Mineral. Soc. Amer. Spec. Pap. 3, 145-153 (1970).

PHYSICAL PROPERTIES OF SULFIDE MATERIALS

STANLEY J. PICKART

U. S. Naval Ordnance Laboratory, White Oak, Silver Spring, Maryland 20910

ABSTRACT

A review is given of basic physical properties of sulfides in order to clarify for mineralogists the interest solid-statephysicists have in these materials. After a brief description of the localized and itinerant approaches to the behavior ofelectrons in solids, some examples of the magnetic and electric properties are detailed, particularly those studied by meansof neutron scattering. Particular topics include the magnetic structures (and their relation to exchange interactions) in thepolymorphic forms of MnS, chalcopyrite, the Eu chalcogenides and Li-substituted MnSe; and the semiconducting, photo-conductive and ferroelectric behavior of the IV-VI compounds, especially the Pb salts. In all these cases an attempt ismade to show how these compounds are interesting in their own right, in providing clear examples of fundamental phe-nomena, and how they show promise of future technological applications.

The title of this review promises a great deal more thanit can deliver. To describe adequately all of the physicalproperties of sulfide materials would be impossible in avolume, let alone an article of this length. Therefore it isfirst necessary to establish clearly the purposes I have inmind and, guided by these, to set out the limitations to thetopic.

SCOPE AND PURPOSE OF THE ARTICLE

Sulfides in the last decade or so have been the subjectof quite intensive research in solid-state physics, primarilybecause they exhibit very clearly many types of basicphenomena, and are thus generators of new theories andproving grounds for existing ones. Since most sulfidesexist as or have prototypes in minerals, the needs for inter-disciplinary communication between physicists and min-eralogists are clear. Beyond the simple transferral of in-formation, interesting as this may be, new motivation maychannel research into mutually profitable directions, thusstrengthening both fields.

Two broad areas have comprised most of the researchon sulfides, magnetic properties and electrical properties,and I intend to cover these more thoroughly, with briefmention of other areas that are not yet fully exploited. Toavoid being encyclopedic in such an effort, the approachwill be to describe qualitatively such general concepts aswill be necessary, and then to list several specific examplesthat illustrate the general phenomena in a particularlystriking way.

Of course, subjective bias is impossible to avoid in theselection of such examples, and mine as an experimentalphysicist working on neutron scattering from magneticmaterials will be apparent. Although many interestingsubjects will thus be omitted, I hope to leave the readerwith some feeling for the genesis of the interest physicistshave in studying sulfides, and some appreciation of thewealth of physical phenomena that are found in this class ofmaterials.

BASIC CONCEPTS IN THE DESCRIPTION OF

ELECTRONS IN SOLIDS

A convenient basis on which to classify the phenomenaunder discussion is the description of electrons in solids-

that is, the types of wave functions 1f;(X,t) whose squaredamplitude is the probability density of finding the electronat position X at time t. There are two models for construct-ing the wave functions appropriate to atoms in the solidstate, which can be described loosely as the localized modeland the itinerant model.

These two approaches trace their ancestry directly backto the first many-body problem by solved quantum mecha-nics, the hydrogen molecule. When two H atoms arebrought together, one must decide what forces constitutethe basic situation and what forces are to be treated as aperturbation. The Heitler-London model takes the wavefunction of one electron moving about each nucleus as thestarting point, and the molecular orbital model takes thetwo electrons moving about the common center of the twonuclei. It is important to realize these are two ways oflooking at the same phenomena: they both give results inagreement for the hydrogen molecule problem and indeed,it can be shown there is a continuous transition betweenthe two as the distance of atomic separation varies. Thelocalized versus itinerant character can thus be thoughtof as a measure of "apartness" of the atoms relative to theparticular interaction they exert on each other. Applied tosolids, these two types of theories lead to descriptions ofionic and covalent bonded compounds on the one handand to the energy band theory of solids on the other.

The energy-band theory of solids starts with a firstapproximation of nearly free electrons moving in theperiodic potential of the atom cores. In order to reviewsome of the basic concepts of this theory, let me discusssome of the language, of band structurists. As the individ-ual atoms are moved together, it is found that the discreteatomic energy levels broaden into bands of allowed energy.The solution to the simplest problem, one electron peratom in a one-dimensional crystal, is shown in Figure 1.The dashed line shows the energy versus wavenumber(k =2'rr/'A.) of the free electron, the familiar parabolicenergy-momentum dependence (E= p2/2M, where p = fik);as a consequence of the periodicity of the potential, dis-continuities are introduced at wavelengths half the spacingbetween the atoms, separating the energies of the electronsinto allowed bands separated by forbidden gaps. Thisfigure also illustrates the concept of the Brillouin zone;

145

146 STANLEY J. PICKART

ENERGY

\ I~

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_L\I"-2eU K 1\-rr'

I

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/ II II II I

/ I/ I

LI III I

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akx -

FIG. 1. Energy versus wave number for an electron in a one-dimensional periodic potential. UK is the K'th Fourier componentof the periodic potential. Light dashed line: free electrons; heavydashed line: electrons in periodic potential; solid lines: removal ofcurve segments from higher zones to the reduced zone. (FromGoodenough, 1963). (Reprinted by permission of the publisher.)

the reciprocal wave-number space illustrated here is ageneralization of the reciprocal lattice familiar to crystal-lographers, and the Brillouin zone is the "unit cell" of thereciprocal lattice-a surface in wave-number space formedby planes erected halfway between each Bragg spot andits neighbor. Again because of the periodic nature of thecrystal, all the information in the problem can be con-tained on one reduced zone, thus the folding back of thesegments labelled by the band indices m =2 and m =3.

The final concept needed is the parameter relating tohow the allowed energy states are populated by the avail-able electrons. This is specified by the Fermi level, anenergy value determined by filling the band states up tothe maximum number of electrons available. In real crys-tals, far more complicated than the simple example il-lustrated here, the energies of the bands vary in three di-mensions in k-space in a way reflecting the symmetry offorces acting between neighbors; and the Fermi level willnot be a constant line, as it is here, but will form a com-plicated boundary. The shape of this boundary, called theFermi surface, is an important quantity characterizing thebehavior of the solid,

Concepts in the localized electron approach are some-what simpler since the picture is essentially one of isolatedatoms held together by ionic, covalent and repulsive forces,

whose densities overlap slightly but not enough to destroythe validity of the atomic energy levels calculated for thefree atom. One of the basic concepts here is the idea ofexchange interactions and covalent bonds. The centralconcept of the covalent bond is that a lower energy can beachieved by sharing electrons between neighboring atomsin directional, hybridized orbitals. The qualitative ideasof electron sharing have had a great influence on the physi-cal understanding of magnetic exchange. In the followingdiscussion, the reader is reminded that it is useful to try"keep track" of an individual electron although electronsare transferred between atoms.

The origin of the concept of exchange force again goesback to the hydrogen molecule problem. In the solution tothat problem a contribution to the energy arises (para-doxically, in the present context) because of the indis-tinguishability of states in which the electrons exchangedplaces. This energy contribution combined with the Pauliexclusion principle (an axiom that states the total wavefunction must be antisymmetric in the exchange of spaceand spin coordinates) makes the singlet state, with the spinsof the two electrons antiparallel, the ground state. It wasrealized by Heisenberg that this energy was identical inform to a scalar product of spin vectors, even though it iselectrical in origin; and he hypothesized that such amechanism could be responsible for ferromagnetism if thewave functions of the atom were such as to make the tripletstate with parallel spins lie lowest. This single idea hasbeen extremely fruitful in theories of magnetism, whichattempt to derive the magnetically ordered state frommicroscopic forces between atoms.

Some of the models of exchange, other than ferromagne-tic, that have evolved from this concept are illustrated inFigure 2. The first, superexchange, applies to cations withspins in d orbitals aligned by Hund's rule, separated by anintervening anion like oxygen with outer electrons in porbitals (Anderson, 1963). In the first case, the sphericallysymmetric case of 5 d electrons, one of the pair of oxygenp electrons is promoted to the d shell of the overlappingcation wave function where it must be antiparallel byHund's rule; the antiparallel coupling of the oxygen bond-ing orbitals makes the net spin of the cations antiparallel,and the excess magnetic energy gained by ordering thesespins stabilizes the postulated excited state. By similararguments, for a less than half-filled shell, superexchangepredicts ferromagnetism. Indirect exchange does not involvepromoting an oxygen electron, but rearranges the polariza-tion of the oxygen electron density to keep electrons ofparallel spin closer together-the same mechanism re-sponsible for Hund's rule; the resulting coupling is alwaysantiparallel or anti ferromagnetic. Double exchange (Zener,1951) is postulated for systems containing mixed valencestates; a simultaneous transfer of electrons from cation tooxygen and oxygen to cation gains kinetic energy by con-tributing to the conductivity. This transfer occurs only ifthe ionic spins are parallel, so ferromagnetism always re-sults. Finally, semicovalent exchange (Goodenough, 1963)

147PHYSICAL PROPERTIES OF SULFIDES

EXCITtD STATEI

SUPEREXCHANGE

WEXCITED STATE

oGROUND STATE

SLATER TYPE INOIRECT EXCHANGE

DOUBLE EXCHANGE

dZ,pl

OCTOHEORAL ORBITALS

SEMI-COVALENT EXCHANGE

dSp!SQUARE COPLANAR ORBITALS

ANTIFERROMAGNETIC FERROMAGNETIC

FIG. 2. Schematic representations of the different types of superexchange mechanisms. (From Shull andWollan, 1956). (Reprinted by permission of the publisher.)

is a refinement of superexchange that takes account ofcovalence and orbital symmetry; it can result in eitherparallel or antiparallel coupling depending on the particularcombination of the hybridized orbitals that are formed.The exchange mechanisms described here have had greatsuccess as phenomenological rules in accounting for manytypes of alignment that were actually observed (Kanamori,1959; Wollan, 1960).It is convenient, and I believe more intuitive, to discuss

the magnetic properties of sulfides on the basis of localizedconcepts and the electrical properties on the basis of bandor itinerant electron concepts. This is not to imply thateach description cannot be used to predict both sets ofproperties-indeed they have been used that way. But, asremarked earlier, each type of theory represents a differentway of looking at, or a different mix of approximations for,the extremely difficult problem of the energy states andwave functions of the 1023 atoms in a unit volume of thesolid.

THE MAGNETIC PROPERTIES OF SULFIDES

The "workhorse" theory of magnetism, the one that canexplain the properties of localized spins, is the molecularfield theory. Starting from the proportionality of thescalar product of spins with the exchange force, the theoryattempts to minimize the exchange energy of the wholemagnetic crystal through the "effective field" approach of

Weiss. The proportionality constant of this field to themagnetization is given by an appropriate sum of exchangeconstants over neighbors-usually restricted to nearestand next-nearest to render the problem tractable. One ofthe first signal successes of this theory was to explain thediffraction effects from magnetic crystals when they werestudied by the method of neutron scattering.

Since the magnetic phenomena described are weighted soheavily toward neutron diffraction, it is necessary to say afew words about the types of information obtainable bythis technique. For the present purpose, the central featureis that, in addition to the neutron-nucleus interaction thatgives rise to Bragg peaks analogous to X-ray diffraction,there exists a comparable magnetic interaction betweenthe neutron spin and atomic moment. This interaction givesrise to a magnetic component of the scattering which is theFourier transform of the magnetic moment density in thecrystal. This magnetic component is diffuse if the spins aredisoriented as in the paramagnetic phase, and its diffrac-tion symmetry tells whether the ordering scheme of thespins, called the magnetic structure, is parallel (ferromag-netism), antiparallel (antiferromagnetism), partly un-compensated (ferrimagnetism), or has some more com-plicated, noncollinear arrangement. A subsidiary feature ofthe technique is that the energy, as well as the momentum(wavelength) of the average thermal neutron in a reactormatches the elementary excitations in the solid-lattice

148 STANLEY J. PICKART

2".--;INELASTIC SCATTERINGELASTIC IBRAGGI SCATTERING

2".T + qkf - kj =,,2

liw = Tn!

FIG. 3. Reciprocal lattice representation of neutron scattering.

vibrations and their analogue, spin waves-hence theirenergy spectrum can be thus directly measured. The con-ditions for energy and momentum conservation in a simplecubic reciprocal lattice are sketched in Figure 3; the in-elastic case may be considered as a generalization of"Ewald's sphere" construction for Bragg scattering wheremomentum is delivered to the individual atoms as well asthe lattice, and the energy change is large enough to be de-tected, contrary to the case of X-rays.

The polymorphic forms of M nS and the magnetic symmetryof chalcopyrite. The three polymorphic forms of MnS allundergo magnetic ordering and the types of magneticstructures observed offer a striking example of the influenceof bonding on the super-exchange interaction. The threestructure types are rock salt, zincblende and wurtzite. EachMn2+ cation has twelve nearest Mn2+, neighbors in allthree forms, but different numbers of S2- anion neighbors

NEAREST NEIGHBOR CONFIGURATION

STRUCTURETYPE ROCK SALT ZINCBLENDE WURTZITE

~~~

~~12JANTI-PARALLEL

PARALLEL

6

6

8

4

8

4

NEXT NEAREST NEIGHBOR CONFIGURATION

ANTI-PARALLEL

PARALLEL

6

o2

4

2

4

FIG. 4. Nearest and next-nearest neighbor spin configurations inthe three polymorphic forms of MnS. Metal atoms only are shown,and open and closed circles represent up and down spins respec-tively. (From Corliss, Elliott and Hastings, 1956). (Reprinted bypermission of the publisher.)

which provide the paths for superexchange. In the rock saltform the Mn2+ is bonded to next-nearest MnH neighborsvia 1800 sulfur p-orbitals while in the other two forms thelinkage is tetrahedral to nearest neighbors.

The magnetic correlations determined by neutron dif-fraction (Corliss, Elliott and Hastings, 1956) are sum-marized in Figure 4, which shows nearest and next-nearestcation configurations for the three cases. The importantresult is that the zincblende and wurtzite forms (with similarbonding but different cation arrangement) have the samemagnetic structure, which differs from the rock salt spinstructure, where the bonding is different. These results areconsistent with the superexchange mechanism, since theantiparallel cation-anion-cation interaction couples next-nearest neighbors in the latter structure and nearest neigh-bors in the former.

The mineral chalcopyrite (CuFeS2) is closely related tothe zincblende form of MnS, the Cu and Fe systematicallyfilling the Mn sites. The magnetic structure was also found(G. Donnay, Corliss, J. Donnay, Elliott and Hastings,1958) to be closely related, in that the two iron atoms con-nected to a common sulfur atom are antiparallel. The solu-tion of this structure is noteworthy in that it represents thefirst application of black-white symmetry to magneticstructure determinations. Figure 5 shows the relations ofthe iron moments to the symmetry elements of the spacegroup I42d determined from these studies.

The europium chalcogenides A system where variation inthe exchange parameters is brought about solely by changesin cell dimensions, while the coordination polyhedra remain

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FIG. 5. Magnetic space group symmetry elements in CuFeS •.The spins are represented as current loops whose transformationproperties are specified by the indicated symmetry elements. The zcoordinates give the elevation and notation for symmetry ele-ments are as in International Tables. (From Donnay ei al., 1958).(Reprinted by permission of the publisher.)

PHYSICAL PROPERTIES OF SULFIDES

the same, is provided by the Eu chalcogenide salts EuO,EuS, EuSe and EuTe. These crystallize in the rock saltstructure with the cell edge (and thus the next-nearestneighbor distance) varying from 5.1 to 6.6 A. By means ofmagnetic susceptibility measurements, the first three werefound to be ferromagnetic, the last antiferromagnetic. Thenearest and next-nearest exchange interactions shown inFigure 6 were deduced (McGuire, Argyle, Shafer and Smart1963) from the temperature dependence of the suscepti-bility, and a molecular field analysis.

If the assumption is made that J1 is positive and J2negative, a coherent picture of the dependence of the ex-change forces on distance follows, as shown by the dashedlines; the net resultant exchange force (solid line) then pre-dicts a change form ferromagnetism to antiferromagnetism.Furthermore, this explantation predicts the EuTe will havethe next-nearest neighbor (n.n.n.) correlation as found inrock salt MnS, and this was confirmed by neutron dif-fraction measurements (Will, Pickart, N athans and Al-perin, 1963). A precarious balance between parallel andantiparallel configuration was indicated by the fact thatEuSe is a complicated antiferromagnetic in a zero externalfield but ferromagnetic when a field is applied (Pickart andAlperin, 1968).

Lithium-substituted M nSe. The rock salt phase MnSe is stillanother example of antiparallel n.n.n. correlation in itsmagnetically ordered phase. But when monovalent lithium

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LATTICE PARAMETER (AU)

FIG. 6. Nearest neighbor (J1) and next-nearest neighbor (J2)exchange interactions derived from molecular field analysis of theEu chalcogenides, (From McGuire et al., 1963).

149

is substituted for divalent manganese, the resulting mag-netic properties (Heikes, McGuire and Happel, 1961) pro-vide a striking instance of the "touchiness" of exchangeforces with respect to the various mechanisms discussedearlier. The substitution creates MnH and Mn2+ pairs sothat one might expect the double exchange mechanism tobe operative.

This is indeed found to be the case, although the re-sulting situation is more complicated than expected. Amagnetic phase diagram for compositions up to thesolubility limit of 11 atomic percent Li is reproduced inFigure 7. One finds clear -cu t evidence for ferromagnetismin the 10 percent Li sample, but it disappears about 200below the Curie transition. N eutron diffraction (Pickart,Nathans and Shirane, 1961) showed that this transitionwas to an antiferromagnetic state, and indeed, one thatdiffered from the lower concentrations by having a morenearly parallel n.n.n. configuration. Thus, although thesmall concentration of double-exchange coupled cationswas able to swing the whole system ferromagnetic, as thetemperature decreased and the mobile electrons becametrapped, antiferromagnetism took over. However, a vestigeof the ferromagnetic coupling remained behind and alteredthe scheme of the antiferromagnetic structure.

Spins as vectors: canted and spiral structures. The struc-tures so far described have been collinear, i.e. the spins canbe represented by plus and minus scalar quantities. Whathappens when an assembly of spins finds itself with com-parable nearest-neighbor forces that dictate parallel align-ment and n.n.n. forces that dictate antiparallelism? Theanswer, as already alluded to in the case of EuSe, is thatnon collinear arrangements are adopted. The first suchverified structure, in fact, was in the hexagonal NiAs phaseof CrSe. The "spin" cell is enlarged to include three Crspins in each basal plane and these adopt a "tepee" orumbrella arrangement that alternates in successive layers(Corliss, Elliott, Hastings and Sass, 1961).

Molecular field calculations, however, show that ingeneral the lowest energy state of such a system is in facta spiral arrangement (Lyons and Kaplan, 1960), of whichthe collinear and non collinear structures are special cases.If the alternation direction is considered the propagationdirection of a spiral helix, the ferromagnetic case cor-responds to a 3600 phase change or turn angle, the anti-ferromagnetic to a 1800 phase change, and so on. It is notnecessary in general for the repeat distance to correspondto the unit cell distance, although this generalization wouldseem at least superficially to hold conceptual difficulties forthe theory of space group symmetry.

Several of such spiral structures have been discovered insulfur compounds. Indeed, the iron series chalcogenidespinels exhibit simple Neel ferrimagnetism (unequal anti-parallel spins) as in FeCr2S4 (Shirane, Cox and Pickart,1964) simple ferromagnetism, as in CrCu2Se4 (Lotgering,1965) and helical antiferromagnetism in ZnCr2Se4 (Plumier,1966). A visual representation of such a spin arrangementin MnS04 is given in Figure 8. This wealth of spin arrange-

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150 STANLEY J. PICKART

• CURIE TEMPERATURE.AHTIFERRO .. A8NETIC .... __ '~ DEFINES POSSIBLE REGION

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• SPIN AXIS CHANGE i.•.ABOVE THIS TEMPERATURESPIN LIE WITHIN (III) PLANESBELOW SPIN LIE 32· OFF AXISPERPENDICULAR TO (111).

FIG. 7. The magnetic phase diagram of the LixMnl_x system.

ments is philosophically satisfying in the sense that almostevery conceivable type of ordering has now been observed.

Seeing the covalent bond. I spoke before of exchange inter-actions being propagated by the overlap of cation andanion electron densities. The question naturally rises, ifsuch polarized spin density indeed exists in ligands, is therea sensitive enough method to observe it directly? Theanswer is yes, and the method is polarized neutron scat-tering, where the neutron spin-electron spin interaction ismaximized by making it interfere constructively with thenuclear scattering. An example is provided by antiferro-magnetic CUS04. The Cu2+ ions in this orthorhombicstructure are sufficiently far apart that super exchange viatwo intervening anions is required, and evidence has beenobtained that intervening S042- groups are very slightlyspin-polarized,

n

fIIIIIII

20

IIIII

40

IIII

50

IIIIII

30

FIG. 8. A representation of the conical spiral in MnS04. Thetransverse (helical) component advances in phase 3600 in six lat-tice spacings along the a direction, (From Will et al., 1965). (Re-printed by permisson of the publisher.)

After measuring as many of the weak magnetic scatter-ing amplitudes as possible, a Fourier synthesis of themagnetization density projected onto the (100) plane,illustrated in Figure 9, was made (Menzinger, Cox, Frazerand Umbayashi, 1968). Note that while the majority of the

I

60

FIG. 9. A Fourier projection of the magnetization density inCUS04 on the (100) plane. Note the anisotropy of the densityabout the Cu positions at y(0,1/2)z(0,1/2) and the smaller pileupof density between them. Positive and negative densities are in-dicated by solid and broken lines respectively. (From Menzingeret al., 1969). (Reprinted by permission of the publisher.)

PHYSICAL PROPERTIES OF SULFIDES 151

magnetization density is localized on the Cu2+ ions (thesolid and dashed lines refer to positive and negative equi-density contours), there are significant densities observedat a projected distance of 2.5 A away, clearly too far tobelong to the Cu2+ ionic density, however, anisotropic.

ELECTRICAL PROPERTIES OF SULFIDES

Turning to a discussion of electrical properties, we findthree major areas where sulfide compounds have been atthe center of activity: semiconductors, photoconductivityand ferroelectricity.

Semiconductors. To discuss semiconducting properties, wereturn to the band theory concepts described earlier. Therewe described the Fermi energy, the level in energy-mo-mentum space up to which energy states were filled,which is well-defined at absolute zero. As the temperature israised the Fermi surface becomes fuzzy; electrons are ex-cited above this level by thermal energies of amount kTand as more and more of them receive enough energy tocross the forbidden gap from the valence band, where theyare relatively tightly bound, to the conduction band, wherethey are nearly free, the conductivity increases. This situa-tion holds in intrinsic semiconductors, which are very pure;in extrinsic semiconductors impurities create additional 10-calized states whose energy lies within the band gap andserve as traps for electrons from the valence band, causinghole conduction (p-type), and sources for electrons for theconduction band, causing electron conduction (n-type).

The tools for the investigation of the band structure andthe topology of the Fermi surface are many: transportphenomena such as resistivity and Hall effect, whichmeasure the number, sign and mobility of charge carriers;optical phenomena, including reflectance and absorptionwhich trace out the transitions near the band edges; cyclo-tron resonance and oscillations in the susceptibility andmagnetoresistance which detail the trajectories of theelectrons on the Fermi surface. These latter measurementshave become more important as high magnetic fields andvery pure samples have become available, because theydepend on the electron being able to complete several pre-cessional orbits in the field before being scattered by im-purities. The frequency of these oscillations, which occurbecause the "free" electrons are quantized according totheir orbital moment, is a measure of extremal orbitsequivalent to cross-sections of the Fermi surface.

1. Fermiology of the lead salt semiconductors. The leadsalts PbS, PbSe, PbSe and PbTe have long been a focalarea of semiconductor research because of the wide vari-ation in carrier concentration that can be obtained by con-trolling the composition and degree of stoichiometry. Trans-port and optical measurements (Scanlon, 1959; Allgaier,1958) established the band gaps and energy surfaces ofthese materials; these measurements stimulated theoreticalcalculation of the energy band structure, which in turn havebeen tested out by more sophisticated measurements de-signed to caliper the Fermi surface.

The degree of detail achieved in current calculations is

w

~ (3/2,3/2,0)

FIG. 10. Details of the calculated band structure in PbTe il-lustrating the calculated band extrema and the forbidden gap inthe [111) direction. Labels refer to the symmetry of the wavefunctions of the individual levels. (From Lin and Kleinman, 1966).(Reprinted by permission of the publisher.)

illustrated in Figure 10. This is indeed a far cry from thesimple parabolic energy bands envisaged in the nearly-freeelectron theory; still, some resemblance to the features ofFigure 1 is there. The good correlation established betweenthese energy level diagrams and the optical, transport andoscillatory measurements (Burke, Houston and Savage,1969) lend credence to the model now generally acceptedfor the lead salts, nearly parabolic extrema in [111] direc-tions of momentum space as indicated in Figure 10.

2. Band crossing in lead-tin telluride. Some interestingexperimental data have recently been obtained on thelead-tin telluride alloy system that suggests that the as-signment of valence and conduction bands is reversed fromone end of the system to the other. The evidence for thisphenomenon appears in resistivity (Dixon and Bis, 1968),and laser emission studies (Dimmock, Melngailis, andStrauss, 1966). It holds out the promise of achieving verynarrow energy gaps by controlling the composition, whichcould lead to extremely long wavelength optical detectorsand lasers.

Photoconductivity in PbS. It has long been known thatpolycrystalline PbS films, when sensitized by baking in sul-fur or oxygen, gave enhanced conductivity when illum-.ina ted by infrared light. The mechanisms for such effectswere never clear because films were not always reproducibleor uniform. Recent advances in the growth of expitaxialsingle crystal PbS films give promise of sorting out theseveral mechanisms that may be responsible for the photo-sensitivity.

One study (Riedl and Schoolar, 1968) involved scanninga microscopic light spot over the area of the films; photo-voltaic effects were observed that could be correlated withrows of defects in the films. Furthermore, the specifics of

152 STANLEY J. PICKART

,~I,

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o 0.2 0.4 0,6 0.8 1.0REDUCED WAVE VECTOR COORDINATE C 'oq/2 tt

FIG. 11. Energy versus wave number relations for the trans-verse (TO) and longitudinal optic (LO) lattice vibrational modesin SnTe as determined from neutron scattering. Note the de-crease in energy or "softening" of the TO made with decreasingtemperature. (From Pawley et al., 1966). (Reprinted by permissionof the publisher.)

the behavior of the photosignal with biasing field indicatedthatan n-p-n junction localized at the defect was responsible.Other uniform epitaxial films were grown in which at leasttwo basic mechanisms other than junctions were identified(Schoolar, 1970), characterized by differing lifetimes: onefrom oxygen-induced defect states that serve as electrontraps from which photo-exitation occurs: the other at-tributed to the intrinsic photo-conductivity due to creationof electron-hole pairs that increase the carrier concentration.These thin film studies not only explain the variety of re-sponses observed in polycrystalline films bu t give promise ofleading to reliable, reproducible photosensitive detectors.

Diatomic ferroelectrics. Ferroelectricity is the electricalanalogue of ferromagnetism in that a spontaneous polar-ization of charge occurs in a crystal at the ferroelectrictransition. There is a large body of evidence (Cochran,1959) that such transitions are occasioned by the simul-taneous, static displacement of atoms participating in atransverse optical mode of the lattice vibrational spectrum,i.e., one where atoms are vibrating 1800 out of phase andtransverse to the propagation direction of the wave. Suchbehavior can be studied by inelastic neutron scattering, foras the temperature decreases toward the transition, theenergy of this particular mode decreases (spoken of as"softening" of the mode) until the crystal becomes un-

stable against the permanent displacement of the atoms(spoken of as a "frozen" mode).

In nature most of the known ferroelectrics are compli-cated ionic structures where the ferroelectric transition canbe detected by an anomaly in the static dielectric constant.The alloys of (Sn-Ge)Te, which have high carrier concen-trations that prevent measurement of the static dielectricconstant, have recently been studied by neutron scattering(Pawley, Cochran, Cowley and Dolling, 1966); their re-sults for SnTe are shown in Figure 11. The decrease inenergy or "softening" of the TO mode with temperature isclearly seen. For this composition the energy never doesreach zero, but on the basis of these results and the knowndisplacive phase transition in the alloys related to this modethe conclusion was drawn that GeTe is the first example ofa semiconducting, diatomic ferroelectric .

UNEXPLORED PATHS AND FUTURE DIRECTIONS

Some fields of investigation that are quite powerful buthave not as yet been fully exploited in the realm of sulfidematerials are listed below. Along with continuing develop-ment of earlier described fields, they show great promise forfu ture progress.

Phase transitions. Recently a growing body of theorytreating the thermodynamic behavior of phase transitionsof many types has been accompanied by experimentalstudies, particularly by the critical scattering of neutronsassociated with these transitions. Again, such criticalscattering can be of magnetic or nuclear origin and candetail the frequency and wave number dependence of themodes involved in the transition, whether vibrational (spinwaves and lattice vibrational) or diffusive. An obvious con-nection exists between this type of microscopic informationand macroscopic phase equilibria determinations.

Atomic correlations in compound liquids and gases. Neu-tron scattering methods can also be used to obtain dif-fraction patterns from disordered systems, such as liquidsor vapors, and the data can be Fourier-inverted to yielda radial distribution or correlation function for the atomicpositions. Studies on liquid alloy systems and gases havebeen limited because of the inherent complexity, but theanalytical difficulties will no doubt be solved in future. Aninteresting application is the study of the degree of atomicsegregration on both sides of the melting point in dis associ-ative versus associative phase transitions.

Magnetic semiconductors. A relatively new area of interestmarries the two broad categories discussed earlier. As amatter of fact, most of the compounds that have beenfound to exhibit both magnetic and semiconductive be-havior are sulfide-type materials-the rare earth chalcoge-nides and the transition metal chalcogenide spinels. Awealth of new effects are being found relating to the in-fluence of spin polarization on the band energies that willno doubt result eventually in practical devices.

Lattice vibrational spectra and force constants. As in the

PHYSICAL PROPERTIES OF SULFIDES153

case of neutron scattering from liquids, this is an activefield that has not yet been extensively applied to sulfides.The lattice vibrational spectrum contains all the informa-tion necessary to specify the interatomic force constantswhich can be correlated with the hardness, melting point,coefficient of thermal expansion and other physical proper-ties.

SUMMARY

This cursory review of the wealth of physical propertiesexhibited by sulfide materials, mineral or synthetic, has,I hope, helped convey the impression that these materials

ALLGAIER,R (1958) Magnetoresistance in PbS, PbSe, and PbTeat 295°,77.4°, and 4.2°K. Phys. Rev. 112, 828-836.

ANDERSON,P. (1963) Exchange in insulators: superexchange,direct exchange, and double exchange. In Magnetism, Vol. I,Rado, G. and H. Suhl, (eds.) Academic Press, New York, 25-83.

BURKE,R, B. HOUSTON,ANDH. SAVAGE(1969) Anisotropy of theFermi surface of p-type PbTe. Phys. Rev. (in press).

COCHRAN,N. (1959) Crystal stability and the theory of ferro-electricity. Phys. Rev. Lett. 3, 412-413.

CORLISS,L., N. ELLIOTT,ANDJ. HASTINGS(1956) Magneticstructures of the polymorphic forms of manganous sulfide.Phys. Rev. 104, 924-928.

---, ---, ---, ANDR SASS(1961) Magnetic structureof chromium selenide. Phys. Rev. 122, 1402-1406.

DIMMOCK,J., 1. MELNGAILIS,ANDA. STRAUSS(1966) Band struc-ture and laser action in PbxSn'_xTe. Phys Rev. Lett. 16, 1193-1196.

DrxON, J., ANDRBIS (1968) Band inversion in the electricalproperties of PbxSn'_xTe. Phys. Rev. 176,942-949.

DONNAY,G., L. CORLISS,J. DONNAY,N. ELLIOTT,ANDJ. HAST-INGS(1958) Symmetry of magnetic structures: magnetic struc-ture of chalcopyrite. Phys. Rev. 112,1917-1923.

GOODENOUGH,J. (1963) Magnetism and the Chemical Bond. JohnWiley and Sons, Inc., New York,

Heikes, R, T. MCGUIRE,ANDR HAPPEL(1961) Role of doubleexchange in the magnetic structure of LixMn'_xSe. Phys. Rev.121, 703-707.

KANAMORI,J., (1959) Superexchange interaction and symmetryproperties of electron orbitals. J. Phys. Chem. Solids 10, 87-98.

LIN, P. ANDL. KLEINMAN(1966) Energy bands of PbTe, PbSe,and PbS. Phys. Rev. 142, 478-489.

LOTGERING,F. (1965) Ferromagnetic interactions in sulfides,selenides, and tellurides with spinel structure. Proc. Int. Conj.Magnetism, Nottingham, Inst. Phys. and Phys. Soc., (London)p. 533-537.

LYONS,D, ANDT. KAPLAN,(1960) Method for determining groundstate spin configurations. Phys. Rev. 120, 1580-1585.

have been intimately involved in the discovery and de-velopment of some of the most fundamental concepts insolid-state physics. The corollary aspect which I havecovered but briefly, because it is outside my area ofspecialization, is that in many cases these materials havegenerated important practical applications or give im-mediate promise of doing so. I hope the reader in the fieldof mineralogy will realize the important contributions hisfield has made in the study and characterization of mineralphases, for ultimately the solid-state physicist can make noprogress without prior advances in the synthesis of ma-terials.

REFERENCES

MENZINGER,F., D. Cox, B. FRAZERANDH. UMEBAYASHI(1969)Polarized neutron study of the magnetic moment density inantiferromagnetic CuSO•. Phys. Rev. 181,936-945.

MCGUIRE, T., B. ARGYLE,M. SHAFER,ANDJ. SMART(1963)Magnetic properties of some divalent europium compounds. J.Appl. Phys. 34, (Pt. II), 1345-1346.

PAWLEY,G., W. COCHRAN,R. COWLEY,ANDG. DOLLING(1966)Diatomic ferroelectrics. Phys. Rev. Lett. 17, 753-755.

PICKART,S, ANDH. ALPERIN(1968) Magnetic structure of EuSe.J. Phys. Chem. Solids 29,414-416.

---, R. NATHANS,ANDG. SmRANE(1961) Magnetic structuretransitions in LixMn'_xSe. Phys. Rev. 121, 707-714.

PLUMIER,R. (1966) Neutron diffraction study of helimagneticspinel ZnCr2Se•. J. Appl. Phys. 37, 964-965.

RIEDL, H., ANDR. SCHOOLAR(1968) Photosensitivity in epitaxialPbS films. J. Appl. Phys. 39,5086-5092.

SCANLON,W. (1959) Recent advances in the optical and electronicproperties of PbS, PbSe, and PbTe, and their alloys. J. Phys.Chem. Solids 8, 423-428.

SCHOOLAR,R. (1970) Epitaxial PbS photovoltaic cells and photo-conductive films. Appl. Phys. Lett. (in press).

SHIRANE,G., D. Cox ANDS. PICKART(1964) Magnetic structuresof FeCr2S. and FeCr20 •. J. Appl. Phys. 35, (Pt. II), 954-955.

SHULL,C., ANDE. WOLLAN(1956) Applications of neutron diffrac-tion to solid state problems. In Seitz, F. and D. Turnbull, (eds.)Advances in Solid State Physics, Vol. II, Academic Press, NewYork.

WILL, G., FRAZER,B., G. SHIRANE,D. Cox ANDP. BROWN(1965)Magnetic structure of MnSO., Phys. Rev. 140, A2139-A2342.

---, S. PICKART,H. ALPERIN,ANDR NATHANS(1963) Anti-ferromagnetic structure of EuTe. J. Phys. Chem. Solids 24,1679-1681.

WOLLAN,E. (1960) Magnetic coupling in crystalline compounds.Phys. Rev. 117, 387-401.

ZENER,C. (1951) Interaction between the d shells in the transi-tion metals. Phys. Rev. 81, 440-444.