PHYSICAL REVIEW B VOLUME 39, NUMBER 7

Correlation between electronegativity and superconductivity

1 MARCH 1989

R. Asokamani and R. Manjula*Department of Physics, College of Engineering, Anna University, Madras 600 025, India

(Received 6 September 1988)This paper brings out one of the striking features exhibited by all oxide superconductors. It is

found that irrespective of the value of T the average eiectronegativity g of all the oxide super-conductors found up until now lies between 2.5 and 2.65 in the Pauling s scale and this is con-sidered to be one of the criteria for oxide materials to be considered superconductors. This nar-row range is in contrast to the elemental superconductors whose values lie in a broad range from1.3 to 1.9. Further, the pressures required to drive some of the elemental metals to become su-perconductors have been calculated on the basis of their electronegativity values. The pressuresso obtained agree well with the experimental observations and those calculated on the basis ofband theory. The average electronegativity of A15 and Chevrel-phase superconductors are alsogiven. Based on the concept of electronegativity the other oxide systems which are likely to be-come superconductors have been suggested.

I. INTRODUCTION

With the advent of high-T, superconductors the questfor speculating a criterion for materials to have high tran-sition temperature has increased. It is seen that by cas-cading more numbers of Cu-0 layers T, has increased inthe recently discovered high-T, compounds. ' In this pa-per we put forward one of the criteria that should besatisfied by all oxide compounds to be superconductors.We have worked out the average electronegativity g of a

- number of oxide superconductors and we observe that allof them have electronegativity values falling in a very nar-row range of 2.5 to 2.65 whereas the electronegativity ofelemental superconductors lies in a rather broad rangevarying from 1.3 to 1.9. It is well known that a numberof elements become superconductors by the application ofhigh pressure. This phenomenon of pressure-induced su-perconductors in metals such as Li, Y, Ba, and Lu hasbeen successfully explained by us on the basis of band-structure calculation with McMillan's formula.

Apart from metals, nonmetals such as Si, P, and S alsobecome superconductors under pressure. Pressure-induced superconductivity in Si has been explained by uson the basis of band-structure results. We now approachthe same problem from the point of view of electronega-tivity. For elemental superconductors we can say thatelectronegativity values are centered around 1.6+ 0.3. Asfar as elemental solids are concerned, the question that weraise is the following: What pressures are required tomake Ba and S become superconductors? Ba and S have0.93 and 2.2 as their respective electronegativity values.From the point of view of electronegativity the abovequestion can be recast as follows: What pressure does Baneed to increase its g value from 0.93 to approximately 1.6and what pressure is to be applied for S to push down its gvalue again in the vicinity of 1.6, from 2.2. The latterquestion carries more significance as it refers to the caseof transformation of the nonmetal into metal and, hence,to a superconductor under pressure. This is analogous toLa2Cu04 and YBa2Cu065. These are magnetic insula-

tors which upon doping are made to become metallic andsuperconducting because of the increase in chemical pres-sure.

This paper is divided into three sections. Section Adeals with the electronegativity of metals and the methodof calculating the pressures required to drive the nonsu-perconducting metals to become superconductors. In Sec.B, we discuss the average electronegativity of all oxide su-perconductors and the variation of the average g value asa function of oxygen concentration in 1:2:3systems. Sec-tion C is devoted to the discussion of average g value pos-sessed by all kinds of compounds of perovskite structuresas well as some of the Chevrel-phase systems. Last, theunique range of g values possessed by superconducting ox-ides leads us to suggest the possible compositions whichwill become superconductors either under application ofexternal pressure or by increasing chemical pressure bymaking substitutions in the matrix. All the calculationsthat have been done here are based on the Pauling's scale.The electronegativity values of the elements used in thispaper are taken from the recent work of Luo and Wang.

II. AVERAGE ELECTRONEGATIVITIES

A. Electronegativity and superconductivity in elements

Pauling introduced the concept of electronegativity bywhich he qualitatively described the transition from ionicto covalent bond. He observed that the electronegativityof metallic elements is less than 2 and that of nonmetallicelements greater than 2. This value of 2 in the electrone-gativity scale distinguishes metals from nonmetals. Luoand Wang have made a detailed study of electronegativi-ty of all elements and found that all superconducting ele-ments are concentrated in a region where g varies from1.3 to 1.9. They observed that both very high and verylow values of electronegativity do not favor superconduc-tivity and all elemental superconductors have their elec-tronegativity values falling in the above range. On this

39 4217 1989 The American Physical Society

4218 R. ASOKAMANI AND R. MANJULA

TABLE I. Variation of g with pressure.

Pressure

(kbar)

Element: Ba0

1020304050

V/ Vo

1

0.9080.8650.7880.7440.707

(Z,g)ez=r

0.9301.0241.0751.1801.3151.345

Element: Y0

1020304050

1

0.9860.9500.9300.9130.866

1.2001.2171.2631.2901.3141.385

basis, they defined this range as the criterion for supercon-ductivity in elemental solids.

It is well known that metals such as Li, Y, Ba, and Ludo not exhibit superconductivity at ambient pressure andthey start superconducting when they are subjected tohigh pressures. This phenomenon which we have ex-plained on the basis of band structure calculations for theabove-mentioned metals is now being approachedfrom the point of view of electronegativity. The elementalmetals such as Ba, Li, Y, and Lu have their electronega-tivity values less than 1.3. For instance the value of g forBa is 0.93. In order to determine the pressure required tomake the material become a superconductor, we calculatethe pressure required to push the value of g in the range1.3-1.9, the range exhibited by elemental superconduc-tors.

g as a function of pressure has been calculated usingGordy's definition of electronegativity, ' g =Z,ae/r whereZ, tr is the unscreened nuclear charge and r is the covalentradius. The variation of r with pressure is found by pro-portionately decreasing the atomic radius from the known

values of change in cell volume as a function of pressure.The changes in cell volumes adopted here have been al-ready used in the band-structure calculations. It is in-teresting to observe that at 40 kbar, the g value of Baenters into the range 1.3-1.9. This is in good agreementwith the experimental observation as well as our theoreti-cal calculations based on band structure approach. Simi-lar calculations that were done for the elements Y, Lu,and Li have been given in Table I. The calculated pres-sures for all the above metals at which g goes above 1.3are in good agreement with the experimental observationsand the theoretical band-structure predictions.

B. Electronegativity of oxide superconductors

We have determined the average electronegativity ofthe different oxide superconductors starting withBaQ ~SrQ9Ti03 which has a T, of 1 K to T128a2Ca2Cu30]Qwhose T, is about 125 K. The striking feature that we ob-served was that the average electronegativity lies in a verynarrow range, from 2.50 to 2.65. Even the newly foundsystem which does not have copper in its composition, viz. ,BaQ6KQ4Bi03, which has a T, of 30 K has a g value of2.63. The average g values were calculated for as many as40 different compositions of 1:2:3system and it was foundthat for all of them g is centered around 2.6. The most re-cently found high-T, compounds (see Refs. 35 and 36 andtheir T, values given in Table II) further strengthens ourcriterion. These values are given in Table II along withother systems.

According to Sanderson, "when two or more atoms ini-tially different in electronegativity combine chemicallythey become adjusted to an equal intermediate electro-negativity in the compound. Further, in the recent workof Villars and Phillips' on high-temperature supercon-ductors, they combine two elements which are chemicallycloser and call it a pseudoelement and proceed to showthat all superconductors with T, & 10 K lie in threegroups in their quantum structural diagrams. Here wecalculate the average electronegativity g of the system forvarious superconductors using the expression

Element: Lu0

10203040

103157191230

1

0.9760.9550.9380.9220.8430.7790.7470.720

1.1001.1271.1521.1731.1931.4201.5401.6061.670

where 1V; is the number of atoms of a particular specieshaving electronegativity g;.

From the above studies, we propose that one of the cri-teria for oxide materials to be superconductors is thattheir average g value should be in the range 2.5-2.65. Butthe converse is not true. This is borne out from the factthat the perovskite compound La(Mgp 5Nbp5)03 has a gvalue of 2.63 and it is not superconducting.

Element: Li0

247

Element: Sc0

170

1

0.520

1

0.765

0.9601.850

1.3001.690

C. Electronegativity of Chevrel phase and other systems

In Table II we have also listed the average g values ofconventional superconductors, Chevrel phase compounds,and those of nonsuperconducting oxides of perovskitestructure. Figure 1 shows the plot of electronegativity

39 CORRELATION BETWEEN ELECTRONEGATIVITY AND. . . 4219

of

Composition T, (K.) Reference

TABLE II. Electronegativity and transition temperaturevarious compositions.

150

D Nonoxlde superconductors0 Oxide superconductors

125g Nonsuperconducting oxides

LuRhB4Mo3A12CMo2BCSc5Rh4Si~pY50s46e~pYbRh (.4Sn4. 6ZrRuPNBPSLaRu4P

~q

Cui. sMo6S6Mo6S6I2Pbp 9Mo6S7.5

Conventional nonoxide1 1.710.07.08.58.78.6

13.012.57.2

10.814.015.2

superconductors1.851.771.971.691.7161.651.832. 132.052. 132.012. 16

131415161718192021222324

50

CPo

NdRh4B4SmRh4B4

Antiferromagnetic superconductors5.36 1.872.72 1.87

2525

1.5

aoo D0oge-

2.0 2.5Average eLectronegativity &

NdMo6S8ErMo6Ses

Chevrel phase superconductors3.3 2.156.0 1.77

2525

FIG. 1. Plot of average electronegativity vs transition temper-ature for nonoxide, oxide superconductors, and nonsupercon-ducting oxides of perovskite structure.

ErRh4B4Reentrant superconductors

8.7 1.87

Hop 5Eup 5Mo6S8

Oxide superconductors1.0 2.551.0 2.60

1.0 2.6310-12 2.6110-12 2.6010-12 2.5913.2 2.6113.7 2.6230 2.6340 2.6483 2.5385 2.6490 2.5790 2.58

118 2.52125 2.5068 2.5157-81 2.60

NboTiOBap. t Srp.9Ti03Lii. )Tii 904L&).2Ti i.804L&~ 3Til.704BaPbp 8Bip 203LiTi204Bap 6Kp 4Bi03I a~,8Srp qCu04T12Ba2Cu06Bi2Sr2CaCu30)pBi2Sr2CaCu208YBa2Cu307T12Ba2CaCu208T12Ba2Ca2Cu30~pPb2Sr2 Yp.5Cap. 5Cu308RBa2Cu408

Ferromagnetic superconductors2.0 2.14

26

27

2814141429303132

1

33333433333536

versus T, of all materials and it is clearly seen that oxidesuperconductors cluster in a narrow region, irrespective ofthe value of T,. We observe that the conventional nonox-ides have g values well below that of oxide systems, whichwe have discussed so far. Chevrel phase compounds aswell as other compounds have low g values. On the otherhand, the nonsuperconducting oxides of perovskite struc-ture are found to have g values above those of the oxidesuperconductors, which are of present interest.

Encouraged by the results we have presented in Sec. Awith regard to elemental substances, we speculate thatmaterials like LaTi03, LaVO3, and La(MgosNbo5)03,which have g in the vicinity of the upper bound of the ox-ide systems, would become superconductors either by ap-plying external pressure or by proper substitution bydiff'erent atoms. Our expectation is in analogy with thenonmetal such as S which is made to become a supercon-ductor under pressure where its g value should be broughtdown below 1.9 from its actual value of 2.6.

Further, from the point of view of electronegativity, wesuggest some of the oxide materials which are similar toT12Ba2CaCu208 as the probable candidates for supercon-ductivity. Their average electronegativity values lie well

NonsuperconductingLa (Cop 5Irp 5)03La(Mgp5Nbp 5)03La(Mnp 5Irp, 5)03La(Mnp 5Rup 5)03La(Nip, 5Rup 5)03La(Nip, 5Tip 5)03LaTi03LaV03

oxides (perovskite~ ~ ~ 2.72~ ~ ~ 2.64~ ~ ~ 2.81~ ~ ~ 2.80

~ ~ 2.74~ ~ 2.73~ ~ 2.70~ ~ 2.70

structure)2828282828282828

Composition

Pb2Ba2CaCu208T12SrpCaCu208T12Sr3Cup08Pb2Sr3Cu208Pb2Ca3Cu208

2.5372.5312.5292.5432.547

TABLE III. Compositions similar to T12Ba2CaCu208 whichare probable candidates for superconductivity.

4220 R. ASOKAMANI AND R. MANJULA 39

within the range of the known oxide superconductorswhich we have discussed so far. These are listed in TableIII.

III. RESULTS AND DISCUSSMN

Using the idea of electronegativity we have been able toexplain successfully the pressure-induced superconductivi-ty in elemental metals. We hope that it is also possible toexplain pressure-induced superconductivity in nonmetalsusing the same reasoning. But in the case of a nonmetalsuch as Si the bonds will be broken at high pressures andthe electrons will be delocalized which will drasticallyaffect the value of Z,g that has been used in the expres-sion for g.

Studies on oxide superconductors make us to claim thatone of the criteria for an oxide material to be a supercon-ductor is that its average electronegativity should be in therange 2.5-2.65. The converse is not necessarily true. Wehave cited the case of La(Mgo5Nbo5)03. Further, itshould be noted that all lanthanide elements have thesame electronegativity so substitution of' Y by alllanthanide elements will give the same g value in the caseof YBa2Cu307. So problems arising with regard toachieving high T, with Ce or Pr substitution in the placeof Y cannot be explained by this simple approach. Simi-larly, this analysis which uses the concept of electronega-tivity which is purely of chemical origin will not be able todifferentiate between La2Cu04 and La2Ni04 even thoughthe latter exhibits magnetic excitations. This is due to thesimple fact that Cu and Ni possess the same electronega-tivity value.

We would like to add that the range that we haveprescribed for the average electronegativity for oxide su-perconductors will not be altered much because of the factthat Cu and 0 exist in different oxidation states. It isknown that the value of g for Cu'+ and Cu + are 1.9 and2.0, respectively. The variations with respect to oxygen'soxidation state are also small and since we are determin-ing the average value of g in a system of 13 atoms theseeffects will hardly affect our conclusion. A similar ex-planation holds good when Ba and/or Sr substitution ismade in the case of La compounds and also for oxygenconcentration variation in 1:2:3systems. Since we are cal-culating only the average g values, the above effects pro-

duce very little change in g. The average g values for pureLa2Cu04 and for the composition La~ 8Sr02Cu04 are2.657 and 2.648, respectively. Similarly, the values ofaverage electronegativity are 2.58, 2.54, and 2.50 for 07,065, and 06, respectively, in the case of YBa2Cu307 p.Normally, one would expect an abrupt change in the elec-tronegativity value since dramatic changes in the proper-ties occur for 065. However, it is obvious that from thenature of our calculations these effects cannot be broughtabout. Based on our work we have also suggested thecompositions which could be probable superconductors.

The underlying physics behind the range of electrone-gativity possessed by oxide superconductors is not difficultto understand. It has been stated earlier that g =2 can beapproximately taken as the demarcation point that divideselements into metals and nonmetals. The fact that thevalue of oxide superconductors is centered around 2.6 in-dicates that they are poor'metals and it is well known thatpoor metals are good superconductors. If this argumentcould be pushed further then flourinated compoundsshould be expected to be good superconductors as Aourineis a superhalogen having an electronegativity of 3,9 incontrast to oxygen which has a value of 3.5. Anotherpoint to be noted is that the constancy of g for all oxides,whether it is NbO or TlpBa2Ca2Cu30~0, can be taken tobe an indication that superconductivity in all materialsmay be only of electronic origin. The former compoundconsists of lighter Nb ions whereas the latter ones haveheavier ionic masses and it seems as if the lattice vibra-tions are unimportant.

ACKNOWLEDGMENTS

One of the authors (R.A.) is thankful to Professor N.Kumar, Professor K. S. Singwi, and Dr. C. M. Varma forthe valuable discussions. He also thanks Professor S. K.Joshi and Professor G. V. Subba Rao for their encourage-ment. Useful suggestions given by Dr. M. A. Subramani-an, Dr. R. Suryanarayanan, and Dr. Shaukat Ali are ac-knowledged. He would also like to express his gratitude toProfessor Abdus Salam for hospitality at InternationalCentre for Theoretical Physics, Trieste, Italy, where partof the work was done. The authors acknowledge withthanks, the financial assistance given by the UniversityGrants Commision, New Delhi, India.

Present address: Physics Department, West Virginia Universi-ty, Morgantown, WV 26506.

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