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Location of excess oxygen atoms in HgBa2CaCu2O6+δ
PHYSlCA ELSEVIER
Physica C 262 (1996) 13-20
Location of excess oxygen atoms in HgBa2CaCu206+ X. Zhang *, S.Y. Xu, C.K. Ong Department of Physics, National University of Singapore, Low Kent Ridge Road, Singapore 0511, Republic of Singapore Received 8 November 1995; revised manuscript received 12 February 1996
Abstract
We have developed a set of interatomic potentials for the simulation of HgBa2CaCu206+ ~ (Hg-1212). These potentials can be used to reproduce the structure of Hg-1212 with a discrepancy in lattice parameter of less than 0.3% and a discrepancy in bond length of less than 1%. Using atomistic simulation techniques, we investigated the possible position of excess oxygen atoms in Hg-1212. We found that for Hg-1212, without partial replacement of Hg by Cu, the most energetically favorable oxygen interstitial position is (½, ~, 0), i.e. the 0(3) site, whereas for Hg-1212 with partial replacement of Hg by Cu, the most likely oxygen interstitial position is (½, 0, z = 0.049), i.e. the 0(4) site. Both our results are in good agreement with the experimental results. We also discussed the possible replacement of Hg by Cu.
I. Introduction
The discovery of the new H g B a 2 C a , - l Cu,O2,+2+8 superconductors with T~ = 94, 128 and 135 K corresponding to n = 1 (Hg-1201), 2 (Hg1212) and 3 (Hg-1223), respectively, has stimulated intense activity aimed at understanding the properties and underlying mechanisms in these materials [1-3]. High-pressure measurements up to 40 GPa show saturation of T~ at 118, 154, and 164 K for Hg-1201, Hg-1212, and Hg-1223, respectively [4]. The observation of superconductivity at 164 K in the Hg-1223 under pressure caused a further increase in interest in these materials, since it raised the hope that suitable
' Corresponding author. Fax: + 65 777 6126.
chemical modifications may increase Tc further. It has been suggested [5,6] that the strong increase in T~ under pressure implies that the CuO 2 planes in Hg1223 are underdoped. To improve our understanding of the increase in Tc under pressure it is crucial to study the doping in the Hg cuprates. The structure of HgBa2Ca ._ iCUnO2n+2+~5has a larger open space surrounded by Hg and Ba in the plane of the Hg ion. The site (½, ½, 0) in the Hg layer (denoted 0(3) in Hg-1201 and Hg-1212, and 0(4) in Hg-1223) is partially filled with interstitial oxygen which accounts for the 8 in the chemical formulas. Measured values of 8 in high-T~ samples are approximately 0.06, 0.22 and 0.4 in Hg-1201, Hg-1212 and Hg-1223 respectively. It is reported that lowered values of t5 yield lower Tc and increasing ~ to 0.35 in Hg-1212 results in lower Tc too [7]. It is clear that understanding of the role of the interstitial oxygen in the Hg layer and related effects
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved PH S 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 1 8 7 - 6
X. Zhang et a l . / Physica C 262 (1996) 13-20
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are crucial for optimizing superconductivity in these compounds. Excess oxygen atoms are the primary doping mechanism for Hg-1201. It is found that as many as 0.06 oxygen atoms per formula unit are present in the 0(3) site [½, ½, 0] for the fully oxygenated compound [2,8,9]. The T~ of Hg-1201 can be reduced to 44 K by processing the samples under reducing conditions. For reduced sample, the 0(3) site is nearly empty [2]. However, the same study suggested that partial doping may be provided by an additional complex defect, which involves partial substitution of Hg by Cu, associated with the presence of oxygen in the 0(4) site [½, 0, z] (z = 0.04). The location of excess oxygen atoms in Hg-1212 is even more complex than that of Hg-1201. It is suggested [3] that in addition to the 0(3) oxygen site, an additional defect may be necessary to explain the sample-to-sample variability. It is reported [10] that the occupancy of the primary doping site 0(3) varies from 0.08 for the argon-reduced sample to 0.22 for the oxygenated sample, but the additional defect site 0(4) [½, 0, z] was found to be almost empty (The 0(3) and 0(4) sites are shown in Fig. 1). A recent work [11] reported that in Hg1212 samples with
•
MJ
~
!
*
Cu
o
Ba
$
Ca
Q
Hg
~
I
-_ - O . ~ O 2
'-)
~:b:~
2. C o m p u t a t i o n a l m e t h o d
Our simulation is based on the shell model generalization of the Born model of the solid, which treats the solid as a collection of point ions with short-range repulsive forces acting between them. This approach has achieved a wide range of success. We have used this simulation technique in studies of La2CuO4 [14-16], Bal_xKxBiO 3 [17], YBaCu307_ x [18-21], and YBa2Cu408 [22-26]. A detailed discussion of these simulation techniques can be found in Refs. [27] and [28]. We shall only give a brief description of the interatomic potentials and defect energy calculation. The short-range potentials used in this classic simulation are described by the Born-Mayer potential supplemented by an attractive r - 6 term: V ( r ) = A exp( -
©o
Fig. 1. T h e s t r u c t u r e o f H g B a 2 C a C u 2 0 6 +
substitution of Cu for Hg of more than 10%, excess oxygen is observed on two sites near the z = 0 plane: at the 0(4) site and at a site close to (½, 0.4, 0), but no oxygen is found at the 0(3) site as reported in their earlier studies of Hg-1212 samples without mixing the Hg and Cu [12]. Another work [13] reported that without partial substitution of Hg by Cu, excess oxygen is found at the 0(3) site, but even when 11% of the Cu is found at the Hg site, still no oxygen is found on 0(4) site. It appears that the location of excess oxygen atoms varies from sample to sample, and depends on the impurity existing in the sample. In this work, we developed a set of interatomic potential which reproduce the crystal structure of Hg-1212 successfully. Using atomistic simulation techniques we studied the locations of excess oxygen atoms in Hg-1212 with and without partial substitution of Hg by Cu.
~ ( 6 = 0).
r/p)
-
Cr -6 ,
(1)
where A, p and C are constants. The polarizability of the individual ions and its dependence on local atomic environment is treated by the shell model [29], in which the outer valence cloud of the ion is simulated by a massless shell of charge Y and the nucleus and inner electrons by a core of charge X. The total charge of the ion is thus X + Y which indicates the oxidation state of the ion. The interac-
X. Zhang et al. / Physica C 262 (1996) 13-20
tion between core and shell of any ion is treated to be harmonic with a spring constant k and represented by V(ri)
= ~' k i d 2i ,
(2)
where d i is the relative displacement of core and shell of ion i. The electronic polarizability of the free ion i is thus given by a, = r,2/k/.
(3)
The defect energy is defined as the energy to create a defect within the perfect lattice (for a full discussion of the terms involved, see Ref. [30]). In this work, we treated the defective lattice by using a two-region strategy [31]. In this approach the crystal is formally divided into an inner region (region I) and a outer region (region II). In the inner region the lattice configuration is evaluated explicitly while the outer region can be viewed from the defect as a continuum. The displacements within the outer region are due solely to the electric field produced by the total charge of the defect centered at the defect origin. The Mott-Littleton method [27] is employed in the outer region and the polarisation P can be represented by P = 4"rr 1 -
R3 ,
(4)
where G0 is the static dielectric constant of the solid and the R is the distance from the defect origin. In order to account consistently for the different treatment of the two regions, an interfacial region (region IIa) is introduced between region I and region II. This approach furnishes a considerable relaxation of the crystal structure around the defect, and the total energy of the system can therefore be written as
E= E~( x) +Ella(X, t) +Ell(t),
(5)
in which E l ( x ) is the energy of the region I, Ella(X, t ) is the interaction energy between region I and II, and E~j(t) is the energy of the region II. Here the argument x is a vector of independent coordinates describing the region I, and t is the magnitude of a corresponding vector of the displacements in the region II. In thisostudy, we used a radius of the inner region of 10.5 A which includes 564 atoms and a radius of the interfacial region of 22 A which in-
15
cludes 5416 atoms. All the atoms in the two regions are fully relaxed in our calculation. For fitting the potential of the HgBa2CaCu206 + ~, the charge of 2 + is assigned to Hg, Ba, Ca and Cu and a charge of 2 - is assigned to O. Ba, Ca, Cu and O are treated using the shell model but Hg is treated using the rigid model (without shell). The potential parameters for HgBa2CaCu2Ot+ 8 are obtained by using an empirical fitting method, known as the "relaxed" fitting approach [32], developed by Bush et al. [33]. In a conventional fitting approach, elastic constants and relative permittivities are only strictly valid at the minimum-energy configuration when the gradient is zero. Hence, calculating properties at the experimental structure when it is not in the equilibrium geometry may be misleading. In this "relaxed" fitting approach, the structure is relaxed to zero strain for every evaluation of the sum of squares and
Table 1 Potential parameters for HgBa2CaCu200 + a ( 6 = 0) (a) Short-range interaction
A (eV)
p (A)
C (eV/~6)
0 ( 1 ) 2- - O ( 1 ) 20 ( 2 ) 2- - 0 ( 2 ) 2 0 ( 2 ) 2- - H g 2÷ Hg 2÷ - H g 2+ Hg 2 + _Ba2 + 0 ( 1 ) 2 - _Cu 2 + 0 ( 2 ) 2- - C u 2+ Cu 2+ - C u 2+ 0 ( 1 ) 2- - B a 2+ 0 ( 2 ) 2- - B a 2+ 0 ( 1 ) 2- - C a 2+ Cu 2+ - B a 2+ Ba 2÷ - B a 2+ 0 ( X ) 2- - H g 2 ÷ 0 ( X ) 2- - C u 2 + 0 ( X ) 2- - B a 2÷ 0 ( X ) 2- - 0 ( 2 ) 2 -
22764.00 22764.00 213.104 11903.30 436.892 2068.04 2486.00 6894.869 1785.272 93869.00 1702.075 168128.60 2663.00 213.104 2486.00 93869.00 22764.00
0.14900 0.14900 0.557036 0.393256 0.154376 0.26876 0.25753 0.152719 0.350281 0.22135 0.315016 0.22973 0.25580 0.557036 0.25753 0.22135 0.14900
43.00 43.00 0.575426 3384.732 3.630410 0 0 1.34953 0 0 0 0 0 0.575426 0 0 43.00
(b) Shell model parameters Species
Y (e)
K (eV ~ - 2 )
Cu 2+ Ba 2+ Ca 2+ O ( I ) 20 ( 2 ) 20 ( X ) 2-
2.0000 9.1173 1.2600 - 3.2576 - 3.2576 - 3.2576
99999.0 426.1 34.0 49.8 49.8 49.8
a 0 ( X ) is the label for 0 ( 3 ) and 0(4).
16
X. Zhang et al./Physica C 262 (1996) 13-20
Table 2 Comparison of calculated and experimental structural data for HgBa 2CaCu206 + ExperiCalculated Differmental a (8 = 0) ence
(%)
Lattice parameters (~,) a 3.8594 c 12.6946 Interatomic distances (.~) Hg-O2 1.995(5) Cu-Ol 1.9279(7) Cu-O2 2.799(6) Ba-O1 2.753(5) Ba-O2 2.849(2) Ca-O1 2.483(3) Bond angles (°) O2-Cu-O1 O1-Cu-Ol Cu-Ol-Cu Hg-O2-Cu
89.5(2) 89.996(3) 179.0(3) 180.00
3.8528 12.7216
0.17 0.21
2.0062 1.9264 2.8159 2.7324 2.8642 2.4615
0.56 0.08 0.60 0.75 0.53 0.87
90.18 90.00 179.64 180.00
0.74 0.004 0.34 0
a From Ref. [12].
the difference between observed and calculated structural parameters is used in place of the derivatives. In each step in the fitting process, the minimization was started from the experimental structure rather than from the last optimized structure, to avoid the possibility that the fit becomes trapped in an undesirable local minimum in either potential or geometry space. It should be stressed that the reliability of the simulations depends on the validity of the potential model used in the calculation and the latter is assessed primarily by its ability to reproduce experimental crystal properties. We note that our potential is an ionic empirical potential without screening. Therefore, we do not expect this potential to give very good structural changes on doping in HgBa2CaCu206+ 8, as changes due to doping on the metallic Hg planes are due to more features than ionic sizes and charges. However, it is possible for this potential to give reasonable structures for the HgBa2CaCu206+ 8, and this potential can give quick indications of the interstitial oxygen sites, although the displacements calculated using this potential has to be used with caution.
3. Results and discussion Our potential parameters for HgBa2CaCu206+ 8 are given in Table 1. The comparison of calculated and experimental data are shown in Table 2. The difference in lattice parameter between calculated and experimental data is less than 0.3%, and the difference in bond length is less than 1%. For the structure of HgBaECaCu206+ 8 without partial replacement of Hg by Cu, our calculation (see Table 3) shows that the defect energy of the oxygen interstitial at the 0(3) site (configuration (1)) is - 17.296 eV whereas the defect energy of the oxygen interstitial at the 0(4) site (configuration (2)) is - 1 5 . 9 6 1 eV, indicating that oxygen interstitial is energetically more favorably located at the 0(3) site
Table 3 Calculated defect energy for various defect configurations in HgBa2CaCu206+ 8 Configurations Defect energy (eV)
OHg •
Cu
©0
(1)~
-17.30
(2)~
-15.96
(3)~
-46.96
(4)0~(4) '
-47.54
(5)~
-43.54
(6)~
-40.74
X. Zhang et al. / Physica C 262 (1996) 13-20
than at the 0(4) site. These results agrees well with the experimental results [10,13]. Fig. 2 shows the structural changes caused by a interstitial oxygen at the 0(3) site. It is found that the interstitial oxygen is exactly at the 0(3) site, i.e. (½, 5,~ 0) position. We found that Hg atoms and Ba atoms move closer to the 0(3) site by 0.12 A and 0.17 A, respectively. But 02 atoms move away from 03 by 0.22 A. Cu atoms are found to be moving closer to the 02 site by 0.11 ~, and O1 atoms do not move significantly. The corresponding structural changes in bond lengths and bond angles are given in Table 4. The larger changes are observed for the Hg-O2 and Cu-O2 bond lengths, and the O 2 - C u O1 and Cu-O1-Cu bond angles. We found that incorporation of interstitial oxygen at the 0(3) site causes a decrease in the lattice parameter, which is in agreement with experiment [12]. We also found that incorporation of interstitial oxygen at the 0(3) site does not change the C u - O 1 - C u bond angle significantly. This result agrees as well with the experiments [10,13]. Experiments [2,11] show that interstitial oxygen can exist at the 0(4) sites with partial replacement of Hg by Cu. For simplicity we consider only the partial replacement of Hg by one Cu atom or two Cu o
17
atoms. Let us consider three types of partial replacement of Hg by Cu: (1) Partial replacement of Hg by two Cu atoms where both Cu atoms are on one side of the Hg square. The defect reaction can be represented by 2CuO + 2Hg~g ~ (Cu( 1)ng-Cu(2)Ug)* + 2HgO. (2) Partial replacement of Hg by two Cu atoms where the Cu atoms are at diagonal positions of the Hg square. Its reaction can be represented by 2CuO + 2HgH8 ~ (Cu(1)Hg-Cu(3)Hg) + 2HgO. (3) Partial replacement of Hg by two Cu atoms where the Cu atoms are separated by a large distance. (This is equivalent to a partial replacement of Hg by one of the Cu atoms.) Its reaction can be represented by 2CuO + 2Hg ~ ~ 2Cu + 2HgO. Our calculation shows that reactions (1), (2) and (3) need an energy of 3.08, 3.34 and 3.40 eV, respectively. This indicates that reaction (1) is the most
Table 4 Comparison of calculated structural changes in HgBa2CaCu206+ ~ with and without 0(3) Experimental a
Calculated without (3)
Interatomic distances (,~) Hg-O2 Hg-O3 Cu-O1 Cu-O2 Ba-O1 Ba-O2 Ba-O3 Ca-O1 Bond angles (°) O2-Cu-O1 O1-Cu-Ol Cu-OI-Cu Hg-O2-Cu Hg-O3-Hg O2-Hg-O3 a From Ref. [ 12].
1.995(5) 2.72904(8) 1.9279(7) 2.799(6) 2.753(5) 2.849(2) 2.814(6) 2.483(3) 89.5(2) 89.996(3) 179.0(3) 180.00
2.0062 1.9264 2.8159 2.7324 2.8642 2.4615 90.18 90.00 179.64 180.00 -
Change (%) with 0(3) 2.1808 2.6002 1.9236 2.5430 2.8520 2.9374 2.7197 2.4258 95.70 91.47 173.66 168.74 90.00 97.48
8.70 4.72 0.15 9.69 4.38 2.56 3.35 1.45 6.12 1.63 3.33 6.26 -
18
X. Zhang et aL / Physica C 262 (1996) 13-20
12)
(6) H
~4)
Fig. 2. The structuralchanges in the unit cell of HgBa2CaCu206 + when the excess oxygen atom is at the 0(3) site (½, ½, 0).
energetically favorable, i.e. the linear Cu clustering is most likely as experiment suggested [2]. Thus, we concentrated our studies on the partial replacement of Hg by two Cu atoms where Cu atoms are on one side of Hg square (configuration ( 3 ) - ( 6 ) as shown in Table 3). Table 3 shows that configuration (4) is the most energetically favorable, i.e. interstitial oxygen favors the 0 ( 4 ) site when two Hg atoms are replaced by Cu atoms. Fig. 3 shows the structural changes in two unit cells o f Hg-1212 due to the oxygen interstitial at the 0 ( 4 ) site when two Hg atoms are replaced by Cu atoms. It is seen that the unit cells have a big structural change. Atoms of 0 4 move upwards to the position (½, 0, z) where z = 0.049. This result is in good agreement with the experimental results of (½, 0, z) where z -- 0.04 [2,11]. This agreement provides encouraging support for the accuracy o f our potential and the general validity of our modelling approach. This result also indicates that the experimental results o f the 0 4 site at (½, 0, 0.04) may occur in the case when two Hg atoms are replaced
Fig. 3. The structural changes in two unit cells of HgBa2CaCu206+ 8 with two Hg atoms replaced by Cu when the excess oxygen alom is at the 0(4) site (½,0, z).
lg
Fig. 4. The structural changes in the unit cell of HgBa2CaCu206+ with two Hg atoms replaced by Cu when the excess oxygen atom I is initially put at the 0(3) site (½, 7, 0). After relaxaaon the excess oxygen atom moves to the position (0.5, 0.35, 0).
x. Zhang et al./ Physica C 262 (1996) 13-20
by two Cu atoms as shown in Fig. 3. The displacement of 0 4 off the Hg plane ( z = 0) causes a large structural change. O1(1) is found to be displaced downwards by 0.49 ,~. The 02(5) and 02(6) are found to move out with displacements of 1.4 A, while Cu(a) and Cu(b) move in with displacements of 0.40 ,~. Interstitial oxygen at the 0 4 site also results in some changes in the Cu-O2 bond length, i.e., a shortening of Cul-O2(1) and Cu2-O2(2), and elongation of Cu3-O2(3) and Cu4-O2(4). We also noted that the top CuO 2 plane is distorted while the bottom CuO 2 plane is almost unchanged. It appears that the interstitial 0(4) could change the nearly perfectly flat CuO 2 plane in Hg-1212. Fig. 4 shows the structural changes caused by interstitial oxygen at the 0(3) site when two Hg atoms are replaced by Cu (configuration (3)). Our calculation indicates that in this case the interstitial oxygen does not stay at the 0(3) site but moves to the position (0.5, 0.35, 0). This result is similar to the experimental result that in Hg-1212 with more than 10% Cu substitution for Hg, one of the interstitial oxygen sites is (0.5, 0.4, 0) [11]. We noted that in this configuration, the atoms in the CuO 2 plane do not displace much from their original positions. o
tg
19
However, some of the 0 2 atoms displace significantly. As configuration (3) just causes 0.5 eV more energy than configuration (4), these two configuration may co-exist in Hg-1212 with partial displacement of Hg by Cu, as reported [l 1]. We also investigated the position of the interstitial oxygen when one Hg is replaced by Cu. In this case, the 0(3) site is more energetically favorable than the 0(4) site. Fig. 5 shows the structural changes caused by interstitial oxygen at the 0(3) site when one Hg atom is replaced by Cu. It is found that the interstitial oxygen does not stay at the 0(3) site but moves to the position (0.41, 0.42, 0). We noted that this position is not reported after experiment. This discrepancy implies that the replacement of one Hg by Cu in Hg-1212 is unlikely. In contrast, the agreement of our oxygen interstitial positions of (½, 0, z) where z = 0.049 and (½, 0.35, 0) with the experimental results [l l] shows that our assumption that two Hg atoms are replaced by Cu seems reasonable. 4. Conclusions
Our newly developed interatomic potential can reproduce the Hg-1212 structure with a discrepancy in lattice parameter of less than 0.3% and a discrepancy in bond length of less than 1%. Our simulation results show that the 0(3) site is the most favorable oxygen interstitial position for Hg-1212 without partial replacement of Hg by Cu. Incorporation of interstitial oxygen at the 0(3) site results in a little structural change and does not change the nearly perfectly flat CuO 2 plane significantly. For Hg-1212 with partial replacement of Hg by Cu, the most likely oxygen interstitial position is the 0(4) site. This interstitial 0(4) can cause bigger structural changes compared to the 0(3) interstitial. Our prediction of the positions of excess oxygen atoms in Hg-1212 is in good agreement with the experimental results. We also found that the partial replacement of Hg by two Cu atoms on one side of Hg square is favorable and can account for the position (½, 0, z) of the interstitial oxygen.
@
Fig. 5. The structuralchangesin the unit cell of HgBa2CaCu206+ with one Hg atoms replacedby Cu when the excessoxygenatom is initiallyput at the 0(3) site (½, ~,~0). Afterrelaxationthe excess oxygen atom moves to the position(0.41,0.42,0).
Acknowledgements
We would like to thank Julian Gale for providing the computing code GULP for potential fitting and to
20
X. Zhang et al./Physica C 262 (1996) 13-20
thank K.W. Yip for help in the earlier stage of potential fitting. References [1] S.N. Putilin, E.V. Antipov, O. Chmaissem and M. Marezio, Nature (London) 362 (1993) 226. [2] J.L. Wagner, P.G. Radaelli, D.G. Hinks, H.D. Gorgensen, H.F. Mitchell, B. Dabrowski, G.S. Knapp and M.A. Bero, Physica C 210 (1993) 447. [3] S.N. Putilin, E.V. Antipov and M. Marezio, Physica C 212 (1993) 266. [4] L. Cao, Y.Y. Xue, F. Chen, Q. Xiong, ER.L. Meng, D. Ramirez, C.W. Chu, J.H. Eggert and H.K. Mao, to be published. [5] C.W. Chu et al., Nature 365 (1993) 323. [6] M. Nunez-Regueiro et al., Science 262 (1993) 97. [7] S.M. Loureiro et ai., Physica C 217 (1993) 253. [8] J. Schwartz, S. Nakamae, G.W. Raban Jr., J.K. Heuer, S. Wu, H.L. Wagner, D.G. Knapp and M.A. Beno, Physica C 210 (1993) 447. [9] O. Chmaissem, Q. Huang, S.N. Putilin, M. Marezio and A. Santoro, Physica C 212 (1993) 259. [10] P.G. Radaelli, J.L. Wagner, B.A. Hunter, M.A. Beno, G.S. Knapp, J.D. Jorgensen and D.G. Hinks, Physica C 216 (1993) 29. [l 1] L.W. Finger, R.M. Hazen, R.T. Downs, R.L. Meng and C.W. Chu, Physica C 226 (1994) 216. [12] Q. Huang, J.W. Lynn, R.L. Meng and C.W. Chu, Physica C 218 (1993) 356. [13] E.V. Abtuoiv et al, Physica C 218 (1993) 348.
[14] X. Zhang, C.R.A. Catlow and W. Zhou, Physica C 168 (1990) 417. [15] X. Zhang and C.R.A. Catlow, J. Mater. Chem. 1 (1991) 233. [16] X. Zhang and C.R.A. Catlow, J. Phys. Chem. Solids 53 (1992) 45. [17] X. Zhang and C.R.A. Catlow, Physica C 173 (1991) 25. [18] X. Zhang and C.R.A. Catlow, Phys. Rev. B 46 (1992) 457. [19] X. Zhang, K.W. Yip and C.K. Ong, Physica C 234 (1994) 99. [20] X. Zhang and C.R.A. Catlow, Molecular Simulation 12 (1994) 115. [21] X. Zhang, K.W. Yip and C.K. Ong, J. Phys. Chem. Solids 56 (1995) 1603. [22] X. Zhang and C.R.A. Catlow, Physica C 193 (1992) 221. [23] X. Zhang and C.R.A. Caflow, Phys, Rev. B 47 (1993) 5315. [24] X. Zhang, Physica C 222 (1994) 227. [25] X. Zhang, K.W. Yip and C.K. Ong, Phys. Rev. B 51 (1995) 1277. [26] X. Zhang, K.W. Yip and C.K. Ong, Physica C 241 (1995) 241. [27] C.R.A. Catlow and W.C. Mac'krodt, ed. Lecture Notes in Physics 166: Computer simulation of solids (Springer, Berlin, 1982). [28] J. Chem. Soc. Farad II (1989) 5. [29] B.G. Dick and A.W. Overhauser, Phys. Rev. 112 (1958) 90. [30] P.E. Cade, A.M. Stoneham and P.W. Tasker, Phys. Rev. B 30 (1984) 4621. [31] M.J. Norgett and A.B. Lidiard, Computational Solid State Physics, ed. F. Herman (Plenum, New York, 1972), p. 385. [32] A.L. Rohl and J.D. Gale, to be published. [33] T.S. Bush, J.D. Gale, C.R.A. Catlow and P.D. Battle, J. Mater. Chem. 4 (1994) 831.
Physica C 262 (1996) 13-20
Location of excess oxygen atoms in HgBa2CaCu206+ X. Zhang *, S.Y. Xu, C.K. Ong Department of Physics, National University of Singapore, Low Kent Ridge Road, Singapore 0511, Republic of Singapore Received 8 November 1995; revised manuscript received 12 February 1996
Abstract
We have developed a set of interatomic potentials for the simulation of HgBa2CaCu206+ ~ (Hg-1212). These potentials can be used to reproduce the structure of Hg-1212 with a discrepancy in lattice parameter of less than 0.3% and a discrepancy in bond length of less than 1%. Using atomistic simulation techniques, we investigated the possible position of excess oxygen atoms in Hg-1212. We found that for Hg-1212, without partial replacement of Hg by Cu, the most energetically favorable oxygen interstitial position is (½, ~, 0), i.e. the 0(3) site, whereas for Hg-1212 with partial replacement of Hg by Cu, the most likely oxygen interstitial position is (½, 0, z = 0.049), i.e. the 0(4) site. Both our results are in good agreement with the experimental results. We also discussed the possible replacement of Hg by Cu.
I. Introduction
The discovery of the new H g B a 2 C a , - l Cu,O2,+2+8 superconductors with T~ = 94, 128 and 135 K corresponding to n = 1 (Hg-1201), 2 (Hg1212) and 3 (Hg-1223), respectively, has stimulated intense activity aimed at understanding the properties and underlying mechanisms in these materials [1-3]. High-pressure measurements up to 40 GPa show saturation of T~ at 118, 154, and 164 K for Hg-1201, Hg-1212, and Hg-1223, respectively [4]. The observation of superconductivity at 164 K in the Hg-1223 under pressure caused a further increase in interest in these materials, since it raised the hope that suitable
' Corresponding author. Fax: + 65 777 6126.
chemical modifications may increase Tc further. It has been suggested [5,6] that the strong increase in T~ under pressure implies that the CuO 2 planes in Hg1223 are underdoped. To improve our understanding of the increase in Tc under pressure it is crucial to study the doping in the Hg cuprates. The structure of HgBa2Ca ._ iCUnO2n+2+~5has a larger open space surrounded by Hg and Ba in the plane of the Hg ion. The site (½, ½, 0) in the Hg layer (denoted 0(3) in Hg-1201 and Hg-1212, and 0(4) in Hg-1223) is partially filled with interstitial oxygen which accounts for the 8 in the chemical formulas. Measured values of 8 in high-T~ samples are approximately 0.06, 0.22 and 0.4 in Hg-1201, Hg-1212 and Hg-1223 respectively. It is reported that lowered values of t5 yield lower Tc and increasing ~ to 0.35 in Hg-1212 results in lower Tc too [7]. It is clear that understanding of the role of the interstitial oxygen in the Hg layer and related effects
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved PH S 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 1 8 7 - 6
X. Zhang et a l . / Physica C 262 (1996) 13-20
14
are crucial for optimizing superconductivity in these compounds. Excess oxygen atoms are the primary doping mechanism for Hg-1201. It is found that as many as 0.06 oxygen atoms per formula unit are present in the 0(3) site [½, ½, 0] for the fully oxygenated compound [2,8,9]. The T~ of Hg-1201 can be reduced to 44 K by processing the samples under reducing conditions. For reduced sample, the 0(3) site is nearly empty [2]. However, the same study suggested that partial doping may be provided by an additional complex defect, which involves partial substitution of Hg by Cu, associated with the presence of oxygen in the 0(4) site [½, 0, z] (z = 0.04). The location of excess oxygen atoms in Hg-1212 is even more complex than that of Hg-1201. It is suggested [3] that in addition to the 0(3) oxygen site, an additional defect may be necessary to explain the sample-to-sample variability. It is reported [10] that the occupancy of the primary doping site 0(3) varies from 0.08 for the argon-reduced sample to 0.22 for the oxygenated sample, but the additional defect site 0(4) [½, 0, z] was found to be almost empty (The 0(3) and 0(4) sites are shown in Fig. 1). A recent work [11] reported that in Hg1212 samples with
•
MJ
~
!
*
Cu
o
Ba
$
Ca
Q
Hg
~
I
-_ - O . ~ O 2
'-)
~:b:~
2. C o m p u t a t i o n a l m e t h o d
Our simulation is based on the shell model generalization of the Born model of the solid, which treats the solid as a collection of point ions with short-range repulsive forces acting between them. This approach has achieved a wide range of success. We have used this simulation technique in studies of La2CuO4 [14-16], Bal_xKxBiO 3 [17], YBaCu307_ x [18-21], and YBa2Cu408 [22-26]. A detailed discussion of these simulation techniques can be found in Refs. [27] and [28]. We shall only give a brief description of the interatomic potentials and defect energy calculation. The short-range potentials used in this classic simulation are described by the Born-Mayer potential supplemented by an attractive r - 6 term: V ( r ) = A exp( -
©o
Fig. 1. T h e s t r u c t u r e o f H g B a 2 C a C u 2 0 6 +
substitution of Cu for Hg of more than 10%, excess oxygen is observed on two sites near the z = 0 plane: at the 0(4) site and at a site close to (½, 0.4, 0), but no oxygen is found at the 0(3) site as reported in their earlier studies of Hg-1212 samples without mixing the Hg and Cu [12]. Another work [13] reported that without partial substitution of Hg by Cu, excess oxygen is found at the 0(3) site, but even when 11% of the Cu is found at the Hg site, still no oxygen is found on 0(4) site. It appears that the location of excess oxygen atoms varies from sample to sample, and depends on the impurity existing in the sample. In this work, we developed a set of interatomic potential which reproduce the crystal structure of Hg-1212 successfully. Using atomistic simulation techniques we studied the locations of excess oxygen atoms in Hg-1212 with and without partial substitution of Hg by Cu.
~ ( 6 = 0).
r/p)
-
Cr -6 ,
(1)
where A, p and C are constants. The polarizability of the individual ions and its dependence on local atomic environment is treated by the shell model [29], in which the outer valence cloud of the ion is simulated by a massless shell of charge Y and the nucleus and inner electrons by a core of charge X. The total charge of the ion is thus X + Y which indicates the oxidation state of the ion. The interac-
X. Zhang et al. / Physica C 262 (1996) 13-20
tion between core and shell of any ion is treated to be harmonic with a spring constant k and represented by V(ri)
= ~' k i d 2i ,
(2)
where d i is the relative displacement of core and shell of ion i. The electronic polarizability of the free ion i is thus given by a, = r,2/k/.
(3)
The defect energy is defined as the energy to create a defect within the perfect lattice (for a full discussion of the terms involved, see Ref. [30]). In this work, we treated the defective lattice by using a two-region strategy [31]. In this approach the crystal is formally divided into an inner region (region I) and a outer region (region II). In the inner region the lattice configuration is evaluated explicitly while the outer region can be viewed from the defect as a continuum. The displacements within the outer region are due solely to the electric field produced by the total charge of the defect centered at the defect origin. The Mott-Littleton method [27] is employed in the outer region and the polarisation P can be represented by P = 4"rr 1 -
R3 ,
(4)
where G0 is the static dielectric constant of the solid and the R is the distance from the defect origin. In order to account consistently for the different treatment of the two regions, an interfacial region (region IIa) is introduced between region I and region II. This approach furnishes a considerable relaxation of the crystal structure around the defect, and the total energy of the system can therefore be written as
E= E~( x) +Ella(X, t) +Ell(t),
(5)
in which E l ( x ) is the energy of the region I, Ella(X, t ) is the interaction energy between region I and II, and E~j(t) is the energy of the region II. Here the argument x is a vector of independent coordinates describing the region I, and t is the magnitude of a corresponding vector of the displacements in the region II. In thisostudy, we used a radius of the inner region of 10.5 A which includes 564 atoms and a radius of the interfacial region of 22 A which in-
15
cludes 5416 atoms. All the atoms in the two regions are fully relaxed in our calculation. For fitting the potential of the HgBa2CaCu206 + ~, the charge of 2 + is assigned to Hg, Ba, Ca and Cu and a charge of 2 - is assigned to O. Ba, Ca, Cu and O are treated using the shell model but Hg is treated using the rigid model (without shell). The potential parameters for HgBa2CaCu2Ot+ 8 are obtained by using an empirical fitting method, known as the "relaxed" fitting approach [32], developed by Bush et al. [33]. In a conventional fitting approach, elastic constants and relative permittivities are only strictly valid at the minimum-energy configuration when the gradient is zero. Hence, calculating properties at the experimental structure when it is not in the equilibrium geometry may be misleading. In this "relaxed" fitting approach, the structure is relaxed to zero strain for every evaluation of the sum of squares and
Table 1 Potential parameters for HgBa2CaCu200 + a ( 6 = 0) (a) Short-range interaction
A (eV)
p (A)
C (eV/~6)
0 ( 1 ) 2- - O ( 1 ) 20 ( 2 ) 2- - 0 ( 2 ) 2 0 ( 2 ) 2- - H g 2÷ Hg 2÷ - H g 2+ Hg 2 + _Ba2 + 0 ( 1 ) 2 - _Cu 2 + 0 ( 2 ) 2- - C u 2+ Cu 2+ - C u 2+ 0 ( 1 ) 2- - B a 2+ 0 ( 2 ) 2- - B a 2+ 0 ( 1 ) 2- - C a 2+ Cu 2+ - B a 2+ Ba 2÷ - B a 2+ 0 ( X ) 2- - H g 2 ÷ 0 ( X ) 2- - C u 2 + 0 ( X ) 2- - B a 2÷ 0 ( X ) 2- - 0 ( 2 ) 2 -
22764.00 22764.00 213.104 11903.30 436.892 2068.04 2486.00 6894.869 1785.272 93869.00 1702.075 168128.60 2663.00 213.104 2486.00 93869.00 22764.00
0.14900 0.14900 0.557036 0.393256 0.154376 0.26876 0.25753 0.152719 0.350281 0.22135 0.315016 0.22973 0.25580 0.557036 0.25753 0.22135 0.14900
43.00 43.00 0.575426 3384.732 3.630410 0 0 1.34953 0 0 0 0 0 0.575426 0 0 43.00
(b) Shell model parameters Species
Y (e)
K (eV ~ - 2 )
Cu 2+ Ba 2+ Ca 2+ O ( I ) 20 ( 2 ) 20 ( X ) 2-
2.0000 9.1173 1.2600 - 3.2576 - 3.2576 - 3.2576
99999.0 426.1 34.0 49.8 49.8 49.8
a 0 ( X ) is the label for 0 ( 3 ) and 0(4).
16
X. Zhang et al./Physica C 262 (1996) 13-20
Table 2 Comparison of calculated and experimental structural data for HgBa 2CaCu206 + ExperiCalculated Differmental a (8 = 0) ence
(%)
Lattice parameters (~,) a 3.8594 c 12.6946 Interatomic distances (.~) Hg-O2 1.995(5) Cu-Ol 1.9279(7) Cu-O2 2.799(6) Ba-O1 2.753(5) Ba-O2 2.849(2) Ca-O1 2.483(3) Bond angles (°) O2-Cu-O1 O1-Cu-Ol Cu-Ol-Cu Hg-O2-Cu
89.5(2) 89.996(3) 179.0(3) 180.00
3.8528 12.7216
0.17 0.21
2.0062 1.9264 2.8159 2.7324 2.8642 2.4615
0.56 0.08 0.60 0.75 0.53 0.87
90.18 90.00 179.64 180.00
0.74 0.004 0.34 0
a From Ref. [12].
the difference between observed and calculated structural parameters is used in place of the derivatives. In each step in the fitting process, the minimization was started from the experimental structure rather than from the last optimized structure, to avoid the possibility that the fit becomes trapped in an undesirable local minimum in either potential or geometry space. It should be stressed that the reliability of the simulations depends on the validity of the potential model used in the calculation and the latter is assessed primarily by its ability to reproduce experimental crystal properties. We note that our potential is an ionic empirical potential without screening. Therefore, we do not expect this potential to give very good structural changes on doping in HgBa2CaCu206+ 8, as changes due to doping on the metallic Hg planes are due to more features than ionic sizes and charges. However, it is possible for this potential to give reasonable structures for the HgBa2CaCu206+ 8, and this potential can give quick indications of the interstitial oxygen sites, although the displacements calculated using this potential has to be used with caution.
3. Results and discussion Our potential parameters for HgBa2CaCu206+ 8 are given in Table 1. The comparison of calculated and experimental data are shown in Table 2. The difference in lattice parameter between calculated and experimental data is less than 0.3%, and the difference in bond length is less than 1%. For the structure of HgBaECaCu206+ 8 without partial replacement of Hg by Cu, our calculation (see Table 3) shows that the defect energy of the oxygen interstitial at the 0(3) site (configuration (1)) is - 17.296 eV whereas the defect energy of the oxygen interstitial at the 0(4) site (configuration (2)) is - 1 5 . 9 6 1 eV, indicating that oxygen interstitial is energetically more favorably located at the 0(3) site
Table 3 Calculated defect energy for various defect configurations in HgBa2CaCu206+ 8 Configurations Defect energy (eV)
OHg •
Cu
©0
(1)~
-17.30
(2)~
-15.96
(3)~
-46.96
(4)0~(4) '
-47.54
(5)~
-43.54
(6)~
-40.74
X. Zhang et al. / Physica C 262 (1996) 13-20
than at the 0(4) site. These results agrees well with the experimental results [10,13]. Fig. 2 shows the structural changes caused by a interstitial oxygen at the 0(3) site. It is found that the interstitial oxygen is exactly at the 0(3) site, i.e. (½, 5,~ 0) position. We found that Hg atoms and Ba atoms move closer to the 0(3) site by 0.12 A and 0.17 A, respectively. But 02 atoms move away from 03 by 0.22 A. Cu atoms are found to be moving closer to the 02 site by 0.11 ~, and O1 atoms do not move significantly. The corresponding structural changes in bond lengths and bond angles are given in Table 4. The larger changes are observed for the Hg-O2 and Cu-O2 bond lengths, and the O 2 - C u O1 and Cu-O1-Cu bond angles. We found that incorporation of interstitial oxygen at the 0(3) site causes a decrease in the lattice parameter, which is in agreement with experiment [12]. We also found that incorporation of interstitial oxygen at the 0(3) site does not change the C u - O 1 - C u bond angle significantly. This result agrees as well with the experiments [10,13]. Experiments [2,11] show that interstitial oxygen can exist at the 0(4) sites with partial replacement of Hg by Cu. For simplicity we consider only the partial replacement of Hg by one Cu atom or two Cu o
17
atoms. Let us consider three types of partial replacement of Hg by Cu: (1) Partial replacement of Hg by two Cu atoms where both Cu atoms are on one side of the Hg square. The defect reaction can be represented by 2CuO + 2Hg~g ~ (Cu( 1)ng-Cu(2)Ug)* + 2HgO. (2) Partial replacement of Hg by two Cu atoms where the Cu atoms are at diagonal positions of the Hg square. Its reaction can be represented by 2CuO + 2HgH8 ~ (Cu(1)Hg-Cu(3)Hg) + 2HgO. (3) Partial replacement of Hg by two Cu atoms where the Cu atoms are separated by a large distance. (This is equivalent to a partial replacement of Hg by one of the Cu atoms.) Its reaction can be represented by 2CuO + 2Hg ~ ~ 2Cu + 2HgO. Our calculation shows that reactions (1), (2) and (3) need an energy of 3.08, 3.34 and 3.40 eV, respectively. This indicates that reaction (1) is the most
Table 4 Comparison of calculated structural changes in HgBa2CaCu206+ ~ with and without 0(3) Experimental a
Calculated without (3)
Interatomic distances (,~) Hg-O2 Hg-O3 Cu-O1 Cu-O2 Ba-O1 Ba-O2 Ba-O3 Ca-O1 Bond angles (°) O2-Cu-O1 O1-Cu-Ol Cu-OI-Cu Hg-O2-Cu Hg-O3-Hg O2-Hg-O3 a From Ref. [ 12].
1.995(5) 2.72904(8) 1.9279(7) 2.799(6) 2.753(5) 2.849(2) 2.814(6) 2.483(3) 89.5(2) 89.996(3) 179.0(3) 180.00
2.0062 1.9264 2.8159 2.7324 2.8642 2.4615 90.18 90.00 179.64 180.00 -
Change (%) with 0(3) 2.1808 2.6002 1.9236 2.5430 2.8520 2.9374 2.7197 2.4258 95.70 91.47 173.66 168.74 90.00 97.48
8.70 4.72 0.15 9.69 4.38 2.56 3.35 1.45 6.12 1.63 3.33 6.26 -
18
X. Zhang et aL / Physica C 262 (1996) 13-20
12)
(6) H
~4)
Fig. 2. The structuralchanges in the unit cell of HgBa2CaCu206 + when the excess oxygen atom is at the 0(3) site (½, ½, 0).
energetically favorable, i.e. the linear Cu clustering is most likely as experiment suggested [2]. Thus, we concentrated our studies on the partial replacement of Hg by two Cu atoms where Cu atoms are on one side of Hg square (configuration ( 3 ) - ( 6 ) as shown in Table 3). Table 3 shows that configuration (4) is the most energetically favorable, i.e. interstitial oxygen favors the 0 ( 4 ) site when two Hg atoms are replaced by Cu atoms. Fig. 3 shows the structural changes in two unit cells o f Hg-1212 due to the oxygen interstitial at the 0 ( 4 ) site when two Hg atoms are replaced by Cu atoms. It is seen that the unit cells have a big structural change. Atoms of 0 4 move upwards to the position (½, 0, z) where z = 0.049. This result is in good agreement with the experimental results of (½, 0, z) where z -- 0.04 [2,11]. This agreement provides encouraging support for the accuracy o f our potential and the general validity of our modelling approach. This result also indicates that the experimental results o f the 0 4 site at (½, 0, 0.04) may occur in the case when two Hg atoms are replaced
Fig. 3. The structural changes in two unit cells of HgBa2CaCu206+ 8 with two Hg atoms replaced by Cu when the excess oxygen alom is at the 0(4) site (½,0, z).
lg
Fig. 4. The structural changes in the unit cell of HgBa2CaCu206+ with two Hg atoms replaced by Cu when the excess oxygen atom I is initially put at the 0(3) site (½, 7, 0). After relaxaaon the excess oxygen atom moves to the position (0.5, 0.35, 0).
x. Zhang et al./ Physica C 262 (1996) 13-20
by two Cu atoms as shown in Fig. 3. The displacement of 0 4 off the Hg plane ( z = 0) causes a large structural change. O1(1) is found to be displaced downwards by 0.49 ,~. The 02(5) and 02(6) are found to move out with displacements of 1.4 A, while Cu(a) and Cu(b) move in with displacements of 0.40 ,~. Interstitial oxygen at the 0 4 site also results in some changes in the Cu-O2 bond length, i.e., a shortening of Cul-O2(1) and Cu2-O2(2), and elongation of Cu3-O2(3) and Cu4-O2(4). We also noted that the top CuO 2 plane is distorted while the bottom CuO 2 plane is almost unchanged. It appears that the interstitial 0(4) could change the nearly perfectly flat CuO 2 plane in Hg-1212. Fig. 4 shows the structural changes caused by interstitial oxygen at the 0(3) site when two Hg atoms are replaced by Cu (configuration (3)). Our calculation indicates that in this case the interstitial oxygen does not stay at the 0(3) site but moves to the position (0.5, 0.35, 0). This result is similar to the experimental result that in Hg-1212 with more than 10% Cu substitution for Hg, one of the interstitial oxygen sites is (0.5, 0.4, 0) [11]. We noted that in this configuration, the atoms in the CuO 2 plane do not displace much from their original positions. o
tg
19
However, some of the 0 2 atoms displace significantly. As configuration (3) just causes 0.5 eV more energy than configuration (4), these two configuration may co-exist in Hg-1212 with partial displacement of Hg by Cu, as reported [l 1]. We also investigated the position of the interstitial oxygen when one Hg is replaced by Cu. In this case, the 0(3) site is more energetically favorable than the 0(4) site. Fig. 5 shows the structural changes caused by interstitial oxygen at the 0(3) site when one Hg atom is replaced by Cu. It is found that the interstitial oxygen does not stay at the 0(3) site but moves to the position (0.41, 0.42, 0). We noted that this position is not reported after experiment. This discrepancy implies that the replacement of one Hg by Cu in Hg-1212 is unlikely. In contrast, the agreement of our oxygen interstitial positions of (½, 0, z) where z = 0.049 and (½, 0.35, 0) with the experimental results [l l] shows that our assumption that two Hg atoms are replaced by Cu seems reasonable. 4. Conclusions
Our newly developed interatomic potential can reproduce the Hg-1212 structure with a discrepancy in lattice parameter of less than 0.3% and a discrepancy in bond length of less than 1%. Our simulation results show that the 0(3) site is the most favorable oxygen interstitial position for Hg-1212 without partial replacement of Hg by Cu. Incorporation of interstitial oxygen at the 0(3) site results in a little structural change and does not change the nearly perfectly flat CuO 2 plane significantly. For Hg-1212 with partial replacement of Hg by Cu, the most likely oxygen interstitial position is the 0(4) site. This interstitial 0(4) can cause bigger structural changes compared to the 0(3) interstitial. Our prediction of the positions of excess oxygen atoms in Hg-1212 is in good agreement with the experimental results. We also found that the partial replacement of Hg by two Cu atoms on one side of Hg square is favorable and can account for the position (½, 0, z) of the interstitial oxygen.
@
Fig. 5. The structuralchangesin the unit cell of HgBa2CaCu206+ with one Hg atoms replacedby Cu when the excessoxygenatom is initiallyput at the 0(3) site (½, ~,~0). Afterrelaxationthe excess oxygen atom moves to the position(0.41,0.42,0).
Acknowledgements
We would like to thank Julian Gale for providing the computing code GULP for potential fitting and to
20
X. Zhang et al./Physica C 262 (1996) 13-20
thank K.W. Yip for help in the earlier stage of potential fitting. References [1] S.N. Putilin, E.V. Antipov, O. Chmaissem and M. Marezio, Nature (London) 362 (1993) 226. [2] J.L. Wagner, P.G. Radaelli, D.G. Hinks, H.D. Gorgensen, H.F. Mitchell, B. Dabrowski, G.S. Knapp and M.A. Bero, Physica C 210 (1993) 447. [3] S.N. Putilin, E.V. Antipov and M. Marezio, Physica C 212 (1993) 266. [4] L. Cao, Y.Y. Xue, F. Chen, Q. Xiong, ER.L. Meng, D. Ramirez, C.W. Chu, J.H. Eggert and H.K. Mao, to be published. [5] C.W. Chu et al., Nature 365 (1993) 323. [6] M. Nunez-Regueiro et al., Science 262 (1993) 97. [7] S.M. Loureiro et ai., Physica C 217 (1993) 253. [8] J. Schwartz, S. Nakamae, G.W. Raban Jr., J.K. Heuer, S. Wu, H.L. Wagner, D.G. Knapp and M.A. Beno, Physica C 210 (1993) 447. [9] O. Chmaissem, Q. Huang, S.N. Putilin, M. Marezio and A. Santoro, Physica C 212 (1993) 259. [10] P.G. Radaelli, J.L. Wagner, B.A. Hunter, M.A. Beno, G.S. Knapp, J.D. Jorgensen and D.G. Hinks, Physica C 216 (1993) 29. [l 1] L.W. Finger, R.M. Hazen, R.T. Downs, R.L. Meng and C.W. Chu, Physica C 226 (1994) 216. [12] Q. Huang, J.W. Lynn, R.L. Meng and C.W. Chu, Physica C 218 (1993) 356. [13] E.V. Abtuoiv et al, Physica C 218 (1993) 348.
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