Optical transitions, XPS, electronic states in NiPS3

Chemical Physics 65 (1982) 289-304 North-HoUand Publishing Company

OPTKAL

7iXANSmONS,

M.‘PIACENTINI*,

XPS, AND EEECTRQNK

F.S. KHUMALO,

Ames Lobora?o~4JSDOE**

C.G.

OLSON,

end Iowa Srate Lhinicersiry, Arm,

J.W.

STATES IN NiPSs ANDEREGG

and D.W.

LYNCH

lawn, 50011, USA

Received 6 July 1!381

We have measured the optical absorptionbelowthe fundamentalthreshold,the normal-incidence reflectivity between 1.5 and 30 eV and the X-ray photoemissionspectra of Nip&. Shake-upsatellitespresentat the Ni 2p and 3p core levels are strong evidence for the ionicity of the M-S bonds. We have also derived a qitalitative molecular orbital model of 5IiP.S~ in which the trigonal crystal field splits the P and S 3p,p,-3p, states, and strong covalent hybridization between P and S plpY orbitak leads to covalent electronic bonding. Vi is envisaged as a divatent ion which plap little role in the electronic bonding and its 3d levels are localized, lying near the top of the valence states. This model accounts well for both the valence band XpS data and the low energy optical transitions. Our model should represent, at the center of the BriUouin zone but not at the boundaries, the energy level sequence in NiPSj and other related M?Xs layer-type compounds where IM--CO~~. MI?, Fe”, Zn*- acd X is sulfur or selenium.

1. Inr_roducrion NiPSj is a prototype member of a family of layer compounds with the general formula IMPX~, where X is either S or Se, and M is a divalent metai, e.g., Co, Mn, Fe, Ni, or Zn. These compounds, synthesized only recently [141, are especially interesting in that both molecules and atoms intercalate easily [5-S]. Straight-chain amine and pyridine molecules have been intercalated into MPX3 layer systems and Li intercalates (for example in Nil?&) to a level much higher than it reaches in TiS2, thus making these MPX3 layer-type compounds promising candidates for cathodes in batteries based on Li” transport. The theoretical ener,7 density of Li’ intercalated NiPSj has been reported (81 to be twice that of the oftenNazionaiedelle Ricerche; (GNSM). Permanentaddress: Gruppo PULS, Laboratori NazionaliINFN. 00044 Frascati, Italy.

* On leave fmm Consiglio

** Operated

for the US Department

of Energy

by Iowa

O&e

Science, WPAS-KC-

UniversiWunder contract No. W-7405Eng-82. This research was supportedby the Director for-Energy State

Research, 02-02-02.

of Basic Energy

0301-0104/82/0000-0000/$02.75

studied Li, TiSr battery. Some electronic and magnetic properties of these compounds have been studied [5,9, lo]. Their band structures, upon which al1 the electronic properties depend, are sti!l un_known, except for a schematic density of states proposed for interpreting high energy reflectivity measurements [ll]. The crystal structures of these compounds have been extensively studied both before [l-4], and after [S], intercalation. Taylor et al. [4] performed crystal structure determinations on severa samples of Nip!& (among other chalcogenophosphidesj reaf?irming the monoclinic unit cell (previously reported by Klingen et al. Cl, 21) space group C2/m, and determining more accurate lattice parameters, uo = 5.811 A, b. = 10.076 A, co = 6.628 A, and p = 106S4 A. The crystal structure of the Ml%& compounds is related to that of TiS2, with the M’+ ions and phosphorus-phosphorus pairs, P7, occupying the Ti sites, and the sulfur atoms in corresponding positions in the two structures, as shown in figs. 1 and 2. In Nip.& this resuits in N& and P& trigonaliy distorted octahedral groups. The P-P bond direction is colinear with the octahedral threefold axis and is parallel to

@ 1982 North-Holland

the hexagonal axis of one of the layers of NiPS;. There are two M atoms for each I?* soup,

hence the formula M&P~)~,~XZ.

There

is a van der Waals gap between the [S Ni2,;(P2)1,zS] slabs as shown irk fig. 1. The

63 P 0

Ni

0/.\s I‘__’ 3

Fig. 2. Position of the atoms in NPS, zs projected on the basal plane. The monoclinic a and b axes are shown, as well as the trigonal F~ and rz axes considered in the single-layer approximaticn. The Ni atoms are located in the z = 0 plane; the phosphorous atoms occupy the _Lu& positions (see table 3). The two inequivalent positions occupied by the sulfur atoms are indicated with letters A and B respectively. The full and dashed circles indicating the sulfur atoms correspond to the *u& and -u; positions (above and below the I = 0 plane, respectively) -see table 3. We also indicate the F& cIuster considered in deriving the energy level diagram of NiP!$

alternate layers of interstices between the &fur planes are unoccupied, thus permitting intercalation by other atoms or molecules [S-8].

Fig. 1. [a) Position of the atoms in NiPS3. as viewed along the 6 axis. The monoclinic D ar.d c axes are shown. The c axis extends over two adjacent S-P-Ni-P-S layers. The letters nez~ each atom indicate the set of positions that they occupy along the b direction in the cell. These positions are: Sulfur: A: at b = 0, i, and 3; B: at b = -2, -6; and f. Nickel: C:arb=fand~;D:atb=~and~.Phosphorus:Eatb=O; F at b = i. (b) Perspective view of the structure of NIPS,. i\t the center of the figure the a ax4 is horizontal. the b axis is normal fo the p:sne of the figure and the t axis is 17” counterclockwise from vertical. The circIes represent P, Ni, and S in order of increasing size.

Studies [4,5,9] of the electric and magnetic properties of Ni& indicate that this material is antiferromagnetic and that Ni is present as highspin, divalent Ni’+ ions. Nips3 has a high electrical resistivity [S]. A few optical measurements [S, lo] on NiP& show that the optical absorption threshold is -i.6 eV. A recent vacuum ultraviolet reflectance study of NiPS3 and orher similar compoufids [ll] suggests that the Ni 3d levels do not participate in high energy optical transitions because these levels exist as discrete, localized states with little hybridization with orbitals on other atoms.

291

M. Piacentini er al. /Electronic statzx in Nip&

In order to give further insight into the electronic structure of these structurally complex compounds, we have measured X-ray induced photoemission spectra (XPS) of NiPS3 and carried out a more extensive study of its optical properties than heretofore done. Measurements of both transmission be!ow the absorption threshold energy (-1.6 eV) and reflectance above it were made, the latter to 30 eV. A Kramers-Kronig analysis of the reflectance gave the complex dielectric function and functions derived from it. Both these and the XPS can be interpreted qualitatively with a tentative model of the bonding in MPXz compounds, which is presented and discussed. Unfortunately, as in the case of other transition metal compounds, the interpretation of the valence band XPS in terms of only the density of states is hindered by the presence of shake-up satellite structures associated with the excitation of the transition metal 3d electrons [12,13]. However, the occurrence of satellites near the transition metal 2p and 3p XPS peaks can be related to the type of bonding that the transition metal atom forms with neighboring ligands [14].

2. Experimental

and results

The XPS were measured on an AEI 200B spectrometer with aii Al Ka~,a? source. The resolution at the S 2p levels was 1.2 eV full width at half maximum (fwhm). The samples were attached to the sample holder with scotch tape and cleaved in a He-filled glove box. They were then introduced directly into the spectrometer vacuum chamber without exposure to air. Weak carbon 1s and oxygen 1s peaks were present in the spectra and these rather weak peaks ori&ated primarily from p2rts of the sample holder or the scotch tape not covered by the sample, but struck by the X-rays. Only the 0 2p peak interfered with the valence band spectrum, shown in fig. 3, but it was identified easily. The weak peak at 10.2 eV binding energy was present only in those spectra showing a strong 0 1s peak. These spectra also showed a strong feature at 26.2 eV which is the

BINDING

ENERGY

(eV1

3. X-ray phoroemissionspectrumof the valence bands of NiPS,. The energies of the structures observed in the spectrum 2nd their assignments are also indicated. Fig.

0 2s peak. The 16 eV separation between the 0 2s and 2p structures is in agreement with the atomic separation [12]. Since the samples were mounted with Scotch tape, they showed some charging. We used the C 1s level as a reference (285 eV). For this reason, the binding energies of the principal core structures reported in table 1 and those given in fig. 3, have only relative significance. We found strong satellite features at the Ni 2~112, 2pj12, and 3p levels, but not at the other Ni levels, nor at the sulfur and phosphorous core 1eveIs. The optical absorption spectrum was measured in the near infrared region, at about 80 K, with 2 Cary 14R spectrophotometer. The spectrum, fig. 4, shows that the absorption threshold is about 1.6 eV for NiPS3. The normal Table 1 Binding energies (in eV) of the principal core structures observed in the NiPSa X-ray photoemission spechwm. The zero of energy has been referenced to the C is peak, taken at 285 eV. It has no absolute meaning

2s 2Pu2 2P,/z 3s 3P

P

S

Ni

190.3 132.5 133.2

227.5 164.1 163.1

873.1 855.5 113.1 68.2

4-f. Pfacenrini et al. / Ekcrronic stares in AW.Sx

Fig. 5. Reflectance spectrum of NiP$ between 0 and 30 eV, obtained by combining several spectra as explained in the text. 6

0.8

I.0 PHOTON

1.2 ENERGY

I.5

1.6

kV1

Fig. 4. A’osorption spectrum NiPS; measured at normal incidence at room temperature (broken line) and at 80 K (continuow line). The assignment of the main structures is also indicated. An estimate of -8 qn for the sample thickness is obtained indirectly from the interference fringes observed in the infrared, using the value c-f 3.03 for the refractive index. With this value for the thickness, the absorption coefficient at the maximum of the 3Tzc bared is about <.6x lO’cmat 80 K We measured the optical density of a much thinner sample ap to 1.7 eV; it showed only a steep rise up to ==2Oxlo3 cm-‘.

incidence reflectance spectrum was measured between 1.5 and 5.5 eV on freshly-cleaved basal Diane layers of single crystal NiPSj by a samplein-sample-out technique, using a Spex 1 m grating monochromator with a variety of light sources and filters to remove or reduce seccnd order scattered radiation. Between 5.5 and 30 eV, the refiectance was measured on similar samples using synchrotron radiation, the techniques having been described earlier [15]. The refiectances have more sample-to-sample differences than is usual due to the differences in the number of cleavage steps on the surfaces, which produce (uncollected) scattered radiation. In all cases the spectral features were identical, but the magnitudes of the reffectances varied. Fig. 5 shows the reflectance of Nil’!&, obtained by combining the different regions and by renormaking the high energy data to the 3.0-S-5 eV spectrum which gave the highest reflectance

measured. The true reflectance may be somewhat higher. For the reason given above, it is difficult to estimate errors. NiPSj is monoclinic. If we fix axes in the crystallographic atis system, the dielectric function tensor has four independent components. To the extent that the material properties are dominated by the near-hexagonal layers, not by the way the layers stack, the off-diagonal components of the dielectric tensor vanish and two of the diagonal components become equal. Thus the anisotropy in the basal plane probably is small. The spectrum of fig. 5 and spectra derived from it represent basal plane spectra, i.e., for Elc. The other component, Eijc, may be quite different, but it is diEcult to measure on thin-layer samples. The reflectance spectrum (including data from ref. [ll] in the 5.5-7.5 eV range) was extrapolated to lower energy by using a smooth curve terminating in an ener,T-independent reflectance in the infrared, represented by R = [(n - l)/(n I l)]’ with II the refractive index, taken as a parameter. The high energy region was extrapolated to 10 000 eV by using a power law refiectance, R OcEp3, a departure from the expectation for a free electron gas because of the core levels and Ni 3d excitations in the spectral region. A Kramer+Kronig analysis was done on the extended reflectance spectrum, resulting in the complex dielectric function E’= Ed-I-iE2 and functions derived from-it. Fig. 6

M. Piacentini et al. / Eiectronic stntes in NipS, i2

,

,

,

,

,

I,,

, .,

PHOTON

ENERGY

, , , ,

kV)

Fig. 6. Reai (dashed line), imaginary (full line) parts of the dielectric function of Nip&, as obtained by a KramersKronig analysisof the refktance. The dashed-dotted line shows the main peak of the energy loss function Im (-l/C).

shows ~1, ~2 and the electron ener,T loss function, Im (-l/Z) = Q/(E: f&z). As often happens in Kramers-Kronig analyses of the reflectance, ~a went negative in a short region below the interband absorption edge. The value of the refractive index was adjusted to minimize this effect and the final value, a = 3.03, should be accurate to within a few percent. This region of negative .s2 could not be removed completely. (The absorption band near 1 eV of fig. 4 is weak enough that it plays a negligible roie in the Kramers-Kronig analysis.)

3. Dbcussion 3.1.

XPS of core teds

in NiPS3

In table 1 we give the binding energies of the core levels observed in ihe Nil?& XPS. We did not attempt to use these binding energies for deriving information on the type of bonds that each atom forms since our energies are referred to the C 1s binding energy and are not absolute_ We. could have obtained such information from the relative energies of the core levels OF different atomic species. For instance, the Ni 2ps/2-S 2p3,~ separation is 692.4 eV in NiPSa

293

while it is 690.6 eV in the conducting compound NiS 1161. Franzen et al. [17] have found that the binding energy of the S 2pjiz line decreases from 162.35 to 160.85 eV in going from conducting to ionic transition metal sulfides. Thus, by comparing NiPSs with NiS, and assuming that in both compounds S is octahedrally coordinated around the Ni atom we can conclude that the Ni-S bonds in Nip!& are ionic, provided the variation of the Ni ~P,,~-S 2~~12 separation is atiributed mainly to the S atom*. Even if this conclusion is correct, as shown below, the analysis itself may not be. In fact, as previously stated, NiPSs is considered as formed by two distinct atomic groups, each with nearoctahedral coordination: NiS6 and P& The latter forms covalent bonds while the former seems to be ionic. Apparently, the S atoms occupy two difierent types of sites with different characters. That this is not the case appears from the fact that the XPS core lines of S are single with a fwhm given by the spectrometer resolution_ Moreover, in the actual crystal, the same S atoms are bound to both Ni and P atoms. Thus, one should take into account not only the ionic bonds with the Ni atoms but also the covalent S-P bonds in using the sulfur core .levels as reference levels. lMuch more valuable and reliable information is obtained from studying the satellite structure observed near the core level spectra. In fig. 7 we show the satellite structures found at the Ni 2~,,~, 2pj,r and 3p levels. In table 2 we report their separations from the principal line, their fwhm, and their intensities calculated as the total area under each line, relative to the principal line. From fig. 7 and table 2, we can see that the ener@s and fwhm’s of the satellite features are almost the same for the corresponding lines at the different Ni levels while their intensities are quite different. Satellites in the XPS of the cation core levels have been observed in many, but not all, transition metal compounds [12-14,19,20]. Those associated with the transition metal 2p and 3p * In genera!, the binding energies of the transition are less sensitive to the type of bonding levels. See, e.g. ref. (181.

metal than the S core

M. Piaccntini et al. / Electronic states ix Nips3

N’~P~,~

I5

IO ENERGY

5

0

kV)

Fig. 7. X-ray photoemission spectra of the satellite structures at the Ni 2p, i2r 2~~1~ and 3p core levels. Energies are Born the main peaks. which have been a!igned for com-

parison. The dashed lines show the decomposition of the XPS st,xctures (after backgrcund subtraction) into several symmetric

peaks.

levels are particularly strong. In particular, large-gap insulating Ni compounds show the satellite lines, while metallic or semimetal compounds do not. Robert 1141 has compared several transition metal compounds, where the transition metal ion is embedded in different environments, and showed that the intensity of the satellite lines that he associated with Iigandto-metal shake-up transitions, depends on the type of bonds that the transition metal forms with its neighbors. In the case of metallic comPounds or totally covalent semiconductors, the valence electrons can screen immediately the core hole created by the X-rays, and no satellites are present. In the case of completely ionic bonds, the satellites are rather weak because of the small overlap between the wavefunctions

centered on the transition metal ion and neighbor iigands. Finally, there is a range of par&y covalent bonds, for which the satellite lines are both favored and strong. Asada and Sugano [Zl, 221 proved theoretically the correctness of Robert’s conclusions [14]. In addition, Asada and Sugano showed that both the shake-up satellites and the principa! lines actually are final state multiplets that merge into broad XPS features because of the hole lifetime and the XPS instrumental resolution. Additional spreading of the multiplet structure, yielding a different intensity distribution, is caused by the itinerant character of the transition metal d electrons [22]. In view of the preceding discussion and the presence of the strong satellite lines at the Ni 2p and 3p core ievels (see fig. 7) we conclude that the Ni-S bonds in Nip& are non-directional and mostly ionic. This result is in agreement with the early crystallographic investigation of Klingen et al. [l] (see also ref. C231) who formulated this compound as Nis+(P&)‘-. Also the magnetic anal electron transport properties of NiPSs lead to the same conclusion [4,5,9]. By comparison with other Ni compounds [12,20], we interpret the Ni 2p satellites at about 5 and 10 eV as ligand-to-metal charge transfer shake-up transitions. The lowest structure at 2.2 eV may be either a final state multiplet partner of the principal one or another shake-up transition_ A similar assignment for the Ni 3p satellites may be more controversial because the stronger interaction between a 3p hole and the 3d empty levels (together with a much smaller spin-orbit splitting and a much stronger exchange) modifies drastically the shake-up and multiplet energies and intensities [20,24]. The si_mikuity between the 3p and 2p satellite patterns observed here for Nip& suggests a common origin for both. Since a shake-up transition can be visualized as the simultaneous excitation of a valence electron and the core photoemitted electron, the energies of the shake-up satellites (with respect to the main line) should correspond to the energies of valence electron transitions. However, the presence of the core hole on the transition

M. Piacentini et al. / Elecrronic states Lr NiPS,

295

Table 2 Satellite structures zssocisted with the Ni 2p,,.,, 2p 3,~ and 3p X-ray photoemission lines of NiPS3. & is the separation from the main line, r the full wid:h a: haif maximum, and I the relative intensity. The last cnlumn gives the energies (referred to the Ni 3d e, structure)

and the widths of-the valence band structures 2Pw

A Main line A B C

I-

I

A 0 2.3 5.0 10.4

0

2.0

1

2.2 4.4 10.3

2.2 3.0 4.4

0.13 0.75 0.58

are in good

agreenent

I

A

1.8

1

0

1.6 2.2 2.6

0.04 0.25 0.1

2.0 4.9 11.4

l-

with the corres-

ponding prominent absorption features [20]. Sources other than charge transfer transitions have been suggested too. In the case of NiPSs, it may be more than coincidence that the energies of the satellites labelled A and C in table 2 are in agreement with the energies of the two prominent reflectivity peaks at 2.0 and 10.5 eV.

(See fig. 5.) 3.2. Energy level scheme For deriving the energy level scheme of NiPS;, we used the single-layer (or twodimensional) approximation instead of considering the full crystal symmetry - monociinic with four molecules per unit cell [l-4]. It is known from studies performed on other layer com-

pounds that the single-layer approximation accounts well for the general properties of the band structure and the electronic properties of

be interpreted

as satellires

Valence bands

3P

hi2

metal atom (ion) modifies the final states localized around it so that the correspondence with the absorption structures is not straightforward [13,25]. It has been shown by calculation that the core hole potential may decrease the charge transfer satellite transition by l-2 eV with respect to the optical transition. However, the Co 2p satellites in Co0 have an energy of 6.3 eV [13] compared with the 0 2p+Co 3d transition of 5.6 eV [26]. In NiCh the first Ni 2p satellite occurs at 5.5 eV [12], while the first strong optical charge transfer structure is at 4.5 eV. Cases are known also where the satellite energies

that ould

I

A

2.2

1

0

I.2

2.0 2.6 3.0

0.2 1 0.22 0.06

5.1 11.4

1.4

l-

I-

the compound [28,29]. Taking into account the interaction between adjacent iayers (threedimensional case) obviously implies a finite, even if small, extension of the Brillouin zone along kz and the dispersion of the bands for . K, Z 0. Significant modifications to the general structure of the bands take place at, and around, particular points of the Brillouin zone, in particular at F, the center of the zone. Such modifications (which we have ignored) are responsible only for a few details of the electronic properties of the compound. In the single-layer approximation, the crystal symmetry of NiPSs is approximated by the space group Did (#12/m) with two molecules per unit cell, as shown in fig. 2. In table 3 we give the trigonai crystal axes, their relation with respect to the monoclinic axes, and the position of the atoms in the unit cell. The following discussion of the energy Ievels will be limited to the center of the Brillouin zone where the full symmetry of the crystal point group occurs. Earlier we mentioned that Ni probably occurs as the Nizi ion in Nip& -i.e., Ni has lost its 4s’ electrons and its 3d states are discrete and localized. Thus, the valence band density of states is dominated by the P and S 3s and 3p levels, on which we will now concentrate. We note that all the S atoms in the unit ceil are equivalent, through a crystal lattice translation, to the S atoms surrounding the P-P pair at the origin (cf. fig. 2) so that at F the S and P atomic orbitals inside the unit cell combine to form molecular-like orbitals as in the trigonal P&,

M. Piacenrini er al. / ElecrroGc

296

slates in Nips3

Tabk 3 Cryxtzi parameters of XiP& for the ;‘ull crystal symmetry (monoclinic-left side) and fcr the single layer approximation used.in this paper to give the energy level sequence (trigonal- right side). Tke cqstailographic axis and the positions of the atoms are ~hoan in fig. 1 and 2. The Iengths of the axis are in A. The monoclinicn and b axes lie in the q~Ca1 basal plaoa. The coorctinntrsof the trigonal axes rIr TV. and : are referred to the monocliaic axes. The positions of the atoms in the monoclinic ccl1 xe given in standard crystallographicnotation, 2nd with their actual positions in tie crystal units of the monoclinicaxes on rhs left and of the trigonal axes on the right. Note that the S atoms actually occupy two inequivalent lattice positions. being closer to the P sites than to the Ni sites. Since the difierence is very small, we have averaged it to obtain the trigond

coordination. 0: and Q; in tha bottom linr are the true V&ES of the transformedu1, ~11site positior,sand are given for comparison

with the valurs used

Xonoclinic (ZC/m)

Single layer (P512/m)

a b e B 5.Sll IO.@76 6.628 106.94 lb! = Z!a/ cos 30’

,,=E(l, LO) C2=f(l, -1.0) = = cc-cos(p)/a.

PJi

(u,. 0, -_,). (Si ItP, ;, -_,I (0,. 0, --z&A (&UP, $, -z&J

2e

v-4 0, I;, (O,O, -2;)

Xi Jq

10.4.0). !k -t, 01 (0. -LO), cf. - ;. 0) (.u,.O, --_,A ($+u*,o, -I,! (-II:, 0. z,), (1-u,. 0. I,)

2c

(f, f, 0) (3:.5.0) tf, f, -2,) (--i> -4, z,)

(ii I,,. -:, z2) (k, b, =?I* (_Ci>. -;, -zz). ct- uz, -;, -;z) ($--rc-, :, z2) (1% i. --A (&&, -f. -z-j (-_(I:. B. - 2,:.

61i

rr, = 0.057, I(! = 0.249, u2 = 0.248 :,=0.171,~*=0.247,~~=0.248

z; = 0.171, u; = 0.332, u; = 0.165 ZI = 0.235

S, Ji Sz 8j

cluster. In table 4 we give the irreducible representations according to which the atomic orbitals transform and the corresponding linear combinations that are basis functions. In fig. S we show schematically the energy level diagram for NiPSj and how it is related to the atomic levels. On the left of fig. 8 we show the P states and on the right the S ones. At the far edges of the figure the a;omic levels are shown with their energies [30]. The strongly asymmetric crystal field along z splits the 3p levels of both P and S into pxpY orbitals, lying at lower energies, and p_ orbitals, lying at higher energies. We compare the present P& cluster with the structurally similar G&S6 cluster that can be recognized in the layer compound Gas. In GaS the S prpr states lie at lower energies than the pz states, while the opposite occurs for the Ga p levels [31]. This different behavior between rhe Ga and the P pxpy-px splitting

6k

li-,[--[+2/=/aj=5.83.& 0. 1) !=I= c sin j3 = 6.34 A

(4,0. z3 (-$,0.&I (0.L :J (0, -4, -=,)

stems from the fact that Ga in GaS behaves like a cation, while P in NiPSj behaves like an anion. The second column in fig. S shows the pxpy-p_ splitting and also a shift to lower energies of the P 3s states. This latter shift has been introduced empirically to account for the valence band XPS. It will be discussed in the next section. In the third column we show further splitting due to the clustering of the atoms. If we neglect the interaction between states localized around S atoms lying on the two opposite faces of the single-layer, crystal orbitals that are even and odd with respect to

inversion will be degenerate in energy. However, the P states localized on the two atoms forming the P-P pair interact rather strongly with each other and the above simplification is not possible. A similar situation was found in the case of GaS [31]. Beginning from the most bound states, the S 3s states gen-

hf. Piacemini er al. [ Eiecffonic sraies in NiP&

297

Table 4 Irreducible representations of tie DJd point group according to which the atomic levels forming the valence bands of NiP& transform (second and first column, respectively). The third_ column gives the basis functions. The fourth column shows very schematically the ckargti distribution of the configurations of the S 3p,p, states. Tke S and P atoms are considered as forming a P&s cluster. The drawing In the lower right corner represents the P&, cluster with tke two P atoms on the threefold axis (perpendicular to the page). In the drawing we have indicated also the “local” reference systetrs chosen at each S atom; the z a& is parallel to the threefold axis; the x and y axes lie in.a plane perpendicular to the threefold axis. with the x axis pointing outwards along the direction connecting, the.P-P axis with the S atom. The symbols of the third column have the following meaning: s, corresponds to the 3s wavefunction centered around atom I of the figure. The other symbols have equivalent meaning. x1, yl. zE stand for pn py. p=. The upper and lower signs in column three correspond to the even (g) and odd (u) representations, respectively, given in the second columns Atomic Ievels

Irreducible representations

Basis functions

Charge distributions

s 3s

S 3P,

S 3PY

SJP:

P 3s

AI,, AI,

P 3PX 3P,

Es, E,

P 3p,

+- o+f29 + ++ + A + A *+ At+--

O-

l

Ni 4s

crate two even-odd pairs of levels. The lowest in energy is the At,LAz, pair, corresponding to the fully symmetric configuration of the S 2s levels centered on the three atoms lying in the same plane, i.e. it is a bonding state. This pair is followed by the E,-E, pair, corresponding to an antibonding combination in the plane. Since the S 3s levels are already rather deep, we do not expect a significant splitting between the AI,AzU-EpEX states. A calculation of the GaS band structure [31] showed that the density of the S 3s states peaks approximately at the same energy as the atomic levelin an. absolute energy scale. For this reason we did not shift the group of S Js-levels in going toward the center column

of fig. 8. The next group of states are formed mostly from the P 3s states, which do split into a bonding Ar, and an antibonding Ai, level. It is much more diflicult to assess the correct sequence for the S and P 3p states for the strong hybridization between each other. From the S 3p,p, states WC expect the following sequence for increasing energy: AQ,~,, (symmetric combination of x orbitals), E,,, (antisymmetric combination of y orbitals), E,., (antisymmetric combination of x orbitals), kze.lu (symmetric combination of y orbitals). The P 3p,p, states transform as E, (bonding) and E, (antibonding) representations. Since they are almost degenerate in energy with the S 3p IeveIs, there

29s

M. Piacenrini et al. / Eiecnoitic siaies in MPS3

4

will be a strong mixing of the S and P 3p,p,. orbitals in all the E,, E, levels that will no longer be degenerate in energy. As mentioned earlier, the p-_ states of both P and S are pushed upwards. A large splitting of the P p_ Ai,, Ai, bonding-antibonding states is expected, for they strongly interact with each other, owing to the directionality of the p- orbitals. A similar situation occurs for the Ga pz levels in GaS and is responsibIe for its fundamental energy gap C311. In the central part of fig. 8 the expected sequence of the IeveIs is indicated. The splittings indicated are not calculated, but only pic-

torial. In addition to the P and S levels, in the center of fig. 8 we have introduced the Ni 3d levels. Since the Ni 3d states are localized and the interaction with states centered on neighbor Ni atoms can be neglected, we have represented them using the traditional tzE-e, nomenclature that holds for d states in an octahedral field [32]. The tzg is further split into ek, aem states by the actual trigonal field. As we shall see in section 3.3, this splitting is very small (~0.2 eV) and we neglect it here. We now proceed to fill the energy level scheme of fig. 8 with electrons for a doubled formula unit NizP&. We do not consider the 16 Ni 3d, the 4 P 3s and the 12 S 3s electrons which are placed easily. We are left with the 6 P 3p, the 24 S 3p, and *be 4 Ni 3s electrons, totalling 34 electrons. The group of S-P prpv bonds shown in fig. 8 can accommodate 2 x 16 electrons, so that the two remaining electrons fill the Al, bonding P p= state. It is clear from this electron counting that the Ni 4s electrons are transferred to the P-S pXpY hybrids. It is likely that most of this extra charge is located around the P atoms, filling their pXpY states. Before concluding this section, it is worthwhile to note that in several cases the assignment of the various states to orbitals centered around the different atoms may not be as clear-cut as we have suggested. For example, we expect some hybridization to occur between the A1,(S 3s) and AI&P 3s) states. The most important is the possible hybridization between the P 3s and P 3p, levels, both generating the same representations. In particular, by comparison with GaS [31], we expect that this interaction affects mostly the Al, antibonding levels, increasing the P 3s A,,-AI, splitting. All these effects could not be taken into account at this rather qualitative level of discussion of the energy levels. They require detaiied calculations_ 3.3.

XPS of the mlence

bands

The valence band XPS of NiPSs is shown in fig. 3. In order to interpret it, we use the energy level diagram-derived in the previous section,

AI_ Piacenhi e; ni. / Electronic states in NipS,

shown in fig. 8. Before making any assignments, some general comments are appropriate. The scheme of fig. 8 is valid oniy at the.center of the two-dimensional Brihouin zone. By moving away.from it, the bands will show dispersion and the most significant structures in the density of states are likely to occur near the zone boundaries rather than near the center. In addition, when the zone boundary is approached, the mixing of the wavefunctions changes and different hybrids form, in particular between p= and pJpY states C311. A serious difficulty has been encountered before in interpreting the valence band WS of other transition metal compounds that show strong satellites at the transition metal p levels [12,19]. In fact, satellites associated with the delectron excitation have been recognized also in the valence band region and they overlap true density of states features 112, 19,331. We expect the same to occur for NiPS3 and we shah suggest more than one assignment for some structures. Let us begin with the Ni 3d levels. The emission of one electron from the transition metal d-states leaves the metal ion in a multiplet of states. In the case of Ni in an octahedral coordination, only three Ieve!s of the 3d7 findstate configuration can be reached from the ground state: ‘Tr,, *Tr, (corresponding to the t&e: configuration) and ‘Ep (t&e, configuration). In the case of several Ni compounds the 4Tr, and ‘Eg levels are almost degenerate in energy [12, 13,341, and the observed splitting of the d peak corresponds to the actual crystalfield splitting of the tZg and e, states. We associate the two structures in fig. 3 at 2.9 and 3.6 eV with the e, and tzs levels, respectiveIy. Their splitting is very ciose to that found in NiC12, NiO, and other insulating Ni compounds, suggesting that the crystai field acting on the Mi d levels is almost the same in all these materials. For the sake of completeness, we note that the XPS technique does not offer enough resolution to see the 0.2 eV a\T+k splitting of the tzp. level in the actual trigonal field of NIP&. Finally, we wznt to comment on the difference between Nip&, NiS [16], and NiSz [35].

299

Assuming for simplicity that in all these compounds the sulfur atoms are octahedrafly coordinated around the Ni atom, in NiS and NiS2 the Ni-S distance is much shorter than in Nip&. Accordingly, the tz,-e, splitting is larger and the Ni 3d e, level is more hybridized with the S 3p molecular orbital e6 [35]. For this reason, NiS and NiSr have covalent Ni-S bonds [35] and lack the shake-up satellites at the Ni core p levels [16], unlike NiPS3. The two features at 8.0 and 15.0 eV (the latter is asymmetric towards lower energies, as if there were an unresolved structure at about 14.3 eV) are separated from the 3d es peak at 2.9 eV by the same amount as the shake-up sateilites are from the Ni p levels (see table 2). Such a.coincidence suggests associating these features with the shake-up satellites of the Ni 3d peak. However, we shall discuss, and probably favor, an alternative interpretation in terms of density of states peaks originating from the P and S 3s and 3p levels. Beginning from the most bound valence states, we associate the 15.0 eV broad peak (in fig. 3) with the S 3s bands. In most sulfur compounds the S 3s states generate a broad peak (=3 eV fwhm) ==13-14 eV below the Fermi energy [16,35]. This occurs also in several transition metat sulfur compounds that do not have core satellite structures, like NiS [16]. The width of the S 3s peak is, in part, the result of band effects that may contribute with l-l.5 eV width, 2s shown, e.g. in GaS [36]. The remaining part of the width is probably due to lifetime. Around 12.5 eV, a second, very weak broad peak is barely discernable in fig. 3. We attribute it to the P 3s states. The separation of 2.5 eV between the P 3s and S 3s bands is smaller than the atomic separation of 3.7 eV [30]. This is consistent with the results of section 3.2, where we showed that the P2S6 clusters pick up the four Ni 4s electrons and that most of this extra charge is located on the P atoms. Thus, the localized levels of phosphorous are pushed to lower energies by the Madelung energy more than those of sulfur. The next group of structures has to be reiated with the S and P 3p,p, states. As we have seen

300

in section 3.2 there is a large number of such levels, some of which contain hybridized orbitals between ? and S and also with p-_ states, especially near the zone boundary. As a rule of thumb, we expect at least two major density of states features, the first arising from states that are wel! localized in the sulfur’s piane and that can be considered as forming the S pxpr bands. The second feature is formed by those states contributing to the S-P bands, having a mixed plpY and pL character. By inspecting fig. 8 we find the latter to lie at lower energies. We associate the XPS structures at 4.9 eV and S eV with these two expected density of states features. The separation of 10.1 eV between the strongest S 3p structure and the S 3s peak is in good agreement with other S compounds [35], and in perfect agreement with GaS [36], where the main XPS peak arises from the S pip,. bands. Also in GaS a second structure at highest binding energies is present that corresponds to a region of high density of states of a split pIpv-pZ band far from the center of the Brillouin zone [36]. Finally, referring to fig. 8, we are unable to identify the A,, bonding P p_ band in our XPS, probably because it gives a weak density of states in the region of the strong Ni 3d peaks. We have compared our proposed energy level scheme and our XPS of the valence bands of Nip& with the density of states calculated by Bullet [37] for FePS3, another MP& compound with properties very similar to those of Nip&. We took into account the different transition metal ions by shifting the caiculated d band peaks to lov;er energies with respect to all the other structures in order to have the Fermi energy at the e6 peak. The ag.reement is very good. In paticuIar, the calculation reflecs the hybridization of the P and S p+pr levels with the consequent two strong density of states peaks at approximately the experimental energies, supporting our assignment of the 4.9 and 8 eV XPS structures. The calculation seems to overestimate the interaction between the localized P and S 3s states, since they seem to be repelling each other in opposite directions with respect to the experimental structures.

3.4.

Opficai spectra

The absorption spectrum measured at room temperature (RT) and at about 80 K between 0.6 and 1.6 eV, shown in fig. 4, consists of a weak absorption peak foliowed by the absorption threshold at 21.6 eV. Our RT spectrum is in good agreement with the absorption measured by Brec et al. [5, lo]. At 80 K we resolved the peak into two structures, a weaker one at 0.92 eV and the stronger at 1.08 eV; a shouider appeared at 1.5 eV on the steep absorption rise. By comparison with other Ni compounds (in particular NiClz and NiBrz), we assign these features to Ni d+d transitions. The small value of the absorption coefficient (=23 x lo3 cm-’ at the stronger peak) is characteristic of electric dipole parity forbidden transitions that become allowed in a higher degree of approximation (magnetic dipole or crystal field effects). The broad peak centered at about 1.0 eV originates from the ‘Ala(t&ei)+ ‘TZg(t&ez) transition between the Ni d levels split by the octahedral field [32]. Its energy corresponds approximately to the trp-e, splitting and is in good agreement with the value of 0.7 eV obtained from the XPS measurement*. The further splitting of the tzg level into a\:, ei- in the trigonal field gives rise to the observed doublet at 0.92-1.08 eV that is assigned to the trigonal final states 3A\:‘, ‘Ehm [38,39]. The shoulder at 1.5 eV corresponds to the 3T1, level of the final state configuration t&e: [32]. It is worth noting that the energies of both the 3Tzs and ‘T1, transitions and the splitting of the ‘T1, state are very close to those measured in the Ni ha!ides [38,39], indicating that the (octahedral+ trigonal) crystal field acting on the Ni ion in NiPS3 is almost the same 2s in the other insulating compounds_ We already arrived at similar conclusions in our analysis of the valence band XPS. This shows that the conclusions drawn from the two types of spectra are mutually consistent. * This statementis not totally correct, since both initial and fin21 states actually are configurationalmultiplets. .

M Piacentini et al. / Elecrronic stats

The refiectivity spectrum of NiiSs between 1 and 30 eV is shown in iig. 5. In fig. 9 we expand the energy scale between 1 and 5.5 eV-in order to show clearly aII the fine structure. In fig. 6 we report the spectra of Ed, ~2 and -1m (l/E). Ail the reflectivity structures are reproduced in ~2 at slightly different energies and with different relative intensities. The interpretation of all the features is almost impossible at the present level of understanding because of the lack of a good calculation, including both the ener,T bands and the excited states of Nip&. As in other insulating transition metal compounds, three main types of transitions may occur [401: (i) promotion transitions from the localized Ni 3d states to conductb; baad states, (ii; charge transfer transitions from the S-P p valence bands to the empty Ni 3d es and 4s states, and (iii) interband transitions from the valence to the conduction bands. We have excluded the _Ni d-d transitions since, because of their very weak oscillator strength, they cannot give significant structure above the absorption threshold. Similarly, we expect the same for the promotion transitions since the oscillator strength for exciting localized d electrons is very small near tliieshold. In support of this statement we note that the spectrum of .iien, the elective number of electrons per molecule contributing to ~2, shown in fig. 10, reaches 25.5 at 30 eV, as if the eight Ni 3d electrons have not yet been excited at 30 eV. The first strong structure in both the Ed (E) and R(E) spectra is the narrow peak at 2.2 eV, accompanied by two shoulders at 2.0 and

;--*t

‘d

in A?&

301

2.5 eV, respectively (cf. fig. 9). We associate this group of structures with charge transfer transitions from the S.3p,p, bands to the Ni 3d eg empty states in analogy with the other insulating transition metal compounds. In NiCL and NiBrz the first prominent charge transfer transition is spiit into two or more components, separated by 0.4-0.6 eV [27,40,41]. In Nip& the charge transfer transition occurs at lower energies than in NiO [26] or Ni halides [27,40,41] because the S 3p,p, valence states lie closer to the Ni 3d leveis than the oxygen or halogen p bands do [12,33,34]. This behavior may be related to the larger Madelung potential acting on the more negatively charged ligands in NiC1, and NiO than in NiPS+ In support of the present assignment we note that the separation of the Ni 3d eg structure and the S 3pxpY structure is 1.5 eV, as obtained from the XPS. Considering that the energies of the XPS features are difficult to determine accurately, since they appear as shoulders, the agreement between the XPS energy separation and the optical charge transfer tiansition is satisfactory. Above 3 eV several features appear in the E2 spectrum. In the case of the other transition. metaf compounds with a degenerate p-like band at I’, seven lines of the type p”(halogen)j” + p5(halogen)dNi’ are allowed and they show up as a sequence of structures of decreasing intensity spread over several eV above the first peak [27]. In the present case the S-P p bands

1

30

4

I

I

1

2

2’

o.eo

,., 1

I

2

’

!

3 PHOTON

5 ENERGY

5

0

6

,ev,

Fig. 9. Reflectance (foil Iine) and s2 (broken line) spectra of NiPSj in the low energy region l-5.5 eV.

0

5

I?

8

2H5TCX

16 EPiEiiGY

20

zi

28

kV)

Fig. 10. Spectrum of the effective number of electrons per molecule participating in optical transitions below energy Ao.

are already split and each of them can give rise of transitions for which peaks between 3.0 and 7.0 eV could be a result. As an alternative (or complementary) interpretation, we think that the struciures bayond 3 eV correspond mostly to peaks of the joint density of states. Khumalo and Hughes [ll] found that the reflectivity of MnPS3, FePS;, and NiPSs are rather identical between 5 and 12 eV, implying that high energy excitations in these materials occur between valence and conduction band states derived from the P& groups (which are common to all the MPS3 compounds) with very little contribution from the transition metal ion. AI1 the narrow peaks in the ez spectrum seem to group in several broad bands centered at 3.7, 6.0, 9.0, 12.5, and 18 eV, respectively*. We suggest that each broad band corresponds to transitions starting in a deeper group of valence bands. Their separations should correspond to the separation of the valence band density of states peaks obtained from XPS. By assigning the second band at 6 eV to the excitation of the S 3p,p, states, we find a separation of 3.0, 6.5, and 12 eV for the lowest S-P p=p,. bands, the P 3s bands and the S 3s bands, respectively. XPS yields 3.2, 7.7, and 10.2 eV, are in fairly good agreement. A discrepancy can be expected from several sources. First, the optical transitions probe the joint density of states between valence and conduction bands, second, the lowest conduction bands are likely to have strong s character from the empty Ni 4s states, hybridizing with P and S, s and pZ states, and from empty S 4s states that we did not consider?. Transitions to all these bands are

to a multiplicity

* l-he structores

at 12 and 1S e\’ zre very weak and difficult to see in the P= spectrum, but they are clearly visible in the spectrum of E’p,. which is proportional KOthe joint densky of states if electric dip& ma:rix elements are assumed constant. f The S 4s band does not appear in the tight binding calculation of ref. [31], but its presence is shown by sevcwl experimental results, as well as by pseudoporcnria1 band calculations. See ref. [42] for a detaiLed discussion. in addition,it has been si:ownthat the AI, antibonding p_ Ga band. the lowest conduction band, conrains very little Ga Ip, admixtture.

allowed from the S-P prpY states but not from the deepest s bands. For this reason the separation between the S pxpY and S-P prpY bands agrees well, while the S 3s band gives structure in the Ed spectrum at higher energy than in XPS. The first group of features around 3.7 eV can be attributed to the excitation of the Ai, bonding P pZ band. We can locate it about 2.3 eV above the S pxpv states, in correspondence with the Ni 3d ez state (see fig_ 8). Our analysis of the structures above 3 eV is supported by the spectrum of N+e (fig. 10); which, along its steady rise, shows some small changes in shape corresponding to the energies of the broad bands, as if it were inflecting towards saturation after each band. Finally, the value of 25.5 electrons/molecule reached by Nd at 30 eV corresponds well to the number of valence electrons/molecule available in NE& (excluding the Ni 3d electrons). En spite of the good agreement, we think that a small fraction of these electrons does come from the Ni 3d electrons. The strong, sharp peak at 7.3 eV in fig. 5 needs more comment. Upon cooling to 85 K it becomes even sharper (about 0.5 eV wide) [ll]. Such behavior is reminiscent of localized excitations. It might be a charge transfer transition from the lowest group of S-P p,
;I% Piacentirri et al. / Ekctronic states in NiPS;

divergent structure is generated from a twodimensional MI critical point. Also MnP& and FePS, show the same dominating sharp peak at a5out the same energy as Nip!!& fll], suggesting that such a peak arises from the P-S states rather than involving transition metal d states. The spectrum of N,, (fig. 10) shows that the 7.3 eV peak contributes several electrons (more than 4) to the total number of electrons per molecule, in support of our assignment of a very high joint density of states peak. 3.5.

303

-4cknowledgement We wish to thank A.H. Thompson of Exxon Research Laboratories for supplying several crystals of Nip!&, H.F. Franzen for useful conversations, and D.W. Bullett for allowing us access to figures of his unpublished calculated partial densities of states for FeP$. We also wish to thank R.C. Burns and S. Critchlow for their help in producing the perspective drawing of the crystal in fig. 1. The storage ring is operated under NSF cantract DMR 8020164.

i%e loss function

The loss function, Im (-l/E), fig. 6, shows one large, rather broad peak. The large height of this peak is unusual, considering its breadthFor a free electron gas, the height and width of the peak in this function are proportional to .G1 and E;I, respectively, both evaluated at the plasma frequency. In Nip& the peak occurs at 21.0 eV, while that for a free electron gas of the same electron density as that in Nip& is 19.27 eV (for 25 electrons/molecule), the diEerence arising in part from interband transitions at lower energy. One expects the electron gas in layered compounds such as NiPSs to be nearly two dimensional, but at an energy above most of the interband transitions the electrons do not fee1 the lattice potential very strongly and the anisotropy is much diminished. 4. summary The XPS spectra and optical properties of NlPSs have been obtdned and interpreted on a qualitative molecular orbital model in which the Ni is a divalent positive ion which plays !ittle role in the bonding. Evidence for such ionicity appears in the optical properties and XPS satellite structures, as well as in the magnetic properties. The mode1 shouId represent qualitatively the band structure at the center of the Brillouin zone, but not at the boundaries. It should also be valid for other compounds similar to NiPSj, i.e., those with other metals in place of Ni and those with Se in piace of S.

References [l] W. Klingen, G. Eulenberger and H. Hahn, Natunviss. 55 (1968) 229. [2] W. K1‘m g en, G. Eulrnherger and H. Hahn, Naturwiss. 57 (1970) 88. [3] 2. Nitsche and P. Wild, Mat. Res. Buil. 5 (1970) 419. [4] B.E. Taylor, 3. Steger and A. WoId, J. Solid State Chem. 7 (1973) 461. [5] R. Brec, D.M. Schleich, G. Ouvrard, A. Louisy and J. Rouxel, Inorg. Chem. 18 (1979) 1814. [6] S. Yamanaka. H. Kabayashi and M. Zanaky, Chem. Letters Japan (1976) 324. [7] F. Kanamam, S. Otani and IU. Kuizumi, Extended Abstracts, 5th International Conference on Solid Compounds of Transition Elements. Uppsala (1976) p. 36. [8] A.H. Thompson and M.S. Whittingham, Mat. Res. Boll. 12 (1977) 741. [9] C. Berthier, Y. Chabre and M. Minier, Solid State Commun. 28 (1978) 327. [lo] R. Brec, D. Schleich, A. Louisy and J. Rouxel, Ann. Chim. Fr. 3 (19%) 347. [ll] F.S. Khuma!o and H.P. Hqhes, Phys. Rev. B 23 (1981) 5375. [12] S. l-i-fner and G.K. Wertheimer. Phys. Rev. B 8 (1973) 4857. [13] KS. Kim, Phys. Rev. B 11 (1975) 2177. [14] T. Robert, Chem. Phys. 8 (1975) 123. [IS] C.G. Olsonand D.W. Lynch, Phys.Rev. B 9 (1974) 31.59. [16] J. Gopalakrishnan, T. Mumgesan. M.S. Hegde and C.N.R. Rao, J. Phys. C 12 (1979) 5255. [17] H.F. Franzea, IM.X. Umaiia, I.R. McCreary and R.J. Thorn, J. Solid State Chem. 18 (1976) 363. [18] H.F. Franzen and G.A. Sawatzky, J. Solid State Chem. 1s (1975) 229. [lY] K.S. Kim, J. Electron Spectry. Relat. Phenom. 3 (1974) 217. [ZO] M. Scrocco. J. Electron Spectry. Re!at. Phenom. 19 (1980) 311.

M Piacentini S. _&ada and S. Sugano,

er CL / Elecnonic

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129.

S. Asada and S. Sugano. I. Phys. C 11 (1975) 3911. F. Jellinek, MIT Inr. Rev. Sci. Inorg. Chem. Ser. 1, 5 (1972) 339. S. _Asada, C. Satoko and S. Sugano, J. Phys. SGC. Japan 37 (1975) 885. J.A. Tosse!, J. E!ectron Specv. Relat. Phenom. 10 (1977) 169. R.J. Powell znd ‘W.E. Spicer, Php. Rev. B 2 (1970) 2182. G. Guizetti, L. Nosenzo and I. Polliai, 5th Intemational Conference on Vacuum Ultraviolet Radiation Physics, Vol. 11. eds. M.C. Castex, M. Pouey and N. Pouey (CNRS. Meudon. 1977) p. 79. A. Balzarotti, R. Girlandz, V. Grasso. E. Doni, F. Antonangeli. M. Piacentini and A. Baldareschi, Solid State Commun. 2-l (1977) 327. C-797 A. Balzamtti, R. Girlanda, V. Grasso, E. Doni, F. Antonangeli and M. Piacentini, Can. J. Phys. 56 (1978) 700. [30] F. Herman and S. Skillman, Atomic structure caiculations (Prentice-Hail, Englewood Cliffs, 1963). [31] E. Doni. R. Girlanda. V. Gra.ssc. A. aalzarotti and M. Piacentini, Nuovo Cimento 5lB (1979) 154.

safes ir: Nip&

[332] S. Su,g~o, Y. Tanabe and H. Kamimua. Multipleo of transition metal ions in crystals (.+ademic Press. New York, 1970). [33] DE. Eastman and J.L. Freeouf, Phyis. Rev. Letters 34 (1975) 395. [34] Y. Sakisaka, T. Ishii and T. Sagawa, I. Phys. Sot. Japan 36 (1954) 1372. [35] E.K. Li, K-H. Johnson, D.E. Eastman andJ.L. Freeauf, Phys. Rev. Letters 32 (1979) 470. [36] F. Antonangeli. M. Piacentini, A. Balzarom‘, V. Grasso, R. Girlanda, and E. Doni, Nuovo Cimento 51B (1979) 18. [37] D.W. Bullett, prhie communication. r381 _ _ M. Kozielski, I. PoIlini and G. Spinolo. J. Phys. C 5 (1972) 1253. [39] J. Pollini. G. Spinolo and G. Benedek, P&s. Rev. B 22 (1950) 6369. [40] G. Guizetti, L. Nosenzo, I. Pollini. E. Regunoni, G. Samo&a 2nd G. Spinolo. Php. Rev. B 14 0976) 4622. [41] Y. Sakisaka, T. I&ii and T. Sagawa, J. Phys. Sot. Japan 36 (1974) 1365. [42] M. Piacenrini, C.G. Olson, A. Balzarotti, R. Girlanda, V. Grass0 and E. Doni. Nuovo Cimento 5JB (1979) 24s.