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Paramagnetic properties of oxygen deficient YBa2Cu3O7−δ polycrystals
PHYSICA
Physica C 178 (1991) 37-40 North-Holland
Paramagnetic properties of oxygen deficient YBa2Cu307_6 polycrystals H. T h e u s s a n d H . K r o n m i i l l e r Instilut fur Physik, Max-Planck-Institut f~r Metallforschung, Heisenbergstr. 1, Pf800665, IV- 7000 Stuttgart 80, Germany Received 20 March 1991 Revised manuscript received 15 May 1991
At a series of oxygen deficient YBa2Cu3OT_~ polycrystals with 0 < ~< 0.6 the temperature dependent magnetic susceptibility was investigated at temperatures above the critical temperature To. Fitting these data to a Curie-Weiss-law Z(T) = C~ ( T - O) +Zo provides a method to derive the number of Bohr magnetons #B per Cu2+ ion in the Cu-O chains. Considering nearly full stoichiometric samples with ~ 0 , this quantity is in accordance with the value normally found in Cu2÷ compounds, but it decreases with increasing ~. The increase of the temperature independent part Zo of the susceptibility with the oxygen stoichiometry 7 - 6 is correlated with an increase of the density of states N(EF) at the Fermi level EF and provides a presupposition for a rising occupation of conducting charge carriers with the oxygen content.
I. Introduction As the superconducting properties of ceramic high t e m p e r a t u r e superconductors ( H T S C s ) d e p e n d very sensitively on the oxygen content [ 1 - 4 ] , an understanding o f the role o f oxygen in these materials will be i m p o r t a n t for understanding the mechanisms o f HTSC. While the existence o f a two-dimensional structure ( C u - O planes) is a characteristic feature o f all HTSCs and seems to be crucial for the superconducting pairing mechanism, the one-dimensional C u - O chains in YBa2Cu3OT_6 are assumed only to act as a charge reservoir for the conductivity in the planes [ 3 ]. Considering the interatomic C u - O distances, Cava et al. calculated the effective valence o f the copper atoms in the chains ( C u ( 1 ) sites) and in the planes (Cu ( 2 ) sites) [ 3 ]. The valence o f the Cu ( 1 ) a t o m was found to increase linearly with increasing oxygen content, whereas the copper located at the Cu ( 2 ) sites follow the step like oxygen d e p e n d e n c e o f the critical t e m p e r a t u r e T~. C a v a et al. concluded, that the C u ( 2 ) site is closely related to the superconducting properties o f YBa2Cu3OT_6, in particular to the hole concentration in the C u - O layers. Never-
theless, concerning magnetic properties, the Cu ( 1 ) sites in the chains provide interesting features, especially in the n o r m a l conducting state above To. Following a simple model introduced by Suzuki et al. [5], YBa2Cu3OT_6 can be described in more detail by the formula Y(BaO)2(Cu3+_2~Cu220~_~) (Cu2+O2)2 . chains (Cu( I ))
(l)
plane~((Cu(2))
This description takes into account the linear decrease of the effective Cu ( 1 ) valence with increasing & On the basis of formula ( 1 ) we will discuss the magnetic properties o f a series o f oxygen deficient YBa2Cu3OT_a samples with special regard to the role o f the copper atoms located in the chains.
2. Experimental procedure and results A series o f oxygen deficient YBa2Cu307_6-polycrystals was p r e p a r e d by a usual sintering technique with a d d i t i o n a l annealing t r e a t m e n t as described in detail in ref. [4]. F o r the magnetic properties o f these samples in the superconducting state below Tc also
0921-4534/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved
38
H. Theuss, tt. Kronmiiller / Paramagnetic properties qf o
see ref. [4]. The normal-state susceptibility was measured with constant applied field ltott~,,= 1.0 T and temperature up to 300 K using a commercial SQUID-magnetometer (SHE, model V T S ) . The temperature dependence o f the susceptibility was found to follow Curie-Weiss laws T-o+Z°"
z(T)=
l
? c>
poh,crvstals
YBa2Cu3Ov_a-Polyc
rys kaI
I
(2)
as illustrated in figs. 1 and 2. Figures 3, 4 and 5 show the Curie constant C the temperature independence susceptibility X0 and the temperature O as a function
'
F~ tl
~
~
~
'
~
~] ~
1
~
d
! 4
YBa2Cu30 ? ~
Fig. 3. Curie constant (2 measured as a function of oxygen stoichiometry.
Polycrystal
1.2
i
CD
X
1 [1
.8
+
© A +
~
7
=6.92
d
7-6
=
6.58
7-~
-
6.50
r
ii,
(9Oo <:,
6
4
,
,
100
,
a
20Q
150
T
~00
[K]
Fig. 1. Temperaturedependence of the magnetic susceptibility of 4 samples with different oxygen content. The lines are fits to eq.
l! +
i],
~:~
25C
1
}
YBa2Cu30v d PolycrysLa
(2). 7
d
Fig. 4. Temperature independent susceptibility Z, as a function of oxygen stoichiometrs. YBa2Ou307_ a - P o l y c r y s t a l
o 7
5 i
B 92
@7-d
=
A 7-~
= 6.58
+7-6
=
6
e O
6.50
ooo°
~
~ ~
z~
z~
><
000000
o
g~
o e
4
,
@q
o
.
.
+ + 4
4
•
"'"
.
I O0
+4
+ 4"
~ ~
+
~ ^
I
150
200 T
250
300
[K]
Fig. 2. Temperature dependent part o f the inverse susceptibility for 4 samples with different oxygen content. The lines are fits to eq. ( 2 ) .
of oxygen stoichiometry 7 - 0 . These parameters were obtained by fitting eq. (2) to the experimental data. The fitting procedure consisted o f a least squares fit, Data points below 100 K, where the beginning transition to the superconducting state leads to deviations from the Curie-Weiss law, were not taken into consideration. The algorithm requires starting values for the fitting parameters C Zo and O, where different starting values lead to different results. Fitting parameters outside the range indicated by the error bars exceed standard deviations o f 10 5 and are not reasonable.
H. Theuss, H. Kronmiiller I Paramagnetic properties of oxygen deficient YBa2CusOT_~polycrystals 60
2
39
0
YBa2Cu3OT_~-Po l y c r y s t a I
YBa2Cu307_ a - P o l y c r y s t a
50
7.
l
6
t
4
t
7
1
0
30
CO 20
{
{{{
10
0 . . . . 6.4
I
6.5
i
J
i
5.6
6.7
5.8
,
,
,
i
++ +
8
6 ,
i
4
6.9
5.4
7-~
6.5
i
66
,
,
i
5.7
5.8
~5 9
7.0
7-c~
Fig. 5. Dependence of the temperature O on the oxygen content.
Fig. 6. Dependence of the effective n u m b e r p of Bohr magnetons ¢tB on the oxygen content.
3. Discussion Once the density N of the atoms responsible for the Curie-Weiss term C / ( T - O) is known, one can evaluate the effective number p of Bohr magnetons pn per atom via the formula
C= ~-b Np2,
(3)
when p2 =g2 j(j+ 1). Because of full stoichiometric samples with 5 = 0 showing no temperature dependent susceptibility [ 68], it is reasonable to assume, that only the Cu 2+ atoms in the chains carry the local magnetic moment, necessary for a material to show Curie-Weiss behaviour. With 25nACu 2+(1) atoms per mol YBa2Cu3OT_~ (cf. formula ( 1 ) ) , we have 25NAt (666.18-- 165) magnetic moments per g. Multiplying this number by the sample density (p=5.5 g/ c m 3) yields the volume density N of magnetic moments and with eq. (3) we get the effective number of Bohr magnetons/IB per Cu 2+ ( 1 ) atom: p = 0 . 2 4 , / IC(\
666"18
16)~6.27~
.
(4)
Figure 6 shows the result, that was computed from the Curie constants (fig. 3). In Cu 2+ compounds, in general the experimentally observed values of p do not correspond to the theoretical expression of the free ion, p=gx/J(Jq- 1 ) ~ 3.55 ( g ~ 1.2, Land6 factor for free Cu 2+ ions; L = 2, S = ½and J = { ) . The reason is, that as a consequence of the crystal field, the ra-
dial symmetry of the electrical field of the C U 2 + ions is destroyed. In the case of many compounds of the iron group, this leads to a quenching of the orbital momentum L, so that the measured value ofF rather corresponds to the term p = 2 ~ 1 ) ( = 1.73 for Cu 2+ ) [9]. With 5--+0 the number of Bohr magnetons/zB in YBa2Cu307_6 seems to approach just this value (cf. fig. 6). The fall o f f t o about a half of this value at lower oxygen concentrations may express a rising interaction between the Cu2+(l ) atoms. The temperature independent part Zo of the magnetic susceptibility mainly results from a Pauli susceptibility Zp due to free charge carriers (holes) in the Cu-O layers. Consequently the increase of Zo with 7 - 5 means an increase of the density of states at the Fermi level EF according to the relation Zp ~ N(Ev). So within the model of Suzuki et al. (cf. eq. ( 1 ) ) [ 5 ], measurements of the Pauli susceptibility Zp ~Zo are fully compatible with the results of Cava et al., who relates the decrease of the effective copper valence at the Cu (2) sites with decreasing oxygen content to a loss of charge carriers in the C u - O layers [31. According to fig. 5 for 5< 0.2 the susceptibility follows approximately a Curie law, i.e. O,~ 0, whereas for higher 6 we found 30 K < O+ 40 K. These values are comparable to the results of Takabatake et al. [10l.
40
H. Theuss, H. Kronmiiller /Pararnagnetic properties" qI'o~Kvgen d¢~&'ient YBa 2( 'usO~ ,~po(vcO'stal.s
4. Summary Investigating the normal-state susceptibility of YBa2Cu307_,~ polycrystals provides a possibility for determining the effective number of Bohr magnetons/xB per Cu 2+ atom in the Cu-O chains as well as the Pauli susceptibility 2'e, which is proportional to the density of states at the Fermi level N(Er). The effective number of Bohr magnetons /~B shows a monotonic decrease with (~ from about p = 2x/A~S+ 1 ) ~ 1.73 for ~ 0 to p ~ 0 . 7 for d~<6.7. The Curie-Weiss behaviour of the susceptibility arises from the localized Cu 2+ spins at Cu( 1 ) sites and the temperature independent part ;(c~Zp from conducting charge carriers in the Cu-O layers. The results are compatible with the model, that oxygen loss in the chains causes a decreasing density of states in the layers.
Acknowledgements The authors are indebted to R. Henes for the preparation of the samples and to Dr. R. Reiger and Dr. M. Seeger for helpful discussions: This work was
subsidized by the Bundesminister fiir Forschung ur, d Technologic (Kennzeichen 13 N 57005).
References [ 1 ] R. Beyers and T.M. Shaw, Solid State Phys. 42 (1989) 135. [2] V.G. Baryakhtar, A.V. Zhalko-Titarenko, V.S. Melnikov. I.G. Mikhailov, A.V. Morozovsky, V.V. Nemoshkalenko. V.M. Pan, N.P. Pshentsova and S.K. Tolpygo, Int. J. Mod. Phys. B 1 (1988)1259. [31 R.J. Cava, A.W. Hewat, E.A. Hewat, B. Batlogg, M. Marezio, K.M. Rabe, J.J. Krajewski, W.F. Peck Jr. and L.W. Rupp Jr., Physica C 165 (1990)419. [4] H. Theuss and H. Kronmfiller, Physica C 177 ( 1991 ) 253. [ 5 ] M. Suzuki, J. Kardiawarman, S.M. Sampere and C.R. Burr. Phys. Rev. B 37 (1988) 5175. [61A. Hofmann, H. Kronmtiller, N. Moser, R. Reisser, P. Schiile and F. Dworschak, Physica C 156 (1988) 528. [7] T.R. McGuire, T.R. Dinger, P.J.P. Freitas, W.J. Gallagher, T.S. Plaskett, R.L. Sandstrom and T.M. Shaw, Phys. Rev. B 36 (1987) 4032. [8]S.-W. Cheong, S.E. Brown, Z. Fisk, R.S. Kwok, J.I). Thompson, E. Zirngiebl, G. Gruner. D.E. Peterson, G.L. Wells, R.B. Schwarz and J.R. Cooper, Phys. Rev. B 3(, (1987) 3913. [91 e.g.C. Kittel in: Introduction to Solid State Physics, 5th ed. (John Wiley & Sons, New York, 1976 ). [1o] T. Takabatake, M. lshikawa and T. Sugano, Jpn. J. Appl. Phys. 26 ( 1987} 1859.
Physica C 178 (1991) 37-40 North-Holland
Paramagnetic properties of oxygen deficient YBa2Cu307_6 polycrystals H. T h e u s s a n d H . K r o n m i i l l e r Instilut fur Physik, Max-Planck-Institut f~r Metallforschung, Heisenbergstr. 1, Pf800665, IV- 7000 Stuttgart 80, Germany Received 20 March 1991 Revised manuscript received 15 May 1991
At a series of oxygen deficient YBa2Cu3OT_~ polycrystals with 0 < ~< 0.6 the temperature dependent magnetic susceptibility was investigated at temperatures above the critical temperature To. Fitting these data to a Curie-Weiss-law Z(T) = C~ ( T - O) +Zo provides a method to derive the number of Bohr magnetons #B per Cu2+ ion in the Cu-O chains. Considering nearly full stoichiometric samples with ~ 0 , this quantity is in accordance with the value normally found in Cu2÷ compounds, but it decreases with increasing ~. The increase of the temperature independent part Zo of the susceptibility with the oxygen stoichiometry 7 - 6 is correlated with an increase of the density of states N(EF) at the Fermi level EF and provides a presupposition for a rising occupation of conducting charge carriers with the oxygen content.
I. Introduction As the superconducting properties of ceramic high t e m p e r a t u r e superconductors ( H T S C s ) d e p e n d very sensitively on the oxygen content [ 1 - 4 ] , an understanding o f the role o f oxygen in these materials will be i m p o r t a n t for understanding the mechanisms o f HTSC. While the existence o f a two-dimensional structure ( C u - O planes) is a characteristic feature o f all HTSCs and seems to be crucial for the superconducting pairing mechanism, the one-dimensional C u - O chains in YBa2Cu3OT_6 are assumed only to act as a charge reservoir for the conductivity in the planes [ 3 ]. Considering the interatomic C u - O distances, Cava et al. calculated the effective valence o f the copper atoms in the chains ( C u ( 1 ) sites) and in the planes (Cu ( 2 ) sites) [ 3 ]. The valence o f the Cu ( 1 ) a t o m was found to increase linearly with increasing oxygen content, whereas the copper located at the Cu ( 2 ) sites follow the step like oxygen d e p e n d e n c e o f the critical t e m p e r a t u r e T~. C a v a et al. concluded, that the C u ( 2 ) site is closely related to the superconducting properties o f YBa2Cu3OT_6, in particular to the hole concentration in the C u - O layers. Never-
theless, concerning magnetic properties, the Cu ( 1 ) sites in the chains provide interesting features, especially in the n o r m a l conducting state above To. Following a simple model introduced by Suzuki et al. [5], YBa2Cu3OT_6 can be described in more detail by the formula Y(BaO)2(Cu3+_2~Cu220~_~) (Cu2+O2)2 . chains (Cu( I ))
(l)
plane~((Cu(2))
This description takes into account the linear decrease of the effective Cu ( 1 ) valence with increasing & On the basis of formula ( 1 ) we will discuss the magnetic properties o f a series o f oxygen deficient YBa2Cu3OT_a samples with special regard to the role o f the copper atoms located in the chains.
2. Experimental procedure and results A series o f oxygen deficient YBa2Cu307_6-polycrystals was p r e p a r e d by a usual sintering technique with a d d i t i o n a l annealing t r e a t m e n t as described in detail in ref. [4]. F o r the magnetic properties o f these samples in the superconducting state below Tc also
0921-4534/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved
38
H. Theuss, tt. Kronmiiller / Paramagnetic properties qf o
see ref. [4]. The normal-state susceptibility was measured with constant applied field ltott~,,= 1.0 T and temperature up to 300 K using a commercial SQUID-magnetometer (SHE, model V T S ) . The temperature dependence o f the susceptibility was found to follow Curie-Weiss laws T-o+Z°"
z(T)=
l
? c>
poh,crvstals
YBa2Cu3Ov_a-Polyc
rys kaI
I
(2)
as illustrated in figs. 1 and 2. Figures 3, 4 and 5 show the Curie constant C the temperature independence susceptibility X0 and the temperature O as a function
'
F~ tl
~
~
~
'
~
~] ~
1
~
d
! 4
YBa2Cu30 ? ~
Fig. 3. Curie constant (2 measured as a function of oxygen stoichiometry.
Polycrystal
1.2
i
CD
X
1 [1
.8
+
© A +
~
7
=6.92
d
7-6
=
6.58
7-~
-
6.50
r
ii,
(9Oo <:,
6
4
,
,
100
,
a
20Q
150
T
~00
[K]
Fig. 1. Temperaturedependence of the magnetic susceptibility of 4 samples with different oxygen content. The lines are fits to eq.
l! +
i],
~:~
25C
1
}
YBa2Cu30v d PolycrysLa
(2). 7
d
Fig. 4. Temperature independent susceptibility Z, as a function of oxygen stoichiometrs. YBa2Ou307_ a - P o l y c r y s t a l
o 7
5 i
B 92
@7-d
=
A 7-~
= 6.58
+7-6
=
6
e O
6.50
ooo°
~
~ ~
z~
z~
><
000000
o
g~
o e
4
,
@q
o
.
.
+ + 4
4
•
"'"
.
I O0
+4
+ 4"
~ ~
+
~ ^
I
150
200 T
250
300
[K]
Fig. 2. Temperature dependent part o f the inverse susceptibility for 4 samples with different oxygen content. The lines are fits to eq. ( 2 ) .
of oxygen stoichiometry 7 - 0 . These parameters were obtained by fitting eq. (2) to the experimental data. The fitting procedure consisted o f a least squares fit, Data points below 100 K, where the beginning transition to the superconducting state leads to deviations from the Curie-Weiss law, were not taken into consideration. The algorithm requires starting values for the fitting parameters C Zo and O, where different starting values lead to different results. Fitting parameters outside the range indicated by the error bars exceed standard deviations o f 10 5 and are not reasonable.
H. Theuss, H. Kronmiiller I Paramagnetic properties of oxygen deficient YBa2CusOT_~polycrystals 60
2
39
0
YBa2Cu3OT_~-Po l y c r y s t a I
YBa2Cu307_ a - P o l y c r y s t a
50
7.
l
6
t
4
t
7
1
0
30
CO 20
{
{{{
10
0 . . . . 6.4
I
6.5
i
J
i
5.6
6.7
5.8
,
,
,
i
++ +
8
6 ,
i
4
6.9
5.4
7-~
6.5
i
66
,
,
i
5.7
5.8
~5 9
7.0
7-c~
Fig. 5. Dependence of the temperature O on the oxygen content.
Fig. 6. Dependence of the effective n u m b e r p of Bohr magnetons ¢tB on the oxygen content.
3. Discussion Once the density N of the atoms responsible for the Curie-Weiss term C / ( T - O) is known, one can evaluate the effective number p of Bohr magnetons pn per atom via the formula
C= ~-b Np2,
(3)
when p2 =g2 j(j+ 1). Because of full stoichiometric samples with 5 = 0 showing no temperature dependent susceptibility [ 68], it is reasonable to assume, that only the Cu 2+ atoms in the chains carry the local magnetic moment, necessary for a material to show Curie-Weiss behaviour. With 25nACu 2+(1) atoms per mol YBa2Cu3OT_~ (cf. formula ( 1 ) ) , we have 25NAt (666.18-- 165) magnetic moments per g. Multiplying this number by the sample density (p=5.5 g/ c m 3) yields the volume density N of magnetic moments and with eq. (3) we get the effective number of Bohr magnetons/IB per Cu 2+ ( 1 ) atom: p = 0 . 2 4 , / IC(\
666"18
16)~6.27~
.
(4)
Figure 6 shows the result, that was computed from the Curie constants (fig. 3). In Cu 2+ compounds, in general the experimentally observed values of p do not correspond to the theoretical expression of the free ion, p=gx/J(Jq- 1 ) ~ 3.55 ( g ~ 1.2, Land6 factor for free Cu 2+ ions; L = 2, S = ½and J = { ) . The reason is, that as a consequence of the crystal field, the ra-
dial symmetry of the electrical field of the C U 2 + ions is destroyed. In the case of many compounds of the iron group, this leads to a quenching of the orbital momentum L, so that the measured value ofF rather corresponds to the term p = 2 ~ 1 ) ( = 1.73 for Cu 2+ ) [9]. With 5--+0 the number of Bohr magnetons/zB in YBa2Cu307_6 seems to approach just this value (cf. fig. 6). The fall o f f t o about a half of this value at lower oxygen concentrations may express a rising interaction between the Cu2+(l ) atoms. The temperature independent part Zo of the magnetic susceptibility mainly results from a Pauli susceptibility Zp due to free charge carriers (holes) in the Cu-O layers. Consequently the increase of Zo with 7 - 5 means an increase of the density of states at the Fermi level EF according to the relation Zp ~ N(Ev). So within the model of Suzuki et al. (cf. eq. ( 1 ) ) [ 5 ], measurements of the Pauli susceptibility Zp ~Zo are fully compatible with the results of Cava et al., who relates the decrease of the effective copper valence at the Cu (2) sites with decreasing oxygen content to a loss of charge carriers in the C u - O layers [31. According to fig. 5 for 5< 0.2 the susceptibility follows approximately a Curie law, i.e. O,~ 0, whereas for higher 6 we found 30 K < O+ 40 K. These values are comparable to the results of Takabatake et al. [10l.
40
H. Theuss, H. Kronmiiller /Pararnagnetic properties" qI'o~Kvgen d¢~&'ient YBa 2( 'usO~ ,~po(vcO'stal.s
4. Summary Investigating the normal-state susceptibility of YBa2Cu307_,~ polycrystals provides a possibility for determining the effective number of Bohr magnetons/xB per Cu 2+ atom in the Cu-O chains as well as the Pauli susceptibility 2'e, which is proportional to the density of states at the Fermi level N(Er). The effective number of Bohr magnetons /~B shows a monotonic decrease with (~ from about p = 2x/A~S+ 1 ) ~ 1.73 for ~ 0 to p ~ 0 . 7 for d~<6.7. The Curie-Weiss behaviour of the susceptibility arises from the localized Cu 2+ spins at Cu( 1 ) sites and the temperature independent part ;(c~Zp from conducting charge carriers in the Cu-O layers. The results are compatible with the model, that oxygen loss in the chains causes a decreasing density of states in the layers.
Acknowledgements The authors are indebted to R. Henes for the preparation of the samples and to Dr. R. Reiger and Dr. M. Seeger for helpful discussions: This work was
subsidized by the Bundesminister fiir Forschung ur, d Technologic (Kennzeichen 13 N 57005).
References [ 1 ] R. Beyers and T.M. Shaw, Solid State Phys. 42 (1989) 135. [2] V.G. Baryakhtar, A.V. Zhalko-Titarenko, V.S. Melnikov. I.G. Mikhailov, A.V. Morozovsky, V.V. Nemoshkalenko. V.M. Pan, N.P. Pshentsova and S.K. Tolpygo, Int. J. Mod. Phys. B 1 (1988)1259. [31 R.J. Cava, A.W. Hewat, E.A. Hewat, B. Batlogg, M. Marezio, K.M. Rabe, J.J. Krajewski, W.F. Peck Jr. and L.W. Rupp Jr., Physica C 165 (1990)419. [4] H. Theuss and H. Kronmfiller, Physica C 177 ( 1991 ) 253. [ 5 ] M. Suzuki, J. Kardiawarman, S.M. Sampere and C.R. Burr. Phys. Rev. B 37 (1988) 5175. [61A. Hofmann, H. Kronmtiller, N. Moser, R. Reisser, P. Schiile and F. Dworschak, Physica C 156 (1988) 528. [7] T.R. McGuire, T.R. Dinger, P.J.P. Freitas, W.J. Gallagher, T.S. Plaskett, R.L. Sandstrom and T.M. Shaw, Phys. Rev. B 36 (1987) 4032. [8]S.-W. Cheong, S.E. Brown, Z. Fisk, R.S. Kwok, J.I). Thompson, E. Zirngiebl, G. Gruner. D.E. Peterson, G.L. Wells, R.B. Schwarz and J.R. Cooper, Phys. Rev. B 3(, (1987) 3913. [91 e.g.C. Kittel in: Introduction to Solid State Physics, 5th ed. (John Wiley & Sons, New York, 1976 ). [1o] T. Takabatake, M. lshikawa and T. Sugano, Jpn. J. Appl. Phys. 26 ( 1987} 1859.