MOSSBAUER STUDIES OF CHEMICAL BONDING By J. F. DUNCAN and R. M. GOLDING (CHEMISTRY DEPARTMENT VICTORIA UNIVERSITY OF WELLINGTON NEW ZEALAND) (CHEMISTRY DIVISION DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH WELLINGTON NEW ZEALAND) SPECTROSCOPY is the study of absorption and/or emission of electro- magnetic radiation between two or more energy levels. In optical absorption spectroscopy we examine transitions (ca. 30,000 cni.-l) between the electronic ground state and the excited states; in infrared spectroscopy between vibrational ground and excited states (ca. I000 cm.-l) ; in electron spin resonance spectroscopy between electron spin states arising from the interaction of the magnetic field with the electron (ca. 0.3 cm.-l) ; and in nuclear magnetic resonance spectroscopy between nuclear spin states arising from interaction of the magnetic field with the nucleus (ca.0.002 cm.-’). Mossbauer spectroscopy is simply a study of the absorption of electromagnetic radiation (y-rays) between the nuclear ground and excited states (ca. lo8 cm.-l). Since the first Mossbauer experiments in 1958,l physicists have used the principle in a variety of investigations especially for studying atomic motions in solids.2 However it is only recently that chemists have realised the importance of Mossbauer spectroscopy for examining electronic con- figurations and the structures of chemical compounds. In this Review we discuss only those features of Mossbauer spectroscopy pertinent to chemistry. 1. Fundamental Features Mossbauer spectroscopy is the study of y-ray absorption (or emission) between the ground and excited states (usually the first) of a specific type of nucleus.The energy difference between the ground and excited states of the transition involved is usually 10-100 kev (1 kev = 8.07 x los cm.-l). When an isolated atom emits a y-ray the total momentum of the system remains constant i.e. the recoil momentum of the atom is equal to the momentum of the y-ray E,/c where c is the velocity of light and E the energy of the y-ray when the decaying nucleus is at rest. Thus for an emitted y-ray \ and for an absorbed y-ray Ey’= E o ( l +&). Mossbauer 2. Physik. 1958 151 124; Naturwiss. 1958 45 538. a Boyle and Hall Proc. Phys. Soc. 1962 25 441. 36 DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 37 The recoil velocity Y depends in general on the thermal motion of the nucleus but when the decaying nucleus is bound in such a way that the recoil momentum is absorbed entirely by the lattice the change in E is negligible and a y-ray spectrum centred at E is obtained (eqn.1). A similar situation obtains when y-ray absorption takes place (eqn. 2). If we now mechanically move the emitter at a velocity v’ the Doppler shift3 in the energy of the emitted y-ray is E,v’/c which corresponds for instance to 4.8 x ev per cm./sec. velocity for the 14.4-kev y-ray emitted in the decay of 57Fe from the first exicted state to the ground state. Since the Doppler shift may be varied by altering the velocity of the source E may be adjusted until allowance has been made for the small difference in the energy level of the first excited state above the ground state in the source compared to that in the absorber (in a chemically different environ- ment).Nuclear absorption of the y-radiation will then occur. 2. Theoretical Aspects As a consequence of the intrinsic nuclear spin 115 (or I in quantum units) the nucleus may interact with magnetic and electric fields in the molecule. These interactions may be represented by the spin-Hamiltonian operator jEp = - hyH.1 + P [(31,2 - 1(1 + 1)) + 5 { I+2 + I-”)]. (3) Here y is the gyromagnetic ratio of the nucleus in a particular state with nuclear spin I ; I+ and I- are step-up and step-down operator^;^ P = e2qQ( 1 - y,)/41(21- l) where eQ the quadrupole moment of the nucleus is non-zero when I > 1 eg is the electric-field gradient parallel to the z axis,5 and (1 - yco) is Sternheimer’s screening factor;6 and r] is the asym- metric parameter of the field-gradient tensor.A magnetic field lifts the degeneracy of the nuclear states into the (21 + 1) Zeeman levels the separations being determined by the magnetic- and electric-field interactions for which MI = I 1-1 . . . . -I + 1 -I. To illustrate the typical energy-level diagram so obtained we can consider the ground (I = Q) and first excited ( I = :) states of the 57Fe nucleus when the magnetic field is parallel to the z axis and the asymmetric parameter q is zero. The spin-Hamiltonian operator now becomes (4) A? = - fiyH,I + P{ 3IS2 -I(I + 1)). The energy-level diagram obtained for the 57Fe nucleus using the constants in Table 1 is shown in Fig. 1. The subscripts ‘g’ and ‘e’ refer to the ground See for example Jenkins and W-hite “Fundamentals of Optics,” McGraw-Hill New York 1950.Griffith “The Theory of Transition-Metal Ions,” Cambridge University Press Cambridge 196 1. Sternheimer Phys. Rev. 1951 84 244; ibid. 1952 86 316; ibid. 1954 95 736. 5 See for example Das and Hahn Solid State Physics 1958 Suppl. 1. 38 QUARTERLY REVIEWS TABLE 1. Nuclear properties of some Mossbauer nuclei. Nucleus Natural Nuclear spin Gyromagnetic ratios abundance (%) Ground state First excited Ground state First excited state state re Y g Ye 3 $0.179 -0.102 Ig 2 - 2.082 f0.448 57Fe 2.25 3 ll9Sn 8.68 t 33.41 0 2 0 & 1-21 Ig7Au 100 2 3 $0.0959 $0.76 3 - 3 166Er - gNPN = k y = p/Z where gN is the nuclear Lande g factor PN the nuclear magneton y the gyromagnetic ratio and p the magnetic moment E t A € I FIG.1. Energy-level diagram for the 67Fe nucleus. LIE is the energy separation of the ground and first excited states. The magnetic-field and the electric-field gradient inter-actions are indicated. (The subscripts ‘g’ and ‘e’ refer to the ground and first excited states respectively.) and first excited states respectively. Similar energy-level diagrams can be obtained for llgSn 125Te 129Xe la9Tm and 171Yb. Knowing the energy levels we may next discuss the intensities of the hyperfine structure of the y-ray absorption spectrum i.e. the transition probabilities between the Zeeman levels. These have been determined from the general theory of multipole radiati~n.~ The angular intensity distribution Iiv(O) for dipole radiation is I M ( 0 ) = Cl(1,l M-m mlIe 1 IgM)12 x { 1 + (3m2 - 2)(3 cos28 - 1)).Here 8 is measured about the axis of quantization the Wigner coefficients ( r e 1 M-m m I Ie 1 I g M ) are known constants and m = 1,0 -1. In Table 2 the relative intensities from the ground to the first excited states and the corresponding relative energies for 57Fe are given. When the ( 5 ) m Fagg and Hanna Rev. Mod. Phys. 1959,31,711. DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 39 TABLE 2. The relative energies and the relative intensities of transitions between the ground and thejirst excited states for 57Fe. Excited state Ground state Relative energies Relative intensities IM - m> I M ) 1 3 emitting nucleus interacts with magnetic and electric fields the y-ray absorption splits into a six-line spectrum. Provided that the absorber has a single-energy resonance the emission spectrum will also be observed as six lines.The energy separations of these transitions depend on the magnitudes of the two interacting fields. Fig. 2 illustrates the relative separation of the six-line spectrum for various magnetic-field and electric- field gradient ratios which we have evaluated for the 57Fe nucleus taking ye/yg = - 0.572. The relative intensities of the six transitions are indicated. Fig. 2 shows that when the effective magnetic field (H,) is zero and only an electric-field gradient is present at the nucleus the spectrum is a doublet. From eqns. 3 and 4 (or Fig. 2) the intensity ratio is In Mossbauer experiments with polycrystalline compounds relative intensities are calculated by averaging over all angles of 8 the average values of sinV and cos28 being 3 and 8 respectively.Consequently the arms of the doublet arising from the interaction of the electric-field gradient with the 57Fe nucleus in a powdered sample of an iron compound are of equal intensity. Deviations from equality are due to preferred orien- tations in the powdem8 When a magnetic field is present either externally applied or inherent in the material the intensities of the six y-ray absorption (or emission) peaks for a powdered iron or iron complex are in the ratio 3 2 1 1 2 3 and if the nucleus is in a preferred orientation the relative intensitiesg are 3:/3:1:1:/?:3 where /3 = 4/(1 + 2cot28) and0</3<4. Boyle Bunbury and Edwards Proc. Phys. Soc. 1962 79 416. Preston Hanna and Heberle Phys. Rev. 1962 128 2207. 40 QUARTERLY REVIEWS I i I l l I I 1 1 I 0 4 I i 0 7'x x/r I +3 t 2 +I s O + sw 1 r,l U -1- -I -2 -3 FIG.2. Separation of the six-line spectrum for the 57Fe nucleus at different magnetic- field and electric-field gradient ratios ye/yg = - 0.572 x = y&H/2 and y = 3P. 2.1 Internal Magnetic Fields in Molecules.-Internal magnetic fields in atoms and molecules arise through the interaction of the s electrons with the nucleus ; this is mathematically expressed in the spin-Hamiltonian by the Fermi contact term. In the usual symbolism where the effective internal magnetic field at the nucleus H, depends on the time-averaged value of the z component of the electron spin (Sz). There is an additional term in the total spin-Hamiltonian contributing to the effective magnetic-field interaction with the nucleus namely that arising from the interactions between the electron and nuclear spins and the electron angular momentum.This the dipolar term is usually much smaller than the Fermi contact term.1° If the electronic ground state of a lo Golding Mol. Phys. in the press. DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 41 typical transition-metal ion were truly represented by ( ls2) (2s2) (2p6) (3s2) (3p6) (3d9 [i.e. using the Aufbau principle] the total s-electron spin density at the nucleus would be zero. However large effective magnetic fields have been observed in these atoms.ll Sternheimer suggests6 that the outer unpaired electrons polarise the core electrons to produce a finite s-electron spin density. We may relate this to observed Mossbauer spectra as follows.The Aufbau principle implies that the wave functions of the two electrons in the same s shell have the same radial function and differ only in the electron spin +& or -4 (a or /?). However if there is an odd a-spin electron present then it will experience different exchange interactions with the remaining wspin electrons (including those in the core) from those with the /?-spin electrons. Consequently the a- and /?-spin s electrons will have different radial functions leading to a net s-electron spin density I$,(O) l2 - I$a(0) 12. Thus the electron spin density for closed s-electron shells is not necessarily zero. Abragam et a1.12 define a parameter where Sdenotes the number of unpaired electrons. They showed that for the first transition-metal series x was approximately constant (- 3 atomic units).This leads to an effective magnetic field through the Fermi contact term of -125 kgauss per unpaired 3d electron. Watson and Freeman13 confirmed this constancy of x from free-ion spin-polarised Hartree-Fock calculations. Thus the magnetic field at the nucleus of a transition-metal comporind is very large being about -500 kgauss. is sensitive to the symmetry and nature of the ligands surrounding the transition-metal ion. For example the calculated value of x for the free Ni2+ ion is -3-9413 whereas for the Ni2+ ion in a cubic field it is -3-27;14 the experimental values for internal magnetic fields at the manganese nucleus in Mn2+ ion complexes depend on the ligand,15 as shown in Table 3. The negative core polarisation is usually less than ex- pected but this can be explained by configurational mixing of the The value of TABLE 3.The observed internal magnetic field at the manganese nucleus for several Mn2+ compounds. Ligand H20 F- CO2- 02- S2- Se2- Te2- lHzl (kgauss) 695 695 665 570-640 490 460 420 1960,4,177; Hanna Meyer-Schutzmeister Preston and Vincent ibid. p. 513. l1 Hanna Heberle Littlejohn Perlow Preston and Vincent. Phys. Rev. Letters l2 Abragam Horowitz and Pryce Proc. Roy. Soc. 1955 A 230 169. l3 Watson and Freeman Phys. Rev. 1961 123,2027. l4 Watson and Freeman Phys. Rev. 1960,120 11 34. Van Wieringen Discuss. Faraday SOC. 1955 19 118. 42 QUARTERLY REVIEWS TABLE 4. ally aligned environments. Nucleus Host H (kgauss) Ref. 57Fe Fe - 342 11 16 17 17 17 18 57Fe c o 57Fe Ni 57Fe3-k Y iron garnet 392 (tetrahedral) 57Fe34- Y iron garnet 474 17 18 (octahedral) 59c0 Fe 300 19 61Ni Ni - 170 20 l19Sn Fe - 81 21 l19Sn c o - 205 21 l19Sn Ni + 185 21 lg8Au Fe 1460 22 3dn4sx excited statesz3 into the ground state this effect giving a positive contribution to the effective magnetic field at the nucleus.It is clear that large magnetic fields are present at nuclei as a result of electronic inter- actions. In Table 4 we quote a few typical examples for different Mossbauer nuclei. The nuclear spin will couple with this field but if the electron- spin-lattice relaxation time is shorter than the Larmor frequency of the nucleus then the time-averaged value of the internal magnetic field affecting the nucleus is zero. This is often (but not always) the case when the Mossbauer atom is not in a magnetically aligned lattice (e.g.for paramagnetic substances in the absence of external magnetic fields). Usually for this internal magnetic field to be observed the electronic structure of all the atoms must be spatially aligned e.g. in a ferro- magnetic complex. The six-line spectrum which results has been used to determine effective internal magnetic fields at iron nuclei in various lattices (see Table 4). In a recent study of the Mossbauer spectra of Fe3+ in corundum (a non-magnetically aligned matrix) at 78 0~,230 this character- istic hyperfine structure was observed which implies that the spin relaxation time must be sufficiently long to present a stationary magnetic field at the iron nucleus. In some cases the magnetic behaviour of a substance depends upon the temperature. For instance the Mossbauer spectrum for iron at or above the Curie temperature (773") is a single line indicating no inter- action between the nucleus and any magnetic-field or electric-field gradient.l8 Nagle Frauenfelder Taylor Cochran and Matthias Phys. Rev. Letters 1960 5 l7 Wertheim Phys. Rev. Letters 1960,4,403; J. Appl. Phys. 1960,32 110s. la Alff and Wertheim Bull. Amer. Phys. SOC. 1960 5 428. l9 Dash Taylor Nagle Craig and Visscher Bull. Amer. Phys. Soc. 1961 6 136. 21 Boyle Bunbury and Edwards Phys. Rev. Letters 1960 5 553; Boyle Bunbury 22 Roberts and Thomson Phys. Rev. 1963 129,664. 23 Walker Wertheim and Jaccarino Phys. Rev. Letters 1961 6 98. 23a Wertheim and Remeika Phys. Rev. Letters 1964 10 14. The magneticJield at the nuclei of Mossbauer atoms in magnetic- I;;;\ 364. Wegener and Obenshain Z .Physik. 1961 163 17. Edwards and Hall Proc. Phys. SOC. 1961 77 129. DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 43 However below the Curie temperature the averaged internal magnetic field is not zero and the spectrum has the characteristic six lines9 with spacings dependent upon the magnetisation of the material.16 2.2 Electric-field Gradients at Nuclei.-Both the experimental quadru- pole interaction P and the internal magnetic field can be determined by fitting the experimental results from a Mossbauer spectrum to the calcu- lated relative energies using energies similar to those shown in Table 2. For example Kistner and S ~ n y a r ~ ~ found an internal magnetic field of 5 10 kgauss and a small quadrupole interaction in antiferromagnetic Fe203. However in diamagnetic and paramagnetic compounds only the quadrupole interaction need appear in the spin Hamiltonian (eqn.3) since the averaged effective internal magnetic field is zero (see above). For 57Fe complexes this leads to doublet Mossbauer spectra with relative intensities as predicted in Fig. 2. The doublet energy separation dE, can be evaluated from eqn. 4 with H = 0. For the 57Fe nucleus so that the term governing the variation of dE, in compounds with the same Mossbauer nucleus is the electric-field gradient (eq) at the nucleus. The energy of Coulomb interaction between the electrons and the protons in an atom can be written as a set of multipole interaction^.^^ The constant term gives rise to the central-field energy and it is of no interest to us here. The dipolar term vanishes leaving the third term the electric quadrupole interaction.The next non-vanishing term is such that interactions from this and higher terms are very small and we shall ignore them. If there is no mixing between the nuclear states then the Hamil- tonian representing the quadrupole interaction can be written as where (r3) is the averaged value of r3 and Z is the nuclear spin. The distance between the hth electron and the nucleus is r,,.26 If we have an 1" electronic configuration then the Hamiltonian (8) may be written2' as e2 Q ( r -3) S f 7/{3(L.1)2 + ; (L.1) - L(L + l)I(I + 1)). (9) xq = * I(2I - 1) Here 24 25 26 27 ~- 21 + 1 - 4s ' = S(21 - 1)(21 + 3)(2L - 1) ' Kistner and Sunyar Phys. Rev. Letters 1960 4 412. Cohen and Reiff Solid State Physics 1957 5 321. Casimir see ref.25. Bleaney and Stevens Reports Progr. Phvs. 1953 16 108. 44 QUARTERLY REVIEWS n 2 S = 4 2 and L = - (21 + 1 - n). The positive sign in this equation is taken when the shell is less than half-filled and the negative sign when the shell is more than half-filled. For the d5 case Fe" I = 2 and n = 5; thus L = 0 and from the Hamiltonian (9) it follows that dE = 0. However for the d6 case Fe2+ L = 2 and thus dEQ is finite. Therefore ionic paramagnetic iron(rr1) complexes will give a single-peak Mossbauer spectrum but ionic ferrous complexes will show a quadrupole splitting (see below). The relative order of magnitude of the quadrupole interactions expected for octahedral iron complexes can be derived simply from the symmetry and multiplicity of the four possible ground states for d5 and d6 configurations by examining the appropriate Tanabe and Sugano2* diagrams arising from the electrostatic and crystal-field interactions.The ground terms arising from the d5 electronic configuration are 6A for the high-spin (Few) and ,T2 for the low-spin (Fern) complexes. The ds electronic configuration yields 5T2 and lA ground terms for the high- spin (Fe2+) and the low-spin (Fen) complexes respectively. We would expect a zero electric-field gradient from a spherical ground state A but not for non-spherical ground wavefunctions such as T2. In the latter case a greater spin multiplicity would produce a greater electric-field gradient. Hence we obtain a semi-quantitative diagram relating the quadrupole moments expected for the four types of octahedral iron Complexes. Fen Fe2+ As discussed later this type of semi-quantitative argument can be used to determine the type of iron complex in symmetrical octahedral fields.The field symmetry may however also be changed by altering the type of ligand in one or more of the co-ordination positions. For example species like [Fe(CN),NOI2- FeCl 2 Fe(o-phenanthroline),(CN), and FeS0,,7H 2O will all have different electric-field gradients because of the symmetry of the ligands nearest to the iron atom. A relationship has recently been found30 between the spin-spin para- meter D obtained from electron spin resonance measurements and the nuclear quadrupole splitting AEQ obtained from Mossbauer experiments. This can be interpreted by means of the theory developed to explain the Tanabe and Sugano J. Phys. SOC. Japan 1954 9 753.Duncan and Golding I.U.P.A.C. meeting August 1964. so Nicholson and Burns Phys. Rev. 1963 129,2490. DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 45 zero-field splitting in 3d5 ions. It has been known for some time that the ground state of ions such as Mn2+ and Fe3+ is split even in the absence of a magnetic field (zero-field splitting). This is usually represented by the spin- Hamiltonian 2 = D(S,2 - Q S(3 + 1)) + E(Sz2 - Sy2) (1 1) where D and E are two experimentally determined parameters. Pryce31 suggested that the splitting in Mn2+ arises from spin-spin coupling of unpaired electrons and also from the electric-field gradient. Using these assumptions Chakra~arty~~ has derived expressions for D and E namely D = - !g2p24 (ao3/e)(DD) and E = - 4 g2p2Tq(a,3/e)(EE) (12) (13) where g is the Landk splitting factor 16 the Bohr magneton and a, the Bohr radius.The parameters ( D D ) and (EE) were determined by using hydrogen-like wavefunctions. These expressions lead to the empirical linear relationship discussed by Nicholson and Burns :30 D = Do + keqQlh (14) in which k is an experimentally determined constant. Chakra~arty~~ plotted the variation of D with eqQ/h for Fe3+ ions in several crystal lattices using eqQ/h values determined by Nicholson and Burns.30 This yields D = 0 when q = 0 which is expected when an ion is in a perfect cubic crystal-field. Any deviation from the spherical symmetry of this crystal field is reflected in the magnitudes of D E and q. 2.3 Isomeric or Chemical Shift.-In this section we are interested in small variations in the energy differences between the ground and first excited states arising from the environment of the nucleus.B ~ d m e r ~ ~ showed that this energy difference dE is d E = F(Z) I#s(O) l2 (15) where F(2) is a complex function of a number of nuclear parameters including 2 the nuclear charge Rn is the radius of the equivalent uniform charge distribution; 8Rn is the difference between the radii of the ground and the first excited states ; and I #,(O) I2 is the total s-electron density at the nucleus. d E is thus a measure of the s-electron density which in turn de- pends upon the number of unpaired electrons and the nuclear environ- ment. Mossbauer results are normally related to a reference emitter by defining the isomeric or chemical shift 8 as 8 = F(Z) sRrJRn( I+AO) I i - I #AO> I )s (16) 81 Pryce Phys.Rev. 1950 80 1 107. sa Chakravarty J. Chem. Phys. 1963,39 1004. 33 Bodmer Nuclear Phys. 1961,21 347. 46 QUARTERLY REVIEWS 02- where Il/ls(0)li and ll/ls(0)li refer to the s-electron densities of the absorber and the emitter respectively. Hence both the isomeric shift and the internal magnetic field discussed previously depend upon the total s-electron density at the nucleus. The expected variation in isomeric shifts may be interpreted in a manner similar to that used in discussing AE above. Since [l/ls(0)li is greatest when the number of unpaired electrons is largest we expect the isomeric shift to decrease in the order 6A . . lA and 5T2 . . 2T2. The s-electron density also depends markedly upon the environment of the Mossbauer nucleus (see Tables 3 and 4) and we can expect the effect of the a-induced polarisation of the s shells to be least for a symmetrical ground state.This is observed and we can therefore qualitatively represent the variation in isomeric shift of octahedral iron complexes as follows FeI" Few j o ; i Fe2+ FeII Few 2.4 The S/dEQ Correlation Diagram.-A diagram of 6 plotted against LIE for the same M6ssbauer nucleus has some interesting ,... *. U - Fe "I Fen Fe 2+ Fern Fe 3+ u- FIG. 3. ~/AEQ correlation diagram for a number of iron complexes. The circles indicate the approximate positions expected for iron complexes of octahedral symmetry. Brady Wigley and Duncan Rev. Pure Appl. Chem. (Australia) 1962,12,165. DUNCAN AND GOLDING M~SSBAUER STUDIES OF CHEMICAL BONDING 47 Fig. 3 shows the correlation diagram for a large number of iron complexes ; the small circles indicate the positions expected for the octahedral iron complexes.The areas indicating Fe3+ FerIr Fe2+ Fe" were obtained experi- mentally from results on about twenty different compounds of all types. With the aid of such a correlation diagram it is possible to assign the electronic configuration and to study the influence of different ligands on the nucleus under examination. 2.5 Temperature-dependence.-In a previous section we discussed the difference in Mossbauer spectra above and below the Curie temperature due to the change in the magnetic properties of the material. Below the Curie temperature an atom in a magnetically aligned environment usually shows hyperfine Zeeman splitting. The experimentally determined internal magnetic field (from the Zeeman splitting) in metals is found to be tem- perature-dependent ; this corresponds closely to the temperature-depen- dence of the ~ a g n e t i s a t i o n .~ ~ ~ ~ For there to be a change in the quadrupole splitting with temperature it is necessary to have an electronic excited state close to the electronic ground state. This has been suggested36 as an explanation of the marked temperature-dependence with Fe2+ salts such as Fe(NH4),(S0,),,6H,0. However in 3d iron complexes the first excited electronic state is fre- quently well above the ground electronic state and consequently a temper- ature-independent AE term is obtained. This is not the case with the 4f rare-earth complexes. Here spin-orbit coupling is very large and the weak crystal-field interactions produce low-lying excited states leading to tern- perature-dependent quadrupole splitting.MOssbauer3' observed such a temperature-dependent quadrupole splitting in thulium metal. 2.6 Other Correlations.-Any physical property dependent on the electronic or nuclear states will be related in some way to AEQ and 6. Two examples must suffice. The first is the linear relation between the magnetic susceptibility and dE over a wide range of values for Fe3+ Any deviation from the expected zero value of d EQ for a d5 Fe3+ ion must arise through an electric-field gradient at the nucleus due to the ligands. In such a case the magnetic-susceptibility variations in Fe3+ complexes must similarly depend upon the ligands. A second example39 is the linear relation between the proton magnetic resonance chemical shifts and the 57Fe isomeric shifts for several cyclo- pentadienyl iron complexes.Such correlations relate variations in the electronic ground and excited 36 Meyer-Schutzmeister Preston and Hanna Phys. Rev. 1961 122 1717. s6 DeBenedetti Lang and Ingails Proc. 2nd Mossbauer Conf. Paris Wiley New 37 Mossbauer Proc. 2nd Mossbauer Conf. Paris Wiley New York 1961. 38 Brady Duncan and Mok unpublished results. York 1961. Herber King and Werthcim Inorg. Chem. 1964 3 101. 48 QUARTERLY REVIEWS states from compound to compound. An interpretation is to be sought in the s-electron density and the electric-field gradients in the atom. Since Mossbauer spectra enable these two quantities to be determined un- equivocally at one place in the atom (the nucleus) the method illuminates in a fundamental way the interpretation of results determined by other methods.3. Practical Aspects In this section we summarise those aspects likely to concern the reader who is considering work of this kind Two practical aspects of importance are (a) the nature of the necessary equipment and (b) the number of suitable isotopes. 3.1 The Apparatus.-Spectra may be determined in a number of ways the cost depending on the degree of sophistication employed.34 Either scintillation or proportional counting methods may be used. The moving parts may be either electronically or mechanically driven. The latter is simpler but the former allows errors in the movement to be eliminated by feedback methods. Both require special construction. The electronic method normally requires a wave-form generator transducer (e.g.high- fidelity loud-speaker) to drive the source and associated components. The mechanical technique involves only workshop time and minor ex- penditure on materials but good machining is essential to avoid loss of resonance intensity caused by vibrations. Mossbauer spectra can be recorded in a variety of ways depending on the method used for driving the source (or absorber). There are two general methods. The spectrum can be determined point by point by moving the source at a constant velocity towards or away from the absorber. About ten minutes may be necessary to determine one point with sufficient accuracy and therefore about five hours for a complete spectrum. Each point may be recorded independently either manually or automatically by using a single scaling unit.The method is relatively cheap but is subject to error from electronic drift. A second more satisfactory arrangement is to drive the source with a constant-acceleration cam (ca. 1 rev./min.). The output froin the scintillation spectrometer is recorded against velocity. A convenient method is to employ a pulse-amplitude analyser with channel selection controlled by a potential related to the velocity at which the events are recorded. Anti-coincidence equipment to reject unwanted pulses may be useful. This reduces errors due to stray radiation background fluctuations etc. 3.2 Isotopes.-Even with 67Fe with which most work has so far been done many possible applications of the Mossbauer effect in chemistry remain to be studied. However there are a number of other isotopes which can be used; the situation is rather similar to that for nuclear magnetic resoname spectroscopy.About eighty isotopes which may be suitable have DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 49 been li~ted,~,~O but not all have been shown experimentally to exhibit the Only l19Sn and 57Fe have been used for any systematic chemical work. In some cases it has been asserted that low temperatures are essen- TABLE 5 . Some suitable Mossbauer Decay Resonant nucleus 57Fe l19Sn 125Te 1291 lZ9Xe scheme energy (kev) 57Co-+67Fe 14.4 (270 day) 119Sn*+119Sn 23.8 (250 day) 129Te-1291 26.8 (70 min.) 1291,129xe 79 (1.6 x lo7 yr.) Mossbauer nuclei. Chemical features Source 5 7 c ~ in copper stainless steel. Absorbers numerous chemical compounds over a wide range of temperatures.Source in SnQ,. Absorbers numerous chemical compounds over a wide range of temperatures. Source 125Sb in copper. Absorbers MnTe CrTe a-TeO,. Source lZgTe in ZnTe. Absorbers iodides io- dates enriched with 1291. Both source and ab- sorber cooled in liquid nitrogen . Source in NaI NaIO,. Absorber clathrate compounds XeF, XeF,. Ref. 47 48 49 50 51 52 42,43 I 44 45 40 Frauenfelder “The Mossbauer Effect,” Benjamin New York 1962. 41 Wertheim Science 1964 144 253. 4a Hien Shapiro and Shpinel’ Soviet Phys. JETP 1962 15 489 (Zhur. eksp. teor. 43 Shikazono J. Phys. SOC. Japan 1963 18,925. 44 de Waard de Pasquali and Hafemeister Phys. Rev. Letters 1963 5 217. 4s de Waard Garrell and Hafemeister Phys. Rev. Letters 1962 3 59. p6 Jha Segnan and Lang Phys. Rev. 1962 128 11 60.47 Bryukhanov Delyagin Opalenko and Shpinel’ Soviet Phys. JETP 1963 16 310 (Zhur. eksp. teor. Fiz. 1962 43 432). Bryukhanov Gol’danskii Delyagin Korytko Makarov Suzdalev and Shpinel’ Soviet Phys. JETP 1963,16,321 (Zhur. eksp. teor. Fiz. 1962,43,448). 4s Aleksandrov Delyagin Mitrofanov Polak and Shpinel’ Soviet Phys. JETP 1963 16,879 (Zhur. eksp. teor. Fiz. 1962 43 1242). so Aleksevskii Hien Shapiro and Shpinel Soviet Phys. JETP 1963 16 559 (Zhur. eksp. teor. Fiz. 1962 43 790). 61 Bryukhanov Gol’danskii Delyagin Makarov and Shpinel’ Soviet Phys. JETP 1962 14,443 (Zhur. eksp. teor. Fiz. 1962,42 637). 62 Boyle Bunbury and Edwards Proc. Phys. Soc. 1962,79,416. 63 Shpinel’ Bryukhanov and Delyagin Soviet Phys. JETP 1962,14,1256 (Zhur. eksp. teor. Fiz. 1961 41 1767). Fiz. 1962 42 703).Perlow and Perlow Rev. Mod. Phys. 1964,36 353. 50 QUARTERLY REVIEWS Mossbauer Decay nucleus scheme 151EU 151Gd,151E~ (140 day) 161Dy 161Dy*+161Dy (7.2 day) (27 hr.) 166Er 166H0+166Er 197AU 197pt+f97AU (18 hr.) TABLE 5-continuqd Resonant Chemical features Ref. energy (kev) 54 55 I 21.7 Source in Nd203 Eu203. Absorber Eu203. 26 Source Gd,03. Absorbers Fe2Er Er 56a Absorber Dy,O,. 80.7 Source HoA1,. ErFe,Mn Er20,. Absorber Au Au in Fe. i'" 77 Source enriched Pt foil. 122 J tial for observing the effect but since the efficiency of recoilless productions and absorption of y-radiation depends on the chemical form of the host material this statement is not generally true. In Table 5 the relevant data are given for the principal isotopes with which the Mossbauer effect has been studied.3.3 Other Experimental Features.-An important feature is the pre- vention of loss in the resonant y-ray energy by nuclear recoil. This is usu- ally accomplished by incorporating the radioactive atom in an ionic lattice so that the whole of the source must recoil for each emission. It is however not satisfactory to choose just any ionic lattice for incorporating the radioactive material since atomic vibrations of the emitting atom which vary from one compound to another can change the y-ray energy sufficiently to preclude resonance. The more tightly bound the radio- active atom is (the higher the vibration frequency and the lower the vibra- tion amplitude) the greater the resonance intensity. Careful source pre- paration is therefore essential. Fortunately several methods for preparing satisfactory sources have already been given.34 The same considerations however also apply to the absorber.Very poor resonances invariably result from poor absorber preparations so that material which easily decomposes or which cannot be easily purified should not be used. Another way of reducing the effect of nuclear vibration is to lower the temperature. This may of course alter the chemical environment owing to phase changes and changes in the electronic ground state. But even if it does not 6 and LIE may be temperature-dependent. However these temperature-dependent variations are small and well-known so that lowering the temperature is a useful method of improving the detection of 64 Shirley Kaplan Grant and Keller Plzys. Rev. 1962 127 2097. 65 Delyagin Shpinel' and Bryukhanov Soviet Pliys.JETP 1962,14,959 (Zhur. eksp. 66 Sklyarevskii Sanioilov and Stepanov Soviet Phys. JETP 1963 16 1316 (Zhur. teor. Fiz. 1961 41 1347). eksp. teor. Fiz. 1961 40 1874). Cohen and Wernick Phys. Rev. 1964 134 B503. DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 51 y-ray absorption. This is often done by using a foam-plastic vessel in which to keep the refrigerant. 3.4 Experimental Mossbauer Spectra.-The experimental features of a Mossbauer spectrum are quite simple. Figs. 4 and 5 show two typical Mossbauer spectra. The y-ray absorption intensity is recorded against the Doppler-shift velocity (cm./sec.). Since the Doppler-shift energy is Eov'/c (Section I) this can be converted into the usual energy units by remember- ing that for 57Fe 1 cm./sec.= 0.00388 cm.-l. The spectrum is recorded in a pulse-amplitude analyser until several-thousand y-ray quanta have been detected. To record a spectrum over a period of a few hours therefore requires a source of about 2 millicuries. FIG. 4. The Mossbauer spectrum for 57Fe in antiferromagnetic Fe203.24 The positions of the six hyperfine lines-intensity ratio 3 :2 1 1 :2 :3-depend on the magnetic-field and electric-field gradient interactions. The arrows indicate the positions of the six lines if the electric-field gradient interaction were zero. -0.4 -0-2 0 +o-2 0 4 Velocity (cm/sec) FIG. 5. The Mossbauer spectrum of iron(u) sulphate AEQ is the quadrupole splitting; 6 is the isomeric (or chemical) shift; and A and B refer to the energy of the stainless- steel single-line y-ray emission and the centre of the iron(I1) sulphate spectrum respect- ively.52 QUARTERLY REVIEWS The Mossbauer spectrum for 57Fe in antiferromagnetic Fe20324 (Fig. 4) shows the six hyperfine lines arising from the magnetic-field interaction (Section 2.1). When the effective magnetic field is zero only the quadrupole interaction is observed; this is shown in Fig. 5 the Mossbauer spectrum of iron(@ sulphate. The quadrupole splitting AE, is in this case 0.320 cm./sec. (= 0.00124 cm.-l). The isomeric shift 6 the difference between the energy of the stainless-steel single-line y-ray emission (A) and the centre of the iron@) sulphate spectrum (B). Here 6 = 0.131 cm./sec. (G 5-08 x cm.-l). The magnetic-field and quadrupole interactions and the isomeric shift can thus readily be evaluated from a Mossbauer spectrum.In general Mossbauer spectra are never more complicated than these unless two or more species are present to give overlapping spectra. 4. Chemical Applications In this Section we discuss some illustrative examples of typical chemical problems. We have made no attempt to discuss the large number of com- pounds which have been studied (see earlier review^).^,^^,^^ Table 6 gives some recent examples of the use of the Mossbauer effect. 4.1 Magaetic Fields in Alloys.-Included in Table 6 are several cases where chemical interest is centred on the source. This technique has been widely used in studying the magnetic fields of binary metallic compounds and alloys (Table 4). Both the magnitude and the sign of the internal magnetic field can readily be found in this way.The internal magnetic field at a nucleus may be either increased or decreased by an externally applied magnetic field. By convention the internal magnetic field in the first case is taken as negative and in the second case as positive. We have assumed here that the internal magnetic field is not affected appreciably by the domain magnetization. Nuclear magnetic resonance studies yield more accurate measurements of internal magnetic fields at nuclei but normally the resonance is so broad that it is difficult to detect without prior know- ledge of its position. 4.2 Structure of Compounds.-In the complex ferrocyanides Prussian Blue Turnbull's Blue and Berlin Green it has been that in all three cases the cation and the anion are in the oxidized and reduced states respectively and that the compound prepared by precipitation from iron(rr1) sulphate and potassium cyanoferrate(r1) is identical with that pre- pared from iron@) sulphate and potassium cyanoferrate(r1).In the SnX series of compounds a linear relationship between the isomeric shift and both the electronegativity of the X atom and the degree 57 Fluck Kerler and Neuwith Angew. Chern. 1963 2 277. 58 Duncan and Wigley J. 1963 1120. TABLE 6. Recent examples of the use of the Mossbauer efect in chemical work. Source 57Fe/57Co in a single crystal of NaI. 57Fe/57Co in silicon and germanium. 57Fe/57Co in stainleqs steel and l19Sn in SnO,. 57Fe/57Co in stainless steel. 57Fe/57Co in copper. 57Fe/57Co in metallic chro- mium. 57Fe/57Co in metallic chro- mium. 57Fe/57Co in metallic chro- mium. 57Fe/57Co in stainless steel.l19Sn in llSSn-enriched SnO,. Absorber Stainless steel. 57Fe-enriched K,[Fe(CN),] . FeSn as powder on beryllium disc. Oriented FeF,. Glasses of Na20,3SiO with Fe203 incorporated. Fe( PO3) cry st als. Ferrocene-type compounds. Fe(CO) and related com- pounds. K,FeO Single-crystals of white tin cut along various crystal planes. Type of work Change in dE observed for different orientations. Positive-hole vacancies and substitutional incorporation. No difference between n- and p-types. Asymmetric positions for FeO and Fe-1 in Ge lattice. Fe is electrically inactive. Internal magnetic field below Curie point measured and effect of this on l19Sn resonances determined Internal magnetic field in antiferromagnetic state measured. Magnetic hyperfine splitting in absence of external field resulting from long electron-relaxation time.Antiferromagnetic below 1 0 " ~ . Bonding of iron atom not affected by ring substitution. Results for Fe(CO) and Fe,(CO) agree with trigonal bipyramid and 333 structures respectively. Fe,(CO), probably is 3333 structure and is not trigonal as X-ray results suggest. Fe(CO),I is low spin. Data indicate complete covalent bonding between iron atom and n-electron distribution of cyclo-octatetraene ring system. Results interpreted in terms of d3s hybridisation. Large anisotropy studied for various orientations and temperature-dependence. Ref. 69 62 60 64 68 65 63 66 67 50 TABLE 6.-continued Source U9Sn in SnO,. l19Sn in SnO,. l19Sn in SnO,. 125Te/125Sb in copper or iron. 1311/131Xe in NaI. 1291/129Xe in NaI or Na12910, or 129~2.161Eu/151Gd in 151Eu-enriched Eu 203. 197A~/197Pt in 19 metals and semiconductors at 4 . 2 " ~ . } Absorber Type of work Ref. SnO, SnO Sn Sn(NO,),. 55 Tin-organic polymers. Investigation of tin-carbon bonding. 51 compounds. TeO, MnTe CrTe. Resonance intensity measurement and dependence of AE on temperature. (C,H,),SnX and related nEQ and 8 vary with electronegativity of X. 49 Determination of internal field and nuclear moment. 68a 131XeF 12%e clathrate. Study of Xe compounds such as XeO,. Eu(EtHSO,) nEQ suggests mixingof 5p56p1 (lo,) and 5p6 (lS,) states. 61 3 E Gold dEQ correlated with electronegativity differences be- 59 E tween host metal and gold. Barrett Grant Kaplan Keller and Shirley J. Chem. Phys. 1963 39 1035. 6o Nikolaev Shcherbina and Karchevskii Zhur. eksp. teor.Fiz. 1963 44 775. Judd Lovejoy and Shirley Phys. Rev. 1962 128 1733. 62 Noreni and Wertheim J. Phjx and Chem. Solids 1962 23 1 1 11. 63 Herber Kingston and Wertheim Inorg. Chem. 1963 2 153. 64 Wertheim Phys. Rev. 1961 121 63. 65 Wertheim and Herber J Chem. Phys. 1963 38 2106. 66 Wertheim and Herber J. Anzer. Chem. SOC. 1962 84 2274. 67 Wertheim and Herber J. Chem. Phys. 1962 36 2497. 6 8 ~ Shikazano J. Phys. SOC. Japan 1963 18 925. 60 Mullen Phys. Rev. 1963 131 1410; 1415. Kurkjian and Buchanan Phys. and Chem. Glasses 1964 5 63. DUNCAN AND GOLDING MOSSBAUER STUDIES OF CHEMICAL BONDING 55 of ionisation of the bond has been found.’O Such a graph gives insight into the type of bonding in similar tin compounds. Any quadrupole splitting observed in these compounds would indicate a deviation from tetrahedral symmetry.For instance the quadrupole splitting in SnF has been attri- buted71 to a polymeric structure in which each tin atom is bound to six fluorine atoms two of which have no additional bonds while four form bridge bonds between the tin atoms. 4.3 Gas-phase Adsorption and Surface Reactions.-Mossbauer spec- troscopy is also applicable to the study of solid-surface phenomena such as gas-phase adsorption and to surface reactions in liquid solutions. Little work of this type has so far been reported. The potentialitizs of the method can be illustrated by the adsorption of cobalt(r1) ion on precipitates of cobalt(r1) and iron(1r) o x a l a t e ~ . ~ ~ One would expect cobalt(I1) to be ad- sorbed on the surface sites of these precipitates in such a way that the en- vironment of the anions is asymmetric and quite different from that due to cations in the body of the solid.Experimentally however the shape of the Mossbauer spectrum using such a source with a stainless-steel absorber is identical within experimental error with that obtained with a copper- backed source and an iron@) oxalate absorber. It is also very similar to that obtained with a cobalt(r1) oxalate adsorbate; it is not affected by the length of time the precipitate is allowed to stand in contact with the active super- natant liquid; and is indistinguishable from spectra obtained when the precipitate is formed in the presence of radioactive material (it?. the 57Fe was formed by decay from the 5 7 C ~ in lattice sites). From these results two conclusions may be drawn.First the environments of iron atoms in cobalt(Ir) and iron(r1) oxalates are very similar. This implies that the crystal- line structures are similar which is not unreasonable in view of the similar ionic radii of the Co2+ and the Fez+ ions. Secondly the environment of surface-adsorbed ions is similar to that of ions within the lattice. 4.4 Single-crystal Studies.-The majority of Mossbauer spectra have been obtained from microcrystalline powders which give only averaged spectra. Consequently information is lost. By using a single crystal we may observe the y-ray absorption in different crystal orientations. It has been shown (Section 2) that in paramagnetic iron complexes the quadru- pole-split doublet in the y-ray absorption spectrum has an intensity ratio of 3(1 + cos28):(5 - 3cos28) where 8 is the angle between the electric- field gradient and the y-ray direction.Hence from the ratio of the in- tensities of the doublet lines the direction of the electric-field gradient in the single crystal can be determined. We have recently used this technique to determine the electric-field gradient in sodium nitroprusside single 70 Gol’danskii Atomic Energy Review vol. 1 No. 4 p. 3 International Atomic 71 Khaiduk see ref. 70. 72 Brady and Duncan J. 1964 653. 73 Duncan and Golding unpublished results. Energy Agency Vienna 1963. 56 QUARTERLY REVIEWS Single-crystal studies can sometimes readily reveal the presence of more than a single site in the lattice. For example Alff and We~theim,'~ using a single crystal of yttrium iron garnet have shown that there are three non- equivalent sites (one octahedral and two tetrahedral) for the 57Fe atoms in the structure.4.5 Electronic Configurations.-From the internal magnetic field or the isomeric shift 6 we can evaluate the s-electron density at the nucleus from the nucleus-electron interaction represented by the Fermi contact term in the spin Hamiltonian (eqn. 5). This term also accounts for the isotropic hyperfine interaction in electron spin resonance spectroscopy12 and the magnitudes of temperature-dependent shifts in nuclear magnetic resonance spectra of paramagnetic complexes.1o Such measurements are therefore important in order to test the validity of an electronic configura- tion for a molecule. For instance the nai've Aufbau principle implies a zero Fermi contact interaction. However we deduce from experiments that this is not the case.The Fermi term probably arises in three ways,4 namely (i) from mixing of excited electronic states containing unpaired s-electrons with the ground state (ii) by a spin-polarisation effect due to different spin-exchange interactions and (iii) by ligand-field mixing of the appropriate electronic configuration with the ground state. These important features of molecular electronic configuration can readily be investigated by means of Mossbauer spectroscopy. This new technique in chemistry thus provides ways in which basic ideas about molecular structure can be investigated and is a valuable extension to the general field of spectroscopy. This work is supported at the Victoria University of Wellington by the United States Air Force. '* Alff and Wertheim Phys. Rev. 1961 122 1414.