 4. Calculated total energy as a function of cell volume in the B1 and B2 phases of NpAs.
Result
Present study
Experiment
Pt (GPa) DV /V0 (%) B0 (GPa) ˚ a 0 (A) ˚ Lattice parameter in the B2 phase (A)
19.8 11.37 71.78 5.7026 3.4402
26 9 70.0 5.8366 3.310
AnX compounds (An5actinide, X5pnictogen or chalcogen). It governs the interactions between various l-states in the compound. The calculated values of d are compared with experiment [7] in Table 2. Thus the cation–anion distance is larger in the B2-type structure. As a consequence, the electronic interaction (d–p and / or f–p band mixing) between neptunium and arsenic is weakened during the transition. The Np–Np distance in the B2 phase after the transition ˚ It is greater than the Hill limit for Np ions is 3.286 A. ˚ Hence, the compound remains in the which is 3.05 A. magnetic state even after the structural phase transition. Thus, the present results establish the validity of Hill’s theory [2] for Np. The B1 to B2 transition induced by pressure in NpAs does not seem to be related to 5f delocalisation. This is also supported by the fact that the variation in interatomic distances across the transition in the case of ThAs (which is a 5f 0 compound) are nearly equal in magnitude, as well as sign, to those for NpAs. This is supported by the fact that the high pressure phase is of higher crystal symmetry. There will only be a change in coordination number during the transition in NpAs. Our calculations for ThAs indicated the value of the bulk modulus at ambient pressure to be 125 GPa, which is greater than that for NpAs. This result also establishes the trend that compressibility increases with a smaller cation.
4. Band structure and pressure induced phase transition of NpTe The ‘‘spin-down’’ electronic structure in the B1 phase of NpTe at ambient pressure is shown in Fig. 6. The bands for the ‘‘spin-up’’ case will be similar. The corresponding total DOS is shown in Fig. 7. Figs. 6 and 7 are typical for an AnX compound. The total energy as a function of cell volume and the enthalpy at various pressures are plotted in
Table 2 Variation in the interatomic distance (Dd) of NpAs during the B1 to B2 transition Between atoms
Fig. 5. Enthalpy versus pressure in the case of NpAs.
Np–Np Np–As
Dd (pm) Present study
Experiment
254.5 113.8
254 114
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22
Fig. 6. ‘‘Spin-down’’ electronic structure for NpTe in the B1 phase at ambient pressure.
21
Fig. 9. Enthalpy as a function of pressure for NpTe in the B1 and B2 phases.
interatomic distances and their variation during the transition were calculated and, as shown in Tables 3 and 4, are in good agreement with experiment [4]. For NpTe, as for NpAs, the Np–Np distance remains ˚ for Np in the B2 phase, above the Hill limit (3.05–3.2 A) indicating that the compound remains in the magnetic state. These results indicate that the transition is not due to 5f electrons. The mechanism for the transition is a geometric effect involving a change in coordination number from 6 in the B1 phase to 8 in the B2 phase.
5. Summary of results Fig. 7. Total DOS in the B1 phase of NpTe at ambient pressure.
Figs. 8 and 9, respectively, which indicate the structural phase stability of NpTe under pressure. The error in the calculation of the lattice parameter a 0 of NpTe at ambient pressure was found to be 2.14%. The
Fig. 8. Calculated total energy versus cell volume in the B1 and B2 phases of NpTe.
An ab-initio band structure study for NpAs and NpTe could successfully explain the crystal phase stability under pressure. The salient conclusions from the present calculations are as follows. (i) Spin-polarized calculations within the local spin density approximation (LSDA) of the von Barth and Hedin exchange-correlation scheme were sufficient to study the pressure induced structural transitions in NpAs and NpTe. Spin–orbit effects, which were not taken into account in the calculation, have no or little role to play in a study concerned with structural properties. (ii) The compound remains in the B1 phase with coordination number 6 over the pressure range in which the ratio of cation to anion radius remains between 0.42 and 0.71. The compound goes to the B2 phase with coordination number 8 at the transition pressure. (iii) The present electronic structure studies have shown that Hill’s criterion is good for 5f electron systems such as NpAs and NpTe. (iv) Variations in interatomic distances were found to play a significant role during the transition. (v) To our knowledge, this is the first time that the electronic structures for NpAs and NpTe have been reported. Spin-polarized PES experiments on NpAs and NpTe would be very useful for a precise comparison of the results on DOS by the present calculations.
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22
22
Table 3 Value of interatomic distances for NpTe Between atoms
Pressure
Distance d (pm) In the B1 phase
Np–Np Np–Np Np–Te Np–Te
Ambient 13 GPa Ambient 13 GPa
Present study
Experiment
438.68 415.39 310.09 293.69
438.68 416 310.19 294
Table 4 Variation in interatomic distances for NpTe during the B1 to B2 transition Between atoms
Np–Np Np–Te
In the B2 phase
Dd (pm) Present study
Experiment
256.16 117.68
255 119
Acknowledgements One of the authors (TCUM) acknowledges a fellowship granted by the Council of Scientific and Industrial Research (CSIR), New Delhi, India.
References [1] U. Benedict, J. Alloys Comp. 223 (1995) 216. [2] H.H. Hill, in: W.M. Miner (Ed.), Plutonium and Other Actinides, Society of AIME, New York, 1970, p. 2. [3] S.S. Dabos, C. Dufour, U. Benedict, J.C. Spirlet, M. Pages, Physica B 144 (1986) 79.
Present study
Experiment
359.84
361.2
311.68
312.8
[4] S.S. Dabos, U. Benedict, S. Heathmann, J.C. Spirlet, M. Pages, J. Less-Common Met. 160 (1990) 35. [5] G. Kalkowski, G. Kaindl, S. Bertram, G. Schmiester, J. Rebizant, J.C. Spirlet, O. Vogt, Solid State Commun. 64 (1987) 193. [6] K. Mattenberger, O. Vogt, J. Rebizant, J.C. Spirlet, F. Bourdarot, P. Burlet, J. Rossat-Mignod, M.N. Bouillet, A. Blaise, J.P. Sanchez, J. Magn. Magn. Mater. 104–107 (1992) 43. [7] S.S. Dabos, U. Benedict, J.C. Spirlet, M. Pages, J. Less-Common Met. 153 (1989) 133. [8] J.P. Sanchez, J. Rebizant, J.C. Spirlet, O. Vogt, Electronic and magnetic properties of NpSb and NpTe studied by 237 Np, 121 Sb and 125 ¨ Te Mossbauer spectroscopies, 17e’me Journees des Actinides Lausanne, 1987, p. 26. [9] O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53 (1984) 2571. [10] M. Rajagopalan, K. Arthi, S. Auluck, G. Kalpana, J. Alloys Comp. 240 (1996) 124. [11] O. Jepsen, O.K. Andersen, Solid State Commun. 9 (1971) 1963. [12] U. von Barth, L. Hedin, J. Phys. C 5 (1972) 629. [13] H.L. Davis, in: A.J. Freeman, J.B. Darby (Eds.), The Actinides Electronic Structure and Related Properties, Vol. II, Academic Press, New York, 1974, p. 1. [14] M.S.S. Brooks, J. Phys. F. Met. Phys. 14 (1984) 857. [15] Ch.U.M. Trinadh, M. Rajagopalan, S. Natarajan, Phys. Status Solidi (b) (submitted).
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A computational study of structural transitions in NpAs and NpTe induced by pressure Ch.U.M. Trinadh, M. Rajagopalan*, S. Natarajan Department of Physics, Anna University, Chennai 600 025, India Received 16 January 1998
Abstract Spin-polarized electronic structure calculations, by the tight binding linear muffin tin orbital (TBLMTO) method within the atomic sphere approximation (ASA), for neptunium compounds NpAs and NpTe at ambient pressure and high pressure are reported. The self-consistently calculated total energies at various cell volumes were fitted to Birch equation of state (EOS) in order to obtain the transition pressure from the B1 to the B2 phase and the volume collapse for each compound. The results indicate good agreement with high pressure X-ray diffraction (HPXRD) experiments. The role of interatomic distances in the transition is also examined. 1998 Elsevier Science S.A. Keywords: Electronic structure ; Interatomic distance; Neptunium compounds; Pressure induced transition
1. Introduction The pressure induced structural phase transition in binary compounds of lanthanides and actinides has received considerable attention recently [1]. Computational physics is an important area which can provide insight into the mechanism of these transitions via electronic structure studies. The element Np, with the 5f 4 valence configuration, is an actinide element (An). The 5f states are considered to be intermediate in localisation between the rare-earth 4f and transition metal 3d electrons. Hill [2] has shown that there is a critical interatomic distance between the lanthanide or actinide atoms below which the compound is non-magnetic and above which the compound is magnetic. On the other hand, in some of these compounds, the phase transition does not seem to have any link to the 5f electrons. The interest in these compounds lies in the following observations: (i) experimental X-ray diffraction (XRD) studies under high pressure (HP) have been reported for these compounds [3,4]; (ii) both compounds are known to possess 5f electrons in a localised state at ambient pressure from X-ray absorption studies [5]; (iii) there have been no reports of calculations of the electronic structure of NpAs and NpTe by band theory, even at ambient pressure. *Corresponding author. 0925-8388 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 98 )00550-7
The outline of this paper is as follows. Section 2 gives details of the calculations. The results are presented in Section 3 and Section 4. Section 5 presents the conclusions. At ambient pressure, neptunium monoarsenide (NpAs) is in the NaCl-type structure (B1 phase). NpAs is an anti-ferromagnetic (AFM) compound with an ordered moment of 2.5 m B [6]. Dabos et al. [3] carried out XRD experiments on NpAs under HP using a diamond anvil cell (DAC) and reported that the compound undergoes a sluggish structural transition to the CsCl structure (B2 phase) which starts at around 26 GPa. Dabos et al. [7] observed that the Np–Np distance decreases by 54 pm and the Np–As distance increases by 14 pm across the transition. Photoemission spectra (PES) and electronic structure calculations of NpAs have not been reported. Neptunium monotelluride (NpTe) crystallises in the B1 phase at ambient pressure with a lattice constant of ˚ Dabos et al. [4] carried out HPXRD studies 6.2021 A. using DAC on single crystals of NpTe and reported a B1 to B2 transition in the range 12–20 GPa with a 7% decrease in cell volume. It is also observed that the Np–Np distance decreases by 55 pm and the Np–Te distance increases by ¨ 19 pm during the transition. Mossbauer spectroscopy on NpTe [8] suggested a trivalent state for Np. At ambient pressure, NpTe shows AFM ordering with an ordered moment of 2 m B . There have been no photoemission
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22
spectroscopic (PES) results nor calculations of the electronic structure reported for NpTe in the literature.
2. Method of spin-polarized calculations on NpAs and NpTe Since these compounds are magnetic, spin-polarized calculations were carried out using the TBLMTO-ASA method [9] for different cell volumes in both the B1 and B2 phases, similar to our earlier studies an Fe 3 Pt [10]. The tetrahedron method [11] was employed to obtain the density of states (DOS). The exchange-correlation scheme employed was that due to von Barth and Hedin [12]. All relativistic corrections except that due to the spin–orbit coupling were included. Two empty spheres are positioned along the body diagonal in the B1 phase for closer packing. The radii of the spheres were chosen according to the electro-negativity criterion. Self-consistent band calculations were carried out for 512 k-points in the entire Brillouin zone (BZ). The valence configurations 7s 2 7p 0 5d 1 5f 4 for Np, 4s 2 4p 3 for As and 5s 2 5p 4 for Te were used.
3. Electronic structure and equation of state studies for NpAs The ‘‘spin-down’’ electron bands for the B1 phase of NpAs at ambient pressure are plotted in Fig. 1. The bands for the ‘‘spin-up’’ case will be similar and are not shown here. As is typical for monopnictides of f-block elements, the lowest-lying bands arise from the 4s states of pnictogen As and the bands in the valence region just below EF are due to the 4p states of As. One of the 5f bands crosses EF , indicating the metallicity of NpAs. The 6d states of Np are in the conduction band region and hybridise with the 5f states of Np. There are no previous calculations of the
Fig. 1. ‘‘Spin-up’’ electron dispersion curves for NpAs in the B1 phase at ambient pressure.
19
electronic structure of NpAs in the literature. However, a comparative study with other neptunium monopnictides can be made. Davis [13] performed ambient band structure calculations for a higher monopnictide, namely NpSb, in various Np valence configurations using the Kohn–Korringa–Rostoker (KKR) method. Of these, the case stated as NpSb1 by Davis [13] corresponds to the electron configuration (f 4 d 1 s 2 for Np) used in the present calculations. Although the calculations of Davis [13] are non-spin polarized and Sb has a higher atomic number than As, there is good agreement in the overall profile of the electronic structure for NpAs plotted in Fig. 1. Brooks [14] calculated the paramagnetic band structure for the lower monopnictide NpN using the non-relativistic as well as the relativistic LMTO method. The results of Brooks [14] show the partial f-occupation number of Np in NpN to be 3.8, which is close to the f-configuration that was used in the present calculations for NpAs and NpTe. The electronic structure calculations for ThAs were performed by the present authors and are reported elsewhere [15]. The resulting band structure for ThAs at ambient pressure is shown in Fig. 2. It can be seen that Th has the 5f 0 configuration. A comparison of Figs. 1 and 2 shows that the overall bandwidth increases as the actinide becomes heavier, as reported by Davis [13]. A histogram of the total density of states (DOS) is shown for NpAs in the B1 phase at ambient pressure in Fig. 3. PES studies on NpAs are not available in the literature for comparison. However, the DOS histogram depicts the following features: (i) a small feature due to the 4s of As around 20.8 Ry; (ii) a small peaked structure appearing from 20.4 to 20.1 Ry; (iii) a sharp peak due to 5f (Np) at 0.1 Ry in the valence region; and (iv) a broad feature due to 6d from about 10.2 Ry and extending over the length of the plot. The overall profile of the total DOS of NpAs qualitatively resembles that of NpN [14]. The total energies calculated for different cell volumes in the B1 and B2 phases of NpAs were fitted to the Birch equation of state (EOS). The total energy as a function of cell volume, and enthalpy as a function of pressure, are
Fig. 2. Band structure of ThAs in the B1 phase at ambient pressure.
20
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22 Table 1 Results for the B1 to B2 transition in NpAs induced by pressure
Fig. 3. Total DOS in the B1 phase of NpAs at ambient pressure.
plotted in Figs. 4 and 5, respectively. The results of EOS studies are given in Table 1. The error in the calculation of a 0 for NpAs was found to be 2.29%. The interatomic distance (d) plays a significant role in
Fig. 4. Calculated total energy as a function of cell volume in the B1 and B2 phases of NpAs.
Result
Present study
Experiment
Pt (GPa) DV /V0 (%) B0 (GPa) ˚ a 0 (A) ˚ Lattice parameter in the B2 phase (A)
19.8 11.37 71.78 5.7026 3.4402
26 9 70.0 5.8366 3.310
AnX compounds (An5actinide, X5pnictogen or chalcogen). It governs the interactions between various l-states in the compound. The calculated values of d are compared with experiment [7] in Table 2. Thus the cation–anion distance is larger in the B2-type structure. As a consequence, the electronic interaction (d–p and / or f–p band mixing) between neptunium and arsenic is weakened during the transition. The Np–Np distance in the B2 phase after the transition ˚ It is greater than the Hill limit for Np ions is 3.286 A. ˚ Hence, the compound remains in the which is 3.05 A. magnetic state even after the structural phase transition. Thus, the present results establish the validity of Hill’s theory [2] for Np. The B1 to B2 transition induced by pressure in NpAs does not seem to be related to 5f delocalisation. This is also supported by the fact that the variation in interatomic distances across the transition in the case of ThAs (which is a 5f 0 compound) are nearly equal in magnitude, as well as sign, to those for NpAs. This is supported by the fact that the high pressure phase is of higher crystal symmetry. There will only be a change in coordination number during the transition in NpAs. Our calculations for ThAs indicated the value of the bulk modulus at ambient pressure to be 125 GPa, which is greater than that for NpAs. This result also establishes the trend that compressibility increases with a smaller cation.
4. Band structure and pressure induced phase transition of NpTe The ‘‘spin-down’’ electronic structure in the B1 phase of NpTe at ambient pressure is shown in Fig. 6. The bands for the ‘‘spin-up’’ case will be similar. The corresponding total DOS is shown in Fig. 7. Figs. 6 and 7 are typical for an AnX compound. The total energy as a function of cell volume and the enthalpy at various pressures are plotted in
Table 2 Variation in the interatomic distance (Dd) of NpAs during the B1 to B2 transition Between atoms
Fig. 5. Enthalpy versus pressure in the case of NpAs.
Np–Np Np–As
Dd (pm) Present study
Experiment
254.5 113.8
254 114
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22
Fig. 6. ‘‘Spin-down’’ electronic structure for NpTe in the B1 phase at ambient pressure.
21
Fig. 9. Enthalpy as a function of pressure for NpTe in the B1 and B2 phases.
interatomic distances and their variation during the transition were calculated and, as shown in Tables 3 and 4, are in good agreement with experiment [4]. For NpTe, as for NpAs, the Np–Np distance remains ˚ for Np in the B2 phase, above the Hill limit (3.05–3.2 A) indicating that the compound remains in the magnetic state. These results indicate that the transition is not due to 5f electrons. The mechanism for the transition is a geometric effect involving a change in coordination number from 6 in the B1 phase to 8 in the B2 phase.
5. Summary of results Fig. 7. Total DOS in the B1 phase of NpTe at ambient pressure.
Figs. 8 and 9, respectively, which indicate the structural phase stability of NpTe under pressure. The error in the calculation of the lattice parameter a 0 of NpTe at ambient pressure was found to be 2.14%. The
Fig. 8. Calculated total energy versus cell volume in the B1 and B2 phases of NpTe.
An ab-initio band structure study for NpAs and NpTe could successfully explain the crystal phase stability under pressure. The salient conclusions from the present calculations are as follows. (i) Spin-polarized calculations within the local spin density approximation (LSDA) of the von Barth and Hedin exchange-correlation scheme were sufficient to study the pressure induced structural transitions in NpAs and NpTe. Spin–orbit effects, which were not taken into account in the calculation, have no or little role to play in a study concerned with structural properties. (ii) The compound remains in the B1 phase with coordination number 6 over the pressure range in which the ratio of cation to anion radius remains between 0.42 and 0.71. The compound goes to the B2 phase with coordination number 8 at the transition pressure. (iii) The present electronic structure studies have shown that Hill’s criterion is good for 5f electron systems such as NpAs and NpTe. (iv) Variations in interatomic distances were found to play a significant role during the transition. (v) To our knowledge, this is the first time that the electronic structures for NpAs and NpTe have been reported. Spin-polarized PES experiments on NpAs and NpTe would be very useful for a precise comparison of the results on DOS by the present calculations.
C.U.M. Trinadh et al. / Journal of Alloys and Compounds 274 (1998) 18 – 22
22
Table 3 Value of interatomic distances for NpTe Between atoms
Pressure
Distance d (pm) In the B1 phase
Np–Np Np–Np Np–Te Np–Te
Ambient 13 GPa Ambient 13 GPa
Present study
Experiment
438.68 415.39 310.09 293.69
438.68 416 310.19 294
Table 4 Variation in interatomic distances for NpTe during the B1 to B2 transition Between atoms
Np–Np Np–Te
In the B2 phase
Dd (pm) Present study
Experiment
256.16 117.68
255 119
Acknowledgements One of the authors (TCUM) acknowledges a fellowship granted by the Council of Scientific and Industrial Research (CSIR), New Delhi, India.
References [1] U. Benedict, J. Alloys Comp. 223 (1995) 216. [2] H.H. Hill, in: W.M. Miner (Ed.), Plutonium and Other Actinides, Society of AIME, New York, 1970, p. 2. [3] S.S. Dabos, C. Dufour, U. Benedict, J.C. Spirlet, M. Pages, Physica B 144 (1986) 79.
Present study
Experiment
359.84
361.2
311.68
312.8
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