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Hyperfine interaction of impurity silver atoms in alkali halide crystals
J. Phys. Printed
Chem. Solids Vol. in Great Britain.
54, No.
3, pp.
301-307,
1993 0
0022-3697/93 S6.00 + 0.00 I!393 Pergamon Press Ltd
HYPERFINE INTERACTION OF IMPURITY SILVER ATOMS IN ALKALI HALIDE CRYSTALS MANPBBD BIJCHER Physics Department, California State University, Fresno, CA 93740-0037, U.S.A. (Received 22 July 1992; accepted 26 October 1992) Abstract-Experimental data from Ago impurities in NaCl, KC1 and KBr hosts are used to extrapolate hyperfine (hf) shifts of Ag” impurities in the remaining 13 alkali halide crystals with rocksalt structure. The extrapolation is based on scaling relations of hf shifts with the host lattice spacing and with orbital moments of host neighbor ions. A comparison of hf shifts of A$ impurities in both alkali halide and rare gas matrices indicates a large contribution from the Madelung potential. As a consequence, a revised determination of neighbor ion displacements from superhyperfine interaction may be necessary. Keyword: Electron spin resonance, silver impurities, ionic crystals, short-range forces, impurity-host interaction.
1. INTRODUCTION
Aala, (Rg : ImO) scales with the orbital-moments
ratio
q = ,/R(*)/P of the Rg host atoms [19]. Here Rc2)is the Impurity silver atoms and ions in alkali halide crystals, AX: Ago and AX: Ag+, respectively, have been studied with ESR [l-6], ENDOR [2, 5,7], spectroscopy [S-14], and quantum mechanical calculations [15-181 for more than three decades. It has been found that the Ag0 atoms and Ag’ ions are substitutionally situated at (or near) cation lattice sites in the AX hosts. The observed disturbances of the electron structures of Ago and Ag+ impurities, caused by the closed-shell ions of the AX hosts, provide information about the configurations of, and interactions in the impurity-host complexes. One of the simplest indicators for impurity-host interaction is the relative shift Aa/u,, of hyperfine (hf) interaction between the nucleus and the 5s electron of an impurity Ago atom. Here Aa = a - a, denotes the difference between the isotropic hf interaction constants a and a,, of the Ago impurity and of a free silver atom, respectively. Such hf shifts have been measured for Ago in LiCl, NaCI, KCl, KBr, KI and RbCl at temperatures of T = 4 K and/or T = 77 K [l-6]. In this paper we extrapolate the T = 4 K data, listed in Table 1, to obtain hf shifts of Ago impurities in the remaining AX crystals with rocksalt structure. The extrapolation is based on findings and trends of hf shifts of substitutional impurity hydrogen and mint metal atoms-Ho, Cue, Ago, Au”-in rare gas (Rg) crystals [19], of interstitial hydrogen atoms HP in AX hosts [20], and of impurity copper atoms Cue and ions Cu+ in AX hosts [21,22]. For impurity atoms (ImO) of ns’ ground state electron structure embedded in Rg crystals, the hf shift
total second orbital moment and i is the first moment of the outermost orbital. Since the orbital moment R(*)is a factor in the van der Waals (vdW) attraction and the moment i is a factor in the short-range (sr) repulsion between Rg and Im” atoms, the ratio q(Rg) serves as a measure [23] for the counteractive effects from these potentials on the hf shift Aala,. More specifically, a large q value indicates a large dominance of vdW attraction over sr repulsion on an Im” atom from the surrounding Rg atoms. This causes less compression (or more expansion) of Im” which in turn gives rise to a less positive (or more negative) hf shift. A similar scaling of da/a, with the orbital-moments ratio q(x- ) of the neighbor halide ions was found [20] for interstitial hydrogen atoms in alkali halides, AX: HP. In addition, the hf shifts of the AX:Hy complexes scale also with the host lattice spacing r, due to an indirect influence from the host cations A+. The present task of extrapolating hf shifts of AX : Ago from the few measured systems to the whole AX family (with rocksalt structure) is complicated by two circumstances. First, the measured Aala, values at T = 77 K and T = 4 K show a substantial temperature dependence [l-6]. In the temperature interval from T = 4K to T = 77 K, the Ago hf shift Aala, shifts by -0.7% in NaCl, by - 1% in KCI, and by -3% in LiCl toward more negative values. The amount of such temperature shifts reaches to the same order of magnitude as the hf shifts of the AX: Ago complexes at T = 0, caused solely by the host crystal environment. Thus, in order 301
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Table 1. Measured and extrapolated values of the relative hf shift s = Au/a, (in %) of impurity Ag atoms in alkali halide
and rare gas crystals at T = 4 K (top value) and nearestneighbor distancetl r0 (in A) in the host crystals at T = 0 (bottom value). The experimental values, marked by references, have error margins of +0.3% or less. The values for lithium halide hosts, marked with asterisks, were obtained with a resealing scheme (see text). The corresponding hf constants a = (s + l)a, are readily obtained with the free atom values a,/h of 1712.56MHz and 1976.94MHz for lo7Ag and IWAg isotopes, $respectively, and Planck’s constant h Li Na K Rb
F
Cl
Br
5.6* 1.996 -0.1 2.295 1.2 2.648 1.7 2.789 Ne 9.7 3.156
0.811 2.539 -4.97 2.789 -3.81 3.116 -3.4 3.259
-1.Of 2.713 -6.5 2.954 -5.4tt 3.262 -5.0 3.410
&t. 3.756
&$ 3.992
I -3.2* 2.951 -8.9 3.194 - 6.2tt 3.489 -7.4 3.628 Xe l.O$% 4.336
tRef. 48. $Ref. 49. #Ref. 50. IJExtrapolated from a graph in Ref. 3. TRef. 5. ttRef. 4. SfRef. 35.
to circumvent the temperature effects, we extrapolate only the T = 4 K data [24]. The second complication for the attempted extrapolation of hf shifts arises from spectroscopic observations [lO-14,221 of KI:Ag+, RbCl:Ag+, and several AX:Cu+ complexes where an impurity Ag+ or Cut ion can occupy off-center positions in AX hosts when the ionic radius of the impurity is smaller
than that of a host cation, r(Im+)
2. EXTRAPOLATION
Assuming a scaling of the impurity hf shift with the host lattice spacing r. [25], as found for the AX : HP systems [20] we extend straight lines through the three basic data points from the NaCl : Ago, KCI : Ago and KBr: Ago complexes in the An/u,, vs r, plot of Fig. 1. At the corresponding r, values we read estimated hf shifts Aala, for Ago in the remaining chlorides, LiCl and RbCl, and potassium halides, KF and KI, off these lines. Guided by analogy with Aala, (AX:HT), we draw a third line through the KBr data point in Fig. 1 running parallel to the NaCl-KC1 line. This permits us to read off As/a, estimates for the Ago hf shift in the remaining bromides LiBr, NaBr and RbBr. From a fourth, extended line through NaCl and NaBr we obtain Aala, of Ago in the other sodium halides, NaF and NaI. Repeated extensions of straight lines through the new points obtained in this way give Aala, estimates of Ago in the final hosts, LiF, RbF, LiI, RbI, at the corresponding r. values in Fig. 1 and, concurrently, very close to the
Fig. 1. Relative hf shift da/a, of impurity Ag” atoms in alkali halide and rare gas crystals vs host lattice spacing r,, (nearest-neighbor distance): triangles show experimental data; open circles represent extrapolated values and full circles resealed values (see text). The diamonds display the hf shifts of substitutional Ago atoms in rare gas crystals vs nearest-neighbor distances from fee interstitial sites (r&/2).
Interaction of silver impurities in alkali halide crystals
Aa 1,
r
I
1
I
I
t (3
0
b
-5
-10 2.8
3.0
3.2
p
3.4
Fig. 2. Measured (triangles) and extrapolated (open circles) relative hf shifts Au/a, of impurity AJ$’atoms in alkali halide and rare gas crystals vs orbital-moments ratio q of anions and rare gas atoms, respectively. Full circles represent resealed values for the lithium halide hosts.
intersections of the straight lines. The extrapolated Au/a, values, except for LiX (see below), are compiled in Table 1. The dependence of the measured and extrapolated hf shifts on the anion orbital-moments ratio [26] q@- ) is shown in Fig. 2. The similarity in the slopes of the lines connecting data from hosts with the same and different anions X-, alkali ions A+ d(Aa/a,,)/dq(X-)I,+ < 0, indicates that increasingly dominant vdW attractions from larger neighbor anions X- tend to expand the impurity Ago atom, causing spin density depletion at the Ag nucleus and, consequently, a negative contribution to the hf shift. The intluence from increasingly dominant vdW attraction over sr repulsion between Ago and neighboring X- ions with increasing anion radius r,_ can also be seen in Fig. 1 by the negative slopes of the lines connecting the data for isocationic hosts, a(Aa/q,)/ar,_l,,+ < 0. On the other hand, the positive slopes of the isoanionic lines in Fig. 1, a(Au/u,,)/gr,+]x_ > 0, result from an indirect influence of the host crystal cations A+ on the Ago hf shift through the cations’ contribution to the host lattice spacing [20]. In these cases the increased lattice spacing [25] r. = (r,,+ + rx_) for AX hosts with the same anions but different cations (of increasing ion radius rA+) reduces the vdW attraction between A$ and the surrounding X- ions which in turn reduces the expansion of the Ago impurity atom.
303
3. CASE DJSCUSSION With increasing temperature the hf shift of Ago is observed to become more negative (by -3.3%, -0.7% and - 1.0%) in the three known cases of LiCl, NaCl and KC1 hosts [2-51. This is qualitatively expected due to diminished spin density (on timeaverage [271) at the Ag nucleus resulting from oscillations of the 5s electron cloud about the nucleus when the Ago atom is thermally agitated by the surrounding host ions. Fitting that trend, the extrapolated hf shift of the RbCl: Ago complex at T = 4 K, Au/a, = -3.4%, in Table 1 comes out appropriately higher (1.6%) than the measured value at T = 77 K, Aala, = -5.0 f 0.6% [3]. On the other hand, the extrapolated value Au/u, = -7.9% in Fig. 1 for the KI:AgO system at T = 4 K is 1.7% lower than the experimental value of -6.2% measured at the same temperature. Since the ionic impurity complex KI: Ag+ is known to have a delicate on-center/off-center stability [12] the possibility of off-center behavior of the atomic impurity complex KI: Ago comes to mind. However, a displacement of the 5s electron cloud relative to the nucleus of an off-center Ago atom, caused by electronic and deformation dipole mechanisms, would give rise to spin density depletion at the Ag nucleus and would lead to a much deeper hf down shift than for an on-center Ago atom. Such a situation of a very large hf down shift, Aala, = - 17.4% at T = 77 K [21], seems to be present for the KCl: Cue complex which is qualitatively in agreement with the spectroscopically [22] established off-center character of the ionic impurity system KC1 : Cu+. Having ruled out an off-center position of the Ago atom in a KI host as the cause for the deviation of the extrapolated hf shift from the experimental value, the 1.7% discrepancy remains unexplained [28]. Much more severe than for the KI host is the discrepancy for the LiCl matrix where a hf shift Au/a, = -5.8% is extrapolated but Au/a, = +0.8% is measured (see Fig. 1). The large discrepancy warrants an exploration of possible irregularities in the experimental data and of circumstantial information. (1) A positive hf shift, Au/u,= +17%, was also measured for Cue impurities in LiCl (at 77 K) [21]. This corroborates the observed positive hf shift of Ago impurities in that host. (2) It has been established from well-resolved ESR signals [3,21] of both LiCl: Ago and LiCl : Cue systems, and also by spectroscopy [22] of the ionic complex LiCl: Cu+, that these impurities occupy on-center positions in LiCl hosts. This rules out the possibility of off-center effects-which in any case would give rise to negative instead of positive hf shifts. (3) The LiCl : Ago hf shift (and also the superhyperhne interaction) shows a
304
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strong, nonlinear temperature dependence, d(Au/ %)/dT < 0, which distinguishes the LiCl matrix from the other AX hosts [3]. The temperature dependence indicates that with rising temperature a thermal relaxation process takes place. Obviously, the present extrapolation of hf shifts of on-center Ago atoms in a LiCl host fails, posing a severe setback to the extrapolation scheme which was quite successful for Rg : Im” and AX: HP impurity systems [19,20]. Taking a clue from the temperature dependence, we believe that the observed, slightly positive hf shift of the LiCl : Ago complex is the result of so strong a compression of the Ago impurities by their closest Cl- host neighbors that it more than compensates the expanding effect from the Madelung potential (to be discussed below). Such a compression is likely to occur when impurity Ago or Cue atoms substitute the much smaller Li+ ions. A rough size comparison is provided by Pauling ionic radii: r(Ag+) = 1.26& r(Cu+) = 0.96& r(Li+) = 0.60 A, r(Na+) = 0.95 A, r(K+) = 1.33 A, r(Rb+) = 1.48 A. If the observed hf shift in the LiCl host is indeed caused by a strong compression of Ago atoms, then the extrapolated As/a, values for the other LiX hosts must be discarded as well. However, the compression mechanism does not necessarily eliminate the vdW influence from neighbor anions on the Ago impurities. Thus, if we assume a similar influence of vdW interaction on hf shifts in the remaining LiX, as employed for Ago impurities in the other AX crystals and as found for Rg hosts [19], then we can obtain new estimates, Aa*/a, (LiX: Ago), which better take into account the compression of Ago atoms. Such resealed Au */a0 (LiX : Ago) values are listed in Table 1 and shown by full circles in Figs 1 and 2. Certainly, their derivation is based on an ad hoc assumption which must be judged by future hf measurements of LiX: Ago impurity systems and by theoretical analysis.
4. COMPARISON WITH RARE GAS HOSTS For an exploration of the influences from crystal structure and binding, a comparison of Ago hf shifts in AX with those of Ago atoms in Rg hosts is in order. Common to the Ago impurities in both AX and Rg matrices is the closed electron shell character of their immediate X- and, respectively, Rg neighbors. This causes similar vdW attraction and sr repulsion of Ago atoms with X- ions and with isoelectronic Rg atoms. Different in these hosts is the number of nearest neighbors (NN) around Ago, namely six X- ions compared to 12 Rg atoms. Another difference arises from the Madelung potential [29], present in AX but absent in Rg crystals.
In order to discern the influence from the closedshell nature of the host neighbors, we compare in Fig. 2 the dependence of the Ago hf shift on the orbital-moments ratio of the host neighbors for both AX and Rg hosts. The almost parallel lines indicate that the same mechanism of balancing vdW attraction and sr repulsion is effective in these different groups of host crystals. Since that mechanism is the basic concept underlying the present extrapolation of hf shifts of the AX: Ago complexes, the systematic finding in Fig. 2 corroborates the extrapolation scheme carried out in Fig. 1. Actually, the vdW/sr influence on Au/u,, as illustrated by the linear q-dependence in Fig. 2, is a secondary effect. It reduces the primary compression of Ago in Rg matrices and enhances the primary expansion of Ago in AX hosts. The primary compression of the oversized Ago atom by its 12 neighbor atoms in an Rg (fee) host lattice, resulting in a positive hf shift, Au/a, > 0, is not very surprising. Not so trivial is the primary expansion of Ago in AX. It is caused by the Madelung potential in the ionic crystals [29]. More familiar than its effect on hf shifts is the effect of the Madelung potential on the band structure [3&32], on ion polarizabilities [33], and on ion cores [34] of AX crystals. In the region inside the shell of NN ions (neighbor shell 1) the Madelung potential forms a potential well at anion lattice sites [29] and a potential plateau (upside-down potential well) at cation lattice sites. The potential wells and plateaus lower and raise, respectively, the electron energy levels in the ions or atoms occupying these sites. The raised electron energy levels of an impurity Ago atom in an AX lattice cause a reduction in the binding of the 5s electron and an extension of its orbital. This in turn results in spin density depletion at the Ag nucleus and thus in a negative hf shift, An/a, < 0.
An assessment of the influence from the Madelung potential by a comparison of Ago hf shifts in AX and Rg hosts is complicated by the different neighbor coordinations of substitutional Ago complexes in these crystals. The difference in neighbor coordination could be circumvented, however, by a comparison of substitutional silver atoms in alkali halide hosts, AX:AgO, with impurity silver atoms at octahedral intersritial sites in rare gas crystals, Rg: Agy . A silver atom at such an interstitial site in a Rg host has six closed-shell neighbors just like the substitutional silver atom in an AX: Ag(’ complex. Ignoring the weak vdW attraction and sr repulsion between the Ago impurity and surrounding ions or atoms beyond the six immediate X- or Rg neighbors, the essential difference left between Rg : Agp and isoelectronic AX: Ago complexes is the
Interaction of silver impurities in alkali halide crystals Madelung potential from the point ions in the AX crystals. Yet, no direct comparison of equally coordinated Ago impurities in Rg and AX hosts is possible, because only substitutional silver atoms in rare gas hosts, Rg:AgO-but no stable complexes with interstitial configuration, Rg: Agy-are observed [35]. On the other hand, impurity hydrogen atoms are embedded in Rg hosts at both substitutional and octahedral interstitial sites with respective hf shifts Aala, (Rg:HO) < Aala (Rg:Hy) [36]. Thus, by analogy, the measured Au/a, (Rg : Ago) values may serve as lower bounds of hf shifts Aala, (Rg : Agy) of interstitial silver atoms in Rg hosts. Such lower bounds are indicated in Fig. 1 by diamond symbols which display the hf shifts of substitutional Ago atoms in Rg hosts not vs neighbor distances r, from substitutional sites but vs the neighbor distances from octahedral interstitial sites in these hosts (r,/,/2). Figure 1 shows that the spacing between the Ago hf shifts in the Ar, Kr and Xe hosts is similar to the spacing of hf shifts in the ACl, ABr and AI hosts [37]. More specifically, the vertical differences of _ 10% between the diamond symbols in Fig. 1 and the AX lines associated with isoelectronic X- ions indicate that the influence from the Madelung potential on the hf shift of Ago impurities is quite large and must not be ignored. Because of the involved assumptions and uncertainties, the figure of 10% should not be considered an accurate value of the Madelung shift but rather an order-of-magnitude estimate. Nevertheless, the present indication of a lowering of the Ago hf shift by the Madelung potential in AX crystals to an extent of 10% (or more) implies a considerable redistribution of 5s electron charge from the region of the Madelung plateau inside the first neighbor shell to higher neighbor regions where the (radial) 5s wavefunction has its tail.
5. NEIGHBOR DISPLACEMENTS If the Madelung potential gives rise to a substantial 5s electron charge redistribution, then this affects the interpretation of superhyperfine (shf) interaction with nuclei of the surrounding ions. Using a wavefunction from Hartree-Fock calculations of a free Ago atom and Gourary-Adrian amplification factors [29] to account for orthogonalization admixture of the Ago envelope wavefunction to neighbor ions in NaCl and KC1 crystals, Holmberg et al. [5] calculated for NN anions on (ideal) host lattice sites larger shf constants than the measured values. The authors estimated, on a qualitative level, that NN outward displacements of -0.3 A, i.e. N 10% of the lattice
305
spacing r. [25], were necessary to obtain agreement with experiment. Barriuso and Moreno [17] analyzed the measured shf interaction of several AX: AgO systems with a molecular-orbital scheme. They obtained NN outward displacements (and values relative to host lattice spacing [25]) of 0.70 A (27%) in LiCl, 0.55 A (19%) in NaCl, 0.54 A (17%) in KCl, 0.51 A (15%) in RbCl, and 0.45A (14%) in KBr hosts [38]. The above values for NN displacements of impurity silver atoms are put in better perspective by a with calculated NN displacements comparison around impurity silver ions in alkali hosts, AX : Ag+. Moine et al. [15], using a multiple-scattering Xa method applied to an embedded (AgCl,$ cluster, obtained NN displacements of 1.22 A (60%) for LiCl:Ag+ and 0.33A (12%) for NaCl:Ag+. These displacements, exceeding even ionic hard-sphere behavior, appear much too large. It seems that the authors’ simulation of the crystal environment through mere charge distributions [15] is insufficient to account for the compressing sr forces from the host crystal on the simulation cluster. Using the unrestricted Hartree-Fock approximation, Meng and Kunz calculated the electronic structure of impurity clusters whose ions relax under sr repulsion and vdW attraction forces [18]. The authors got surprisingly small NN displacements of 0.03 8, (1%) for the NaCl: Ag+ complex. In an interpolation scheme of host lattice spacings, supported by a simple force model [39] and combined with a resealing of ionic radii [40], the following average values of NN displacements around Ag+ impuritied.23 A (9%) in LiX, 0.13 A (4%) in NaX, 0.04A (1%) in KX, and -0.12A (-4%) in RbX hosts-were obtained by this author. Compared to displacements around impurity silver ions, two changes occur for displacements around impurity silver atoms. We explore these changes here only on a qualitative level. The first change concerns the charge neutrality of the Ago impurities. The absence of Coulomb attraction between Ago atoms and surrounding X- ions causes outward NN displacement of these ions. Very simple cases where only this effect is present exist for vacancies in AX crystals. Atomistic calculations with Born-Meyer potentials and a deformation dipole model [41] by Leutz [42] and Potstada [43] gave NN displacements around cation vacancies of 7% in AF, 4% in ACl, 2% in ABr, and 1% in AI crystals [37,44]. Similar contributions to NN displacements can be expected from the charge neutrality of impurity Ago atoms in AX hosts. The second change, compared to an impurity Ag+ ion, is the expanded size of an impurity Ago atom
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resulting from both an expanded atom core and the additional 5s orbital. The increase of the Ago atom’s core is well represented by the difference between the 4d orbital moment of an Ago core and that of an Ag+ ion, 0.80 8, - 0.73 8, = 0.07 A [23,46]. Since most of the sr repulsion between NN atoms and ions originates from overlap of the outermost closed electron shells [41] the Ago core expansion contributes -2% (of ro) to the NN displacements in the AX hosts. The repulsion from the (open-shell) 5s’ orbital of Ago on the X- neighbor ions is more difficult to determine but it can be considered small, causing very little NN displacements-probably less than 1%. Combining all these contributions amounts to NN displacements in AX: Ago complexes from close to 10% in the fluorides down to -3% in the iodide hosts. The present estimates of NN displacements around Ago impurities, based on interaction potentials and atomistic calculations [4143] are about half as large as the estimates from calibrations with a free-atom wavefunction by Holmberg et al. [5] and about a quarter of the values calculated by Barriuso and Moreno with a molecular-orbital scheme [17]. The indication in Fig. 1 of substantial Madelung contributions to the hf shift of AX : Ago complexes suggests that the large and, respectively, very large apparent NN displacements obtained by these authors could be an artifact resulting from the neglect of the Madelung potential in both the free-atom calibration [5] and the molecular-orbital calculation [17].
6. CONCLUSION
Three experimental values of Ago impurity hyperfine shifts-in NaCl, KCl, and KBr hosts-are used to extrapolate hf shifts of substitutional Ago impurities in the remaining 13 alkali halide crystals with rocksalt structure. The extrapolation is based on scaling relations of hf shifts with the host lattice spacing and with orbital moments of host neighbor ions (or atoms). Such scaling relations have been successful for hydrogen and mint metal impurities in rare gas matrices and for interstitial hydrogen atoms in alkali halide hosts. The extrapolated values are in reasonable agreement with measured hf shifts in RbCl and KI hosts, although some problems remain in the latter case. However, the original scaling relations break down for the LiX hosts and an ad hoc resealing scheme is used to account for strong compression of the oversized Ago impurities in the LiX matrices. The finding of unsystematic (non-scaling) features in the data from KX hosts makes a remeasurement of hf shifts of the KBr: Ago and KI:AgO complexes desirable. Equally interesting will be experiments with the re-
maining impurity-host systems to test the predicted hf shifts. A comparison of hf shifts of Ago impurities in both alkali halide and rare gas hosts indicates a large contribution from the Madelung potential. The influence of the Madelung potential on the Ago 5s orbital affects the derivation of neighbor ion displacements from the measured superhyperfine interactions with host neighbor nuclei. Taking the Madelung potential into account could give neighbor displacements considerably smaller than previously obtained and closer to estimates from atomistic calculations of similar lattice defects. Note added After submission of the manuscript I learned that the hf shift of the system KF : ‘OS Ago had been recently measured [47]. The experimental hf constant is a/h = 2002.4 MHz + 0.5% compared to the predicted value from Table 1, a/h = 2000.7 MHz, differing 0.1% from experiment, i.e. less than the experimental uncertainty. This finding supports the present interpolation scheme and the choice in selecting the underlying basic data.
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50.
307
isoanionic host sequence AC1 (A = Li, Na, K, Rb) is in differences accordance with decreasing size r(A$)-r(A+). However, contrasting Ref. 17, no decrease of absolute NN displacements would be expected when going from KC1 to KBr because of the wider lattice spacing in the latter, isocationic host. Shih C. K.. Snicer W. E., Harrison W. A. and Sher A., Phys. Reu.‘B-31, 1139 (i985). Bucher M., Phys. Rev. B 45, 7444 (1992). Bucher M., Phys. Rev. B 30, 947 (1984). Leutz R. K., thesis, University of Stuttgart 1977, cited in Ref. 41. Pot&da H. H., thesis, University of Frankfurt (1980), cited in Ref. 41. Slightly larger NN displacements than around cation vacancies were obtained (in Refs 42 and 43) around anion vacancies: 9% in LiX, 7% in NaX, 5% in KX and 3% in RbX. The overall larger NN displacements around anion vacancies than around cation vacancies originates from the stronger (non-Coulombic) anion-anion interaction compared to cation*tion interaction in AX crystals. In another calculation with Born-Mayer potentials and a polarization shell model (Ref. 45) NN displacements of 8% around anion vacancies in KC1 were obtained. The latter value for cation displacements (around anion vacancies), cited in Ref. 17, does not directly relate to anion displacements around Ags impurities. Heder G., Spaeth J. M. and Harker A. H., J. Phys. C 13, 4965 (1980). Bucher M., Phys. Rev. B 27, 5919 (1983). Yu C., thesis, Michigan Technological University (1991). Ghate P. B., Phys. Rev. A 139, 1666 (1965). Bell R. J. and Zucker I. J., in Rare Gas Solids (Edited by M. L. Klein and J. A. Venables), Vol. 1, p. 161. Academic Press, London (1976). Wessel G. and Lew H., Phys. Rev. 92, 641 (1953).
Chem. Solids Vol. in Great Britain.
54, No.
3, pp.
301-307,
1993 0
0022-3697/93 S6.00 + 0.00 I!393 Pergamon Press Ltd
HYPERFINE INTERACTION OF IMPURITY SILVER ATOMS IN ALKALI HALIDE CRYSTALS MANPBBD BIJCHER Physics Department, California State University, Fresno, CA 93740-0037, U.S.A. (Received 22 July 1992; accepted 26 October 1992) Abstract-Experimental data from Ago impurities in NaCl, KC1 and KBr hosts are used to extrapolate hyperfine (hf) shifts of Ag” impurities in the remaining 13 alkali halide crystals with rocksalt structure. The extrapolation is based on scaling relations of hf shifts with the host lattice spacing and with orbital moments of host neighbor ions. A comparison of hf shifts of A$ impurities in both alkali halide and rare gas matrices indicates a large contribution from the Madelung potential. As a consequence, a revised determination of neighbor ion displacements from superhyperfine interaction may be necessary. Keyword: Electron spin resonance, silver impurities, ionic crystals, short-range forces, impurity-host interaction.
1. INTRODUCTION
Aala, (Rg : ImO) scales with the orbital-moments
ratio
q = ,/R(*)/P of the Rg host atoms [19]. Here Rc2)is the Impurity silver atoms and ions in alkali halide crystals, AX: Ago and AX: Ag+, respectively, have been studied with ESR [l-6], ENDOR [2, 5,7], spectroscopy [S-14], and quantum mechanical calculations [15-181 for more than three decades. It has been found that the Ag0 atoms and Ag’ ions are substitutionally situated at (or near) cation lattice sites in the AX hosts. The observed disturbances of the electron structures of Ago and Ag+ impurities, caused by the closed-shell ions of the AX hosts, provide information about the configurations of, and interactions in the impurity-host complexes. One of the simplest indicators for impurity-host interaction is the relative shift Aa/u,, of hyperfine (hf) interaction between the nucleus and the 5s electron of an impurity Ago atom. Here Aa = a - a, denotes the difference between the isotropic hf interaction constants a and a,, of the Ago impurity and of a free silver atom, respectively. Such hf shifts have been measured for Ago in LiCl, NaCI, KCl, KBr, KI and RbCl at temperatures of T = 4 K and/or T = 77 K [l-6]. In this paper we extrapolate the T = 4 K data, listed in Table 1, to obtain hf shifts of Ago impurities in the remaining AX crystals with rocksalt structure. The extrapolation is based on findings and trends of hf shifts of substitutional impurity hydrogen and mint metal atoms-Ho, Cue, Ago, Au”-in rare gas (Rg) crystals [19], of interstitial hydrogen atoms HP in AX hosts [20], and of impurity copper atoms Cue and ions Cu+ in AX hosts [21,22]. For impurity atoms (ImO) of ns’ ground state electron structure embedded in Rg crystals, the hf shift
total second orbital moment and i is the first moment of the outermost orbital. Since the orbital moment R(*)is a factor in the van der Waals (vdW) attraction and the moment i is a factor in the short-range (sr) repulsion between Rg and Im” atoms, the ratio q(Rg) serves as a measure [23] for the counteractive effects from these potentials on the hf shift Aala,. More specifically, a large q value indicates a large dominance of vdW attraction over sr repulsion on an Im” atom from the surrounding Rg atoms. This causes less compression (or more expansion) of Im” which in turn gives rise to a less positive (or more negative) hf shift. A similar scaling of da/a, with the orbital-moments ratio q(x- ) of the neighbor halide ions was found [20] for interstitial hydrogen atoms in alkali halides, AX: HP. In addition, the hf shifts of the AX:Hy complexes scale also with the host lattice spacing r, due to an indirect influence from the host cations A+. The present task of extrapolating hf shifts of AX : Ago from the few measured systems to the whole AX family (with rocksalt structure) is complicated by two circumstances. First, the measured Aala, values at T = 77 K and T = 4 K show a substantial temperature dependence [l-6]. In the temperature interval from T = 4K to T = 77 K, the Ago hf shift Aala, shifts by -0.7% in NaCl, by - 1% in KCI, and by -3% in LiCl toward more negative values. The amount of such temperature shifts reaches to the same order of magnitude as the hf shifts of the AX: Ago complexes at T = 0, caused solely by the host crystal environment. Thus, in order 301
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302
Table 1. Measured and extrapolated values of the relative hf shift s = Au/a, (in %) of impurity Ag atoms in alkali halide
and rare gas crystals at T = 4 K (top value) and nearestneighbor distancetl r0 (in A) in the host crystals at T = 0 (bottom value). The experimental values, marked by references, have error margins of +0.3% or less. The values for lithium halide hosts, marked with asterisks, were obtained with a resealing scheme (see text). The corresponding hf constants a = (s + l)a, are readily obtained with the free atom values a,/h of 1712.56MHz and 1976.94MHz for lo7Ag and IWAg isotopes, $respectively, and Planck’s constant h Li Na K Rb
F
Cl
Br
5.6* 1.996 -0.1 2.295 1.2 2.648 1.7 2.789 Ne 9.7 3.156
0.811 2.539 -4.97 2.789 -3.81 3.116 -3.4 3.259
-1.Of 2.713 -6.5 2.954 -5.4tt 3.262 -5.0 3.410
&t. 3.756
&$ 3.992
I -3.2* 2.951 -8.9 3.194 - 6.2tt 3.489 -7.4 3.628 Xe l.O$% 4.336
tRef. 48. $Ref. 49. #Ref. 50. IJExtrapolated from a graph in Ref. 3. TRef. 5. ttRef. 4. SfRef. 35.
to circumvent the temperature effects, we extrapolate only the T = 4 K data [24]. The second complication for the attempted extrapolation of hf shifts arises from spectroscopic observations [lO-14,221 of KI:Ag+, RbCl:Ag+, and several AX:Cu+ complexes where an impurity Ag+ or Cut ion can occupy off-center positions in AX hosts when the ionic radius of the impurity is smaller
than that of a host cation, r(Im+)
2. EXTRAPOLATION
Assuming a scaling of the impurity hf shift with the host lattice spacing r. [25], as found for the AX : HP systems [20] we extend straight lines through the three basic data points from the NaCl : Ago, KCI : Ago and KBr: Ago complexes in the An/u,, vs r, plot of Fig. 1. At the corresponding r, values we read estimated hf shifts Aala, for Ago in the remaining chlorides, LiCl and RbCl, and potassium halides, KF and KI, off these lines. Guided by analogy with Aala, (AX:HT), we draw a third line through the KBr data point in Fig. 1 running parallel to the NaCl-KC1 line. This permits us to read off As/a, estimates for the Ago hf shift in the remaining bromides LiBr, NaBr and RbBr. From a fourth, extended line through NaCl and NaBr we obtain Aala, of Ago in the other sodium halides, NaF and NaI. Repeated extensions of straight lines through the new points obtained in this way give Aala, estimates of Ago in the final hosts, LiF, RbF, LiI, RbI, at the corresponding r. values in Fig. 1 and, concurrently, very close to the
Fig. 1. Relative hf shift da/a, of impurity Ag” atoms in alkali halide and rare gas crystals vs host lattice spacing r,, (nearest-neighbor distance): triangles show experimental data; open circles represent extrapolated values and full circles resealed values (see text). The diamonds display the hf shifts of substitutional Ago atoms in rare gas crystals vs nearest-neighbor distances from fee interstitial sites (r&/2).
Interaction of silver impurities in alkali halide crystals
Aa 1,
r
I
1
I
I
t (3
0
b
-5
-10 2.8
3.0
3.2
p
3.4
Fig. 2. Measured (triangles) and extrapolated (open circles) relative hf shifts Au/a, of impurity AJ$’atoms in alkali halide and rare gas crystals vs orbital-moments ratio q of anions and rare gas atoms, respectively. Full circles represent resealed values for the lithium halide hosts.
intersections of the straight lines. The extrapolated Au/a, values, except for LiX (see below), are compiled in Table 1. The dependence of the measured and extrapolated hf shifts on the anion orbital-moments ratio [26] q@- ) is shown in Fig. 2. The similarity in the slopes of the lines connecting data from hosts with the same and different anions X-, alkali ions A+ d(Aa/a,,)/dq(X-)I,+ < 0, indicates that increasingly dominant vdW attractions from larger neighbor anions X- tend to expand the impurity Ago atom, causing spin density depletion at the Ag nucleus and, consequently, a negative contribution to the hf shift. The intluence from increasingly dominant vdW attraction over sr repulsion between Ago and neighboring X- ions with increasing anion radius r,_ can also be seen in Fig. 1 by the negative slopes of the lines connecting the data for isocationic hosts, a(Aa/q,)/ar,_l,,+ < 0. On the other hand, the positive slopes of the isoanionic lines in Fig. 1, a(Au/u,,)/gr,+]x_ > 0, result from an indirect influence of the host crystal cations A+ on the Ago hf shift through the cations’ contribution to the host lattice spacing [20]. In these cases the increased lattice spacing [25] r. = (r,,+ + rx_) for AX hosts with the same anions but different cations (of increasing ion radius rA+) reduces the vdW attraction between A$ and the surrounding X- ions which in turn reduces the expansion of the Ago impurity atom.
303
3. CASE DJSCUSSION With increasing temperature the hf shift of Ago is observed to become more negative (by -3.3%, -0.7% and - 1.0%) in the three known cases of LiCl, NaCl and KC1 hosts [2-51. This is qualitatively expected due to diminished spin density (on timeaverage [271) at the Ag nucleus resulting from oscillations of the 5s electron cloud about the nucleus when the Ago atom is thermally agitated by the surrounding host ions. Fitting that trend, the extrapolated hf shift of the RbCl: Ago complex at T = 4 K, Au/a, = -3.4%, in Table 1 comes out appropriately higher (1.6%) than the measured value at T = 77 K, Aala, = -5.0 f 0.6% [3]. On the other hand, the extrapolated value Au/u, = -7.9% in Fig. 1 for the KI:AgO system at T = 4 K is 1.7% lower than the experimental value of -6.2% measured at the same temperature. Since the ionic impurity complex KI: Ag+ is known to have a delicate on-center/off-center stability [12] the possibility of off-center behavior of the atomic impurity complex KI: Ago comes to mind. However, a displacement of the 5s electron cloud relative to the nucleus of an off-center Ago atom, caused by electronic and deformation dipole mechanisms, would give rise to spin density depletion at the Ag nucleus and would lead to a much deeper hf down shift than for an on-center Ago atom. Such a situation of a very large hf down shift, Aala, = - 17.4% at T = 77 K [21], seems to be present for the KCl: Cue complex which is qualitatively in agreement with the spectroscopically [22] established off-center character of the ionic impurity system KC1 : Cu+. Having ruled out an off-center position of the Ago atom in a KI host as the cause for the deviation of the extrapolated hf shift from the experimental value, the 1.7% discrepancy remains unexplained [28]. Much more severe than for the KI host is the discrepancy for the LiCl matrix where a hf shift Au/a, = -5.8% is extrapolated but Au/a, = +0.8% is measured (see Fig. 1). The large discrepancy warrants an exploration of possible irregularities in the experimental data and of circumstantial information. (1) A positive hf shift, Au/u,= +17%, was also measured for Cue impurities in LiCl (at 77 K) [21]. This corroborates the observed positive hf shift of Ago impurities in that host. (2) It has been established from well-resolved ESR signals [3,21] of both LiCl: Ago and LiCl : Cue systems, and also by spectroscopy [22] of the ionic complex LiCl: Cu+, that these impurities occupy on-center positions in LiCl hosts. This rules out the possibility of off-center effects-which in any case would give rise to negative instead of positive hf shifts. (3) The LiCl : Ago hf shift (and also the superhyperhne interaction) shows a
304
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strong, nonlinear temperature dependence, d(Au/ %)/dT < 0, which distinguishes the LiCl matrix from the other AX hosts [3]. The temperature dependence indicates that with rising temperature a thermal relaxation process takes place. Obviously, the present extrapolation of hf shifts of on-center Ago atoms in a LiCl host fails, posing a severe setback to the extrapolation scheme which was quite successful for Rg : Im” and AX: HP impurity systems [19,20]. Taking a clue from the temperature dependence, we believe that the observed, slightly positive hf shift of the LiCl : Ago complex is the result of so strong a compression of the Ago impurities by their closest Cl- host neighbors that it more than compensates the expanding effect from the Madelung potential (to be discussed below). Such a compression is likely to occur when impurity Ago or Cue atoms substitute the much smaller Li+ ions. A rough size comparison is provided by Pauling ionic radii: r(Ag+) = 1.26& r(Cu+) = 0.96& r(Li+) = 0.60 A, r(Na+) = 0.95 A, r(K+) = 1.33 A, r(Rb+) = 1.48 A. If the observed hf shift in the LiCl host is indeed caused by a strong compression of Ago atoms, then the extrapolated As/a, values for the other LiX hosts must be discarded as well. However, the compression mechanism does not necessarily eliminate the vdW influence from neighbor anions on the Ago impurities. Thus, if we assume a similar influence of vdW interaction on hf shifts in the remaining LiX, as employed for Ago impurities in the other AX crystals and as found for Rg hosts [19], then we can obtain new estimates, Aa*/a, (LiX: Ago), which better take into account the compression of Ago atoms. Such resealed Au */a0 (LiX : Ago) values are listed in Table 1 and shown by full circles in Figs 1 and 2. Certainly, their derivation is based on an ad hoc assumption which must be judged by future hf measurements of LiX: Ago impurity systems and by theoretical analysis.
4. COMPARISON WITH RARE GAS HOSTS For an exploration of the influences from crystal structure and binding, a comparison of Ago hf shifts in AX with those of Ago atoms in Rg hosts is in order. Common to the Ago impurities in both AX and Rg matrices is the closed electron shell character of their immediate X- and, respectively, Rg neighbors. This causes similar vdW attraction and sr repulsion of Ago atoms with X- ions and with isoelectronic Rg atoms. Different in these hosts is the number of nearest neighbors (NN) around Ago, namely six X- ions compared to 12 Rg atoms. Another difference arises from the Madelung potential [29], present in AX but absent in Rg crystals.
In order to discern the influence from the closedshell nature of the host neighbors, we compare in Fig. 2 the dependence of the Ago hf shift on the orbital-moments ratio of the host neighbors for both AX and Rg hosts. The almost parallel lines indicate that the same mechanism of balancing vdW attraction and sr repulsion is effective in these different groups of host crystals. Since that mechanism is the basic concept underlying the present extrapolation of hf shifts of the AX: Ago complexes, the systematic finding in Fig. 2 corroborates the extrapolation scheme carried out in Fig. 1. Actually, the vdW/sr influence on Au/u,, as illustrated by the linear q-dependence in Fig. 2, is a secondary effect. It reduces the primary compression of Ago in Rg matrices and enhances the primary expansion of Ago in AX hosts. The primary compression of the oversized Ago atom by its 12 neighbor atoms in an Rg (fee) host lattice, resulting in a positive hf shift, Au/a, > 0, is not very surprising. Not so trivial is the primary expansion of Ago in AX. It is caused by the Madelung potential in the ionic crystals [29]. More familiar than its effect on hf shifts is the effect of the Madelung potential on the band structure [3&32], on ion polarizabilities [33], and on ion cores [34] of AX crystals. In the region inside the shell of NN ions (neighbor shell 1) the Madelung potential forms a potential well at anion lattice sites [29] and a potential plateau (upside-down potential well) at cation lattice sites. The potential wells and plateaus lower and raise, respectively, the electron energy levels in the ions or atoms occupying these sites. The raised electron energy levels of an impurity Ago atom in an AX lattice cause a reduction in the binding of the 5s electron and an extension of its orbital. This in turn results in spin density depletion at the Ag nucleus and thus in a negative hf shift, An/a, < 0.
An assessment of the influence from the Madelung potential by a comparison of Ago hf shifts in AX and Rg hosts is complicated by the different neighbor coordinations of substitutional Ago complexes in these crystals. The difference in neighbor coordination could be circumvented, however, by a comparison of substitutional silver atoms in alkali halide hosts, AX:AgO, with impurity silver atoms at octahedral intersritial sites in rare gas crystals, Rg: Agy . A silver atom at such an interstitial site in a Rg host has six closed-shell neighbors just like the substitutional silver atom in an AX: Ag(’ complex. Ignoring the weak vdW attraction and sr repulsion between the Ago impurity and surrounding ions or atoms beyond the six immediate X- or Rg neighbors, the essential difference left between Rg : Agp and isoelectronic AX: Ago complexes is the
Interaction of silver impurities in alkali halide crystals Madelung potential from the point ions in the AX crystals. Yet, no direct comparison of equally coordinated Ago impurities in Rg and AX hosts is possible, because only substitutional silver atoms in rare gas hosts, Rg:AgO-but no stable complexes with interstitial configuration, Rg: Agy-are observed [35]. On the other hand, impurity hydrogen atoms are embedded in Rg hosts at both substitutional and octahedral interstitial sites with respective hf shifts Aala, (Rg:HO) < Aala (Rg:Hy) [36]. Thus, by analogy, the measured Au/a, (Rg : Ago) values may serve as lower bounds of hf shifts Aala, (Rg : Agy) of interstitial silver atoms in Rg hosts. Such lower bounds are indicated in Fig. 1 by diamond symbols which display the hf shifts of substitutional Ago atoms in Rg hosts not vs neighbor distances r, from substitutional sites but vs the neighbor distances from octahedral interstitial sites in these hosts (r,/,/2). Figure 1 shows that the spacing between the Ago hf shifts in the Ar, Kr and Xe hosts is similar to the spacing of hf shifts in the ACl, ABr and AI hosts [37]. More specifically, the vertical differences of _ 10% between the diamond symbols in Fig. 1 and the AX lines associated with isoelectronic X- ions indicate that the influence from the Madelung potential on the hf shift of Ago impurities is quite large and must not be ignored. Because of the involved assumptions and uncertainties, the figure of 10% should not be considered an accurate value of the Madelung shift but rather an order-of-magnitude estimate. Nevertheless, the present indication of a lowering of the Ago hf shift by the Madelung potential in AX crystals to an extent of 10% (or more) implies a considerable redistribution of 5s electron charge from the region of the Madelung plateau inside the first neighbor shell to higher neighbor regions where the (radial) 5s wavefunction has its tail.
5. NEIGHBOR DISPLACEMENTS If the Madelung potential gives rise to a substantial 5s electron charge redistribution, then this affects the interpretation of superhyperfine (shf) interaction with nuclei of the surrounding ions. Using a wavefunction from Hartree-Fock calculations of a free Ago atom and Gourary-Adrian amplification factors [29] to account for orthogonalization admixture of the Ago envelope wavefunction to neighbor ions in NaCl and KC1 crystals, Holmberg et al. [5] calculated for NN anions on (ideal) host lattice sites larger shf constants than the measured values. The authors estimated, on a qualitative level, that NN outward displacements of -0.3 A, i.e. N 10% of the lattice
305
spacing r. [25], were necessary to obtain agreement with experiment. Barriuso and Moreno [17] analyzed the measured shf interaction of several AX: AgO systems with a molecular-orbital scheme. They obtained NN outward displacements (and values relative to host lattice spacing [25]) of 0.70 A (27%) in LiCl, 0.55 A (19%) in NaCl, 0.54 A (17%) in KCl, 0.51 A (15%) in RbCl, and 0.45A (14%) in KBr hosts [38]. The above values for NN displacements of impurity silver atoms are put in better perspective by a with calculated NN displacements comparison around impurity silver ions in alkali hosts, AX : Ag+. Moine et al. [15], using a multiple-scattering Xa method applied to an embedded (AgCl,$ cluster, obtained NN displacements of 1.22 A (60%) for LiCl:Ag+ and 0.33A (12%) for NaCl:Ag+. These displacements, exceeding even ionic hard-sphere behavior, appear much too large. It seems that the authors’ simulation of the crystal environment through mere charge distributions [15] is insufficient to account for the compressing sr forces from the host crystal on the simulation cluster. Using the unrestricted Hartree-Fock approximation, Meng and Kunz calculated the electronic structure of impurity clusters whose ions relax under sr repulsion and vdW attraction forces [18]. The authors got surprisingly small NN displacements of 0.03 8, (1%) for the NaCl: Ag+ complex. In an interpolation scheme of host lattice spacings, supported by a simple force model [39] and combined with a resealing of ionic radii [40], the following average values of NN displacements around Ag+ impuritied.23 A (9%) in LiX, 0.13 A (4%) in NaX, 0.04A (1%) in KX, and -0.12A (-4%) in RbX hosts-were obtained by this author. Compared to displacements around impurity silver ions, two changes occur for displacements around impurity silver atoms. We explore these changes here only on a qualitative level. The first change concerns the charge neutrality of the Ago impurities. The absence of Coulomb attraction between Ago atoms and surrounding X- ions causes outward NN displacement of these ions. Very simple cases where only this effect is present exist for vacancies in AX crystals. Atomistic calculations with Born-Meyer potentials and a deformation dipole model [41] by Leutz [42] and Potstada [43] gave NN displacements around cation vacancies of 7% in AF, 4% in ACl, 2% in ABr, and 1% in AI crystals [37,44]. Similar contributions to NN displacements can be expected from the charge neutrality of impurity Ago atoms in AX hosts. The second change, compared to an impurity Ag+ ion, is the expanded size of an impurity Ago atom
MANFRF.D BUCHER
306
resulting from both an expanded atom core and the additional 5s orbital. The increase of the Ago atom’s core is well represented by the difference between the 4d orbital moment of an Ago core and that of an Ag+ ion, 0.80 8, - 0.73 8, = 0.07 A [23,46]. Since most of the sr repulsion between NN atoms and ions originates from overlap of the outermost closed electron shells [41] the Ago core expansion contributes -2% (of ro) to the NN displacements in the AX hosts. The repulsion from the (open-shell) 5s’ orbital of Ago on the X- neighbor ions is more difficult to determine but it can be considered small, causing very little NN displacements-probably less than 1%. Combining all these contributions amounts to NN displacements in AX: Ago complexes from close to 10% in the fluorides down to -3% in the iodide hosts. The present estimates of NN displacements around Ago impurities, based on interaction potentials and atomistic calculations [4143] are about half as large as the estimates from calibrations with a free-atom wavefunction by Holmberg et al. [5] and about a quarter of the values calculated by Barriuso and Moreno with a molecular-orbital scheme [17]. The indication in Fig. 1 of substantial Madelung contributions to the hf shift of AX : Ago complexes suggests that the large and, respectively, very large apparent NN displacements obtained by these authors could be an artifact resulting from the neglect of the Madelung potential in both the free-atom calibration [5] and the molecular-orbital calculation [17].
6. CONCLUSION
Three experimental values of Ago impurity hyperfine shifts-in NaCl, KCl, and KBr hosts-are used to extrapolate hf shifts of substitutional Ago impurities in the remaining 13 alkali halide crystals with rocksalt structure. The extrapolation is based on scaling relations of hf shifts with the host lattice spacing and with orbital moments of host neighbor ions (or atoms). Such scaling relations have been successful for hydrogen and mint metal impurities in rare gas matrices and for interstitial hydrogen atoms in alkali halide hosts. The extrapolated values are in reasonable agreement with measured hf shifts in RbCl and KI hosts, although some problems remain in the latter case. However, the original scaling relations break down for the LiX hosts and an ad hoc resealing scheme is used to account for strong compression of the oversized Ago impurities in the LiX matrices. The finding of unsystematic (non-scaling) features in the data from KX hosts makes a remeasurement of hf shifts of the KBr: Ago and KI:AgO complexes desirable. Equally interesting will be experiments with the re-
maining impurity-host systems to test the predicted hf shifts. A comparison of hf shifts of Ago impurities in both alkali halide and rare gas hosts indicates a large contribution from the Madelung potential. The influence of the Madelung potential on the Ago 5s orbital affects the derivation of neighbor ion displacements from the measured superhyperfine interactions with host neighbor nuclei. Taking the Madelung potential into account could give neighbor displacements considerably smaller than previously obtained and closer to estimates from atomistic calculations of similar lattice defects. Note added After submission of the manuscript I learned that the hf shift of the system KF : ‘OS Ago had been recently measured [47]. The experimental hf constant is a/h = 2002.4 MHz + 0.5% compared to the predicted value from Table 1, a/h = 2000.7 MHz, differing 0.1% from experiment, i.e. less than the experimental uncertainty. This finding supports the present interpolation scheme and the choice in selecting the underlying basic data.
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Interaction of silver impurities in alkali halide crystals 22. Payne S. A., Phys. Rev. B 36, 6125 (1987). 23. Bucher M., Phys. Rev. B 35, 5985 (1987). 24. In view of the experimental uncertainty of f 0.3% in the Aala, data in Table 1, we can, for the present purpose, identify the T = 4 K data with hf shifts at T = 0. 25. The term “lattice spacing” and the symbol r, are used for the nearest-neighbor distance in a pure AX or Rg host crystal. 26. The values q(Cl-) = 3.06, q(Br-) = 3.17, q(I-) = 3.31, q(Ar) = 3.08, q(Kr) = 3.22 and q(Xe) = 3.39 were obtamed from first-principles calculations (Ref. 23). An empirical value q = 2.75 was adopted for F- which has proved useful in the scaling of hf shifts of AX:HP complexes (Ref. 20). 27. Bucher M., Phys. Rev. B 35, 2923 (1987). 28. I have also attemotcd to use. besides the NaCl: AaO and KCl: Ago data, the experimental hf shifts of boih the KBr: Ago and KI: Ag” complexes (via minimum deviation) as the third cornerstone for an extrapolation procedure. Such attempts produced unsystematic features and were therefore discarded. 29. Gourarv B. S. and Adrian F. J.. in Solid Stale Phvsics (Edited- by F. Seitz and D.. Turnbull), Vol.. 10, pp. 128-247. Academic Press, New York (1960). 30. Seitz F., Reu. Mod. Phys. 23, 328 (1951). 31. Zunger A. and Freeman A. J., Phys. Rev. B 16, 2901 (1977). 32. Kunz A. B., Phys. Rev. B 26, 2056 (1982). 33. Ruffa A. R., Phys. Rev. 130, 1412 (1963). 34. Broughton J. Q. and Bagus P. S., Phys. Rev. B NJ,4761 (1984). 35. Kasai P. H. and McLeod D., J. Chem. Phys. 55, 1566 (1971). 36. Foner S. N., Cochran E. L., Bowers A. V. and Jen C. K., J. Chem. Phys. 32, 963 (1960). 37. The letter A stands for alkali elements. 38. A decrease of absolute NN displacements in the
39. 40. 41. 42. 43. 44.
45.
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46. 47. 48. 49.
50.
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isoanionic host sequence AC1 (A = Li, Na, K, Rb) is in differences accordance with decreasing size r(A$)-r(A+). However, contrasting Ref. 17, no decrease of absolute NN displacements would be expected when going from KC1 to KBr because of the wider lattice spacing in the latter, isocationic host. Shih C. K.. Snicer W. E., Harrison W. A. and Sher A., Phys. Reu.‘B-31, 1139 (i985). Bucher M., Phys. Rev. B 45, 7444 (1992). Bucher M., Phys. Rev. B 30, 947 (1984). Leutz R. K., thesis, University of Stuttgart 1977, cited in Ref. 41. Pot&da H. H., thesis, University of Frankfurt (1980), cited in Ref. 41. Slightly larger NN displacements than around cation vacancies were obtained (in Refs 42 and 43) around anion vacancies: 9% in LiX, 7% in NaX, 5% in KX and 3% in RbX. The overall larger NN displacements around anion vacancies than around cation vacancies originates from the stronger (non-Coulombic) anion-anion interaction compared to cation*tion interaction in AX crystals. In another calculation with Born-Mayer potentials and a polarization shell model (Ref. 45) NN displacements of 8% around anion vacancies in KC1 were obtained. The latter value for cation displacements (around anion vacancies), cited in Ref. 17, does not directly relate to anion displacements around Ags impurities. Heder G., Spaeth J. M. and Harker A. H., J. Phys. C 13, 4965 (1980). Bucher M., Phys. Rev. B 27, 5919 (1983). Yu C., thesis, Michigan Technological University (1991). Ghate P. B., Phys. Rev. A 139, 1666 (1965). Bell R. J. and Zucker I. J., in Rare Gas Solids (Edited by M. L. Klein and J. A. Venables), Vol. 1, p. 161. Academic Press, London (1976). Wessel G. and Lew H., Phys. Rev. 92, 641 (1953).