THE BONDING AND VALENCE PROPERTIES OF IRON GROUP IMPURITIES IN NaF BY W. HAYES The Clarendon Laboratory, University of Oxford Received 30th June, 1958 The paramagnetic resonance spectra of iron group ions present as trace impurities in NaF have been investigated and the ions Cr+, Mn2+, Fe+, Co2+, Co+ and Ni+ have been observed. The monovalent ions are produced by irradiating a crystal containing the corresponding divalent impurity with prays, X-rays or electrons and are stable to about 140°C. Each impurity ion forms a weak covalent complex with the surrounding octa- hedron of fluorine ions resulting in a fluorine hyperfine structure in the resonance spectrum. The bonds are of the o-type and for Cr+, Mn2+ and Fe+ the amount of electron transfer is estimated. The properties of a crystalline lattice are considerably affected by the presence of impurity ions and these effects have been studied in a number of ways.The luminescence of many phosphors is associated with the presence of impurities and in some cases these are paramagnetic, for example ZnS and CdS activated with copper or manganese ions. Other phosphors of interest are the alkali halides activated with thallium and calcium fluoride with rare earths. The properties of impurities in these crystals have been investigated through their optical ab- sorption spectra, luminescence spectra, paramagnetic resonance spectra, dielectric loss and electrical conductivity. Interesting changes in the properties of crystals containing impurities may occur upon irradiation with ionizing radiations and the investigation of effects of this type has been largely confined to alkali halides.In these crystals, well-defined colour centres are found which are associated with the presence of impurity ions.1 Many impurities are effective electron traps and irradiation under suitable conditions may produce a metastable valence state. In general, an impurity ion will distort the host lattice to some extent; the degree of distortion will depend on its valence, bonding characteristics and size and will determine the ease with which the impurity is incorporated into the lattice. It is of interest to know whether the impurity ion is present substitution- ally or interstitially. In cases where the charge on the impurity cations and the host cations are not the same, charge compensation must occur since the crystal as a whole must remain neutral and the mechanism by which this is achieved is also of interest.When the impurity ion is paramagnetic and the electron resonance spectrum is observable it is sometimes possible to obtain precise answers to these questions. The nature of the resonance spectrum gives information about the spectroscopic state of the ion and the symmetry and strength of the crystalline electric field in which it is placed. With NaF a fluorine hyperfine structure is observed in the resonance spectra of iron group impurity ions due to the formation of a weak covalent complex with the six nearest neighbour fluorine ions ; this structure arises from the interaction of the magnetic electrons with fluorine nuclei through bond formation.Analysis of the fluorine h.f.s. enables one to estimate the per- centage covalent character of the bonds and gives aztailed information about the environment of the impurity ion. In the preseni paper we shall be concerned mainly with structures of this kind and with the cbange of valence of the impurity ions which occurs upon irradiation of the crystals. 58W. HAYES 59 EXPERIMENTAL The crystals of NaF used in these experiments were grown by the Stockbarger tech- nique2 with known quantities of impurity added. An “Extra Pure” grade of NaF produced by B.D.H. Ltd. was used. The appropriate amount of salt containing the element required as impurity was mixed with NaF powder before loading into the graphite crucible. The type of salt used and the molar concentration of impurity added are given in table 1.TABLE 1 salt added to molar concentration of molar concentration of the melt impurity added impurity observed CrCl3-nH20 -01 % Cr -003 % MnF2 a 0 1 % Mn -002 % FeS04-7H20 -01 % Fe -0001 % CoC12.6H20 1.0 % c o *0004 % NiC12-6H20 -02 % Ni 402 % The measurements were made at 9200 Mc/sec with a paramagnetic resonance spectro- meter of the type described by Llewellyn.3 A high sensitivity was achieved by modulating the external magnetic field at 465 Kc/sec. Estimates of the concentration of impurity present in the crystal were made from the strength of the resonance signal and these are given in table 1 ; the error in the estimates amounts to about a factor of five. The irradiation of the NaF crystals was performed with (a) 6OCo y-rays at 40°C, or (b) 150 kV X-rays at room temperature, or (c) about 5 pA of 1 MeV electrons for 2 min at room temperature.The observed effects produced by each of these irradiations were substantially the same. THE INTERACTION OF THE MAGNETIC IONS WITH THE LATTICE A brief summary of the work on iron group impurities in NaF has already been given.% 5 NaF has the cubic NaCl type structure and each sodium ion is surrounded by a regular octahedron of fluorine ions. When singly charged impurity cations enter the lattice substitutionally the octahedral cubic symmetry will in general be maintained since vacancies are not introduced. Consider, however, a solid solution of MnF2 in NaF in which Mn2+ ions occupy sites normally occupied by Naf ions.In order to conserve charge the crystal will in general contain one cation vacancy for each Mn2+ ion incor- porated into the lattice. Vacancies are expected to occur near doubly charged impurity ions because of the electrostatic attraction between them. The degree of association of the vacancy-impurity complex appears to depend on the method of crystal growth and the concentration of impurity added. A vacancy in positions P or Q (fig. 1) will introduce an axial component about a cube edge into the crystal field seen by the impurity ion at A ; the lower symmetry will be apparent in the resonance spectrum and three distinguish- able magnetic complexes will be observed since there are three distinguishable cube edges. A vacancy in position R or S will introduce rhombic symmetry with principal axes along two face diagonals and a cube edge and six distinguishable magnetic centres will be found.Charge compensation for doubly charged impurity cations may also be achieved by introducing doubly charged impurity anions, for example, 02-, S2-. An example of such a system is described by Watkins 6 who suggests that charge compensation for Mn2+ ions in NaCl results from the presence of a doubly charged impurity anion at T (fig. 1). With NaF a check on this type of system is possible since the number of nearest neighbour fluorine ions may be determined from an analysis of the fluorine h.f.s. The first detailed description of extra-nuclear h.f.s. in the spectrum of a paramagnetic ion was given for Ir4+(5&) in the complex FrC16]2-.7, * , 9 Subsequently a fluorine h.f.s. was observed in the spectra of iron group (34 impurity ions in ZnF2 by Tinkham 10 and in CaF2 by Baker, Bleaney and Hayes.11 The fluorine h.f.s.arises from a partial transfer of the unpaired d electrons to orbits on fluorine ions and its order of magnitude may be estimated from the product of the h.f.s. of the free fluorine atom and the probability of finding the d-electrons on fluorines. The following discussion of the bonding follows van Vleck,l2 Owen 9 and especially Tinkham.10 Consider a complex AX6 where A is an iron group ion (3d9 surrounded by a regular octahedron of fluorine ions X. If we consider the bonding to be perfectly ionic then the60 orbitals of the magnetic electrons on A are of the form dx2-y2, d322-r2, d,,, d,,, dZx.The first two orbitals (dy type) have a higher energy than the remaining three (de type) which form a ground state orbital triplet. For Mnz+(d5) each of these orbitals is singly occupied and the ground state (6s) has zero angular momentum. If we consider the mixing which occurs between the central dy orbitals on A and the 2s and 2p orbitals on X then the modified dy orbitals become IRON GROUP IMPURITIES IN NaF 03~2-r2 Nu{&2-r2 + [au/l2f](pfc - P: + P: - P: - 2~: + 2~ :))a oX2-,,2 = NU{dx2-y2 + 8.X- P: + P: + P; - ~:)}u. I + - 8 - + + + - + - + - + FIG. 1.-Methods by which charge compensation may be achieved for a doubly charged cation A in NaF. P, Q, R and S are positive ion vacancies ; T is a doubly charged anion. The numbers 1, 2, 3 and 4, 5, 6 refer to nearest neighbour fluorine positions on positive and negative x, y , z axes respectively.The p orbitals are made up of 2s and 2p orbital- on X and = a: + &. The mixing between de orbitals on A and pn orbitals on X will lead to augmented de orbitals of the form nxy = Nn{&y + P; - P;" + P; - P;)l*. The admixtures in this case are expected to be smaller than for a-bonds and do not con- tribute measurably to the bonding in the cases to be described. The interaction between the magnetic electrons and the fluorine nuclei may be expressed in the form where I = Q is the spin of the fluorine nucleus and the summation is over the six nearest neighbour fluorine ions. Fluorine h.f.s. components occur at energies displaced from the zero interaction position by N N where Bz, is the angle between the external magnetic field and the bond axis to the Nth fluorine ion.The term arises from the s electron contact interaction through the fluorine 2s orbital. When the orbital angular momentum is completely quenched and when, as for Cr+, Mn2+ and Fe+, both o-bonding orbitals are singly occupied this becomes In this expression p is the Bohr magneton, f l is the magnetic moment of the Nth fluorine nucleus, S is the true electronic spin and s(0) is the amplitude at the fluorine nucleus ofW. HAYES 61 the 2s fluorine orbital. Where the observed multiplicity of the ground state is 2 an effective spin S’ = 4 may be used to describe the resonance spectrum.13 In such cases a correction factor 2 < IS[ > = gs/2 must be introduced such that gs A: = A“.This correction factor is unity for Cr+, Mn2+ and Ni+ and 1.6 for Fe+ where S = 9. The term A: includes (a) the coupling A; with the Nth fluorine nucleus through the Pa orbital, and (b) the direct magnetic dipole interaction gn13,gp/r3 between the Nth fluorine nucleus and the electronic wave function located on the central ion ; g and g, are the electronic and nuclear g-factors and /3, is the nuclear magneton. Both interactions have the same angular dependence and in general are comparable in magnitude (g,flngfl/r3 = 2.0 x 10-4 cm-1 for g = 2). If the orbital angular momentum is completely quenched then the expression for Ap”. becomes (7) where Y is the radius of the 2p wavefunction. In the calculations which follow we assume n = 2 orbitals and take I s ( 0 ) 12 = 75 x 1024 cm-3 and <r-3 > = 38 x 1024 cm-3.14915 In cases where the quenching approximation is poor and the g-factor departs considerably from 2 then the interaction between the electronic orbital magnetic moment and the fluorine nuclear spin should be considered ; ignoring the effect will introduce errors of around 20 % into the calculation of the anisotropic bonding for Fe+ and Ni+ and it will be neglected.When the external magnetic field is in the (111) orientation, (3 cos2 BZ,, - 1) = 0, and the interaction with six equivalent fluorines will give a seven-line h.f.s. with intensities in the ratio 1 : 6 : 15 : 20 : 15 : 6 : 1 ; 4 the spacing of the lines gives a direct measurement of A,. The parameter A , may now be determined by examination of the spectra in other orientations.Since both a-bonding orbitals are occupied in the case of Cr+, Mn2+ and Fe+ the probability that the magnetic electrons will be found in a fluorine 2s orbital is +A’?: and in a 2pa orbital is *I$$,; values for these expressions are given in table 2. TABLE 2 probability of probability of occupation of a orbital orbital Cr + 12.8 f 0.2 0 f 1.5 -42 % - Mn2+ 14.4 f 0.3 0.8 rt 0.7 -47 % 0.7 % Fe + 28.3 f 1.0 6.0 f 1.0 -35 % 2.0 % Ni + type I fluorines 41 f 2 14 f 2 - - type I1 fluorines 10 f 1 O f 2 occupation of a AS $0 fluorine 2s fluorine 2p0 ion - - The values of A, and A,, are expressed in units of 10-4 cm-1. DESCRIPTION OF THE RESONANCE SPECTRA CHROMIUM Clear crystals of NaF to which Cr3f ions were added to the melt do not show a resonance down to 20°K; the absence of a resonance is not unexpected if chromium is present in the lattice as Cr2+.After irradiation, however, a single isotropic line with a resolved fluorine h.f.s. appears at g = 2.000. The crystals are now a pink colour which is associated with an optical absorption band at 500 mp and probably arises from M centres.1 The resonance spectrum is assigned to chromium since a hyperfine structure due to 53Cr ( I = 3/2, natural abundance 9.5 %) is observed. An analysis of the fluorine h.f.s. shows that the bonding is of the o-type and that the centre is present substitutionally and is surrounded by a complete octahedron of fluorine ions. A fine structure is observed in the spectrum characteristic of the effect of a cubic crystal field on a 6S ground term.All this suggests that the chromium is present as Cr+ which is isoelectronic with62 Mn2+ (3d5,6S). It appears that Cr2f ions are stable electron traps and chromium can exist in the NaF lattice at room temperature in the monovalent form. IRON GROUP IMPURITIES IN NaF MANGANESE Before irradiation a complex spectrum is observed due to Mn2+; there are two types of Mn2+ centre present, each presumably arising from a different degree of association of the vacancy-impurity complex. The stronger spectrum has axial symmetry about a cube edge and the fluorine h.f.s. indicates that the Mn2+ ion is on a cation site and is surrounded by a complete octahedron of fluorine ions. The weaker spectrum which contains about 1 % of the total number of centres has a principal axis of symmetry along a cube edge.The splitting of the fine structure is greater in this orientation than that observed in the stronger spectrum suggesting that the vacancy is on a closer lattice site in this case. An analysis of the fluorine h.f.s. in the weaker spectrum was not possible because of insufficient intensity. After irradiation the intensity of the Mn2+ spectrum is reduced by 90 % but no new resonances are observed down to 4°K. It may be that the irradiation induced reduction of intensity is due to the conversion of Mn2f ions to Mnf ions which are isoelectronic with Fe2+ (3d6, 5 0 ) . Mn+ transi- tions may not be observed in the presence of crystal field components of low symmetry. IRON When crystals of NaF to which Fe2+ ions had been added are irradiated and the resonance spectrum investigated at 20"K, a single line is observed with a resolved fluorine structure.The g-value (g = 4,344) may be compared with the g-value of Co2+- in MgO (g = 4.278).16 However, for Co2+ a large eight-line h,f.s. due to the nucleus of the cobalt ion is observed; in the present case no h.f.s. due to the nucleus of the magnetic centre is found. Since both NaF and MgO have the NaCl structure the results indicate that the irradiation induced centre is Fe+ which is isoelectronic with Co2+ (3d7). No resonance was observed before or after irradiation down to 4°K which could be attributed to Fez+. COBALT Before irradiation a complex spectrum due to Co2+ is observed at 20°K.There are six distinguishable magnetic ions with similar spectra. Each ion has rhombic symmetry with two face diagonals and a cube edge as principal axes. The fluorine h.f.s. was resolved but a detailed analysis was not possible. Irradiation removes completely the spectrum described above and two iso- tropic lines now appear. One line is observed at 20"K, has a g-value of 4.5 and is about 400 gauss wide. It appears that the centres involved are Co2+ ions in slightly distorted cubic surroundings ; the departure from cubic symmetry prob- ably arises from vacancies at distant lattice sites. The second line appears at 90°K with a g-value of 2-31 and has a flat top about 200 gauss long. The g-value is close to the g-value of Ni2+ in MgO (g = 2-22> 17 suggesting that the magnetic ion is Co+ which is isoelectronic with Ni2+ (d8).The absence of a resolved struc- ture on the line is due to the presence of cobalt h.f.s., fluorine h.f.s. and line broadening due to slight distortions of the crystal field. NICKEL After irradiation a spectrum is observed at 20°K ; there are three similar centres each with axial symmetry about a cube edge. The details of the spectrum are explained by assuming the centres are Ni+ ions which are isoelectronic with Cu2+ ions (d9). A cubic field leaves a " non-magnetic " orbital doublet (dxz-yz, d3zz-rz) lowest; the degeneracy is raised by a tetragonal distortion of the octahedron which in this case arises from a Jab-Teller effect 18 (cf. Bleaney, Bowers, Trenam 19). The g-values (811 = 2-766, gL = 2-114) indicate that the octahedron is extendedW.HAYES 63 along a cube edge. If the distortion of the octahedron is pure tetragonal then the single unpaired spin is expected to be in the dx2,,2 ground state and bonding only to the four fluorines (type I) in the plane perpendicular to the symmetry axis should occur. However, an appreciable bonding to the two fluorines (type II) on the symmetry axis is observed indicating an admixture of the d3z~-r2 level into the ~'z-,,z state. This may result from a rhombic distortion which is not observable however in the g-values. The charge transfer has not been calculated since the admixture coefficient is not known. No resonance is observed before or after irradiation which can be assigned to Ni2f. The spectrum of the Nif ion whose axis is directed along (001) is shown in fig.2 for the (110) orientation of the external magnetic field. The interaction with the 1.0 I I I I f = 9150 MC~EC- gauss 3000 3100 3 200 FIG. 2.-Chart recording of differential of absorption lines in the spectrum of Ni+ showing fluorine h.f.s. four type I fluorines splits the resonance line into 5 components with intensities in the ratio 1 : 4 : 6 : 4 : 1 ; a further splitting of each of these lines into 3 com- ponents with intensities in the ratio 1 : 2 : 1 is produced by the weaker interaction with the two type I1 fluorine ions. CONCLUSION Earlier investigations of the effect of divalent impurities (for example, Ca2+ and Sr2+) in alkali halides showed the presence of 21 optical absorption bands following irradiation.These bands were attributed by Seitz to electrons trapped on the divalent ions. It was further assumed that the positive ion vacancy which was initially associated with the divalent ion moves away, possibly to join the electron deficient centre left behind by the captured electron. In the present work the resonance spectra of two divalent ions, Co2+ and Mn2+ have been ob- served. In both cases the symmetry of the surroundings is less than cubic due presumably to association with positive ion vacancies. No spectra are observed which can be attributed to Cr2f, Fe2f or Ni2+ ions; vacancies associated with these ions may reduce the symmetry in such a way as to prevent observation of64 IRON GROUP IMPURITIES I N NaF a resonance. The observation of Cr+, Fe+ and Co+ ions with cubic symmetry indicates that vacancies which may have been originally associated with the di- valent ions have migrated.Some of the electrons released during the irradiation are trapped as F-centres and M-centres. No resonances have been observed which can be attributed to the electron deficient centres and the nature of these centres is unknown. The trapping efficiency of the divalent iron group ions may be partly due to the fact that the radii of the ions are less than that of Na+ and the strain energy of the lattice due to misfit of the impurity ion will be less in the monovalent form. The metastable monovalent ions are annealed out by heating to about 140°C. The analysis of the fluorine h.f.s. shows that the largest interaction comes from magnetic electrons in fluorine 2s orbitals.The smaller anisotropic contribution from 2p orbitals comes mainly from a-bonding ; the contribution from r-bonding is inside the error of measurement. These results may be compared with the work of Tinkham on iron group impurities in ZnF2,lo of Baker, Bleaney and Hayes on iron group impurities in CaF2,11 and of Shulman and Jaccarino on fluorine nuclear resonance shifts in MnF2.20 The measurements on Mn2+ are the most complete and the contact interactions are shown in table 3 ; included TABLE 3 Mn : ZnF MnF2 Mn : NaF Mn : CaF2 As 16.5 f 1.5 15.7 f 0.3 14.4 & 0.3 9.5 f 0-3 probability of occupation of a fluorine 2s orbital, % 5 3 -5 1 -47 -30 cation-anion distance, A 2.03 2.1 1 2.3 1 2.36 The values of A , are expressed in units of 10-4 cm-1.also are the amount of charge transfer to each fluorine 2s orbital and the separa- tions of the bonding ions. The bonding in Mn : ZnF2 and MnF2 should be similar since the systems are isomorphous; it is found that the contact interactions and o-bonding agree closely and for MnF2 it is estimated that the =-bonding is about 30 % of the o-bonding. The contact interaction in Mn : NaF is slightly smaller than that found in Mn : ZnF2 and MnF2 and in Mn : CaF2 is reduced by about 40 %. Inspection of table 3 shows a slight reduction of the contact interaction with increased bond length in the octahedrally co-ordinated compounds ZnF2, MnF2 and NaF and a sudden change in CaF2. However, for CaF2 each manganese ion is at the centre of a cube of eight fluorine ions so that the reduction in the total charge transfer is not so pronounced.The o-bonding orbitals are now d . rather than dy because of the different symmetry involved. The inability to resolve =-bonding in NaF and CaF2 indicates that for most of the impurity ions involved the r-bonding is less than 30 % of the a-bonding. In NaF the probability of finding the magnetic electrons of the impurity ions on a nearest neighbour fluorine ion is approximately 2 %. This value is con- sistent with the ionic nature of the crystal and should be a good indication of the amount of charge transfer which occurs in the pure crystal. I would like to thank Prof. B. Bleaney, Dr. B. R. Judd, Dr. M. C. M. O’Brien, Dr. J. M. Baker and Dr. J. Owen for valuable discussions. I am particularly indebted to Dr. D. A. Jones of the University of Aberdeen for the crystals and Mr. J. Orton and the Atomic Energy Research Establishment, Harwell, for the irradiation facilities. The work was done during the tenure of an 1851 Overseas Scholarship and the report was written while the author was a member of the staff of the Argonne National Laboratory.W. HAYES 1 Seitz, Rev. Mod. Physics, 1954, 26, 7. 2 Stockbarger, J. Opt. SOC. Amer., 1949,39,731. 3 Llewellyn, J. Sci. Instr., 1957, 34, 236. 4 Bleaney and Hayes, Proc. Physic. SOC. B, 1957,70,626. 5 Hayes and Jones, Proc. Physic. SOC., 1958, 71, 503. 6 Watkins, Bull. Amer. Physic. Soc., 1958, 3, 135. 7 Griffiths and Owen, Proc. Roy. SOC. A, 1954,226,96. 8 Owen, Proc. Roy. SOC. A , 1955,227, 183. 9 Owen, Faraday SOC. Discussions, 1955, 19, 127. 10 Tinkham, Proc. Roy. SOC. A , 1956, 236, 535, 549. 11 Baker, Bleaney and Hayes, Proc. Roy. SOC. A, 1958, 247, 141. 12 van Vleck, J. Chem. Physics, 1935, 3, 807. 13 Bowers and Owen, Reports Prog. Physics, 1957, 18, 314. 14 Hartree, Proc. Roy. SOC. A , 1935, 151, 96. 15 Lowdin, Physic. Rev., 1953, 90, 120. 16 Low, Physic. Rev., 1958, 109,256. 17 Low, Physic. Rev., 1958, 109, 247. 18 Jahn and Teller, Proc. Roy. SOC., A, 1937, 161, 220. 19 Bleaney, Bowers and Trenam, Proc. Roy. SOC. A, 1955,228, 157. 20 Shulman and Jaccarino, Physic. Rev., 1957, 108, 1219. 65