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Absence of a phase transition in ZrTe5
Solid State Communications, Printed in Great Britain.
Vol. 42, No. 9, pp. 69 l-693,1982.
ABSENCE OF A PHASE TRANSITION
0038-1098/82/210691-03$03.00/0 Pergamon Press Ltd.
IN ZrTes
D.W. Bullett School of Physics, University
of Bath, Bath BA2 7AY, England
(Received 7 January 1982 by R.A. Cowley) Electronic structure calculations suggest that ZrTes is a semi-metal. Thus it appears much more probable that the electrical resistivity peak at 150 K originates in the strong temperature dependence of the carrier density and carrier mobility than that a structural phase transition occurs, as previously proposed.
THE ANOMALOUS TEMPERATURE dependence [ 1,2] of the electrical resistivity of the group IV transition-metal pentachalcogenides ZrTe, and Hffes has led to speculations [ 1 ] that these materials may undergo structural phase transitions, arising from the strong anisotropy in their crystallographic structure [3]. This stimulated the present calculation of the electronic structure of ZrTes. We find no evidence for an inherent one-dimensional charge-density-wave instability in the atomic arrangement. The calculation yields semi-metallic band overlap between valence and conduction levels, with a very low density of states at the Fermi level. It appears more likely that the resistive peak in these materials arises from the temperature dependence of the carrier density and carrier mobility, than that a structural phase transition occurs. The atomic arrangement with ZrTes and HfTes is depicted in Fig. 1. The crystals are orthorhombic, with space group Cmcm. The room-temperature lattice constants determined by Furuseth et al. [3] for ZrTe5 are a = 3.988.&, b = 14.502&c = 13.727-k A full structural determination has been made only for HfTe5, but, since the lattice constants for the hafnium compound are very close to those of ZrTes, it was assumed in the present study that the HfTe, atomic coordinates could be transferred directly to ZrTes. The structure contains one-dimensional chains of end-sharing ZrTee trigonal prisms, reminiscent of the transition-metal trichalcogenides 14-71. Instead of being linked directly (as in ZrTes), in the ZrTes structure the trigonal ZrTe, chains are linked along the c-axis through intermediate “Tez” chains. We have discussed elsewhere the origin of the semiconducting gap in the zirconium trichalcogenides [6] and the driving force responsible for the structural phase transition in the group V material NbSes [6,7]. In this investigation the same computational techniques were applied to derive the electronic structure of ZrTes. The only input to the calculation is a knowledge of the
Fig. 1. The crystal structure of ZrTes projected along [ 10 01. Open circles are at height zero, shaded circles at height f . Zig-zag chains of Te atoms separate trigonal prismatic ZrTes chains in layers perpendicular to the b-axis. crystal structure and the atomic wave-functions and valence-level energies (Table 1) of the isolated constituent atoms. It was assumed that charge-transfer effects were negligible; selfconsistency was required only to the extent that the atomic energy level of the Zr d-orbital in the calculation of the crystal wave-function was made consistent with that of a neutral isolated Zr atom containing the same number of d-electrons. The resulting Zr configuration in ZrTes was d’.‘. Figure 2 shows the calculated energy band structure along some of the edges of the irreducible Brillouin zone. States in the energy range - 17 eV to - 12 eV are 691
ABSENCE OF A PHASE TRANSITION
692
Table 1. Valence-level one-electron energies (eV) calculated for isolated neutral Zr and Te atoms
eV
Te: 5s’ - 14.5 5p4 - 6.7
- 5.0 -2.9 - 4.7 - 35
Zr: 5s 5P 4d (d’ configuration) (d 3 configuration)
Vol. 42, No. 9
IN ZrTeS
-6 p-bands
essentially Te s-states, while the band ranges - 10 to - 4 eV and - 4 to - 1.5 eVmay be conveniently labelled as Te p-bands and Zr d-bands respectively. The lowest Zr 5s and 5p bands occur several volts higher in energy. In order to simplify the diagram, only the limiting bands of each group are shown. Corresponding densities of states and the component contributions from Zr and the three types of Te site are displayed in Fig. 3. Because of the large (58 x 58) matrices involved, these histograms were calculated from a rather restricted sample of 100 regularly spaced kpoints in the Brillouin zone. Although this small sample obviously cannot represent detailed density-of-states features, it was sufficient to determine the self-consistent d-electron configuration of Zr atoms and to indicate the main contributions to the density of states. The band structure of Fig. 2 predicts quite clearly that ZrTes should be a semi-metal. While along most of the Brillouin zone edges (and within most of the interior) a semiconducting gap - 1 eV separates the highest occupied p-bands from the lowest unoccupied d-bands, a semi-metallic band crossing occurs along the (0, k?, 0) and (1, kz, 0) edges (which are related by symmetry). This band overlap arises from coupling between adjacent ZrTes layers, which each lie in the crystallographic a-c cleavage plane.
-16
[OOOI [ooll
[loll l1001
DO01 10101[011110011
11101[I111
10111 ~0101
1~101mO111011m11
Fig. 2. Calculated electron energy-band limits along the edges of the irreducible Brillouin zone, showing the semi-metallic band crossing along (0, kz, 0) and (1, kzt 0). The incipient semiconducting gap in the electron spectrum is easily understood. Formally, in each ZrTea unit the Zr atom donates two electrons to fill the Ter p-shell and one electron to each Terr atom; because the Terr pair of atoms are closely spaced (2.76 A in HfTes) the corresponding antibonding p-orbital is forced up into
;.ic Zr
-16
-14
-12
-10
-8
-6
-4
-2ev
-10
-8
-6
-4
Fig. 3. Density of states histogram for electrons in ZrTes, with the contributions lated from 100 k-points in the irreducible Brillouin zone.
-2
-10
-8
-6
-4
-2eV
from different atomic sites, calcu-
Vol. 42, No. 9
ABSENCE OF A PHASE TRANSITION
the conduction bands and remains empty. The zig-zag chains of Terrr atoms (with bond angles of 86” in HfTe5) retain the formal p4 configuration of elemental tellurium, with two p-electrons per atom in Te-Te bonding orbitals, two electrons occupying non-bonding orbitals, and two Te-Te antibonding orbitals remaining unoccupied. This formal classification provides a useful guide, even though considerable hybridization takes place between Zr and Te orbitals, as evident in Fig. 3. The actual orbital occupations of atoms were calculated to be Zr: ~~~~p~*‘d**~; Te,: s1*9p4-7; Terr: s1*9p4*4; Terrr: s 1.9 p 4.0 . The electronic structure calculated for ZrTe5 contrasts significantly with that of NbSe, [6,7]. NbSea contains excess electrons beyond the number required to fill states up to the incipient semiconducting gap. The excess electrons enter broad, partially-occupied, quasione-dimensional bands which drive the periodic lattice distortions at 144 and 59 K. There is no corresponding electron excess in ZrTe, : formally the electron number is exactly right to fill the valence bands, but the interlayer coupling is just sufficient to induce the band overlap typical of semi-metal. Thus while the physical properties of the pentatellurides show a pronounced
IN ZrTes
693
anisotropy by virtue of their crystallographic structure, there is no reason to expect charge-density-wave instabilities. It is more likely that the resistivity peaks at 150 K in ZrTes and at 40 K in HfTes originate in the strong temperature dependence of the carrier density and carrier mobility. Supporting experimental evidence is provided by the suppression of the resistivity anomaly by doping with Ta, which increases the carrier density [2]. Measurements of the temperature dependence of the Hall coefficient may provide further support of the present model. REFERENCES 1. 2. 3. 4 ’ s. 6. 7.
S. Okada, T. Sambongi & M. Ido,J. P&s. Sot. Japan 49,839 (1980). F.J. Di Salvo, R.M. Fleming & J.V. Waszczak, Phys. Rev. B24,2935 (1981). S. Furuseth, L. Brattas & A. Kjekshus, Actu Chem. &and. 27,2367 (1973). V.W. Kronert & K. Plieth, 2. Anorg. Allg. Chem. 336,207 (1965). S. Furuseth, L. Brattas & A. Kjekshus, Actu Chem Scand. A29,623 (1975). D.W. Bullett,J. Phys. C12,277 (1979). D.W. Bullett,J. Phys. C (to be published).
Vol. 42, No. 9, pp. 69 l-693,1982.
ABSENCE OF A PHASE TRANSITION
0038-1098/82/210691-03$03.00/0 Pergamon Press Ltd.
IN ZrTes
D.W. Bullett School of Physics, University
of Bath, Bath BA2 7AY, England
(Received 7 January 1982 by R.A. Cowley) Electronic structure calculations suggest that ZrTes is a semi-metal. Thus it appears much more probable that the electrical resistivity peak at 150 K originates in the strong temperature dependence of the carrier density and carrier mobility than that a structural phase transition occurs, as previously proposed.
THE ANOMALOUS TEMPERATURE dependence [ 1,2] of the electrical resistivity of the group IV transition-metal pentachalcogenides ZrTe, and Hffes has led to speculations [ 1 ] that these materials may undergo structural phase transitions, arising from the strong anisotropy in their crystallographic structure [3]. This stimulated the present calculation of the electronic structure of ZrTes. We find no evidence for an inherent one-dimensional charge-density-wave instability in the atomic arrangement. The calculation yields semi-metallic band overlap between valence and conduction levels, with a very low density of states at the Fermi level. It appears more likely that the resistive peak in these materials arises from the temperature dependence of the carrier density and carrier mobility, than that a structural phase transition occurs. The atomic arrangement with ZrTes and HfTes is depicted in Fig. 1. The crystals are orthorhombic, with space group Cmcm. The room-temperature lattice constants determined by Furuseth et al. [3] for ZrTe5 are a = 3.988.&, b = 14.502&c = 13.727-k A full structural determination has been made only for HfTe5, but, since the lattice constants for the hafnium compound are very close to those of ZrTes, it was assumed in the present study that the HfTe, atomic coordinates could be transferred directly to ZrTes. The structure contains one-dimensional chains of end-sharing ZrTee trigonal prisms, reminiscent of the transition-metal trichalcogenides 14-71. Instead of being linked directly (as in ZrTes), in the ZrTes structure the trigonal ZrTe, chains are linked along the c-axis through intermediate “Tez” chains. We have discussed elsewhere the origin of the semiconducting gap in the zirconium trichalcogenides [6] and the driving force responsible for the structural phase transition in the group V material NbSes [6,7]. In this investigation the same computational techniques were applied to derive the electronic structure of ZrTes. The only input to the calculation is a knowledge of the
Fig. 1. The crystal structure of ZrTes projected along [ 10 01. Open circles are at height zero, shaded circles at height f . Zig-zag chains of Te atoms separate trigonal prismatic ZrTes chains in layers perpendicular to the b-axis. crystal structure and the atomic wave-functions and valence-level energies (Table 1) of the isolated constituent atoms. It was assumed that charge-transfer effects were negligible; selfconsistency was required only to the extent that the atomic energy level of the Zr d-orbital in the calculation of the crystal wave-function was made consistent with that of a neutral isolated Zr atom containing the same number of d-electrons. The resulting Zr configuration in ZrTes was d’.‘. Figure 2 shows the calculated energy band structure along some of the edges of the irreducible Brillouin zone. States in the energy range - 17 eV to - 12 eV are 691
ABSENCE OF A PHASE TRANSITION
692
Table 1. Valence-level one-electron energies (eV) calculated for isolated neutral Zr and Te atoms
eV
Te: 5s’ - 14.5 5p4 - 6.7
- 5.0 -2.9 - 4.7 - 35
Zr: 5s 5P 4d (d’ configuration) (d 3 configuration)
Vol. 42, No. 9
IN ZrTeS
-6 p-bands
essentially Te s-states, while the band ranges - 10 to - 4 eV and - 4 to - 1.5 eVmay be conveniently labelled as Te p-bands and Zr d-bands respectively. The lowest Zr 5s and 5p bands occur several volts higher in energy. In order to simplify the diagram, only the limiting bands of each group are shown. Corresponding densities of states and the component contributions from Zr and the three types of Te site are displayed in Fig. 3. Because of the large (58 x 58) matrices involved, these histograms were calculated from a rather restricted sample of 100 regularly spaced kpoints in the Brillouin zone. Although this small sample obviously cannot represent detailed density-of-states features, it was sufficient to determine the self-consistent d-electron configuration of Zr atoms and to indicate the main contributions to the density of states. The band structure of Fig. 2 predicts quite clearly that ZrTes should be a semi-metal. While along most of the Brillouin zone edges (and within most of the interior) a semiconducting gap - 1 eV separates the highest occupied p-bands from the lowest unoccupied d-bands, a semi-metallic band crossing occurs along the (0, k?, 0) and (1, kz, 0) edges (which are related by symmetry). This band overlap arises from coupling between adjacent ZrTes layers, which each lie in the crystallographic a-c cleavage plane.
-16
[OOOI [ooll
[loll l1001
DO01 10101[011110011
11101[I111
10111 ~0101
1~101mO111011m11
Fig. 2. Calculated electron energy-band limits along the edges of the irreducible Brillouin zone, showing the semi-metallic band crossing along (0, kz, 0) and (1, kzt 0). The incipient semiconducting gap in the electron spectrum is easily understood. Formally, in each ZrTea unit the Zr atom donates two electrons to fill the Ter p-shell and one electron to each Terr atom; because the Terr pair of atoms are closely spaced (2.76 A in HfTes) the corresponding antibonding p-orbital is forced up into
;.ic Zr
-16
-14
-12
-10
-8
-6
-4
-2ev
-10
-8
-6
-4
Fig. 3. Density of states histogram for electrons in ZrTes, with the contributions lated from 100 k-points in the irreducible Brillouin zone.
-2
-10
-8
-6
-4
-2eV
from different atomic sites, calcu-
Vol. 42, No. 9
ABSENCE OF A PHASE TRANSITION
the conduction bands and remains empty. The zig-zag chains of Terrr atoms (with bond angles of 86” in HfTe5) retain the formal p4 configuration of elemental tellurium, with two p-electrons per atom in Te-Te bonding orbitals, two electrons occupying non-bonding orbitals, and two Te-Te antibonding orbitals remaining unoccupied. This formal classification provides a useful guide, even though considerable hybridization takes place between Zr and Te orbitals, as evident in Fig. 3. The actual orbital occupations of atoms were calculated to be Zr: ~~~~p~*‘d**~; Te,: s1*9p4-7; Terr: s1*9p4*4; Terrr: s 1.9 p 4.0 . The electronic structure calculated for ZrTe5 contrasts significantly with that of NbSe, [6,7]. NbSea contains excess electrons beyond the number required to fill states up to the incipient semiconducting gap. The excess electrons enter broad, partially-occupied, quasione-dimensional bands which drive the periodic lattice distortions at 144 and 59 K. There is no corresponding electron excess in ZrTe, : formally the electron number is exactly right to fill the valence bands, but the interlayer coupling is just sufficient to induce the band overlap typical of semi-metal. Thus while the physical properties of the pentatellurides show a pronounced
IN ZrTes
693
anisotropy by virtue of their crystallographic structure, there is no reason to expect charge-density-wave instabilities. It is more likely that the resistivity peaks at 150 K in ZrTes and at 40 K in HfTes originate in the strong temperature dependence of the carrier density and carrier mobility. Supporting experimental evidence is provided by the suppression of the resistivity anomaly by doping with Ta, which increases the carrier density [2]. Measurements of the temperature dependence of the Hall coefficient may provide further support of the present model. REFERENCES 1. 2. 3. 4 ’ s. 6. 7.
S. Okada, T. Sambongi & M. Ido,J. P&s. Sot. Japan 49,839 (1980). F.J. Di Salvo, R.M. Fleming & J.V. Waszczak, Phys. Rev. B24,2935 (1981). S. Furuseth, L. Brattas & A. Kjekshus, Actu Chem. &and. 27,2367 (1973). V.W. Kronert & K. Plieth, 2. Anorg. Allg. Chem. 336,207 (1965). S. Furuseth, L. Brattas & A. Kjekshus, Actu Chem Scand. A29,623 (1975). D.W. Bullett,J. Phys. C12,277 (1979). D.W. Bullett,J. Phys. C (to be published).