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Correlation of metastability, icosahedral symmetry and high-critical-temperature superconductivity
Physica C 153-155 (1988) 1205-1206 North-Holland, Amsterdam
CORRELATION OF METASTABILITY,
ICOSAHEDRAL SYMMETRY AND HIGH-CRITICAL-TEMPERATURE
SUPERCONDUCTIVITY
Andras SZASZ Laboratory of Surface Physics, Eotvos University,
Muzeum krt. 6-8. Budapest, H-I088, HUNGARY.
and Derek J FABIAN Scottish Surface and Materials Analysis Centre, Department of Physics and Applied Physics, University of Strathclyde, 48 North Portland Street, Glasgow G1 IXN, SCOTLAND, UK.
We observe a n icosahedral-like co-ordination of 12 in the first co-ordination sphere of the copper atom in the new high-T c superconductor materials. We propose a relation between this icosahedral co-ordination and the superconductivity in these perovskite-like and earlier enhanced-T c materials.
i. INTRODUCTION Many questions on the mechanism of superconductivity in high-T c materials are as yet unanswered. Recent proposals have suggested nonphonon explanations, mostly by two-dimensional and one-dimensional mechanisms. We propose a three-dimensional effect, arising from 'icosahedral seeking' symmetry in these as well as in earlier (AI5) enhanced-T c materials. Our model involves the familiar 3-dimensional Fermisurface Jones-zone interaction invoked in two dimensions, with 'nesting' of Brillouin zone and Fermi surface. We have proposed a relation [I] between icosahedral symmetry and metastability based on electronic structure and we extend this to the possibility of icosahedral-seeking symmetry in high-T c superconductor materials.
gapped' Fermi-surface that Allender and others [4] suggest contributes to the high-T c superconductivity. We propose that dis-torted icosahedral symmetry gives rise to the high Tc, through JZ Fermi-surface interaction. We note a striking correlation (fig. i) of minima in structural total energy, on varying the valence electron concentration (VEC), with maxima in VEC-dependence of Tc, for the A3B group of AI5
Tc
K 10--
Figure i
I
(b) VEC-dependence of T c, for amorphous transition-metal alloys
It
b /
2. THE JONES ZONE EFFECT Generally a Jones-zone (JZ) effect on T c has been well substantiated for metallic materials. An enhancement of T c arises with Fermi-surface JZ interaction [2]. The Jones zone is a complex polyhedron bounded by a number of planes determined by the number of atoms in the elementary cell of the real crystal. For complicated crystalline structures the JZ is bounded by more and more planes and becomes nearer and nearer to spherical. For icosahedral co-ordination [I] the JZ is effectively spherical. Contact with the Fermi surface over a large proportion of an effectively spherical JZ surface, causes a joint van Hove singularity. The energy gap produced at the Fermi surface on interaction with the JZ polyhedron is then small and extends over a large part of the Fermi surface, which is said to be 'partially gapped' [3]. On slight shift of the surface in kspace, within limits set by the JZ inscribed and circumscribed spheres [i], the position and direction in k-space in which the gapping occurs will alter but the average 'partial' gap will main constant and be associated always with the Fermi surface. This produces the 'partially
0 9 2 1 - 4 5 3 4 / 8 8 / $ 0 3 . 5 0 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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II
f~t
i
/
x
10
-evE
W //
'
; p ,, J, ", ,
'}
,~'c
,,
!~ ,,-:!,, x
-
/
'JL,~
(c) VEC-dependence of T c , for A3B group of AI5 transition-metal alloys
Ii
I! x
0
0,01
i
(a) dependence of total structural energy on valence electron concentration (VEC) for transition metals. 5
10
N
1206
A. Szasz and D.J. Fabian / Correlation of metastability, icosahedral symmetry
enhanced-T c , as well as amorphous (metastable), transition-metal alloys [5]. We propose the origin for these almost identical dependences, of both T c and structural stability on VEC, to be the same and to be related to the existence of icosahedral coordination symmetry in both classes of material. Indeed there is no other feature that these two entirely different classes of alloys have in common. The amorphous alloys have short-range icosahedral co-ordination symmetry when seen from the B-ions [7]. Turning to the new 'perovskite' high-T e superconductors, we observe [8] that their elongated octahedral basic cell has chemical bonding, with icosahedral close-packed coordination, of 4 O-atoms and 8 Ba-atoms. It should be noted that in both the lanthanum and yttrium-based (YBaCuO) structures the FrankKasper co-ordination number is 12; i.e. characteristic of close-packing, which therefore indicates icosahedral packing since the geometry is far from either fcc or hcp. Displacements of Cu and O-atoms in these structures have been detected, both theoretically and experimentally, for single crystals of lanthanum based 'layered' perovskites. These displacements can produce structures very close to icosahedral and we propose that 3-dimensional periodic 'breathing' displacements account for the observed features of these highT c materials. We note that the new high-T c superconductors generally have highly distorted extended grainboundary structures. In these the disorder is localised to the grain boundary, where we believe that icosahedral short range cluster coordination occurs even more readily. Observations of twinning in x-ray diffraction studies of the new high-T c perovskite-type superconductors are indicative of intra-granular distortion of the basic 'perovskite' cube giving a structure that indeed is closer to icosahedral.
A gliding CDW without damping, in three dimensions, would be caused by a 'breathing' of microscopic icosahedral cluster regions - in the crystal. Periodically occurring distorted icosahedral 'neighbourhood' regions will allow for the complete filling of real space needed. It is important to note that a Peierls distortion, hitherto accepted only in 2-dimensional models, has recently been observed experimentally in z-bonding in liquid arsenic [12], supporting our contention that 3-dimensional 'breathing' distortions can occur in the solid (since this is an amorphous state). Further support for our suggestion comes from recent measurement [12] of a CDW without damping; and of its effective depinning [13]. Enhancement of N(E) at EF, relative to the generally low N(E) in the vicinity of E F, has also been observed experimentally in studies of highT c materials by UPS and XPS. These results support our proposal of a 'joint' van Hove singularity, although we note that the Peierls instability itself can partially suppress the N(E) enhancement, making its experimental observation all the more significant. Support is found also in far infra-red measurements of the (BCS) superconductor energy gap, showing it to be highly anisotropic and to vary with direction in k-space while its temperature dependence - characterizing the Peierls instability - remains BCS in 'functional form' which is consistent with our 'partially gapped' Fermi-surface model - whereas no full explanation of many such effects has been offered todate.
3- THE CHARGE DENSITY WAVE EFFECT We suggest that a 3-dimensional charge density wave (CDW), in the layers involving the Ba-La cubes and the dense Cu-O chains, is produced for the new high-T c systems. The Mattheiss calculation [9] for pure LaCuO involves a 2-dimensional Peierls distortion (or frozen in CDW), with either a planar or a 2dimensional quadrupolar 'breathing' of the Oatoms. The presence of the divalent metal atom (Ba or Sr) prevents the CDW from being 'frozen in'; it allows O-atom 'breathing' in two dimensions (a 'warping' of the CuO crystal planes) without destroying the superconductivity [i0]. The displacements would bring about a closepacked tetrahedral arrangement, producing (microscopic) icosahedral co-ordination regions with tetrahedral Frank-Kasper packing.
[4]
REFERENCES [i] [2] [3]
[5] [6] [7] [8] [9]
A Szasz and D J Fabian, Solid State Comm., 65 (1988) 1085. E E Havinga and M M van Maaren, Phys Reports I0 (1986) i07. M B Maple et al, Phys. Rev. Lett. 56 (1986) 185. D Allender et al, in Glassy Metals I, eds. H J Guntherodt and H Beck, (SpringerVerlag, Berlin, 1981). Yu A Izumov and E Z Kurmaev, Sov. Phys. Usp. (English Translation), 19 (1976) 26. M Widom, Phys. Rev. B31 (1985) 6456. J S Kasper, in Theory of Alloy Phases (American Soc. Metals), (1957) pp.265. A Szasz and D J Fabian, submitted to Phys. Star. Solidi (1988). L F Mattheiss, Phys. Rev. Lett., 58 (1987)
1028. [10] M S t a v o l a et a l ,
Phys. Rev. L e t t .
58 (1987)
1571. [ii] R Bellisent et al, Phys. Rev. Lett. 59 (1987) 661. [12] G Mihaly and P Beauchene, Sol. State Comm., 63 (1987) 911. [13] J Bardeen, Z. Phys. B. 67 (1987) 427.
CORRELATION OF METASTABILITY,
ICOSAHEDRAL SYMMETRY AND HIGH-CRITICAL-TEMPERATURE
SUPERCONDUCTIVITY
Andras SZASZ Laboratory of Surface Physics, Eotvos University,
Muzeum krt. 6-8. Budapest, H-I088, HUNGARY.
and Derek J FABIAN Scottish Surface and Materials Analysis Centre, Department of Physics and Applied Physics, University of Strathclyde, 48 North Portland Street, Glasgow G1 IXN, SCOTLAND, UK.
We observe a n icosahedral-like co-ordination of 12 in the first co-ordination sphere of the copper atom in the new high-T c superconductor materials. We propose a relation between this icosahedral co-ordination and the superconductivity in these perovskite-like and earlier enhanced-T c materials.
i. INTRODUCTION Many questions on the mechanism of superconductivity in high-T c materials are as yet unanswered. Recent proposals have suggested nonphonon explanations, mostly by two-dimensional and one-dimensional mechanisms. We propose a three-dimensional effect, arising from 'icosahedral seeking' symmetry in these as well as in earlier (AI5) enhanced-T c materials. Our model involves the familiar 3-dimensional Fermisurface Jones-zone interaction invoked in two dimensions, with 'nesting' of Brillouin zone and Fermi surface. We have proposed a relation [I] between icosahedral symmetry and metastability based on electronic structure and we extend this to the possibility of icosahedral-seeking symmetry in high-T c superconductor materials.
gapped' Fermi-surface that Allender and others [4] suggest contributes to the high-T c superconductivity. We propose that dis-torted icosahedral symmetry gives rise to the high Tc, through JZ Fermi-surface interaction. We note a striking correlation (fig. i) of minima in structural total energy, on varying the valence electron concentration (VEC), with maxima in VEC-dependence of Tc, for the A3B group of AI5
Tc
K 10--
Figure i
I
(b) VEC-dependence of T c, for amorphous transition-metal alloys
It
b /
2. THE JONES ZONE EFFECT Generally a Jones-zone (JZ) effect on T c has been well substantiated for metallic materials. An enhancement of T c arises with Fermi-surface JZ interaction [2]. The Jones zone is a complex polyhedron bounded by a number of planes determined by the number of atoms in the elementary cell of the real crystal. For complicated crystalline structures the JZ is bounded by more and more planes and becomes nearer and nearer to spherical. For icosahedral co-ordination [I] the JZ is effectively spherical. Contact with the Fermi surface over a large proportion of an effectively spherical JZ surface, causes a joint van Hove singularity. The energy gap produced at the Fermi surface on interaction with the JZ polyhedron is then small and extends over a large part of the Fermi surface, which is said to be 'partially gapped' [3]. On slight shift of the surface in kspace, within limits set by the JZ inscribed and circumscribed spheres [i], the position and direction in k-space in which the gapping occurs will alter but the average 'partial' gap will main constant and be associated always with the Fermi surface. This produces the 'partially
0 9 2 1 - 4 5 3 4 / 8 8 / $ 0 3 . 5 0 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
/
TC
..K
II
f~t
i
/
x
10
-evE
W //
'
; p ,, J, ", ,
'}
,~'c
,,
!~ ,,-:!,, x
-
/
'JL,~
(c) VEC-dependence of T c , for A3B group of AI5 transition-metal alloys
Ii
I! x
0
0,01
i
(a) dependence of total structural energy on valence electron concentration (VEC) for transition metals. 5
10
N
1206
A. Szasz and D.J. Fabian / Correlation of metastability, icosahedral symmetry
enhanced-T c , as well as amorphous (metastable), transition-metal alloys [5]. We propose the origin for these almost identical dependences, of both T c and structural stability on VEC, to be the same and to be related to the existence of icosahedral coordination symmetry in both classes of material. Indeed there is no other feature that these two entirely different classes of alloys have in common. The amorphous alloys have short-range icosahedral co-ordination symmetry when seen from the B-ions [7]. Turning to the new 'perovskite' high-T e superconductors, we observe [8] that their elongated octahedral basic cell has chemical bonding, with icosahedral close-packed coordination, of 4 O-atoms and 8 Ba-atoms. It should be noted that in both the lanthanum and yttrium-based (YBaCuO) structures the FrankKasper co-ordination number is 12; i.e. characteristic of close-packing, which therefore indicates icosahedral packing since the geometry is far from either fcc or hcp. Displacements of Cu and O-atoms in these structures have been detected, both theoretically and experimentally, for single crystals of lanthanum based 'layered' perovskites. These displacements can produce structures very close to icosahedral and we propose that 3-dimensional periodic 'breathing' displacements account for the observed features of these highT c materials. We note that the new high-T c superconductors generally have highly distorted extended grainboundary structures. In these the disorder is localised to the grain boundary, where we believe that icosahedral short range cluster coordination occurs even more readily. Observations of twinning in x-ray diffraction studies of the new high-T c perovskite-type superconductors are indicative of intra-granular distortion of the basic 'perovskite' cube giving a structure that indeed is closer to icosahedral.
A gliding CDW without damping, in three dimensions, would be caused by a 'breathing' of microscopic icosahedral cluster regions - in the crystal. Periodically occurring distorted icosahedral 'neighbourhood' regions will allow for the complete filling of real space needed. It is important to note that a Peierls distortion, hitherto accepted only in 2-dimensional models, has recently been observed experimentally in z-bonding in liquid arsenic [12], supporting our contention that 3-dimensional 'breathing' distortions can occur in the solid (since this is an amorphous state). Further support for our suggestion comes from recent measurement [12] of a CDW without damping; and of its effective depinning [13]. Enhancement of N(E) at EF, relative to the generally low N(E) in the vicinity of E F, has also been observed experimentally in studies of highT c materials by UPS and XPS. These results support our proposal of a 'joint' van Hove singularity, although we note that the Peierls instability itself can partially suppress the N(E) enhancement, making its experimental observation all the more significant. Support is found also in far infra-red measurements of the (BCS) superconductor energy gap, showing it to be highly anisotropic and to vary with direction in k-space while its temperature dependence - characterizing the Peierls instability - remains BCS in 'functional form' which is consistent with our 'partially gapped' Fermi-surface model - whereas no full explanation of many such effects has been offered todate.
3- THE CHARGE DENSITY WAVE EFFECT We suggest that a 3-dimensional charge density wave (CDW), in the layers involving the Ba-La cubes and the dense Cu-O chains, is produced for the new high-T c systems. The Mattheiss calculation [9] for pure LaCuO involves a 2-dimensional Peierls distortion (or frozen in CDW), with either a planar or a 2dimensional quadrupolar 'breathing' of the Oatoms. The presence of the divalent metal atom (Ba or Sr) prevents the CDW from being 'frozen in'; it allows O-atom 'breathing' in two dimensions (a 'warping' of the CuO crystal planes) without destroying the superconductivity [i0]. The displacements would bring about a closepacked tetrahedral arrangement, producing (microscopic) icosahedral co-ordination regions with tetrahedral Frank-Kasper packing.
[4]
REFERENCES [i] [2] [3]
[5] [6] [7] [8] [9]
A Szasz and D J Fabian, Solid State Comm., 65 (1988) 1085. E E Havinga and M M van Maaren, Phys Reports I0 (1986) i07. M B Maple et al, Phys. Rev. Lett. 56 (1986) 185. D Allender et al, in Glassy Metals I, eds. H J Guntherodt and H Beck, (SpringerVerlag, Berlin, 1981). Yu A Izumov and E Z Kurmaev, Sov. Phys. Usp. (English Translation), 19 (1976) 26. M Widom, Phys. Rev. B31 (1985) 6456. J S Kasper, in Theory of Alloy Phases (American Soc. Metals), (1957) pp.265. A Szasz and D J Fabian, submitted to Phys. Star. Solidi (1988). L F Mattheiss, Phys. Rev. Lett., 58 (1987)
1028. [10] M S t a v o l a et a l ,
Phys. Rev. L e t t .
58 (1987)
1571. [ii] R Bellisent et al, Phys. Rev. Lett. 59 (1987) 661. [12] G Mihaly and P Beauchene, Sol. State Comm., 63 (1987) 911. [13] J Bardeen, Z. Phys. B. 67 (1987) 427.