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Silver atom center in α-quartz
SILVER ATOM CENTER IN a-QUARTZ P. H. DAVISand J. A. WHLt Department
of Chemistry and Chemical Engineering, University of Saskatchewan, S7N OWO Canada
Saskatoon, Saskatchewan,
(Received 27 September B77; accepted 14 November B77) Abstract-A new paramagnetic center, A&a, in silver-diffused aquartz is descni and its spin-Hamiltonian parameters are presented. The center is formulated as a silver atom (S = l/2) situated in a c-axis channel, bonded weakly to a normal silicon cation, with four oxygen anions as neighbors. A,+s is created by X-irradiation and is unstable at room temperature.
INTRODUCTlOh’ In a recent paper[ 11, a stable (300°K) paramagnetic center, Ati4,, consisting of a neutral silver atom associated with a germanium 4+ ion substituted at a silicon site in a-quartz (Fig. 1) was discussed. In this center the silver atom is thought to reside at a site in the large c-axis channels present in a-quartz, adjacent to the germanium ion and surrounded by 4 oxygen anions forming a distorted tetrahedral cage. In the present ivork we discuss an analogous center, A-,, in which the silver atom is found adjacent to a normal silicon site. This new center is unstable at room temperature. Electron paramagnetic resonance (EPR) measurements on Aand A-. reveal appreciable spin density at the silicon and germanium nuclei respectively and thus one can speak of the formation of a chemical bond between Ag and Si and between Ag and Ge, respectively. This is in contrast to the situation observed in the structurally similarAH (this latter symbol will be used herein for the atomic hydrogen species described in Ref.[21) in which no large “Si hyper6ne splitting has been observed. By way of further contrast, in the 1.
case of the centers AO+U and Ao+N,[~], the unpaired electron is much more localized on the germanium. No paramagnetic centers with neutral hydrogen adjacent to a substitutional germanium or with sodium or lithium cations adjacent to a normal silicon site have thus far been reported. 2. -AL.
Samples used in this study consisted of single crystals of a-quartz (natural rose quartz and synthetic germanium-doped quartz) cut either in the form of orthorhombic plates or right circular cylinders with the longest dimension of the plate or the axis of the cylinder parallel to one (=a,) of the three symmetry-equivalent crystallographic two-fold axes. We introduced silver into the crystals by chemo-plating metallic silver onto the surface of the crystal normal to the c-axis, followed by electrodifTusion. The Brashear process[4] was used for plating most samples; however, a micro-technique involving in-situ reduction of aqueous Ag(N&k+ ion by acetaldehyde vapor was developed for the preparation of the sample containing isotopically enriched silver (98.2% ““Ag) used for the collection of the rotational data. The electro-diffusions were carried out at co. 650°K with an applied field cn. lo’V/cm for several hours. We terminated the diffusion when the initial current of lo20 pA had stabilized at l-2 PA. The paramagnetic A-i center was created by Xirradiation at 77°K using a Machlett AEG-SOS tube with T tungsten target and beryllium window (SOmA, 50 kV, 1 hr). The crystal was located co. 2.5 cm from the window of the X-ray tube and was rotated during irradiation to produce more uniform exposure. The sample was transferred without warm-up to the cavity of a Displex EPR system[5] and all EPR measurements made at ca. 20°K. The EPR spectrometer Fig. I. SiO, tetrahedron in right-handed (P3~21) aquartz. Symbols o and @ locate possible inequivalent sites for an interwas a Varian V4500-10, with Mark II Fieldial, :: !nc stitial in the middle of the large c-axis channels at the inter100kHz field modulation. The Zeeman field .‘cs section of a three-fold smw c and the two-fold (D,) symmetry measured with a Perkin-Elmer M2 NMR gaussmeter and axis the f denote the sign of tbt charge developed on the the microwave frequency monitored with a Hewletttwo-fold axis when the crystal is compressed in this die&n. Results herein have been expressed in Cartesian coordinates Packard 5245L frequency counter used in conjunction (xI,x2. x3) in a right-handed coordinate system delined by the unit with a Hewlett-Packard 5257A transfer oscillator. The vectors i, j and t. I and k lie along crystallographic axes a, and c natural constant B/v, = 2.348740x lo-‘T-Hz-‘(61 was respectively with positive values of x, associated with the end of used in the magnetic field calculations. We estimate the a, developing a negative (-) charge on compression. experimental uncertainty in the determination of .line tAuthor for correspondence. positions to be about 0.002 mT. A correction was applied
776
P.
H. DAVIS and J. A. WIN
to the measured line positions to take into account the difference in the magnetic field at the sample and gaussmeterprobe. t
3. REWLTs ANDANALYsls EPR spectra taken with the magneticfield B parallelto the c-axis of a crystal (natural Braxihan rose quartz) which had been ditfused with IWAg(Z= 112, 98.2% abundance)gave the pattern shown in Fig. 2. Centered about each line of the primary ‘@‘Ag doublet (333.056and 372.581mT at 9.8946GHx) is a doublet (splitting12.0mT) due to hyper8ne interaction with a single “Si nucleus (I = l/2,4.7496abundant).Additionalsmall“Si sphttings (ca. 0.18 and 0.23mT) were observed but not analyzed. The primary (even-Si isotope) doubkt due to ‘OpAg (Z= l/2, 1.8%abundant) is just vi&k. The additional lines are from other centers as indicated. The same spectra have been observed in silverditfused synthetic quartz Rotation about axis aI gave data used to obtain the matrices in the spin-Hamiltonian
where i indexes the nuclei (?‘*rWAg,=Si) considered. All matrices were assumed to be symmetric and the nuclear Zeeman matrices gr taken to be isotropic. The electronic Zeeman and hy@ne splittingmatrices were obtained by computer least squares fitting of the experimentally determined line positions using exact matrix diagonalixation of X(7). A root-mea&square deviation S of 0.003qT was obtained in fhting 94 line positions (18 angks over 180”range) of the primary doublet and 8 = 0.004mT was obtained in Wing 96 line positions(18 angks over 180”range) for the “Si doubkt. The variations of the Zeeman parameter g = [d . g’ - d]ln (with d = B/M) and silver and silicon hyperfbre parameters A = [fi - A2 - &In, as a function of rotation about the 2-fold axis, are shown in Fig. 3. The
AS (mT)
8
(DEG.) -
pir.3. hiltion of (1) the zeemln
psrametu#, (h) the ‘OrA8 and (c) the ?gi hypcrtkecou& pw~ters as a functionof
rotation aboutthe 2-fold axis I,. The the traces in each mph comapond to the three mq4cally iaequivlknt pairs of A, sites observedwhen the ma~netk fkld B is in a plane perpendicular to a,. The three sites becomemagnetkally hlktin&brMc when *, i.e. B = V.
principalvalues and directionsof the best-titmatricesare given in Tabk 1. It was observed that the two members of the “Si doublet did not exhibit the same linewidth, one being E//C Y = 9.696
GHr
T-20.K
o
b
-
d
a
a
b -+:
a ’
i? IOmT
in 77K X-h&ted rose quartzdopedwithtilvw @6.25&g). ?gf bypr86m Fu. 2. EPR spectrum of AM lines (a) arc visible on either side of each peak of the primuv (even% isotope) m& doubkt. Alao vi8W b the primary doubkt (b) arising from the residual ‘“4. Centers &in# rise to otbcr lines inch& Al& (c) WI. AI/Li (4 M and0 (e) 131.
m
Silver atom center in aqnartz in right-handed aquartz (P&21) at cu. ZV’K.Hyperfine Table I. The matrices f in the spin Hamiltonian for AM parameters are in magnetic field units of mT, obtained by dividing A-vahes in energy units of I by g& (where g,, = 2.002319 and f3, = 9.284832 x 10-“JT-‘). x,, x2 and x, are the dire&o cosines of the principal diions witb respect to the unit vectors I, J and k forming the right-handed coordinate system described in Fig. I. The polar and azimuthal angks, 19and d, are defined in the usual fashion with respect to this same coordinate system
ttstrix
P
Principal Directions
Principal Values Xl
1.99978
-0.00018
-0.00003
1.99383~-0.00258 1.99726 -40.870
-14.230
e
0
X3
1.99978
0.99851
-0.04436
0.03170
1.99864
0.04888
0.47077
-0.88090
151.75
84.07
1.99244
0.02415
0.88114
0.47224
61.82
88.43
88.18'
-2.54'
-0.006
-0.002
-39.220
-0.00360
0.82053
0.57159
55.14
90.25
39.259
0.057
-39.341
-0.00102
0.57159
-0.82054
145.14
90.10
39.301
-40.870
-0.99999
-0.00353
-0.00124
90.07
180.00
-0.008
-0.002
-11.904
-0.00339
0.91200
0.41017
65.78
90.21
-11.920
0.035
-11.999
-0.00074
0.41017
-0.91201
155.78
90.10
-11.983
-14.230
-0.99999
-0.00339
-0.00072
90.04
narrower than the associated primary (even-% isotope) line and the other broader. On warming the crystal from 20”K, there was virtually no change in the EPR characteristics up to 77°K. Above this, line broadening and the decay (co. 200”K), was observed with the formation of other centers (some thought to be species in which silver is associated with ahuninum). Re-irradiation with X-rays at 770K regenerated the Acenter quantitatively but did not appreciably affect any of the other centers present.
+DLWUSSKM It is
x2
assumed (Table 1) that the principal values of 4, all have the same sign, as do those of &, so that Aand Aa, both are almost isotropic and close to ~:niaxial. The deviation from uniaxiahty is real, i.e. considerably outside of our experimental uncertainty. The largest principal value of g lies very nearly along the two-fold axis, aI, as is seen from Table 1. (There are, of course, five other matrices related to ,J by the symmetry operations of the point- group (4) appropriate to aquartz, but we need not consider these explicitly). Likewise, the unique principal value of each hypertine matrix, &, and &, has its axis along the same 2-fold axis. Constrain@ the unique axis of both hype&e matrices to lie _exactly along al (i.e. setting A12= A12 = 0 in A4 and As) did not produce a serious degradation of the fit to the experimental data; however, a similar constraint on g caused 6 to increase to 0.015 mT from the value of 0.004 mT observed in the unconstrained case. Thus the slight deviation from perfect 2-fold axis symmetry is real, i.e. well outside the limits of our experimental uncertainty, but can be attributed entirely to 8. A likely cause for this effect is the mixing in of an excited state having decreased symmetry. For all three matrices the principal vafnes m the plane perpendicular to II tie very close to the projections onto this plane of the Si-0 bonds (Fig. 4). It should be noted that for almost uniaxial matrices the accuracy with which
lEO.!lO
the principal directions belonging to the nearly equal principal values can be determined is limited: A change in the matrix elements A22 and A22 by 6A = f 0.003 mT (i.e. the mean deviation in our field positions) produced changes in 0 (Table 1) of ca. 1.3”(IwAg) and 1.4”(?Si). The orientations of the principal axes are very similar to those observed in A-[ 11 and AH-&~] (in which cases, however, rigorous 2-fold axis symmetry was found) and support the model shown in Fig. 1. IO patticular, the orientation of the unique axis of AT, strongly suggests that the silver atom lies on 8l (at least on the time average) and presumably in the c-axis channel nearest (B in Fig. 1) to the silicon giving the large “Si hyperhoe splitting. The decrease in g from the free-silver atom value of 2.0022+ 0.0002[8] is consistent with observed values from atomic silver in frozen solutions[S] and in KC1[9]. One aspect of A-i not yet clearly understood is the presence of only one strong =Si hypertine coupling, rather than two. The suggested c-axis channel site for the silver atom is between two silicon ions, both located on the two-fold axis aI, one at 2.61 A and the other at 2.31 A from the channel midpoint (Fii. 1). Neither A-, nor Ashow an appreciable coupling to a second silicon. We note that the silver need not be located in mid-channel (r,~ = 1.45A, r4+= 1.2A, rtid - 2A), but presumably is as close as possible to the closer silicon ion. Thus, bonding combination between orbit& on Ag and the closer Si, with anti-bonding between Ag and the farther silicon, may enhance this effect. We now wish to estimate the wavefunction for the unpaired electron. The isotropic hypertine component (Table 2) for ““Ag yields an orbital coefficient for the 5s function by use of the relation ([I], eqn 10).
Ai, 39.81 a:.*=-=fi= AL .
o.65.
Compression effects[lO], such as have been observed in the analogous hydrogen ceuter AHa, would decrease
P. H. DAVIS and 1. A. WUL
Al tio7Ag)
, \ \ \ \ \ \
loo
Fig. 4. Wulff net representationof the principal directionsof the Zeeman and the ““Ag and ?3 hypertinecoupling matrices for the A-4 center. Hlkd circles represent poks in the lower hemisphere.Also shown arc the Si-0 directionswith oxygen ions lab&d accordingto Fis. I. The polar and azimuthalangles B and 4 are definedin the usual mannerrelative to the Cartesian coordinatesystem set out in Fig. I.
b 0.760 a:.sc=~=~=0.13.
T$@ 2. Hypefine parametersfor AS-M, ..
b (mT)
*iso fmTl
this
l”‘Ag
-39.810
-0.530
lO9,,
-45.961
-0.612
29Si
-12.711
-0.760
Further, the observed value of b can be accounted for by assuming a point dipole interaction with all spin density located at the silver nucleus and a silicon-silver distance of co. 1 A. In this latter case we note that the sum H o? is
value. Similarly, for Sp of silver, b
0.530
dp_Q=j-prc=~=
1.30
(3)
if one were to assume no mixing in of silver 4d functions. However the large value a:, > I strongly suggests, as with A-. [ 11,that this is not the case. For mixing in of 4d,t with no 5p contribution,
which is much more reasonable in light of the need for Ca12-
1.0, if the silver orbital is assumed to be composi of 5s and 4d only, so that little spin density on oxygen ions is expected. Comparison between Aand A-, using Table 3, shows that much weaker bond formation and electron transfer from the silver atom occurs with silicon than with gennaaium. This is consistent with the relative free ion ionization energies for Si+3 (45.1 eV) and Ge3’ (44.7 eV), respectively[lll. The relative stabilities of the two centers also imply weaker bonding in tbe silicon species. the center A”_S(, in which virtually no bond Like Ad, formation would appear to occur, is thermally unstable. Another thermally unstable center which may be Am has been reported[ 121;although the data available do not permit a quantitative comparison with tbe centers
I. Tabk 3. Orbital coe&knts fsquarai) for silver casters A+x
’ The spin density on the silicon ion is not large, as can be seen from the estimates (see Appendix A): Aso (j:,*Si=~=-= Ai,
‘2-7’ 0.051 250
(
Silver atom
center
considered herein, its reported properties appear to be consistent with the trends observed here. For a somewhat more quantitative analysis of our data, we have used a modification of the 2nd-order perturbation technique employed by McGarvey[l31 for “Cr in CrG,3-. We have added the terms necessary for inclusion of considerable s-character, and thus use a ground state wavefunction
which is the appropriate combination for a somewhat distorted tetrahedron, with actually assumed symmetry of C2.. Our calculations gives the same expressions as McGarvey published for the principal values g,, g2 and g,. The principal hyperfine values. however, are:
-& - &
[~(a+~(3)b)+J(~)C](t/(3)o-b)
I=
AZ=-K+P
2(V(3)0 + bJ2
I(
@aI
2 4v3 -$+Tab+fb2
-LC v/s
-z,/(;)bC)-&-(yab+2\1(;) -&2(t/(3)0 12 -JO A,=-K+P
;
c
I(
bC)
- bJ2 --&
I
(V(3)a + b)
w
?(a
-d/36)
@b)
;a2-!b2+L
1
d5
w valid for (AJ*(PI. Here gl and A, (i = 1,2,3) have the same principal axis and i = 3 refers to the 2-fold axis. Parameter K is the isotropic contact term
K=-;TAi++g.-Tg,)
(9)
where g. = 2.0023 (free electron value) and P = @d4n) g,g&&(r-‘)ti-,,,, for which restricted nonrelativistic Hattree-Fock calculations give a value of -O.O0633cm- (see [I]). Here ~4 is the permeability of free space. Parameter C-ac. where CY= (r-3)~-J(r-3)~-.,, is estimated to be co. 5.92~ IO-’ from hydrogenic orbit&. The spin-orbit coupling JFCS Vc: 19. No. 7-F
in a-quartz
779
parameter A for Ago (4dp5~~,~0) has a value in cm-’ of - 1769,and doesn’t appear to be very dependent on ionic charge of the silver[l4]. A best-fit computer calculation using our principal values ITable I] was carried out as a function of c (- I -B + I). For each c, the values of a and b were varied to best-fit the hyperfine principal values. The principat g-values were used to evaluate the terms involving AlAE in (8). The normalization sum a2 + b2 t c2 was set equal to a constant value, i.e. to I or 0.27 +0.65 = 0.92 (see Table 3), as desired; parameter a was taken to be positive and best-fits to the hyperfine principal values for a as large as possilble were sought. The data in Table 3 suggest values [cl = d(O.65) = 0.81 and d/(0’+ b2) = v(0.27) = 0.52: for mixing in primarily of dz2 into the s orbital, one expects [a( * b. Thus one obtains exact fitting to the three hyperfine principal values with any of the (very similar) parameter sets given in Table 4. We note that AE,, is indeed small (ca. 930 cm-‘), as would be expected with tetrahedral ligand field splitting of d-orbitals, whereas A&.,, are lo’-ld cm-’ for excited state 4d95s2 in Ago (see [ 11;Fig. 5). The value of P is close to the Hartree-Fock calculated value; admixture of silver Sp, as well as relativistic corrections, would tend to decrease (r-q and hence (PI. We note that K is found by the above procedure to be positive as is to be expected for a 5s electron (“‘Ago beam data yield K = +O.O5713cm- ([I], see Appendix A)). For a 4d electron in Ag”, on the other hand. K arising from core polarization is negative, with estimated value of - 0.00438cm-’ [ 151.Thus coefficient c estimated above is likely to be somewhat too small, and a2 t b2 too large. Hence, to fit the observed hyperfine anisotropy. the calculated P would have a somewhat larger magnitude than the actual value. In view of the many assumptions (zero spin density on silicon and oxygen ions, no silver p-function contribution, symmetry C2.. g and i co-axial), the actual parameters obtained, while being reasonable, must of course be used with caution. The failure to observe an EPR signal in silver-diffused a-quartz prior to x-irradiation suggests that the silver is present initially in a diamagnetic form, probably Ag’. We propose that the mechanism for formation of A,,_s is by trapping at such an Ag’ ion (located adjacent to a silicon site in the lattice) of an electron released by irradiation. Monovalent cationic interstitial impurities in a-quartz are generally thought to be present to provide charge compensation for trivalent substitutional impurities. In fact, Kats[ IS] used this notion as the basis of an indirect method for determining the quantity of hydrogen present in a-quartz. Further evidence of the special affinity of these monovalent interstitial cations for sites adjacent to trivalent substitutional impurities, especially aluminum, is the observation that when ordinary a-quartz is irradiated at 77°K (at which temperature ionic mobility is presumably negligible), the aluminum-related trapped-hole centers exhibit hypefine splitting due not Only to “Al but also to a nearby interstitial (‘H, ‘Li, “Na, ‘m.‘OsAg[171, etc.) while the trapped-electron centers associated, e.g. with substitutional germanium.
780
P. H. DAVIS and J. A.
WEIL
Table 4. Best-fit parameters,usiw a2 + b’+ c2 = 0.92 and a = 5.92x 10e3in eqns (8); K is given for ‘07Ag a
b
c
P cm-1
0.514
-0.0127
-0.810
-0.00660
0.0373
1.93
0.00227
r.514
-0.0128
0.810
-0.00624
0.0372
1.90
0.00227
0.00644
0.513
0.0237
-0.810
-0.00663
0.0373
0.556
0.00247
0.00594
0,513
0.0250
0.810
-0.00626
0.0373
0.499
0.00248
0.00593
exhibit no such hyperfine structure[3]. However, the formation of A-s, by low temperature irradiation and its subsequent quantitative (within the limits of our exponential measurements) regeneration following annealing (2:2WK) and re-irradiation at 77“K suggest that the bulk of the Ag+ ions are distributed randomly throughout the lattice. In summary, it has been shown that atomic silver can exist in the large c-axis channels in aquartz, and that there is weak bonding to silicon cations; the latter is not surprising in view of the penchant shown by silver to form species such as AgH’. Ag2+. At room temperature, the Ago species is unstable with respect to cation formation. Acknowledgements-We would like to thank Mr. C. Y. Huang for his valued assistancewith the silver-platingprocedure. We are grateful to ResearchCorporation for a grant to purchasecertain equipment.We wish also to thank Prof. B. R. McGarvey for his helpfuladvice.This researchwascarriedout underthe auspicesof the National Research Council of Canada.
I. Laman F. C. and Weil J. A.. 1. Phys. Chcm. So/ids 36. 949
16. McGarvey B. R.. 1. Phys. Chnn. 71.51 (1967). 17. We have observed a silver (cation) compensatedaluminum center (see FM. 2) following low temperature irradiation which wilI be describedin this journal: Davis P. H., Huang C. Y. and 1. A. We& 18. Ckmenti E. and Roetti C., Atomic Dota and Nucfear fbra Tables 14, I77 (1974). 19. Froe.se-FischerC., Atomic Jbla 4,301 (1972); Atomic Doto and Nuclear Lhxta Tables 12, 87 (1973); Comput. Phys. Comm. 4. 107 (1972). 20. Julian C. L. and Lane, F. 0. Jr., 1. Appl. Phys. 39. 2316 (1968). 21. Shirley D. A.. Rev. Mod. Phys. 36,339 (1964). 22. Dcsclaux J. P., Atomic l&a and Nuclenr lhta Tables 12. 31I (1973). 23.’ Kusch P. and Taub H., Phys. Rev. 75. 1477 (1949).
APPmrmA Estimation of orbital parameters The quantitiesI$(O$, and (r-3)3pfor silicon may be estimated from Roothaan-Hartree-Fock wavefunctions. using computer programsby Ckmenti[ll] or by Fiscber[l9]. Both quantitiesare sensitiveto the oxidation state. Thus for Si’:
(1977). 2. Perlson B. D. and Weil J. A., 1. Magn Rcs. 15.594 (1974).
3. Mackey 1. H.. Jr., 1. Chem. Phys. 39.74 (l%3). 4. Handbook of Chemistry andPhysics (Edited by c. H. H&_ man). 44th Edn, p. 3428. Chemical Rubber Company, Ck_ veland (1962). 5. Perlson B. D. and Weil 1. A., Reu. Sci. Inshm. 46, 874 (1975). 6. Cohen E. R. and Taylor B. N., 1. Phys. f&m. Ref. Dora 2,663 (1973). 7. RinnebergH. and WeiI J. A., 1. Cha. Phys. 56.2019 (1972). 8. Zhitnikov R. A. and Orbeli A. L.. Soviet Physics-&lid Slorr7.1559(1966); wans&fromFizTocrd Tda7,1926(1965): (a) Zhitnilov R A. and Pm A. P., ibid 8,1429 (1966); trans. fromlbidE,1796(1%6);(b)ShieldsL.,Tmns.F~ySoc.62, 1042(1966); (c) ShieldsL., I. Chem. Phys. U,l685 (l%6); (d) Kevan L., Hase H. and Kawabata K., L Chem. Phys. 663834 (1974). 9. Delbecq C. J., Hayes W., O’Brien M. C. M. and Yuster P. H., Proc. R. Sot. A 271, 243 (1963). IO. Suryanarayana D. and Weil J. A., I. Chem. Phys. 64, 510 (1976). I I. Handbook of Chemistryand Physics (Edited by R C. Weast), 54th Eda. p. E67. Chemical Rubber Company, Ckveland (1973). 12. Amanis 1. K., Kliiva J. G. purans I. J. and Truhin A. N., Phys. Staws Solidi (b). 31, Kl65 (1975). 13. McClarvey B. R., Electron Spin Resonance of Metal Complexes (Edited by Teh Fu Yen), pp. l-11. Pknum press. New York (1969). 14. Fmga S., Karwowski J. and Saxena K. M. S., Handbook of Atomic Doto.p. 280. Blsevier, Amsterdam (1976). IS. Kats A., Philips Res. Rep. 17. 133.201 (1962).
0.00644
n -I 0 +I +2 +2 +3 +3
Configuration
Ground term
3s’3p’ 3?3p’ 3sz3p 3sz 3s3p 3s 3P
‘S
‘P ‘P ‘S
‘P ‘S
I$(OG (cm-‘) ;;:;;
;o$
28.9 x 32.8x 34.5 x 38.7 x
Id’ Id’ IOU IOU
(r-3),p (cm-‘) 10.3x 13.7x 17.8x 22.5 x
2P
Id4 Id’ lp lp
27.5: IP
In a-quartz, one has co. 50% covakncy. For example. Julian and Lane[20] give +2.7 as an effective charge for (nominal) Si”. Since the silicon spin density for Ati is so small, and negkctin8 relativistic effects which are small for silicon[21.22], we shall use (r-J)3p = 26.0x IOU cm-’ and IHO)& = 37.4 x I@ cm-‘. However, it is well known that Hartree-Fock results underestimate I$(Oj’. due primarily to core polarization. Since experimental values for atomic hyperfhte data seen not to be available for d’, one can estimate the effect from such data for Na’, which is isoelectronic with S?. Thus Ah= 8.85805~ IO'Hz for “Na”[23] leading to I&.(o)~:,...~ = Hartree-Fock 5.0570X IOU cm-?. From restricted calculations[l8], one obtains IJrw.(0)lj,.H_~= 3.5688x lp cm-‘. Thus one estimatesfor silicon&: I+(O$,=$$j37.4+
ffzTfi:
IoU=53X IOUcm-‘.
= -250 mT. The above value of (f’h,
yields b- -
of Chemistry and Chemical Engineering, University of Saskatchewan, S7N OWO Canada
Saskatoon, Saskatchewan,
(Received 27 September B77; accepted 14 November B77) Abstract-A new paramagnetic center, A&a, in silver-diffused aquartz is descni and its spin-Hamiltonian parameters are presented. The center is formulated as a silver atom (S = l/2) situated in a c-axis channel, bonded weakly to a normal silicon cation, with four oxygen anions as neighbors. A,+s is created by X-irradiation and is unstable at room temperature.
INTRODUCTlOh’ In a recent paper[ 11, a stable (300°K) paramagnetic center, Ati4,, consisting of a neutral silver atom associated with a germanium 4+ ion substituted at a silicon site in a-quartz (Fig. 1) was discussed. In this center the silver atom is thought to reside at a site in the large c-axis channels present in a-quartz, adjacent to the germanium ion and surrounded by 4 oxygen anions forming a distorted tetrahedral cage. In the present ivork we discuss an analogous center, A-,, in which the silver atom is found adjacent to a normal silicon site. This new center is unstable at room temperature. Electron paramagnetic resonance (EPR) measurements on Aand A-. reveal appreciable spin density at the silicon and germanium nuclei respectively and thus one can speak of the formation of a chemical bond between Ag and Si and between Ag and Ge, respectively. This is in contrast to the situation observed in the structurally similarAH (this latter symbol will be used herein for the atomic hydrogen species described in Ref.[21) in which no large “Si hyper6ne splitting has been observed. By way of further contrast, in the 1.
case of the centers AO+U and Ao+N,[~], the unpaired electron is much more localized on the germanium. No paramagnetic centers with neutral hydrogen adjacent to a substitutional germanium or with sodium or lithium cations adjacent to a normal silicon site have thus far been reported. 2. -AL.
Samples used in this study consisted of single crystals of a-quartz (natural rose quartz and synthetic germanium-doped quartz) cut either in the form of orthorhombic plates or right circular cylinders with the longest dimension of the plate or the axis of the cylinder parallel to one (=a,) of the three symmetry-equivalent crystallographic two-fold axes. We introduced silver into the crystals by chemo-plating metallic silver onto the surface of the crystal normal to the c-axis, followed by electrodifTusion. The Brashear process[4] was used for plating most samples; however, a micro-technique involving in-situ reduction of aqueous Ag(N&k+ ion by acetaldehyde vapor was developed for the preparation of the sample containing isotopically enriched silver (98.2% ““Ag) used for the collection of the rotational data. The electro-diffusions were carried out at co. 650°K with an applied field cn. lo’V/cm for several hours. We terminated the diffusion when the initial current of lo20 pA had stabilized at l-2 PA. The paramagnetic A-i center was created by Xirradiation at 77°K using a Machlett AEG-SOS tube with T tungsten target and beryllium window (SOmA, 50 kV, 1 hr). The crystal was located co. 2.5 cm from the window of the X-ray tube and was rotated during irradiation to produce more uniform exposure. The sample was transferred without warm-up to the cavity of a Displex EPR system[5] and all EPR measurements made at ca. 20°K. The EPR spectrometer Fig. I. SiO, tetrahedron in right-handed (P3~21) aquartz. Symbols o and @ locate possible inequivalent sites for an interwas a Varian V4500-10, with Mark II Fieldial, :: !nc stitial in the middle of the large c-axis channels at the inter100kHz field modulation. The Zeeman field .‘cs section of a three-fold smw c and the two-fold (D,) symmetry measured with a Perkin-Elmer M2 NMR gaussmeter and axis the f denote the sign of tbt charge developed on the the microwave frequency monitored with a Hewletttwo-fold axis when the crystal is compressed in this die&n. Results herein have been expressed in Cartesian coordinates Packard 5245L frequency counter used in conjunction (xI,x2. x3) in a right-handed coordinate system delined by the unit with a Hewlett-Packard 5257A transfer oscillator. The vectors i, j and t. I and k lie along crystallographic axes a, and c natural constant B/v, = 2.348740x lo-‘T-Hz-‘(61 was respectively with positive values of x, associated with the end of used in the magnetic field calculations. We estimate the a, developing a negative (-) charge on compression. experimental uncertainty in the determination of .line tAuthor for correspondence. positions to be about 0.002 mT. A correction was applied
776
P.
H. DAVIS and J. A. WIN
to the measured line positions to take into account the difference in the magnetic field at the sample and gaussmeterprobe. t
3. REWLTs ANDANALYsls EPR spectra taken with the magneticfield B parallelto the c-axis of a crystal (natural Braxihan rose quartz) which had been ditfused with IWAg(Z= 112, 98.2% abundance)gave the pattern shown in Fig. 2. Centered about each line of the primary ‘@‘Ag doublet (333.056and 372.581mT at 9.8946GHx) is a doublet (splitting12.0mT) due to hyper8ne interaction with a single “Si nucleus (I = l/2,4.7496abundant).Additionalsmall“Si sphttings (ca. 0.18 and 0.23mT) were observed but not analyzed. The primary (even-Si isotope) doubkt due to ‘OpAg (Z= l/2, 1.8%abundant) is just vi&k. The additional lines are from other centers as indicated. The same spectra have been observed in silverditfused synthetic quartz Rotation about axis aI gave data used to obtain the matrices in the spin-Hamiltonian
where i indexes the nuclei (?‘*rWAg,=Si) considered. All matrices were assumed to be symmetric and the nuclear Zeeman matrices gr taken to be isotropic. The electronic Zeeman and hy@ne splittingmatrices were obtained by computer least squares fitting of the experimentally determined line positions using exact matrix diagonalixation of X(7). A root-mea&square deviation S of 0.003qT was obtained in fhting 94 line positions (18 angks over 180”range) of the primary doublet and 8 = 0.004mT was obtained in Wing 96 line positions(18 angks over 180”range) for the “Si doubkt. The variations of the Zeeman parameter g = [d . g’ - d]ln (with d = B/M) and silver and silicon hyperfbre parameters A = [fi - A2 - &In, as a function of rotation about the 2-fold axis, are shown in Fig. 3. The
AS (mT)
8
(DEG.) -
pir.3. hiltion of (1) the zeemln
psrametu#, (h) the ‘OrA8 and (c) the ?gi hypcrtkecou& pw~ters as a functionof
rotation aboutthe 2-fold axis I,. The the traces in each mph comapond to the three mq4cally iaequivlknt pairs of A, sites observedwhen the ma~netk fkld B is in a plane perpendicular to a,. The three sites becomemagnetkally hlktin&brMc when *, i.e. B = V.
principalvalues and directionsof the best-titmatricesare given in Tabk 1. It was observed that the two members of the “Si doublet did not exhibit the same linewidth, one being E//C Y = 9.696
GHr
T-20.K
o
b
-
d
a
a
b -+:
a ’
i? IOmT
in 77K X-h&ted rose quartzdopedwithtilvw @6.25&g). ?gf bypr86m Fu. 2. EPR spectrum of AM lines (a) arc visible on either side of each peak of the primuv (even% isotope) m& doubkt. Alao vi8W b the primary doubkt (b) arising from the residual ‘“4. Centers &in# rise to otbcr lines inch& Al& (c) WI. AI/Li (4 M and0 (e) 131.
m
Silver atom center in aqnartz in right-handed aquartz (P&21) at cu. ZV’K.Hyperfine Table I. The matrices f in the spin Hamiltonian for AM parameters are in magnetic field units of mT, obtained by dividing A-vahes in energy units of I by g& (where g,, = 2.002319 and f3, = 9.284832 x 10-“JT-‘). x,, x2 and x, are the dire&o cosines of the principal diions witb respect to the unit vectors I, J and k forming the right-handed coordinate system described in Fig. I. The polar and azimuthal angks, 19and d, are defined in the usual fashion with respect to this same coordinate system
ttstrix
P
Principal Directions
Principal Values Xl
1.99978
-0.00018
-0.00003
1.99383~-0.00258 1.99726 -40.870
-14.230
e
0
X3
1.99978
0.99851
-0.04436
0.03170
1.99864
0.04888
0.47077
-0.88090
151.75
84.07
1.99244
0.02415
0.88114
0.47224
61.82
88.43
88.18'
-2.54'
-0.006
-0.002
-39.220
-0.00360
0.82053
0.57159
55.14
90.25
39.259
0.057
-39.341
-0.00102
0.57159
-0.82054
145.14
90.10
39.301
-40.870
-0.99999
-0.00353
-0.00124
90.07
180.00
-0.008
-0.002
-11.904
-0.00339
0.91200
0.41017
65.78
90.21
-11.920
0.035
-11.999
-0.00074
0.41017
-0.91201
155.78
90.10
-11.983
-14.230
-0.99999
-0.00339
-0.00072
90.04
narrower than the associated primary (even-% isotope) line and the other broader. On warming the crystal from 20”K, there was virtually no change in the EPR characteristics up to 77°K. Above this, line broadening and the decay (co. 200”K), was observed with the formation of other centers (some thought to be species in which silver is associated with ahuninum). Re-irradiation with X-rays at 770K regenerated the Acenter quantitatively but did not appreciably affect any of the other centers present.
+DLWUSSKM It is
x2
assumed (Table 1) that the principal values of 4, all have the same sign, as do those of &, so that Aand Aa, both are almost isotropic and close to ~:niaxial. The deviation from uniaxiahty is real, i.e. considerably outside of our experimental uncertainty. The largest principal value of g lies very nearly along the two-fold axis, aI, as is seen from Table 1. (There are, of course, five other matrices related to ,J by the symmetry operations of the point- group (4) appropriate to aquartz, but we need not consider these explicitly). Likewise, the unique principal value of each hypertine matrix, &, and &, has its axis along the same 2-fold axis. Constrain@ the unique axis of both hype&e matrices to lie _exactly along al (i.e. setting A12= A12 = 0 in A4 and As) did not produce a serious degradation of the fit to the experimental data; however, a similar constraint on g caused 6 to increase to 0.015 mT from the value of 0.004 mT observed in the unconstrained case. Thus the slight deviation from perfect 2-fold axis symmetry is real, i.e. well outside the limits of our experimental uncertainty, but can be attributed entirely to 8. A likely cause for this effect is the mixing in of an excited state having decreased symmetry. For all three matrices the principal vafnes m the plane perpendicular to II tie very close to the projections onto this plane of the Si-0 bonds (Fig. 4). It should be noted that for almost uniaxial matrices the accuracy with which
lEO.!lO
the principal directions belonging to the nearly equal principal values can be determined is limited: A change in the matrix elements A22 and A22 by 6A = f 0.003 mT (i.e. the mean deviation in our field positions) produced changes in 0 (Table 1) of ca. 1.3”(IwAg) and 1.4”(?Si). The orientations of the principal axes are very similar to those observed in A-[ 11 and AH-&~] (in which cases, however, rigorous 2-fold axis symmetry was found) and support the model shown in Fig. 1. IO patticular, the orientation of the unique axis of AT, strongly suggests that the silver atom lies on 8l (at least on the time average) and presumably in the c-axis channel nearest (B in Fig. 1) to the silicon giving the large “Si hyperhoe splitting. The decrease in g from the free-silver atom value of 2.0022+ 0.0002[8] is consistent with observed values from atomic silver in frozen solutions[S] and in KC1[9]. One aspect of A-i not yet clearly understood is the presence of only one strong =Si hypertine coupling, rather than two. The suggested c-axis channel site for the silver atom is between two silicon ions, both located on the two-fold axis aI, one at 2.61 A and the other at 2.31 A from the channel midpoint (Fii. 1). Neither A-, nor Ashow an appreciable coupling to a second silicon. We note that the silver need not be located in mid-channel (r,~ = 1.45A, r4+= 1.2A, rtid - 2A), but presumably is as close as possible to the closer silicon ion. Thus, bonding combination between orbit& on Ag and the closer Si, with anti-bonding between Ag and the farther silicon, may enhance this effect. We now wish to estimate the wavefunction for the unpaired electron. The isotropic hypertine component (Table 2) for ““Ag yields an orbital coefficient for the 5s function by use of the relation ([I], eqn 10).
Ai, 39.81 a:.*=-=fi= AL .
o.65.
Compression effects[lO], such as have been observed in the analogous hydrogen ceuter AHa, would decrease
P. H. DAVIS and 1. A. WUL
Al tio7Ag)
, \ \ \ \ \ \
loo
Fig. 4. Wulff net representationof the principal directionsof the Zeeman and the ““Ag and ?3 hypertinecoupling matrices for the A-4 center. Hlkd circles represent poks in the lower hemisphere.Also shown arc the Si-0 directionswith oxygen ions lab&d accordingto Fis. I. The polar and azimuthalangles B and 4 are definedin the usual mannerrelative to the Cartesian coordinatesystem set out in Fig. I.
b 0.760 a:.sc=~=~=0.13.
T$@ 2. Hypefine parametersfor AS-M, ..
b (mT)
*iso fmTl
this
l”‘Ag
-39.810
-0.530
lO9,,
-45.961
-0.612
29Si
-12.711
-0.760
Further, the observed value of b can be accounted for by assuming a point dipole interaction with all spin density located at the silver nucleus and a silicon-silver distance of co. 1 A. In this latter case we note that the sum H o? is
value. Similarly, for Sp of silver, b
0.530
dp_Q=j-prc=~=
1.30
(3)
if one were to assume no mixing in of silver 4d functions. However the large value a:, > I strongly suggests, as with A-. [ 11,that this is not the case. For mixing in of 4d,t with no 5p contribution,
which is much more reasonable in light of the need for Ca12-
1.0, if the silver orbital is assumed to be composi of 5s and 4d only, so that little spin density on oxygen ions is expected. Comparison between Aand A-, using Table 3, shows that much weaker bond formation and electron transfer from the silver atom occurs with silicon than with gennaaium. This is consistent with the relative free ion ionization energies for Si+3 (45.1 eV) and Ge3’ (44.7 eV), respectively[lll. The relative stabilities of the two centers also imply weaker bonding in tbe silicon species. the center A”_S(, in which virtually no bond Like Ad, formation would appear to occur, is thermally unstable. Another thermally unstable center which may be Am has been reported[ 121;although the data available do not permit a quantitative comparison with tbe centers
I. Tabk 3. Orbital coe&knts fsquarai) for silver casters A+x
’ The spin density on the silicon ion is not large, as can be seen from the estimates (see Appendix A): Aso (j:,*Si=~=-= Ai,
‘2-7’ 0.051 250
(
Silver atom
center
considered herein, its reported properties appear to be consistent with the trends observed here. For a somewhat more quantitative analysis of our data, we have used a modification of the 2nd-order perturbation technique employed by McGarvey[l31 for “Cr in CrG,3-. We have added the terms necessary for inclusion of considerable s-character, and thus use a ground state wavefunction
which is the appropriate combination for a somewhat distorted tetrahedron, with actually assumed symmetry of C2.. Our calculations gives the same expressions as McGarvey published for the principal values g,, g2 and g,. The principal hyperfine values. however, are:
-& - &
[~(a+~(3)b)+J(~)C](t/(3)o-b)
I=
AZ=-K+P
2(V(3)0 + bJ2
I(
@aI
2 4v3 -$+Tab+fb2
-LC v/s
-z,/(;)bC)-&-(yab+2\1(;) -&2(t/(3)0 12 -JO A,=-K+P
;
c
I(
bC)
- bJ2 --&
I
(V(3)a + b)
w
?(a
-d/36)
@b)
;a2-!b2+L
1
d5
w valid for (AJ*(PI. Here gl and A, (i = 1,2,3) have the same principal axis and i = 3 refers to the 2-fold axis. Parameter K is the isotropic contact term
K=-;TAi++g.-Tg,)
(9)
where g. = 2.0023 (free electron value) and P = @d4n) g,g&&(r-‘)ti-,,,, for which restricted nonrelativistic Hattree-Fock calculations give a value of -O.O0633cm- (see [I]). Here ~4 is the permeability of free space. Parameter C-ac. where CY= (r-3)~-J(r-3)~-.,, is estimated to be co. 5.92~ IO-’ from hydrogenic orbit&. The spin-orbit coupling JFCS Vc: 19. No. 7-F
in a-quartz
779
parameter A for Ago (4dp5~~,~0) has a value in cm-’ of - 1769,and doesn’t appear to be very dependent on ionic charge of the silver[l4]. A best-fit computer calculation using our principal values ITable I] was carried out as a function of c (- I -B + I). For each c, the values of a and b were varied to best-fit the hyperfine principal values. The principat g-values were used to evaluate the terms involving AlAE in (8). The normalization sum a2 + b2 t c2 was set equal to a constant value, i.e. to I or 0.27 +0.65 = 0.92 (see Table 3), as desired; parameter a was taken to be positive and best-fits to the hyperfine principal values for a as large as possilble were sought. The data in Table 3 suggest values [cl = d(O.65) = 0.81 and d/(0’+ b2) = v(0.27) = 0.52: for mixing in primarily of dz2 into the s orbital, one expects [a( * b. Thus one obtains exact fitting to the three hyperfine principal values with any of the (very similar) parameter sets given in Table 4. We note that AE,, is indeed small (ca. 930 cm-‘), as would be expected with tetrahedral ligand field splitting of d-orbitals, whereas A&.,, are lo’-ld cm-’ for excited state 4d95s2 in Ago (see [ 11;Fig. 5). The value of P is close to the Hartree-Fock calculated value; admixture of silver Sp, as well as relativistic corrections, would tend to decrease (r-q and hence (PI. We note that K is found by the above procedure to be positive as is to be expected for a 5s electron (“‘Ago beam data yield K = +O.O5713cm- ([I], see Appendix A)). For a 4d electron in Ag”, on the other hand. K arising from core polarization is negative, with estimated value of - 0.00438cm-’ [ 151.Thus coefficient c estimated above is likely to be somewhat too small, and a2 t b2 too large. Hence, to fit the observed hyperfine anisotropy. the calculated P would have a somewhat larger magnitude than the actual value. In view of the many assumptions (zero spin density on silicon and oxygen ions, no silver p-function contribution, symmetry C2.. g and i co-axial), the actual parameters obtained, while being reasonable, must of course be used with caution. The failure to observe an EPR signal in silver-diffused a-quartz prior to x-irradiation suggests that the silver is present initially in a diamagnetic form, probably Ag’. We propose that the mechanism for formation of A,,_s is by trapping at such an Ag’ ion (located adjacent to a silicon site in the lattice) of an electron released by irradiation. Monovalent cationic interstitial impurities in a-quartz are generally thought to be present to provide charge compensation for trivalent substitutional impurities. In fact, Kats[ IS] used this notion as the basis of an indirect method for determining the quantity of hydrogen present in a-quartz. Further evidence of the special affinity of these monovalent interstitial cations for sites adjacent to trivalent substitutional impurities, especially aluminum, is the observation that when ordinary a-quartz is irradiated at 77°K (at which temperature ionic mobility is presumably negligible), the aluminum-related trapped-hole centers exhibit hypefine splitting due not Only to “Al but also to a nearby interstitial (‘H, ‘Li, “Na, ‘m.‘OsAg[171, etc.) while the trapped-electron centers associated, e.g. with substitutional germanium.
780
P. H. DAVIS and J. A.
WEIL
Table 4. Best-fit parameters,usiw a2 + b’+ c2 = 0.92 and a = 5.92x 10e3in eqns (8); K is given for ‘07Ag a
b
c
P cm-1
0.514
-0.0127
-0.810
-0.00660
0.0373
1.93
0.00227
r.514
-0.0128
0.810
-0.00624
0.0372
1.90
0.00227
0.00644
0.513
0.0237
-0.810
-0.00663
0.0373
0.556
0.00247
0.00594
0,513
0.0250
0.810
-0.00626
0.0373
0.499
0.00248
0.00593
exhibit no such hyperfine structure[3]. However, the formation of A-s, by low temperature irradiation and its subsequent quantitative (within the limits of our exponential measurements) regeneration following annealing (2:2WK) and re-irradiation at 77“K suggest that the bulk of the Ag+ ions are distributed randomly throughout the lattice. In summary, it has been shown that atomic silver can exist in the large c-axis channels in aquartz, and that there is weak bonding to silicon cations; the latter is not surprising in view of the penchant shown by silver to form species such as AgH’. Ag2+. At room temperature, the Ago species is unstable with respect to cation formation. Acknowledgements-We would like to thank Mr. C. Y. Huang for his valued assistancewith the silver-platingprocedure. We are grateful to ResearchCorporation for a grant to purchasecertain equipment.We wish also to thank Prof. B. R. McGarvey for his helpfuladvice.This researchwascarriedout underthe auspicesof the National Research Council of Canada.
I. Laman F. C. and Weil J. A.. 1. Phys. Chcm. So/ids 36. 949
16. McGarvey B. R.. 1. Phys. Chnn. 71.51 (1967). 17. We have observed a silver (cation) compensatedaluminum center (see FM. 2) following low temperature irradiation which wilI be describedin this journal: Davis P. H., Huang C. Y. and 1. A. We& 18. Ckmenti E. and Roetti C., Atomic Dota and Nucfear fbra Tables 14, I77 (1974). 19. Froe.se-FischerC., Atomic Jbla 4,301 (1972); Atomic Doto and Nuclear Lhxta Tables 12, 87 (1973); Comput. Phys. Comm. 4. 107 (1972). 20. Julian C. L. and Lane, F. 0. Jr., 1. Appl. Phys. 39. 2316 (1968). 21. Shirley D. A.. Rev. Mod. Phys. 36,339 (1964). 22. Dcsclaux J. P., Atomic l&a and Nuclenr lhta Tables 12. 31I (1973). 23.’ Kusch P. and Taub H., Phys. Rev. 75. 1477 (1949).
APPmrmA Estimation of orbital parameters The quantitiesI$(O$, and (r-3)3pfor silicon may be estimated from Roothaan-Hartree-Fock wavefunctions. using computer programsby Ckmenti[ll] or by Fiscber[l9]. Both quantitiesare sensitiveto the oxidation state. Thus for Si’:
(1977). 2. Perlson B. D. and Weil J. A., 1. Magn Rcs. 15.594 (1974).
3. Mackey 1. H.. Jr., 1. Chem. Phys. 39.74 (l%3). 4. Handbook of Chemistry andPhysics (Edited by c. H. H&_ man). 44th Edn, p. 3428. Chemical Rubber Company, Ck_ veland (1962). 5. Perlson B. D. and Weil 1. A., Reu. Sci. Inshm. 46, 874 (1975). 6. Cohen E. R. and Taylor B. N., 1. Phys. f&m. Ref. Dora 2,663 (1973). 7. RinnebergH. and WeiI J. A., 1. Cha. Phys. 56.2019 (1972). 8. Zhitnikov R. A. and Orbeli A. L.. Soviet Physics-&lid Slorr7.1559(1966); wans&fromFizTocrd Tda7,1926(1965): (a) Zhitnilov R A. and Pm A. P., ibid 8,1429 (1966); trans. fromlbidE,1796(1%6);(b)ShieldsL.,Tmns.F~ySoc.62, 1042(1966); (c) ShieldsL., I. Chem. Phys. U,l685 (l%6); (d) Kevan L., Hase H. and Kawabata K., L Chem. Phys. 663834 (1974). 9. Delbecq C. J., Hayes W., O’Brien M. C. M. and Yuster P. H., Proc. R. Sot. A 271, 243 (1963). IO. Suryanarayana D. and Weil J. A., I. Chem. Phys. 64, 510 (1976). I I. Handbook of Chemistryand Physics (Edited by R C. Weast), 54th Eda. p. E67. Chemical Rubber Company, Ckveland (1973). 12. Amanis 1. K., Kliiva J. G. purans I. J. and Truhin A. N., Phys. Staws Solidi (b). 31, Kl65 (1975). 13. McClarvey B. R., Electron Spin Resonance of Metal Complexes (Edited by Teh Fu Yen), pp. l-11. Pknum press. New York (1969). 14. Fmga S., Karwowski J. and Saxena K. M. S., Handbook of Atomic Doto.p. 280. Blsevier, Amsterdam (1976). IS. Kats A., Philips Res. Rep. 17. 133.201 (1962).
0.00644
n -I 0 +I +2 +2 +3 +3
Configuration
Ground term
3s’3p’ 3?3p’ 3sz3p 3sz 3s3p 3s 3P
‘S
‘P ‘P ‘S
‘P ‘S
I$(OG (cm-‘) ;;:;;
;o$
28.9 x 32.8x 34.5 x 38.7 x
Id’ Id’ IOU IOU
(r-3),p (cm-‘) 10.3x 13.7x 17.8x 22.5 x
2P
Id4 Id’ lp lp
27.5: IP
In a-quartz, one has co. 50% covakncy. For example. Julian and Lane[20] give +2.7 as an effective charge for (nominal) Si”. Since the silicon spin density for Ati is so small, and negkctin8 relativistic effects which are small for silicon[21.22], we shall use (r-J)3p = 26.0x IOU cm-’ and IHO)& = 37.4 x I@ cm-‘. However, it is well known that Hartree-Fock results underestimate I$(Oj’. due primarily to core polarization. Since experimental values for atomic hyperfhte data seen not to be available for d’, one can estimate the effect from such data for Na’, which is isoelectronic with S?. Thus Ah= 8.85805~ IO'Hz for “Na”[23] leading to I&.(o)~:,...~ = Hartree-Fock 5.0570X IOU cm-?. From restricted calculations[l8], one obtains IJrw.(0)lj,.H_~= 3.5688x lp cm-‘. Thus one estimatesfor silicon&: I+(O$,=$$j37.4+
ffzTfi:
IoU=53X IOUcm-‘.
= -250 mT. The above value of (f’h,
yields b- -