Oxygen nonstoichiometry and high-temperature conductivity of DyBa2Cu3O7−δ

PHYSICA Ii

PhysicaC 195 (1992) 145-156 North-Holland

Oxygen nonstoichiometry DyBa,Cu30, --6

and high-temperature

conductivity of

Hiroya Ishizuka, Yasushi Idemoto and Kazuo Fueki Department of Industrial Chemistry, Faculty of Science and Technology, Science University of Tokyo, 2641 Yamazaki, Noda-shi. Chiba 278, Japan

Received 3 March 1992

The oxygen nonstoichiometry and high-temperature conductivity of DyBa2Cu,0,_6 were measured as functions of temperature and oxygen partial pressure P( 0,). When the &log P( 0,) data points at each temperature are shifted in parallel in the abscissa direction by a distance characteristic of temperature, a single smooth curve called “the master curve” was formed. A proposed model, based on chemical equilibria among electronic defects, ionic defects and oxygen well, interpreted “the master curve”. The high-temperature conductivity was plotted against the excess copper valence Az( =z- 1.67) calculated from the oxygen nonstoichiometty. All the data points were found to fall on a single curve, irrespective of temperature. Assuming that CL&, ions are the charge carrier, the mobility was calculated from the conductivity. The lattice parameters as a function of 6 have suggested that the increase in mobility with increasing average copper valence could be due to the concentration change of oxygen on the Cu( 1)-O plane.

1. Introduction

One of the most characteristic features of LnBa2Cu307_-6is the large oxygen nonstoichiometry 6, which changes from around 0 to 1 as a function of temperature and oxygen partial pressure. The nonstoichiometry S is closely related to the average copper valence, carrier concentration, hightemperature conductivity and superconductivity [ 1,2]. In order to elucidate the relation between oxygen nonstoichiometry and conductivity in equilibrium state, measurements at high temperatures are necessary because the equilibrium can be reached in a relatively short period. Several papers have been published on the high-temperature conductivity measurements so far [3-l 01, most of the studies having been made on the conductivity as a function of temperature. Freitas et al. [ 91 are one group that has carried out the measurements on both the oxygen content and high-temperature conductivity, but they did not enter a discussion on the carrier concentration and mobility. Grader et al. [ lo] have carried out measurements on the Hall coefficient and conductivity, and calculated the carrier concentra-

tion and mobility. However, no mention has been made on the role of oxygen content. The purpose of the present study is to determine the oxygen nonstoichiometry and high-temperature conductivity of DyBa2Cu307_-6 as functions of temperature and oxygen partial pressure, and to calculate the carrier concentration and mobility for the elucidation of conduction in superconductors.

2. Experimental 2. I. Sample preparation

One mol/l aqueous solution of DY(NO~)~ and CU(NO~)~, and 0.25 mol/l Ba(N03)z solution were prepared and their concentrations determined by a standard EDTA solution using, respectively, X0, PAN and BT as indicators. These solutions were mixed so that a ratio of Dy : Ba: Cu = 1: 2 : 3 was obtained. Oxalic acid equivalent to 1.5 times the number of cations was dissolved in a volume of ethanol 4 times that of the mixed aqueous solution, and the oxalic acid-ethanol solution was added to the mixed

0921-4534/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

146

H. Ishizuka et al. /Oxygen nonstoichiometry ofDyBa,Cu30,_8

aqueous solution with stirring at pH=3.0 to complete the precipitation. Then, the solution was aged for one night. After filtration, the precipitate was dried, decomposed at 400” C for 4 h to form the oxide, and calcined at 850°C to form DyBa2Cu30,_6. The resulting oxide was confirmed to be single phase by means of an X-ray diffractometer. Then, the oxide powder was pressed into a pellet, 10 mm in diameter, and heated at 950°C for 12 h for sintering. 2.2. Determination of copper valence The average copper valence of DBCO was determined by two kinds of iodometry. First, a quantity of the sample was placed in RI solution and concentrated HCl solution was added to dissolve the sample. The amount of I2 liberated by Cu3++31--CuI+I

21

(1)

cu~++21--CuI$~I

2 2,

(2)

was determined with a standard 1/ 10 N Na2S203 solution. Secondly, a quantity of the sample was dissolved with concentrated HCl solution, so that Cu3+ (or O-) and Cu+ in the oxide could change into Cu2+

2.4. Measurement of oxygen nonstoichiometry The oxygen nonstoichiometry was measured gravimetrically as a function of temperature and oxygen partial pressure, by means of an apparatus equipped with a gas system and a TGA41 microbalance supplied by Shimazu. The microbalance provides the weight difference between two states. So, the example annealed at 350°C in 1 atm of oxygen and analyzed by the iodometric technique mentioned above was employed for the determination of a reference. The sample placed in a platinum basket was suspended from an arm of the microbalance, and equilibrated in 1 atm of oxygen at 350°C. Then, the temperature was raised to 1000°C in the same oxygen partial pressure and the equilibrium weight was determined. The determination of weight was carried out at fifty degree steps with decreasing temperature from 1000°C to 350°C. A similar procedure was employed at different oxygen partial pressures. The oxygen partial pressure range of logP(0,) (atm) =0 to -3.3 was employed. 2.5. Determination of the chemical stability region of the superconductor

by 2Cu3++H20+2Cu2++$02+2H+,

(3)

2Cu++f02+2H++2Cu2++Hz0.

(4)

Then, RI was added to liberate I2 by Reaction (2 ), and the amount of I2 was titrated for the determination of the total amount of copper. From these two kinds of iodometry, the average valence was calculated. 2.3. Determination of critical temperature T, In order to obtain the relation between T, and 6, the pellets with different 6 values were prepared by annealing at various temperatures and oxygen partial pressures. A part of the sample was ground and subjected to iodometry to determine the average copper valence. The critical temperature was determined by the DC four probe method. The temperature measurement was made using a Au (O.O7%Fe)Ag thermocouple.

In order to determine the chemical stability region, the melting point and decomposition pressure were ascertained. In the case of melting point determination, the sample suspended from the microbalante was heated up gradually at a constant rate of increase and the temperature at which the weight decreases suddenly owing to melting was determined. The decomposition pressure was determined by the EMF method using a solid state electrochemical cell. The superconductor sample was divided into two portions, one of which was subjected to decomposition at a low oxygen partial pressure. The decomposition was confirmed by means of an X-ray diffractometer. Then, the decomposed portion was mixed together with the undecomposed portion and pressed into a pellet. A Ni-NiO pellet was employed as the reference electrode and a calcia-stabilized zirconia (CSZ) tube with one open end was used as electrolyte. From the EMF of the cell, the decomposition pressure was calculated.

147

H. Ishizuka et al. / Oxygen nonstoichiometry of DyBa2Cu307_s

2.6. Determination of lattice parameters 0.8 100.

The samples for which oxygen nonstoichiometry was determined by iodometry were used for the lattice parameter measurement. The diffraction measurement was carried out at a scanning speed of 0.2”/ min from 15” to 100” of 26. Rietvelt analysis (Rigaku Denki RIETAN) was made for all diffraction peaks to determine lattice parameters.

0.7

Oxygen Deficit 0.6 0.5 0.4

6 0.3

0.2

I

0.1

90 - D~Ba~=u~o~_~

2.7. High-temperature conductivity measurement [Ill

A pellet, 10 mm in diameter, was prepared by pressing powder at a pressure of 400 kg/cm*, and sintered at 950°C in 1 atm of oxygen for 12 h. The density of the sintered pellet was determined by the Archimedes method using benzene. A rectangular coupon was cut from the pellet and four fine platinum wires were attached with silver paste. The coupon was set in a conductivity measurement apparatus and the equilibrium conductivity was measured as a function of temperature and oxygen partial pressure in a range of logP(0,) =O- - 3.6.

Fig. 1. Plot of T, (zero) vs. average copper valence.

3. Results and discussion 3. I. Average copper valence and T,

Figure 1 shows the relation between average copper valence and T,. As the copper valence increases, T, increases and reaches a maximum value of around 90 K. A plateau was observed at around 60 K. The relation between copper valence and T, is quite similar to that for YBCO [ 12- 15 1. 3.2. Stability boundaries of DBCO 3.2. I. Phase diagram and partial molal quantities

The melting point and oxygen nonstoichiometry 6 are given in fig. 2 as a function of oxygen partial pressure. The oxygen deficiency S is nearly the same as the other 90 K class superconductors [ 16- 19 1, and increases with increasing temperature and decreasing oxygen partial pressure. The &log P( Oz ) ctnves at constant temperatures in fig. 1 were converted into the T-log P( 0,) relation at constant S values. Figure

-3

-2 log ( PoZ/atm)

Fig. 2. Oxygen nonstoichiometry and oxygen partial pressure.

-1

as a function

0

of temperature

H. Ishizuka

148 ,

1400

I

I

I

et al. /Oxygen

1

nonstoichiometry

ofDyBa2CuJ07_-6

vet-ted into the Ri%P(O&T relation. Figure 4 shows the R7ln P(02)-T relation at constant 6 values. In the figure, the open triangles give the melting point as a function of oxygen partial pressure. The plot shows a good linearity and is expressed by

I

1300 1200 -

RnnP(0,)

(J/mo102)=-4.24~102+318T.

1100 -

(9)

G 1000 Y b

The solid triangles express the decomposition pressure as a function of temperature. A good linearity is seen for the plot. The expression is

900

RnnP(O*)

t 800

700

I

600_‘6

(J/mo102)=-2.51x102+162T. (10)

-5I

-41

-2I

-3I

-11

0I

log (Po2jatm) Fig. 3. T-logP(0,)

diagram.

3 gives the T-log P( 0,) plot. The open triangles provide the melting point as a function of oxygen partial pressure. On this line, DBCO decomposes into Dy,BaCuOS and a liquid phase by

The Rnn P( 02)-Tplot at constant 6 values is linear. From the slope of the plots, the partial molal entropy of oxygen AS( 0,) can be determined. As( 0,) means the entropy change when one mole of oxygen dissolves into DBCO with a deficiency 6. The intercept of these lines with the ordinate provides the partial molal enthalpy m( 0,). M( 0,) means the enthalpy change when one mole of oxygen is dissolved into DBCO with a deficiency 6. Figures 5(a) and 5(b) give As(O,) and m( 0,) as a function of 6,

4DyBa, Cu3 0, = 2Dy, BaCuO, + liquid phase (composition;

2Ba3 CQO,)

+ O2 (5)

with the evolution pressed by logP(O1)

of oxygen. The equilibrium

(atm) = 16.6-2.21 x 104 T-l

.

is ex-

(6)

The solid triangles give the decomposition pressure determined by the EMF measurement. The decomposition reaction is i DyBa, Cu3 O6 = : Dy, BaCuOS

+y The equilibrium logP(Oz)

BaCuzO,

is expressed

(atm)=8.45-

Also the T-logP(02)

+ 3 BaO+02.

-

-90

-

by

1.31 x 104T-’ relation

-80

(7)

-loo .

(8)

in fig. 2 can be con-

700

800

900

1000 1100 1200 1300 T(K)

Fig. 4. T-p( 0,) diagram

149

H. Ishizuka et al. /Oxygen nonstoichiometty of DyBazCuJO,_-d

log

-120

PO2

b)

Fig. 6. Principle of master curve. I

ature, one smooth curve, shown in fig. 7, is obtained. Let us call this curve “the master curve”. The master curve represents a general &log P( 0,) relation that is independent of temperature.

-200’

’ 1.8

I 1.9 Average

L 2.0 Copper

2.1

2.2

I 2.3

Valence

Fig. 5. Partial molal entropy and enthalpy of oxygen.

respectively. ti( 0,) increases with increasing 6. This tendency is quite similar to that of YBCO. AR( 0,) has a maximum at 8~0.6. The maximum seems to correspond to the ortho-tetra transition. The mean value of AR(O,) is - 153 kJ/mol O2 and the variation is 11 kJ/mol Oz. This result indicates that M(O,) is nearly constant, irrespective of crystal structure change. 3.2.2. &log P(0 j master curve As mentioned above, M(O,) is nearly constant regardless of& Since aln P(O,)/a( l/T) =M(O,)/ R, the T-log P(0,) plots at constant 6 values are parallel. Figure 6 schematically shows two Tlog P(02) lines with different 6 values. If the AB portion at 1/T, is shifted in parallel along two lines with 6, and &, the AB portion will coincide with the CD portion at 1/T,. Accordingly, if the &log P( 0,) curve at 650°C is taken as the standard one and the &log P( 0,) curves for other temperatures are shifted along the abscissa by log K characteristic of temper-

3.2.3. Interpretation of the master curve a) region of 6> 0.5. A thermodynamic treatment of the master curve will be given below. According to the bond valence sum theory by Brown [ 201, the valence of copper ions on the Cu( 2)-O2 planes is +2 and the copper valence on the Cu ( 1)-O planes changes with oxygen content when 6 is higher than 0.5. It has been said that holes reside on oxygen to form O-; however, in this treatment, we assume that the oxygen valence is always - 2 and that the copper valence changes with 6. Let us denote copper ions Cu3+, Cu2+ and Cu+ on copper sites by Cue-, CUE, and Cu&, respectively, and let us represent an oxygen ion on an anion site and an oxygen ion vacancy by 06 and Vg, respectively. The change in copper valence due to dissolution of oxygen can be expressed by 4CUE” + 2v;

+ 02 = 4CU,” + 2Wo )

(11)

4cu;,

+ 02 = 4CU23”+ 2% .

(12)

+ 2v;

The mass action law yields

[cu,“14[0c512 [cu~“]4[v;;]2P(02)

=K1 ’

(13)

=K2 ’

(14)

[cu~“14[o~12 [cu&“]4[v;]2P(02)

H. Ishizuka et al. /Oxygen nonstoichiometry ofDyBa2Cuj0,_-d

150

1.0 -7

-5

-6

-4

I

I

-3

-2

log

-1 PO2

-log

I

I

I

I

1

0

1

2

3

4

5

K1=93,K2=0.06(d 20.5) K

K3=0.038,K4=2x104(6<0.5)

Fig. 7. &log P(02) master curve.

-I/2

in terms of the where [ ] denotes the concentration number of atoms per unit cell and K, and K2 are the equilibrium constants. According to the result by Brown [ 201, the change in copper valence occurs only on the Cu( 1)-O plane. Since the number of copper atoms on the Cu ( 1) -0 plane is unity in unit volume, the site conservation law provides [Cu,“]+[Cu~“]+[Cu&“]=l. If the average copper 3.2~ 7 - 2S, accordingly,

[CUE”1.

[Cu&,]=(K2Po,)-"4

Combination

(21)

of (20)) (2 1) with ( 15 ) and ( 16 ) gives

(15) valence

is denoted

by z,

(22)

3[Cu,,]+2[Cu&]+[Cu&]=3z-4=3-26. (16) [C&l

In the region of 6> 0.5, the crystal structure is almost tetragonal. Therefore, the number of oxygen sites on a Cu( 1)-O plane is two per unit cell. Accordingly,

(23) From

[v,]+[og]=2

(22) and (23),

(17)

l/2 + (26-

and [vb’]=l+s,

Insertion yields

(19) of these equations

[CU;c”] = (K,P(02))“4

into l/2

( > E

(13)

[CUE"1

and

,

1) --1/2

(18)

[O&1=1-s.

=3-26.

+(26-2)

(&P(O,))-"4

(14)

=o.

(24) Putting

(20)

l/Z =x,

(25)

H. Ishizukaet al. / Oxygen nonstoichiometryof DyBa2Cu30,_d

151

one can obtain

I/*

26(K,)“4x2+(2S-1)x+(26-2)=0. This equation

(26)

is the quadratic

one, so the solution

is

[C&,1

=

[C&,1,

(W’(02))“4

[Cu;,I=(K,P(O,))-114($-d)-“2

(33)

[CL&].

112

P(O*)“4

( > E

(l-26)+&26-1)*-

=

(34)

166(6-

By inserting eqs. (33) and (34) into eqs. (28) and (29) and rearranging them, one can obtain

1) (K,/K,)“4

46Ki/4

(27) This equation gives the relation between S and logP(0,). Putting K,=93 and K2=O.O6, one can obtain a Slog P(0,) relation, which is given by a solid line in a region of 6> 0.5. in fig. 7. This line is well fitted to the master curve. b) Region of ScO.5. According to Brown [ 201, the average copper valence in the Cu(I)-0 plane increases with the decrease in 6, and that in the Cu( 2)-O2 plane increases from 2.0 to around 2.25 as 6 decreases from 0.5. Accordingly, we assume that in the region of 6< 0.5 the copper valence is even in both Cu (I )-0 and Cu (2 )O2 planes. The same equilibrium equations as ( 11) to ( 14) hold in the case of 6< 0.5; however, KS and K4 are used as the equilibrium constants for eqs. ( 13 ) and (14), respectively. The site conservation law yields [Cl&“] + [CU&“] + [Cl&,]=3 because the number The electroneutrality 3[Cu&]+2[CuE,]

(28)

{ (K~Pt02))‘/~

+ (K,P(O,)

(+$)“*

+ 1

)- 114(+J2},Cu&]

=3,

(35)

+ (K4P(O*))-“4

(1 “J”l

[CUE,] =7-2s. (36)

By combining eqs. (35) and (36) and eliminating the [Ct.& ] term, one obtains (2J+2)

(K,P(O2)

)1’4

+ (2S-4)

of copper ions per unit cell is 3. condition gives + [Cu&] =3z=7-26,

(29)

(37) Putting I/*

where z is the average copper valence. In the region of 6~0.5, the crystal structure is orthorhombic and the concentration of the oxygen site is unity. Accordingly, [v,]+[oo]=l

(30)

and [V;;]=S, [Ob]=l-s.

(31)

P(02)1’4

( > $8

we get a quadratic equation is

=x’

,

(38)

equation,

the solution

of which

I/*

P(O*)“4

( > j$

=

(l-26)+&26-1)*-16(6+1) 4(6+

(6-2)

(KJK4)“4

1)Kf’”

(32)

(39)

Insertion of eqs. (31) and (32) into eqs. ( 13) and ( 14) and rearrangement yields

The values of KS and K4 were determined so that two curves for 6>0.5 and 6~0.5 can be connected

H. Ishiruka et al. /Oxygen nonstoichiometry of DyBazCu307_d

152

smoothly at 6~0.5. It was found that the best lit is obtained when KS= 0.038 and K4= 2 x 104. The result is given by the solid line in a range of 6< 0.5 in fig. 7. The solid line is smooth in the whole S range and fits well the master curve. 3.3. High-temperature conductivity 3.3.1. High-temperature conductivity as a function of djcygen partial pressure and temperature The relative density of samples used for conductivity measurement was 98%. The Arrhenius plot for high-temperature conductivity is given in fig. 8. At a constant oxygen partial pressure, the conductivity decreases with the increase in temperature, but it turns up when the oxygen partial pressure is below lo-* atm and the temperature is higher than about 650°C. Such a behavior has been found for YBCO by Fisher et al. [ 41. Using the data in fig. 2, the oxygen nonstoichiometry 6 was plotted on the conductivity-temperature curves in fig. 8. The dotted lines show the conductivity-temperature relation at constant 6 values. These lines are nearly parallel to the

900

800

abscissa. This fact means that the conductivity at constant 6 value is independent of temperature. Such an independence of conductivity at constant 6 has been found in the case of YBaZCu307_-6 and seems a characteristic feature of 90 K class LnBa@,O,_+ It is concluded that the high-temperature conduction of LnBa2Cu@_6 is not the thermal activation type. Figure 9 gives the log a-log P( 0,) relation at constant 6 obtained by converting the Arrhenius plot given in fig. 8. In the high oxygen partial pressure range, log r~increases with the increase in log P( 0,). This result indicates that the majority carriers would be holes. However, the conductivity increases with decreasing oxygen partial pressure in a low oxygen partial pressure region. This feature indicates that electrons would be the majority carrier. The hole concentration is the same as the electron concentration at the minimum conductivity, if the hole mobility is equal to the electron mobility. In fig. 8, the conductivity at constant 6 values was shown to be temperature independent. From this fact, it is considered that both the hole and electron mobilities at minimum conductivity are the same and tempera-

Temperature(“C1 700 600 500

400

2.5 t - 2.0I E 1;1 1.5-

I+

:

0.5-

og(Po2/atm)=-3.6 0

I

0.8

0.9

1.0

1.1

1.2

1/Tx104(

1.3

1.4

l/K)

Fig. 8. Arrhenius plots for high temperature conductivity.

1.5

1.6

H. Ishizuka et al. /Oxygen nonstoichiometry of DyBazCuJ07_-6

153

*'E 0. I-' !: .:0. NE b

51 m 0.

1/Tx104(1/K)

Fig. 10. Arrhenius plots for oki,. 0

-J

-1

-2

log

(Po,/atm)

Fig. 9. Relation between log u and log P( O2) .

ture independent. At the conductivity minimum, a portion of electrons in the valence band are thermally excited to the conduction band by NullSe-

+ h+ ,

(40)

where e- and h+ represent the conduction electron and the electron hole, respectively. If the electron concentration and hole concentration are denoted by n and p, respectively, the mass action law gives n-p= Ki where Ki is the equilibrium ductivity minimum, n=p=p,

(41) constant.

At the con-

(42)

so pi=Ki.

(43)

Near the conductivity minimum the mobilities are considered to be temperature independent. Accordingly, the temperature dependence of g&n is considered to be due to pa. The Arrhenius plot of oLin is given in fig. 10. The plot is linear, and from the slope of the plots the activation energy corresponding to band gap is calculated to be 1.48 eV +0.06 eV. According to the result of bond valence sum calculation

by Brown [ 201, the copper valence of Cu (I) is a little higher than unity and that of Cu(2) is 2, when the copper average valence is near 1.8 where the conductivity minimum is observed. From this result, it is concluded that Gmi, corresponds to the thermal excitation of an electron from the valence band due to the conduction band of the Cu(2)-O2 plane. Humlicek et al. [21] and Yasuoka et al. [ 221 have studied the optical absorption of YBCO and determined the band gap of Cu( 2)-O* plane to be 1.77 eV and 1.5 eV, respectively. The present result agrees well with their results, though the methods of measurement are different. From this result, it is concluded that the band gap of the Cu(2)-O2 plane for DyBa2Cu307_-6 is fairly close to that for YBazCuJO,_a, when the copper valence of Cu (I ) is almost unity. 3.3.2. Oxygen nonstoichiometry and hightemperature conductivity From figs. 2 and 8, the relation between (Tand average copper valence has been derived. Figure 11 shows the result. All the c-average copper valence plots at different temperatures fall on a single curve, and (Tincreases with the copper valence. The present result clearly shows that the high-temperature conductivity is temperature independent and oxygen content dependent. It is easily seen that the slope increases steadily with the increase in oxygen content in a range of 6 < 0.5 and becomes constant in a range of S> 0.5. The linear increase of D with oxygen con-

154

H. Ishizuka et al. /Oxygen nonstoichiometry ofDyBa2Cu307_6

15o,o;8

0;7

0;6

0;5du;4

0;3

0;2

I

”

/

I

2

In fig. 12, line A is the curve obtained by the calculation mentioned above. For comparison, the relation obtained by assuming that 3Az is equal to the number of carriers per unit cell is given by line B in the same figure. Comparison of the two lines indicates that the fraction of Cu,, in the total number

o;l,

I

/

I 7

6

5 o:ooo”c

m

0

1.8

1.9 Average

2.0 Copper

2.1 2.2 Valence

2.3

, 0.1

0.2

0.3

0.4

0.5

0.6

AZ

'5 4 N" 0 43 x a

Fig. 11. Relation valence.

between

tent has been YBa2Cu307_-6.

reported

conductivity

by Freitas

and

average

2

copper

et al. [ 91 for 1.8

I 3.3.3. Carrier concentration and mobility As shown in fig. 11, (Tapproaches zero when S becomes 1. That is, DyBa,Cu,O, is considered to be an insulator. The conductivity increases with decreasing 6 from 1 and the superconductivity appears around 6=0.5, when DyBa2Cu307--6 is cooled to low temperature. Let us denote (z- 1.67) by AZ. If 3A.z is equal to the number of carriers per unit cell, a linear relation should hold between r~ and AZ, but the observed ~-AZ relation is curved. This fact means that 3Az is not equal to the number of carriers per unit cell. Assuming only Cu3+ ions are the charge carriers, the carrier concentration, p, in unit cell volume is represented by

where V, is the unit cell volume. [CL&,, ] can be calculatedusingeqs. (20)-(22) and (27) with K,=93 and K2=0.06, when 6 is larger than 0.5. In the case where 6 is smaller than 0.5, [CL& ] can be calculated using eqs. (33)-( 35) and (39) with K,=O.O38 and K,=2x 104.

1.9 2.0 2.1 2.2 Average Copper Valence

0.2

0.3

0.4

0.5

2.3

0.6

AZ

Fig. 12. Relation valence.

between

0.8 0.7 o.15r-l-Lkl

carrier

0.6

Average

Fig. 13. Relation

0.5

density

0.4

Copper

between mobility

and average

0.3

0.2

copper

0.1

0.0

ValenCe

and average copper valence.

H. Ishizuka et al. /Oxygen nonstoichiometry ofDyBa2Cu30,_s

of copper ions per unit cell increases with the increase in average valence, and p is 6.3x IO” cmp3 when 6= 0. Grader et al. [ lo] have measured the Hall coefficient and conductivity and obtained p = 2 x 10 22 cme3 in a temperature range 350-550°C. However, their value is much higher than that calculated assuming that 3Az is equal to the number of carriers per unit cell, and the interpretation of high carrier concentration is difficult. Probably, the accuracy of the Hall coefficient would become lower when the carrier concentration is high. Assuming that the carrier concentration changes with the average valence as shown by line A in fig. 12, one can calculate the mobility from the conductivity data. The highest mobility is 0.13 cm2 V-’ s-r, which is in good agreement with 0.13 cm2 V-r s-’ by Grader et al. [lo]. It is interesting that the mobility is quite small but the activation energy of conduction is zero. This is one of the most important phenomena to be studied further. Also, it is noteworthy that the change in average copper valence brings not only the change in carrier concentration but also the change in mobility, which would be closely connected with the change in electronic structure. In order to get information on the relation between mobility and lattice parameter, the lattice parameters of DBCO were determined. Figure 14 gives

6 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1 I I,, I I3.89 -

-11.8

3.88-

_ 3.0704 3;

b)/2 -11.7*$

' 3.86-

3.85 -

3.84 -

-11.6 1.8

Fig. 14. Relation valence.

I I I 1 2.0 1.9 2.1 2.2 Average Copper Valence between

lattice parameters

155

the result. The mean lattice parameter, (a+b)/2, slightly decreases with increasing average copper valence, and reaches a constant value at around 6=0.2. The decrease in (a + b) /2 means the decrease in the average Cu-0 distance in the Cu ( 2)-O2 plane. The decrease in average Cu-0 distance would increase the mobility of carriers. The decrease in mobility with decreasing average valence in a region where the average copper valence is small would be due to the decrease in oxygen concentration in the Cu (I)-0 plane, since oxygen bridges two adjacent copper ions.

4. Summary ( 1) The &logP(O,) plots at various temperatures form a single smooth curve called the master curve by shifting the plots in the direction of the abscissa by a distance characteristic of temperature. A proposed model based on chemical equilibria among electronic defects, ionic defects and oxygen interpreted the master curve well. (2) It was found that the log o-logP(0,) curve has a minimum in a high-temperature and low-oxygenpressure region. The Arrhenius plot for o&in was straight, and the activation energy determined from the slope of the plot agreed well with the band gap for the undoped Cu( 2 )-0, plane. (3) From the oxygen nonstoichiometry and hightemperature conductivity, the conductivity cr was plotted against excess copper valence AZ. All the data points fell on a single curve and the ~-AZ relation _ was found to be temperature independent. (4) From the chemical equilibrium calculation on defects and oxygen partial pressure, the concentration of CL&, ions was obtained. The mobility was calculated from the conductivity by assuming that Cu,, ions are charge carriers. It was found that the mobility increases with the increase in average copper valence. The dependence of mobility on average copper valence was interpreted on the basis of the concentration change of oxygen which bridges adjacent copper ions in the Cu(I)-0 plane.

2.3

Acknowledgements

and average copper

This work has been partly supported

by a Grant-

H. Ishizuka et al. / Oxygen nonstoichiometry of DyBa2Cu307_6

156

in-Aid of Scientific Research on Chemistry of New Superconductors from the Ministry of Education, Science and Culture of Japan. The authors wish to acknowledge K. Akasaka, T. Ito and I. Ohyagi for their experimental assistance.

References [ I] R.S. Kwok, SW. Cheong, J.D. Thompson, 12

]3

]4 ]5

]6 17

2. Fisk, J.L. Smith and J.O. Willis, Physica C 152 (1988) 240. M. Kogachi, S. Nakanishi, K. Nakahigashi, H. Sasakura, S. Minamigawa, N. Fukuoka and A. Yanase, Jpn. J. Appl. Phys. 28 (1989) L609. F. Munakata, K. Shinohara, H. Kanesaka, N. Hirosaki, A. Okada and M. Yamanaka, Jpn. J. Appl. Phys. 26 (1987) L1292. B. Fisher, E. Polturak, G. Koren, A. Kessel, R. Fisher and L. Harel, Solid State Commun. 64 (1987) 87. H.C. Yang, M.H. Hsieh, H.H. Sung, C.H. Chen, H.E. Homg, Y.S. Kan, H.C. Chen and J.C. Jao, Phys. Rev. B 39 (1989) 9203. D.S. Patil, J. Karthikeyan, N. Venkatramani and V.K. Rohatgi, J. Mat. Sci. Lett. 8 (1989) 1199. G. Chiodelli, G. Campari-Vigano and G. Flor, 2. Naturforsch. Teil A 44 (1989) 1167.

[ 81 G.S. Grader, P.K. Gallagher and E.M. Gyorgy, Appl. Phys. Lctt.51 (1987) 1115. [ 91 P.P. Freitas and T.S. Plaskett, Phys. Rev. B 37 (1988) 3657. [lo] G.S. Grader, P.K. Gallagher and A.T. Fiory, Phys. Rev. B 38 (1988) 844. [ 111 Y. Idemoto, S. Fujiwara and K. Fueki, Physica C 176 ( 199 1) 325. [ 121 R.J. Cava, B. Batlogg, C.H. Chen, E.A. Rietman, S.M. Zahurak and D. Werder, Phys. Rev. B 36 ( 1987) 5719. [ I3 ] J.D. Jorgensen, H. Shaked, D.G. Hinks, B. Dabrowski, B.W. Veal, A.P. Paulikas, L.J. Nowicki, G.W. Crabtree, W.K. Kwok, L.H. Nunez and H. Claus, Physica C 153- 155 ( 1988) 381. [ 141 S. Yamaguchi, K. Terabe, A. Imai and Y. Iguchi, Jpn. J. Appl. Phys. 27 ( 1988) L220. [ 151 Y. Nakazawa and M. Ishikawa, Physica C 158 ( 1989) 38 1. [ 161 K. Kishio, J. Shimoyama, T. Hasegawa, K. Kitazawa and K. Fueki, Jpn. J. Appl. Phys. 26 (1987) L1228. [ 171 P. Strobel, J.J. Capponi, M. Marezio and P. Monod, Solid State Commun. 64 ( 1987) 5 13. [ 181 S. Yamaguchi, K. Terabe, A. Saito, S. Yahagi and Y. Iguchi, Jpn. J. Appl. Phys. 27 (1988) L179. [ 191 R. Liang and T. Nakamura, Jpn. J. Appl. Phys. 27 ( 1988) L1277. [20] I.D. Brown, J. Solid State Chem. 82 (1989) 122. [21] J. Humlicek, M. Garriga and M. Cardona, Solid State Commun. 67 (1988) 589. [ 221 H. Yasuoka, H. Mazaki, T. Terashima and Y. Bando, Physica C 175 (1991) 192.