MossbauerSpectroscopyN. N. GreenwoodProfessor of Inorganic and Structural Chemistry,University ofLeedsT. C. GibbLecturer in Inorganic andStructural Chemistry,University ofLeedsChapman and Hall Ltd LondonFirst published 1971by Chapman and Hall Ltd,11New Fetter Lane, London EC4P 4EEPrinted in Great Britain byButler & Tanner Ltd, Frome and LondonSBN4121071041971T. C. Gibb and N. N. GreenwoodAll rights reserved. No part of thispublication may be produced, stored ina retrieval system or transmitted inany formor by any means, electronic,mechanical, photocopying, recording,or otherwise, without the prior writtenpermission of the publisher.Distributed in the U.S.A. byBarnes and Noble Inc.ContentsPreface page Xl1. The Mossbauer Effect 1Introduction 11.1 Energetics of free-atom recoil and thermal broadening 21.2 Heisenberg natural1inewidth 51.3 Energy and momentum transfer to the lattice 61.4 Recoil-free fraction and Debye-Waller factor 91.5 Cross-section for resonant reabsorption 111.6 AMossbauer spectrum 152. Experimental Techniques 172.1 Velocity modulation of gamma-rays 172.2 Constant-velocity drives 192.3 Repetitive velocity-scan systems 21(a) Pulse-height analysis mode 23(b)Time-mode (multiscalar-mode) spectrometers 25(c) On-line computers 262.4 Derivative spectrometers 262.5 Scattering experiments 272.6 Source and absorber preparation 302.7 Detection equipment 352.8 Cryogenic equipment and ovens 382.9 Velocity calibration 392.10Curve fitting by computer 413. Hyperfine InteractionsIntroduction3.1 Chemical isomer shift, 03.2 Second-order Doppler shift and zero-point motion3.3 Effect of pressure on the chemical isomer shift3.4 Electric quadrupole interactionsv464646505354vi ICONTENTS3.5 Magnetic hyperfine interactions 593.6 Combined magnetic and quadrupole interactions 633.7 Relative intensities of absorption lines 663.8 Relaxation phenomena 723.9 Anisotropy of the recoilless fraction 743.10The pseudoquadrupole interaction 764. Applications of the MossbauerEffect 804.1 Relativity and general physics 804.2 Nuclear physics 824.3 Solid-state physics and chemistry 845. 5 7Fe - Introduction 875.1 The ,,-decay scheme 875.2 Source preparation and calibration 895.3 Chemical isomer shifts 905.4 Quadrupole splittings 965.5 Magnetic interactions 1025.6 Polarised radiation studies 1045.7 Energetic nuclear reactions 1095.8 The 136-keV transition 1106. High-spin Iron Complexes 112A. HIGH-SPINIRON(II) COMPLEXES 1126.1 Iron(lI) halides 1136.2 Iron(lI) salts of oxyacids and other anions 1306.3 Iron(lI) complexes with nitrogen ligands 140B. HIGH-SPINIRON(III) COMPLEXES 1486.4 lron(IlI) halides 1486.5 Iron(llI) salts of oxyacids 1556.6 Iron(llI) complexes with chelating ligands 1591. Low-spin Iron(II) and Iron(III) Complexes 1697.1 Ferrocyanides 1697.2 Ferricyanides 1737.3 Prussian blue 1787.4 Substituted cyanides 1827.5 Chelating ligands 1878. Unusual Electronic Configurations of Iron 1948.1 Iron(lI) compounds showing5TrlA1 crossover 1948.2 lron(lIl) compounds showing6A 1_2T2 crossover 2028.3 Iron(I1) compounds with S =1 spin state8.4 lron(III) compounds with S =~ spin state8.5 Iron1,2-dithiolate complexes8.6 Systems containing iron(I), iron(IV), and iron(Vl)CONTENTSIVII2052062122169. Covalent Iron Compounds 2219.1 Binary carbonyls, carbonyl anions, and hydride anions 2229.2 Substituted iron carbonyls 2269.3 Ferrocene and othern-cyclopentadienyl derivatives 23310. Iron Oxides and Sulphides 23910.1 Binary oxides and hydroxides 24010.2 Spinel oxides AB20 425810.3 Other ternary oxides 26910.4 Iron(IV) oxides 28010.5 Iron chalcogenides 28310.6 Silicate minerals 28610.7 Lunar samples 29411. Alloys and Intermetallic Compounds 30411.1 Metallic iron 30511.2 Iron alloys 30811.3 Intermetallic compounds 31712. 57Fe - Impurity Studies 32912.1 Chemical compounds 33012.2 Metals 34012.3 Miscellaneous topics 34413. Biological Compounds 35213.1 Haemeproteins 35313.2 Metalloproteins 36514. Tin-119 37114.1 y-Decay scheme and sources 37114.2 Hyperfine interactions 37514.3 Tin(I1) compounds 38114.4 Inorganic tin(IV) compounds 39014.5 Organotin(IV) compounds 39914.6 Metals and alloys 41715. Other Main Group Elements 43315.1 Potassium (4K) 433viiiICONTE N TS15.2 Germanium (73Ge) 43415.3 Krypton (83Kr) 43715.4 Antimony (l21Sb) 44115.5 Tellurium (l25Te) 45215.6 Iodine (l27I,1291) 46215.7 Xenon (l29Xe, 131Xe) 48215.8 Caesium (l33CS) 48615.9 Barium (l33Ba) 48816. Other Transition-metal Elements 49316.1 Nickel (61Ni) 49316.2 Zinc (67Zn) 49716.3 Technetium (99Tc) 49916.4 Ruthenium (99Ru) 49916.5 Silver (l07Ag) 50416.6 Hafnium (l76Hf, 177Hf, 178Hf, 180Hf) 50416.7 Tantalum (l81Ta) 50716.8 Tungsten (l82W, 183W, 184W, 186W) 50916.9 Rhenium (l87Re) 51416.10Osmium (l860 s, 1880S, 1890S) 51416.11 Iridium (l91Ir, 193Ir) 51816.12Platinum (l95Pt) 52416.13Gold (l97Au) 52616.14Mercurye01Hg) 53011. The Rare-earth Elements 53617.1 Praseodymium (l41Pr) 53717.2 Neodymium (l45Nd) 53717.3 Promethium (l47Pm) 53917.4 Samarium (l49Sm, 152Sm, 154Sm) 53917.5 Europium (l51Eu, 153Eu) 54317.6 Gadolinium (l54Gd, 155Gd, 156Gd, 157Gd, 158Gd, 16Gd) 55817.7 Terbium (l59Tb) 56317.8 Dysprosium (l6Dy, 161Dy, 162Dy, 164Dy) 56317.9 Holmium (l65Ho) 57317.10Erbium(l64Er, 166Er, 167Er, 168Er, 170Er) 57417.11 Thulium (l69Tm) 57917.12Ytterbium (i70Yb, 171Yb, 172Yb, 174Yb, 176Yb) 58518. The Actinide Elements18.1 Thorium e32Th)18.2 Protactinium e31Pa)18.3 Uranium e38U)596596596597CONTENTSI ix18.4 Neptunium (237Np) 60018.5 Americium (243Am) 604Appendix 1. Table of nuclear data for Mossbauer transitions 607Appendix 2. The relative intensities of hyperfine lines 612Notes on the International System of Units (SI) 619Author Index 621Subject Index 645PrefaceRudolph Mossbauer discovered the phenomenon of recoil-free nuclearresonancefluorescencein1957-58 and the first indications ofhyperfineinteractions in a chemical compound were obtained by Kistner and Sunyarin1960. Fromthesebeginningsthetechniqueof Mossbauerspectroscopyrapidly emerged and theastonishing versatility of this new techniquesoonled to its extensive application to a wide variety of chemical and solid-stateproblems. This book reviews the results obtained by Mossbauer spectroscopyduring the past ten years in the belief that this will provide a firm basis forthe continued development and application of the technique to new problemsin the future.Ithasbeenouraimtowriteaunifiedandconsistent treatment whichfirstly presents the basic principles underlying the phenomena involved, thenoutlines the experimental techniques used, and finally summarises the wealthof experimental and theoretical results which have been obtained. We havetried to give some feeling for the physical basis of the Mossbauer effect with-out extensive use of mathematical formalism, and some appreciation of theexperimental methods employed without embarking on a detailed discussionof electronics and instrumentation. However, full references to theoriginalliterature are provided and particular points can readily be pursued in moredetail if required.The vast amount ofwork which has been published using the 57Fe resonanceis summarisedinninechapters andagainfull references totherelevantliterature are given. The aim here has been to give a critical treatment whichprovides perspective without loss of detail. The text has been updated to thebeginning of 1970 and numerous referencesto important resultsafter thattime have also been included.A similar approach has been adopted for tin-119 and for each of the fortyother elements for which Mossbauer resonances have been observed. Thoughthe results here aremuch less extensive than for iron, many new points oftheoryemerge andnumerous ingenious applications have beendevised.Indeed, one of the great attractions of Mossbauer spectroscopy is its applic-ability to a wide range of very diverse problems. At all times we have tried toxii \ PREFACEemphasise the chemical implications of the results and have indicated boththe inherent advantages and the occasional limitations of the technique.Our own interest in Mossbauer spectroscopy dates from1962 and, fromthe outset, we were helped immeasurably by that small international band ofenthusiasts who in the early days so generously shared their theoretical insightand instrumental expertise with us. As more chemists became aware of thetechnique, various international conferences were arranged and, in thiscountry, theMossbauer Discussion Group was formed. Thewiderange oftopics discussed at these meetings testifies to the metamorphosis of Mossbauerspectroscopy from its initial 'technique oriented phase' to its present, moremature'problemorientedphase'. Accordingly, Mossbauerspectroscopyisnowwidelyemployedasoneof avarietyof experimental techniquesap-propriate to the particular problem being studied. With this maturity comesthe realisation that in future it will no longer be feasible, or indeed desirable,to revieweachindividual application of Mossbauer spectroscopy or todelineate its distinctive contribution to the solution of a particular problem.However, thepresent book, inreviewingthe first decadeof Mossbauerspectroscopy, enables an overall view of the scope of the method to be ap-preciated. We hope that it will serve both as an introductorytext forthosewishing to become familiar with the technique, and as a detailed source-bookof references and ideas for those actively working in this field.Thebookwas writtenwhilst wewereintheDepartment of InorganicChemistry at the University of Newcastle upon Tyne, and it is a pleasure torecord our appreciation of the friendly and stimulating discussions we havehad over the years with the other members of staff, graduate students, and visit-ing research fellows in theMossbauer Group which grewupthere. Weareindebted toMrs MaryDalglieshfor her good-humouredpersistenceandtechnical skill in preparing the extensive and often complex typescript, andwould alsolike to thank Mrs Linda Cook, Mrs Millie Fenwick, andMiss AnneGreenwood for their help in checking proofsandpreparing theindexes.T.C.G., N.N.G.Department of Inorganic Chemistry,University of Newcastle upon Tyne.May 1971.1 The Mossbauer EffectThe phenomenon of the emission or absorption of a y-ray photon withoutloss of energy due to recoil of the nucleus and without thermal broadening isknownastheMossbauer effect. It wasdiscoveredbyRudolphMossbauerin 1957 [I] and has had an important influence in many branches of physicsand chemistry, particularly during the last five years. Its unique feature is inthe production ofmonochromaticelectromagneticradiationwitha verynarrowly defined energy spectrum, so that it can be used to resolve minuteenergy differences. The direct application of the Mossbauer effect tochemis-try arises from its ability to detect the slight variations in the energy of inter-action between the nucleus and the extra-nuclear electrons, variations whichhad previouslybeen considered negligible.The Mossbauer effect has been detected in a total of 88 y-ray transitions in72 isotopes of 42different elements. Although intheory it ispresent for allexcited-state-ground-state y-ray transitions, its magnitude can be so low astoprecludedetectionwithcurrent techniques. As will beseenpresently,there are several criteria which define a useful Mossbauer isotope for chemicalapplications, andsuch applicationshaveso farbeenrestrictedtoaboutadozen elements, notably iron, tin, antimony, tellurium, iodine, xenon,europium, gold, andneptunium, andtoalesser extentnickel, ruthenium,tungsten, andiridium. Thesituationthus parallels experienceinnuclearmagnetic resonancespectroscopywherevirtually all elementshaveat leastone naturally occurring isotope with a nuclear magnetic moment, though lessthan a dozen can be run on a routine basis (e.g. hydrogen, boron, carbon-B,fluorine, phosphorus, etc.). However, advances in technique will undoubtedlyallow the development of other nuclei for chemical Mossbauer spectroscopy.To gain an insight into the physical basis of the Mossbauer effect and theimportance of recoilless emission of y-rays, we must consider the interplayof a variety of factors. These are best treated under five separate headings:1.1Energetics of free-atom recoil and thermal broadening.1.2Heisenberg naturallinewidth.1.3Energy and momentum transfer to the lattice.[Refs. on p. 16]2 I THE MOSSBAUEREFFECT1.4Recoil-free fraction and Debye-Waller factor.1.5Cross-section for resonant absorption.1.1 Energetics of Free-atom Recoil and Thermal BroadeningLet usconsideranisolatedatom inthegas phase anddefine the energydifference between the ground state of the nucleus (Eg) and its excited state(Ee) asE= Ee- EgThe following treatment refers forsimplicity to one dimension only, that inwhich a y-ray photon is emitted and in which the atom recoils. This simpli-fication causes no loss of generality as the components of motion in the othertwo dimensions remain unchanged. Ifthe photon is emitted from a nucleus ofmassMmoving with aninitialvelocityVxin thechosen direction x atthemoment of emission(seeFig. 1.1), thenitstotal energyabovethegroundBefore Afteremission emission~ ~y.~=~E+ !MV}VelocityEnergyVx+v)-Ey +!MIVx+v;2EyMomentum MVx= .M(Vx+v)+cFig. 1.1The energy and momentum are conserved in the gamma emission process.state nucleus at rest is (E + !MVx2). After emissionthey-raywill haveanenergy Ey and the nucleus a new velocity (Vx + v) due to recoil (note that vis a vector so that its direction can be opposite toVx)' The total energy of thesystem isEy + !M(Vx +V)2. By conservation of energyE +!MVx 2= Ey +!M(Vx + t-)lThe difference betweenthe energyofthe nuclear transition(E) and theenergy of the emitted y-ray photon (Ey) isbE =E - Ey =!Mv2+ MrVxbE =ER +ED 1.1The y-ray energy is thus seen to differ from the nuclear energy level separa-tion by an amount which depends firstly on the recoil kinetic energy(ER =!Mv2) whichis independent of thevelocityVx, andsecondly on thetermED =MvVxwhichisproportional totheatomvelocity Vxandisa[Refs. on p. 16]ENERGETICS OF FREEATOMRECOIL I 3Doppler-effect energy. SinceVx and v are both much smaller than the speedof light it is permissible to use non-relativistic mechanics.Themeankineticenergy pertranslational degreeof freedomofafreeatom in a gas with random thermal motion is given byEK =-!-MV/ ~ d k Twhere Vx2isthemeansquarevelocityof theatoms, kis theBoltzmannconstant and T the absolute temperature.Hence (VX2)t =y(2EK/ M) and the mean broadening1.2Thus referring to equation 1.1, the y-ray distribution is displaced by ER andbroadened by twice the geometric mean of the recoil energy and the averagethermal energy. The distribution itselfis Gaussian and is shown diagrammatic-ally in Fig. 1.2. For E and Ey having values of about104eV ERandED areER ( )0 __yFig. 1.2The statistical energy distribution of the emitted y-ray showing the inter-relationship of E,ER,and ED.about 10-2eV.(The144-keV57Fetransitionat300KhasER =195X10-3eV andEDr-.J 10X 1O-2eV).The values of ER andED can be more conveniently expressed in terms ofthe y-ray energy Ey ThusE - l.M2 _ (Mv)2_LR- 2 V - 2M- 2Mwherep is therecoil momentumof theatom. Sincemomentummust beconserved, thiswill beequalandoppositetothemomentumofthe y-rayphoton, Py,Eyp= -p =--y C[Refs. on p. 16]4 I THE MOSSBAUEREFFECTI.32E - yR - 2Mc2Expressing Ey in eV, Min a.m.u., andwith c =2998 X lOll mm S-1 giveshenceE2ER (eV) =5369x 10-10 -y-M1.4Likewisefromequations1.2 and1.3J2EKED =2y(EKER) =Ey (Mci)1.5The relevance of ER and ED to gamma resonance emission and absorptioncannowbediscussed. Fundamental radiationtheorytellsusthatthepro-portion of absorption is determined by the overlap between the exciting andexcited energy distributions. In this case the y-ray has lost energy ER due torecoil of the emitting nucleus. It can easily be seen that for the reverse processwhere a y-ray is reabsorbed by a nucleus a further increment of energy ER isrequired since the y-ray must provide both the nuclear excitation energy andthe recoil energy of the absorbing atom(E +ER). For example, forEy =104eV andamassof M =100 a.m.u., it isfoundthat ER =54X10-4 eV and ED '" 5X10-3 eV at 300 K. The amount of resonance overlapisillustrated(nottoscale)astheshadedareainFig. 1.3andisextremelysmall.~ I < :t-ER +ER_EyFig. 1.3The resonance overlapforfree-atomnuclear gammaresonanceissmalland is shown shaded in black.It is interesting to note that the principles outlined above are also relevantto the resonance absorption of ultraviolet radiation by atoms. However, forthetypicalvaluesof E =62 eV(50,000 cm-I) andM =100 a.m.u. ERisonly 21 x10-10 eV and ED is'" 3X 10-6 eV. In this case strong resonanceabsorptionis expected becausetheemission andabsorptionprofiles over-lap strongly. The problems associatedwithrecoil phenomenaare thus onlyimportant for very energetic transitions.[Refs. on p. 16]1.6the meanHEISENBERGNATURALLINEWIDTH I 5The earliest attempts to compensate forthe energy disparity 2ERinvolvedthe provision of a large closing Doppler velocity of about 2v.2v= 2p= p.J'. = 2EyM M MeThis was first successfullyachievedbyMoon[2] in 1950usinganultra-centrifuge. Amercuryabsorber was used, together witha 198AufJ-activesource togenerate anexcitedstate of 198Hg. The requiredvelocity wasabout 7X105 mm S-1 (1600 mph). Since that time recoil has been compen-satedbyavarietyof techniquesincluding priorradioactivedecay, nuclearreactions, and the use of high temperatures to increase the Doppler broaden-ing of the emission and absorption lines and so improve the resonant overlap.It is important to note that in all these techniques the recoil energy is beingcompensatedfor, whereasintheMossbauer effect therecoil energyiseli-minated and no compensation for recoil is required.1.2Heisenberg Natural LinewidthOne of themost important influencesonay-rayenergydistributionisthemean lifetime of the excited state. The uncertainties inenergy and timearerelated to Planck's constant h (= 2nli) by the Heisenberguncertainty principle!j.Et i r ~ IiThe ground-state nuclear level has aninfinite lifetime andhence azerouncertainty in energy. However, theexcited state of thesource hasameanlifeT of a microsecond or less, so that there will be a spread of y-ray energiesof width Ts at half height whereTsT= IiWhence, substituting numerical values and remembering thatlifeT is related to the half-lifet1 by the relationT= In 2 X t1:4562 X 10-16T s (eV) = ()t! sFor a typical case C7Fe), t1 is 977 ns and T s is 4'67 X 10-9 eV. This is some106_107times less than the values of ER andED for a free atom and so canbeneglected in that case; thiswasdoneimplicitly inthepreceding sectionwhere the y-transition energy E was represented as a single value rather thanas an energy profile. However, it can beseen that if the recoil and thermalbroadening could be eliminated, radiation with a monochromaticity ap-proaching1 part in1012 could be obtained.[Refs. on p. 16]6 I THE MOSSBAUEREFFECT1.3Energy and Momentum Transfer to the LatticeChemical binding and lattice energies insolids are of theorder of 1-10 eV,andareconsiderablygreaterthanthefree-atomrecoil energiesER If theemittingatomis unabletorecoil freelybecauseof chemical binding, therecoiling mass can be considered tobe the mass of the whole crystal ratherthan the mass of the single emitting atom. Equation1.3 willstill apply, butthe mass Mis now that of the whole crystallite which even in a fine powdercontains at least 1015 atoms. This diminution of ER by a factor of 1015 makesit completelynegligible. Fromequation 1.5, EDwill alsobenegligibleinthese circumstances.However, the foregoingtreatment issomewhat of anover-simplification.The nucleus is not bound rigidly in the crystal as assumed above, but is freeto vibrate. In these circumstances it is still true that the recoil momentum istransferredtothecrystal as awhole, sincethemeandisplacement of thevibrating atom about its lattice position averages essentiallytozeroduringthetimeof thenucleardecay, andtheonlyrandomtranslational motioninvolves the whole crystal, and is negligible. However, the recoil energy of asinglenucleus can be takenup either by the whole crystal as envisaged aboveor it can be transferred to the lattice by increasing the vibrational energy ofthe crystal, particularly as the two energies are ofthe same order 'of magnitude.The vibrational energy levels of the crystal are quantised : only certain energyincrements are allowedandunless the recoil energycorresponds closelywithoneof theallowed incrementsit cannot betransferredtothelattice,thus ensuringthat the whole crystal recoils, leadingto negligible recoilenergy. It can be seen that the necessary condition for theMossbauer effecttooccuristhat thenucleusemittingthey-photonshouldbeinanatomwhich has established vibrational integrity with the solid matrix. In practicethis criterion can be relaxed slightly (see p. 346) and the effect can sometimesbe observed in viscous liquids.The vibrational energy of the latticeasawholecanonly changeby dis-crete amounts 0, liw, 2Iiw, etc. If ER6X10-2eVandvalues arenormally intherange (0'1-5) x10-2 eV.[Refs. on p. 43]32 I EXPERIMENTALTECHNIQUES(5) The method of generation of the source y-rays should ideally be such thatasource can be encapsulated and then used for a long period with only theminimum of handling precautions. This implies a long-lived precursor whichis easilyobtained inhigh activity, and explainsthepopularity of those fJ-,E.C., and I.T. sources, which can be purchased commercially. The Coulomb,(n, y), and (d, p) reactionsrequireaccess toveryexpensiveequipment. Forroutine chemical applications particularly, sources having lifetimes of monthsor years are preferable so that prolonged series of experiments become botheconomical and self-consistent.All theabovecriteriaconcernpropertieswhicharecharacteristic of thetransition concerned and cannot be altered. There are, however, a nnmber ofotherconsiderationsover whichtheexperimentalist has some measureofcontrol, and which are equally important:(6) The source should generate y-rays with an energy profile approaching thenatural Heisenberg Iinewidth andshouldnot besubject toanyappreciableline broadening. It is also a convenience in general work to have a single-linesource unsplit as aresult of hyperfine effects,as this splitting results in verycomplicatedspectra; multiple-linesources can, however, be used for specialpurposes.(7) The effective Debye temperature of the source matrixshould be highsothat the recoil-free fraction is substantial. High-melting metals and refractorymaterials such as oxides are the obvious choices.(8)Thereshouldbenoappreciablequantity of theresonant isotopeinitsground state in the source, otherwise the self-resonant source term in equation1.20 becomes important. This will result in an effective source linewidth whichis greater than the Heisenberg natural linewidth. In this respect it is interestingtonotethat thelinewidth of a 57Coj(iron)sourceisgreaterthanthat for57Coj(ironenrichedinS6Fe) becauseof thegreater self-resonanceintheformer case [48].(9) Non-resonant scattering inside the source can be reduced, either by carefulchoiceof anyotherelementsinthematrix, or, inthecaseof metal foilsdoped with a radioisotope which is the Mossbauer precursor, by controllingthe depth to which this generating impurity is diffused.(10) The ground-state isotope should ideally be stable and have a high naturalabundance, otherwiseit maybecomenecessarytouseartificiallyenrichedcompounds at greatly increasedcost and inconvenience. Isotopic enrich-ment is, however, a very important method of improving resolution of spec-tra and may become essential in work with biological materials or in the studyof dopedsolids where the actual concentration of the element of interest isextremely small.An important consideration is the chemical effects of the nuclear reactionspreceding the occurrence of aMossbauer event. If, forexample, thesourcepreparation involves a long neutron irradiation of the intended source matrix[Refs. on p. 43]SOURCE ANDABSORBERPREPARATION I 33at highflux as in 118Sn(n, y)119mSn, considerableradiationdamagemayoccur with the formation of lattice defects. Since ideally all the excited atomsshouldbeinidentical chemical environments, suchdefects will result inunwanted line-broadening effects.For this reason it may be desirable eitherto annealthe sourceso asto restorethe regularityof thecrystal lattice, ortoextract the radioisotope chemicallyandthenincorporateit ina newmatrix.Very high-energy processes immediately preceding the Mossbauer y-emissionmust alsobeconsidered. The ~ - d e c a y of 241Amtogive 237Npis sufficiently energetic to displace the daughter nucleus from its initial latticesite. At thesametimeaconsiderablenumber of neighboursarethermallyexcited. The fact that aMossbauer spectrum is recordedat all inthis caseshows that the Np atom comes to rest on a normal lattice site and establishesvibrational integrity with the lattice as a whole in a time which is short com-paredtothelifetimeof the5954-keV level, i.e. 63ns. Complications canoccur if the displaced atom is capable of residing on more than one type ofchemical site in the crystal.Similar situations arise, for example, inCoulombexcitationreactions.In the 73Ge case, the low Debye temperature of the Ge metal produces a verylow recoil-free fraction. As mentioned in more detail later (p. 109), it is pos-sible to displace the excited atoms completely out of the target material andimplant themintoanewmatrixwithahighDebyetemperature, therebyobtaining a considerable improvement in the quality of the spectra.Electroncapture involves the incorporationofaninner-shell electron(usuallytheK-shell) intothenucleus(therebyconvertingaprotonintoaneutron and emitting a neutrino). This event is followed by an Auger cascadewhich results in production of momentary charge states on the atom of upto +7. Manypapers on 57Feexperiments have reported the apparentdetection of decaying higher charge states resulting from E.C. in57CO, butas detailed in Chapter 12 it has since been proven that although such statesare indeed generated by the after-effects of electron capture, they have alreadyreached stable equilibrium with thesolidbefore thesubsequent Mossbauertransition occurs. It would appear that all transient nuclear decay after-effectsare over within 10-8 of a second. It is important, however, to avoid the pro-duction of multiple charge states if the source is not intended to be the subjectof a special study designed to detect such states but is tobe used only as asource of monochromatic radiation. Some of these topics will be consideredin more detail under specific isotopes in later chapters.Although the preparation of a good source may in some cases be difficult,an adequate absorber can usually be made quite easily. A few general remarksmay be useful to illustrate the balance of factors involved, and several textswith full mathematical equations are available [49-52]. Integration of equa-tion 1.20 for simplified cases shows that the measured linewidth will increase[Refs. on p.43]2.234 I EXPERIMENTAL TECHNIQUESabove2F as the absorber thickness increases. This will decrease the resolu-tionof a multiple-linespectrumortheprecisionwithwhicha singlelinecanbelocated. Furthermore, anincreaseinabsorber thicknessalsodimi-nishes thetransmissionof resonant radiationas a result of non-resonantscattering. However, it is equally clear that the absorber must have a finitethickness for the resonance to be observed at all, hence it follows that theremust be an optimum absorber thickness for transmission geometry.Integration of equation 1.20 for a uniform resonant absorber and an ideallythin source gives the transmission at the resonance maximum asT(O) =e-l'ata{(1- Is) +Is e-tTaJo(1-iT.)} 2.1where Jo is the zero-order Bessel functionx 2( ~ ) 4 ( ~ ) 6Jo(ix) =1 +(2) +12.22+P.22.32...................... 1-0--...... _---------Non-resonant0'2040'6andT. = fan.a.Got. The functionT(O) is plotted in Fig. 2.8 for 57Fe using10.::.::------------------7(0).30 10 20fa/(mg cm-2af iran}Fig. 2.8The solid linesare the functionT(O) plotted forazerovalueof fl. andfour different values offa' together with parameters appropriate to5 7Fe (14'4 keY).The dashed curve represents the non-resonant attentuation with fl. = 0067.the parameters It. =0 (i.e. no non-resonant scattering), a. =0,0219,Go= 257X10-18 cm2,.fs = 07 and for.fa values of 0,2, 0'4,0'7, and 10 (thethickness has beenconvertedtomgcm-2of natural iron). Theresonantabsorption shows a saturation behaviour with increasing thickness. Thedashedcurveshowsthenon-resonant scatteringattenuation. Thequantityto optimise is obviously the absorption in the final transmitted radiation whichis e-I'ata_ T( 0) =~ T ( O ) .~ T ( O ) =e-I'ata.fs[1- e-tTaJo(!-iT.)] 2.3[Refs. on p.43]DETECTIONEQUIPMENT I 35A series of curves for 5 7Fe with fla =0067 (the value for natural iron) areshown inFig. 2.9. The optimum value isseentobe about 10 mg cm-2of0420 30fa/(mg cm-'ofironlFig. 2.9The function ~ T ( O ) for 57Fe(14,4keY) plotted for fourvalues of fatoshow the optimum absorber thickness.total iron. Fortunately, this value isvirtually independent of the recoil-freefraction, a parameter which cannot always be determined in advance. Com-pounds of iron can be visualised using the same thickness scale, but with ahigher non-resonant attenuationcoefficient, sothat themaximuminthecurves moves to lower ta values.This type of calculation is only of limited value. The major problem is thepossibility of additional non-resonant intensity at the counter produced bytheComptonscatteringof higher-energyy-rays. Anotherfactor concernsparticlesize. Thepresenceof largegranules intheabsorbercancauseasignificant reduction in the observed absorption. Calculations [53] show thatreductioninparticlesizeeventuallyresultsinareversiontotheuniformabsorber model.A discussion of the effects of orientation of the granules andtheuseofsingle-crystal absorbers will be deferred until Chapter 3 when the intensitiesof hyperfine components are discussed.Ingeneral, absorberscanbemetal foils, compactedpowders, mixtureswith inert solid diluents, mixtures with inert greases, frozen liquids, or frozensolutions. The only limitation is on the material used for the windows of thesample container; this must be free of the resonant isotope and have a lowmass attenuation coefficient for the y-ray being studied. Organic plastics andaluminium foilare most commonly used.2.7Detection EquipmentOf the four principal types of y-ray detector used in Mossbauer spectroscopy,[Refs. on p.43136 I EXPERIMENTAL TECHNIQUESthree are conventional instruments and requireonlybrief mention. Furtherdescriptive material and detailed references are readily available [54, 55].The scintillation-crystal type of detector is frequently used for y-rays withenergies in the range 50-100 keY. A typical example is the NaljTI scintillator.The resolutionofscintillators deteriorates withdecreasingenergyofthey-photon as shown in Fig. 2.10, and such detectors can only be used for very50'2010-0-.e-::g.,:J10:: 5AProportional counterNaI(n)Scintillator50 100 150 200Energy/keVFig. 2.10Typical resolution of commonly used y-ray detectors.soft y-rays if the radiation background is low and there are no other X-ray ory-ray lines with energies near that of the Mossbauer transition. The scintilla-tion unit has a prime advantage of a high efficiency.Below 40keY, thegas-filledproportional countergivesbetterresolutionbut at theexpenseof alowefficiencyandgenerallylowerreliability.It ispossible to lower the radiation background in some cases by the choice of asuitable 'filter'; for example a copper foil will absorb the 27,5- and31'0-keV125Te X-raysstrongly and transmitmost of the35'5-keV y-raysbecause ofthe higher mass attenuation coefficient for the former.[Refs. on p. 43]DETECTIONEQUIPMENT I 37A morerecent developmenthasbeenthe introduction of lithium-driftedgermanium detectors. As shown in Fig. 2.10 these give a very highly resolvedenergyspectrum, but at theexpenseof lowsensitivity, andsomeincon-venienceinuse. Theyareof obviousapplicationwherethereareseveraly-rays of similar energy as often found in the complicated decay schemes ofthe heavier isotopes. Again the resolution drops drastically with decreasingenergy, and they are only of use at the higher end of the Mossbauer energyrange. Other drawbacks include a high cost and the necessity for maintainingthem indefinitely at liquidnitrogen temperature; irreparable damage resultsif they are allowed to warm to room temperature.Comparative examples[56]of theresolution fora sourceof1251 popu-lating the 125Te35'5-keV level are given in Fig. 2.11. Although only the Li-driftedGecrystal gives goodresolutionof the 35'5keYy-rayfromtheNar/nScintillatorXelMe proportional counterEnergyFig. 2.11The energy spectrum of an1251 source as recorded with three differentdetection systems.27,5- and 31'O-keV X-rays, in this particular instance the other two systemscanmakeuse of the'escape peak' which isproducedbyloss of aniodine(or xenon)KX-ray fromthe capturing medium. Thetellurium X-raysaretoo low in energy to generate an escape peak.The fourth detector system is to use a resonance scintillation counter [57].A standard type of plastic scintillator for tJ-detection is doped with the reso-nant absorber. It is insensitivetothe non-resonant background of primary[Refs. on p.43]38 I EXPERIMENTAL TECHNIQUESy- and X-photons, but willdetect thesecondary conversion electronsaftery-capturebytheresonantnuclei. Although effective, themaindifficulty isone of inconvenience, becauseanew plasticscintillator mustbemadeforeach compound used as an absorber. Alternatively, one can use an ordinaryGeiger or proportional counterwithits innersurfacethinlycoated withacompoundof theisotopebeingstudied[58] orwiththeproperabsorberitself located insidethecounter[59]. Again, therecoillessy-raysarereso-nantlyabsorbedbythecoating on theinternal absorber, andtheinternalconversion electrons or low-energy X-rays emitted in thesubsequent decayof theexcitedstatearethencountedwithalmost 100%efficiencyin 4:>7:-geometry. The counter has been used for57Fe [59], 119Sn [60], and169Tm[61], and can be used in principle for any Mossbauer isotope in a compoundwhich has a large recoil-free fraction at room temperature.Other closelyrelatedmeansof recordingaMossbauerresonancearetorecord the conversion X-rays scattered from the surface of an absorber [62]or transmitted through it [63], or to count the conversion electrons emitted[64].2.8Cryogenic Equipment and OvensThe verylowrecoil-free fraction ofmany y-ray transitions at ambienttemperatures frequentlynecessitates experimentation at lower temperatureswheretheMossoauer effectwill bestronger. In addition, thetemperaturedependence of hyperfine effects is also frequently of interest. If a good sourcewith a high recoil-free fraction at room temperature is available, it may onlybe necessary to cool the absorber which is stationary. Otherwise, it may benecessary to cool both source and absorber, one of which must also be mov-ing. Standard cryogenic techniquesare used[55, 65]andvacuum cryostatsare commercially available for work between 42 K and 300 K. The two mainconsiderations peculiar to Mossbauer spectroscopy are (a) there must be novibration insiCte the cryostat, and (b) there must be a path through the systemwhich is transparent to the y-rays being studied. Vibration can be eliminatedby careful design. It has been found, for example, that a rigid interconnectionbetween a helium container and theouter walls canbemadebymeans oftwostacks of several hundredaluminisedMylar washers loosely threadedtogether, between two nylon washers for support, the large number of contactsurfaces lowering the heat transmission to acceptable limits [66]. Cooling thevibrating source as well as the absorber can only be accomplished by insertingthe entire transducer unit inside the vacuum space.Although work below liquid nitrogen temperature necessitates a precision-engineered vacuum cryostat, it is quite easy to work between 78 K and 300 Kwithout a vacuum by using styrofoam insulation. Standard coolants are liquidnitrogen (b.p. 773 K), liquidhydrogen (b.p. 204 K), and liquid helium[Refs. on p.43]VELOCITYCALIBRATION I 39(b.p. 42 K). Temperatures below these boiling points can also be maintainedby pumping on the liquid coolant. Some work calls for more flexible variable-temperature control and in such cases it is possible to use either a tempera-ture gradient along a conducting metal rod regulated by a heating element,or a cold-gas flow technique. Many systems are briefly described in the litera-ture, and there are also some detailed texts available [55, 65, 67-69].The windowmaterial used in vacuumcryostats is usually beryllium,aluminium, oraluminisedmylar.Itshouldbenoted, however, that com-mercial berylliumandaluminiumoftencontainsufficient ironto give adetectable 57Pe (14keY) resonance, and this has been known to causeproblems when working with this isotope.Temperatures above300 K aresometimes desirable for 57Pe work, anda controlled-temperature furnace is then required [68, 69]. The sampleis frequently sandwiched between thin discs of beryllium, graphite, oraluminium(m.p. 660C)attachedtoanelectricheatingcoil inavacuum.Alternatively [70], the sample canbe placed in a furnace with thin entranceandexit windows andcontaininganatmosphereof hydrogentopreventoxidation. A vacuum furnace capable of providing temperatures up to 1000Chas been described [71] and temperatures of 1700C have been reached with ahelium-filled oven with beryllium windows [72].High-pressure work has beenpublished byrelativelyfewlaboratoriesbecause pressure cells requirespecial experience and engineering [73-75].If alarge external magneticfieldistobe applied toanabsorber, this isusually done with a superconducting magnet installation which also requiresaliquidheliumcryostat foritsoperation[76]. Again, several commercialinstruments are available.2.9Velocity CalibrationOneof themore difficultexperimental aspectsof Mossbauerspectroscopyis the accurate determinationofthe absolute velocityofthe drive. Thecalibration is comparatively easy for constant-velocity instruments, but mostspectrometers nowuse constant-acceleration drives. The least expensivemethod, and therefore that commonly used, istoutilise thespectrum of acompound which has been calibrated as a reference. Unfortunately, suitableinternational standards and criteria for calibration have yet to be decided. Asa result, major discrepancies sometimesappear in theresults from differentlaboratories. The problemis accentuatedbyhavingfigures quotedwithrespect to several different standards, necessitating conversion of data beforecomparison canbemade. However, calibration of data fromanarbitrarystandard spectrum will at least give self-consistency within each laboratory.Several systems fora more direct absolute-velocity calibration havebeendeveloped. Inone such method[31], theoutput of themonitoring pick-up[Refs. on p. 43]40 I EXPERIMENTAL TECHNIQUEScoil is fedto a voltage-to-frequency converter and thence to the time-modemultichannel analyser asatrainof pulseswiththesamefrequency. Thecounting rate in a channel is thus a function of the instantaneous velocity,provided of course that the linearities of the pick-up coil and the voltage-to-frequency converter are both accurate. Thismethod gives a good check onMirror3 ~ ; = ~ ttm= ~DriveCo}0( &:1 119/;;/. LampMovingpri$mStationaryprismlb)Fig. 2.12Absolute calibration of constant-acceleration drives using (a) diffractiongrating, (b) optical interferometer.the day-to-day linearity and stability of the drive, but is not easily calibratedin absolute terms from a known hyperfine spectrum.An absolute calibration can be obtained by mounting a diffraction grating[Refs. 011 p. 43)CURVE FITTINGBYCOMPUTER I 41(typically8 p,mspacing)onthereverseend of thesourcedrive-shaft [77].Reflectionof thediffractionimagewill producealight intensitywhichisperiodic by interference because of the varying velocity of the grating. Thefluctuations can be detected and converted to pulses which after accumula-tion in the time-mode analyser give a calibration similar to that mentionedabove. Thebasiccomponents areillustratedschematicallyinFig. 2.12a.The absolute accuracy is claimed to be as good as that of the best mechanicaldrives.Asimilar methoduses anoptical interferometer as illustratedinFig.2.12b[78]. Themotion of thesmall prism, which is attachedtothedrive,causes a time-dependent interference which is again converted to pulses andregistered in the analyser. Neither method is widely applicable because of theprohibitive cost of the precision optical equipment.Calibration in terms of a known frequency has also been accomplished bymounting the absorber on a quartz crystal and calculating the velocity scalefrom the spectrum sidebands produced by frequency modulation [79].2.10Curve Fitting by ComputerMuch of the Mossbauer spectroscopic data which is published comes frominstitutions which also have large computer facilities. Since the raw data of aspectrum are already digitised, it is in a very convenient form for automatedanalysisbydigitalcomputer. Themajorityof multichannel analysershaveoutput signals which are either directly compatible with or easily adapted forappropriatetypes of punchedpapertapeormagnetictapeunits, sothataccumulated spectra can be printed out in a formwhich is compatible withthe computer installation.The information which may be required from the computer analysis of thedata are the parameters of a selected function which are the best possible fitto the observed spectrum. In the simplest caSes this function will be one ormore Lorentziancurves. However, morecomplextypesof functionmaysometimes be required, for example when fitting multi-line spectra which aresubject to motional narrowing (see p. 72).The general problem canbe describedasfollows. The data compriseNdigitised values Yj The function which is tobe fittedcontainsnvariables,represented by the vector V, and will give a calculated value at data point iof A(V)!. The error thereby incurred isei = Yi- A(V)! 2.4The best possible fit to the N data points, which is the answer required, mustbesuchthattheoverall errorisaminimum. Thestatistics of radioactivecounting processes[80] tell us that the values ofYiwill be distributed as aPoisson distribution with a variance equal to the mean, and hence the stan-dard deviation inYkis V Yk The quantity to be minimised for a best fit is[Refs. on p.43]42 I EXPERIMENTAL TECHNIQUESthereforethe'goodness of fit' functionNF(V) = 6{[Y1- ~ ( V ) i l 2 }2.5which at the minimum is a chi-squared function and can be used to determinethe probability of the fit being a valid one.Equation2.5isnon-linearinthevariables Vandrepresentsacomplexmathematical problem even for high-speed digital computers. Considerableeffort has been expended since 1959 in developing appropriate methods, andtheirapplicationtoMossbauerspectroscopyhasbeenspecificallydetailedin several papers [80-82]. "The chi-squared(X2) function, F(V),hasN- n degrees of freedom, andthe validity of the result can be determined from standard tables [83]. As ageneral rule, thestatistical significance of the fit decreasesrapidlyasF( V)rises in value. For example, a computed fitwith 400 degrees of freedom iswithin the 25-75% confidence limits ofaX2 distribution if380 < F(V) < 419,and within the 5-95% limits if 355 < F(V) < 448.TheX2values obtained inMossbauer spectroscopy are frequentlyhigherthan one would expect because the functionused isnot absolutely correct.Thus, peaksmay not bestrictlyLorentzian in shape, as in cases of order-disorder phenomena where they may be distorted by a large number of smallvariations in the electronic state of the absorbing atoms due to environmentfluctuations. Again, if the counting rate is greater than aboutlOs counts persecondinthedetectionsystemthe'dead-time' effectswhichoccurintheinstrumentationwill distort thePoisson distribution. In thiscase thetotalregistered count-rate could still be low if the rejection fraction at the single-channel discriminatorwerehigh. Other factorswhichaffect theX2valuesinclude instrumental drift, counting geometry, cosine effects, and the propor-tion of the spectrum being computed which is zero-absorption baseline.Introducing additional variables will invariably lower the value ofF( V), butthe decrease may not be large enough to justify the new fit. The final decisionregarding the valid interpretation of the data must and should remain with theexperimenter, using his full experience and chemical knowledge.One useful feature of some of the mathematical methods of solution is thattheyalsoprovideinformationontheprecisionof thefinal valuesof thevariables [80], but the effects ofinstrument drift are likely to beunder-estimatedasit isassumed that thevelocityof anygivenchannel isnotafunction of time.Althoughdataareusually analysedby specifying anexact mathematicalfunction, it ispossible(withslightlydifferent methods) touseanexperi-mentally defined peak-shape if the former is not known with precision [84].One obvious development of these variousmethodsis the application of[Refs. on p. 43JREFERENCES I 43direct on-linetime-sharingcomputer techniques. Inprinciple, this enablesthe analyser output tobe transmitted directly to the central processing unitfrom the laboratory, and the results of the calculation can then be returnedat least in abbreviatedformto a remote terminal for rapid preliminaryassessment of the experiment.REFERENCES[1] R. L. Mossbauer, Z. Physik, 1958, 151, 124.[2] R. L. Mossbauer, Naturwiss., 1958,45,538.[3] K. Cassell and A. H. Jiggins, J. Sci. Instr., 1967, 44, 212.[4] R. Booth and C. E. Violet, Nuclear Instr. Methods, 1963,25, 1.[5] C. E. Johnson, W. Marshall, and G. J. Perlow, Phys. Rev., 1962, 126, 1503.[6] C.W. Kocher, Rev. Sci. Instr., 1965, 36, 1018.[7] A. J. Bearden, M. G. Hauser, and P. L. Mattern, 'Mossbauer Effect Metho-dology Vol. 1', Ed.1. J. Gruverman, Plenum Press, N.Y., 1965, p. 67.[8] H. M. Kappler, A. Trautwein, A. Mayer, and H. Vogel, Nuclear Instr. Methods,1967,53, 157.[9] P.A. Flinn,Rev. Sci.Instr., 1963, 34, 1422.[10] P. Flinn, 'Mossbauer Effect Methodology Vol. 1', Ed. 1. J. 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Methods, 1968,61,213.3IHyperfine InteractionsIt was shown in Chapter1 that theMossbauer effect produced monochro-matic y-radiation with a definition of the order of 1 part in1012 and we nowseek ways to use this extremely high precision to obtain chemical information.The key to the problem lies in the total interaction Hamiltonian for the atom,which contains terms relating to interactions between the nucleus on the onehand and the electrons (and hence the chemical environment) on the other.The Hamiltonian can be written as = 0 + Eo + M1 + E2 + ... 3.1whereJlt' 0 represents all terms in theHamiltonian forthe atom except thehyperfineinteractions being considered; Eo refers to electric monopole(i.e. Coulombic) interactions betweenthenucleus andtheelectrons; M1refers tomagneticdipolehyperfineinteractions; andE2referstoelectricquadrupole interactions. Higher terms are usually negligible.TheEoCoulombicinteractionalterstheenergyseparationbetweenthegroundstate andtheexcitedstateof thenucleus, therebycausing aslightshift in the position of the observed resonance line. The shift will be differentin various chemical compounds, and for this reason is generally known as thechemical isomer shift. It is also frequently referred to as the isomer shift orchemical shift, but in view of the earlier use of these terms in optical spectro-scopy and nuclear magnetic resonance spectroscopy respectively, the longerexpression is preferred. A less frequently used synonym is centre shift.Theelectricquadrupoleandmagneticdipoleinteractionsbothgeneratemultiple-line spectra, and consequently can give a great deal of information.All three interactions can be expressed as the product of a nuclear term whichis a constant for a givenMossbauer y-ray transition and an electronic termwhich canbevariedandrelatedtothe chemistry of theresonantabsorberbeing studied.3.1 Chemical Isomer Shift, bFor many purposes it is adequate to consider the nucleus as a point chargewhichinfluencestheelectronsviatheCoulombicpotential. However, the[Refs. on p. 78]CHEMICAL ISOMERSHIFT, t5I 47nucleus has a finite volume, and this must be taken into account when con-sideringnucleus-electroninteractions because ans-electronwavefunctionimplies a non-zero electron charge density within the nuclear volume. Duringthe course of a nuclear y-transition, it is usual for the effective nuclear size toalter, thereby changing the nucleus-electron interaction energy. This changeis only a minute fraction of the total Coulombic interaction but is dependenton chemical environment. Although we cannot measure this energy changedirectly, it ispossibletocomparevaluesbymeansof asuitablereferencewhich can be either the y-ray source used in recording the Mossbauer spec-trum or another absorber. The observed range of chemical isomer shifts fora given nuclide is frequently within an order of magnitude of the Heisenbergnaturallinewidth of the transition (i.e. QlT-IOT). The Mossbauer resonancelinerecordedby velocity scanning may thusbemeasurably displaced fromzerovelocity if thechemical environment of thenuclideinthesourceandabsorber differ. For convenience, the chemical isomer shiftt5 is usually quotedin mm S-l rather than in energy units, but it is important to remember that,becauseof therelation t5 =(v/c) XBy, agivendisplacement velocity, v,represents a different energy for each particular Mossbauer transition.The mathematical' expression of the above concepts is virtually identical tothat for theoptical isomeric shift in electronic spectra, and assuch iswelldocumented[1-5]. Oneformof thetheoryisgivenin thefollowingpara-graphs.Electronsof charge -einthefieldof apoint nucleus of charge+Zeexperienceanormal Coulombicpotential andtheintegratedelectrostaticenergy will beEo= ~ Z e 2 JPe ~ ~K r3.2whereKis the dielectric constant of a vacuum, ris the radial distance fromthenucleus, and-epeisthechargedensityof theorbital electrons inthevolume element dr. For a spherical nucleus of finite radiusR, equation3.2is still correct forr >R, but is invalid if r e dr 3.33.4whereepnis thechargedensityof thenucleusand ef>e istheelectrostaticpotential of theelectrons. The integrand becomes equivalent to that in3.2for r >R. Thechange Wintheelectrostaticenergycausedbythefiniteradius of the nucleus can therefore be expressed asJR Ze2JR drW =e Pnef>e dr - - Pe -o K 0 r[Refs. on p. 78]3.548 I HYPERFINEINTERACTIONSThe probability density of an s-electronintheneighbourhood of apointcharge is given in the Dirac theory by= 2(p +I)l1fJs(O)12(2Z)2P-2r2P_2Pe r2(2p + l) 0Hwhere p =y(1- (X2Z2), (X =e2Inc, 0His the first Bohr radius, V',(O) is thenon-relativisticSchrodingerwavefunctionat r = 0, andnil)isthegammafunctionr(n) = f:e-Xxn-ldx n>0 3.6Equation 3.5 ignores distortion of1fJ.(0) by the finitenuclear size which willcause an overestimation of the shift. It should alsobementioned that thereis a secondpossiblecontributiontoelectrondensity at the nucleus if Ptelectronic states of the atom are occupied. However, this term will always bemuch less than the equivalent s-term.Furthermore, the Pt electronicstate isnot usually encountered in applications of Mossbauer spectroscopy andwilltherefore not be considered further.Thelackof knowledgeof the precisechargedistributionand potentialinsidethenucleusnecessitatesfurtherapproximationstoequation3.4. Thecustomary method is toassume a potential equationwhichhas the value ofthe point charge Coulombic potential at r =R and also has the same gradient.This ensures that the potential is continuous. If the nuclear charge density istaken to be a uniform sphere, the change in the electrostatic energy betweenthe point-charge and finite-radius models is given byw= 24n(p +I)l1fJs(O) 12Ze2(2Z)2P-2 R2p 37K2p(2p +1)(2p + 3)r2(2p +1) 0H The difference in energy caused by the nuclear radius change lJR will then bed W =_24Jl:0 + l)l1fJs(O) J2Ze22 R2p lJR 3.8K(2p + 1)(2p + 3)r2(2p +1) 0H RThe appropriate potential curves are illustratedinFig. 3.1.The chemical isomer shift, (j, as measured in aMossbauer experiment isadifference in energy between two chemical environmentsA andB andfrom3.8 is seen to be(j = 24n(p +l){l1fJs(O)A12- 11fJ.(O)B 2 R2pbl! 3.9K(2p +l)(2p + 3)r2(2p +l) 0H RThis equation is rather intractable, and is commonly simplified by assuming[Refs. on p. 78J3.10CHEMICAL ISOMERSHIFT, ~ I 49that p =1. This is not strictly valid for the heavier elements (for Z =26(Fe)p =098 and for Z =80(Hg)p =0'80). WithK =1 andp =14 bRb =Sn:Ze2{IV's(0)A12- I V's(O)B12}R 2 RThe nucleus will usuallybe slightlynon-spherical, andthe chemical isomerRgr/(cmxlO-12)0 10 15IIII1IIII I Vxx I ensures that0andlIz')are two different quantum states of the orientation andCJ1z'lzis aKronecker delta such that CJ1 'I =0 unless Iz'=Iz In other wordsthez zmatrix is diagonal in form and the energy levels are given directly by3.34[Refs.on p. 78156 \ HYPERFINEINTERACTIONSInstead of a single energy level we now haveaseriesof Kramers' doubletsidentifiedbythe I Iz I quantumnumber. For1 =-!- thereisonly one level,but for 1 =1-therearetwodistinct eigenvalues of energy+(e2qQ/4)(forI z =!) and -(e2qQ/4) (for Iz =-!-).In general, a Mossbauer transition occurs between two nuclear levels, eachof which may have a nuclear spin and quadrupole moment. This means thatboth the ground-state and excited-state levels may show a quadrupole inter-action. Because the energy separations due to these quadrupole interactionsare very small, all the levels connected with a given nuclear spin are equallypopulated at temperatures above1 K. A change intheI zquantum numberis allowedduringthe y-raytransition, and we shall discuss the relativeprobabilities oftransitions between sublevels more fully in Section 3.7.Basically the laws of conservation of angular momentum and of parity leadto the formulation of definite selection rules which characterise the transitionbetween the two states and these ensure that thereis a high probability fortransitions in which the change in the z quantum numbers [(lz). - (lz)lI] =mis 0 or 1. The very important example of a y-transition between states with1 = ! and1 =-!- results intwo transitions fromthe {I = ! I !>} and{I = ! I -D} sublevelstotheunsplit {I =-11 -D} level. Theresultantspectrum will comprise two lines, which are in fact of equal i'ntensity if thesampleisanisotropic powder, andtheenergy separation betweenthetwolines is I(e2qQ/2) I. The centroid of the doublet corresponds to the energy ofthe y-transition without a quadrupole interaction so that we can still measurethe chemical isomer shift. The energy level schemes and observed spectra foran 1 = ! ~ 1 = t transition and an 1 =~ ~ 1 =1- transition are representedin Fig. 3.3.Alack of axialsymmetry in theelectric fieldgradient introducesmatrixelements which are off-diagonal with [(Iz). - (Iz)lI] =2. Exact solutions ofthe secular equations for the eigenvalues can only be given for 1 =~ . Thesearee2qQ ( l)Z)!EQ =4/(21 _ 1)[31/ - I(I + 1)] 1 + 33.35For higher spin states, convergent series canbe calculatedbyperturbationprocedures, or else the energies can be solved accurately by matrix diagonalisa-tion on a computer. It is interesting to note, however, that as1) can never begreater than unity(equation 3.30), the maximumdifference betweenthequadrupolesplittingsderivedfromequations3.34 and3.35isabout 16%.Amethodforanalysingspectrawithanon-zerovalueof1) hasbeen des-cribed [16].The magnitude of the quadrupole interaction is a product of two factors,eQisanuclear constant forthe resonant isotope, whileeq is a functionofchemical environment. For a t ~ ! transition it is not possible to determine[Refs. on p. 78]ELECTRICQUADRUPOLEINTERACTIONS I 57the sign of e2qQ or the magnitudeof'YJ from the line positions alone. This isnot the case forhigher spin states wherethesign of e2qQ canbeuniquelydeterminedfromtheunequallyspacedlines. If bothIe andIgaregreaterthan !. there is little difficulty in estimating eq as the ground-state quadrupole>-)6 78! 5)+-I-2I345

\, 21+1-2L--IIII.....\ .....\\ 2\\\\ [-OJ.)-2//I/I!l>IID//

[-2 I I !>-2

'\.!DUI I1 32 ' 46 5 7 8- -Velocity VelocityFig.3.3Typical energy level schemes and observed spectra for t -+ t and t -+ 1transitions with quadrupole hyperfine interactions.momentwillbe accurately known fromother measurements. If Ig =0 or tthen Qfor the excited state is usually calculated from estimated values of eqin chemical compounds and will not be known with any great accuracy.Althoughthe quadrupolecoupling constant e2qQ andasymmetrypara-meter'YJ can easily be evaluated from a Mossbauer spectrum, it is much more(Refs. on p. 78J58 I HYPERFINEINTERACTIONSdifficult to relate these parameters to the electronic structure which generatesthem. Although frequent referenceismadetothesign of the electric fieldgradient, this ismisleading because the latter is atensor quantity. What isactually meant is the sign of the principal component, Vzz Confusion over thesign conventionusedcan beavoidedby considering thecoupling constante2qQ. If the sign of Q is known, that of q is immediately implied. Throughoutthis work we have deliberately chosen to refer to the sign of e2qQ rather thanof eq toavoid any ambiguity, and have taken considerable care in quotingpublished data not given in this convention. The observed sign of e2qQ maybe an important factor in deciding the origin of the electric field gradient.The electric field gradient is the negative second derivative of the potentialat the nucleus of all surrounding electric charge. It therefore embraces con-tributions from both the valence electrons of the atom and from surroundingions. In ionic complexes it is customary to consider these separately, and towrite q asVzz=q =(I- R)qion +(1- Y3.44The expression contained in the angular bracketsisthe expectation value ofthe spin density, 'i being theradialcoordinate oftheith electron. flBis the[Refs. on p. 781MAGNETIC HYPERFINEINTERACTIONS161Bohr magneton. Hsis usually referred to as the Fermi contact term. Its actualorigin may be from intrinsic impairing of the actual s-electrons, or indirectlyas a result of polarisation effects on filled s-orbita1s. These can occur if theatom has unpaired electrons in d- or .f-orbitals, or if it is chemically bondedto such an atom. Intuitively one can see that the interaction of an unpaired63 52 4"1--'"--I-D1+ !>I + ~ >1=!--!!:---h-l-----:s,:--l~VelocityFig. 3.4Magnetic splittingfora ! -+!.transition. The relativeinversionof thet and! muItiplets signifies a change in sign of the nuclear magnetic moment. Onlytransitions for a change in ml of 0, 1 are shown.d-electron with the s-electrons of parallel spin will bedifferent to that withthes-electronsofopposedspin. Theresult is a slight imbalanceof spindensityat the nucleus. Inthecaseofmetals, direct conduction-electronpolarisationaswell asindirect core-polarisation effectsmaybeimportant.[Refs. on p.78]3.4562 I HYPERFINEINTERACTIONSAs mentioned at the end of Section 3.3, application of pressure can also causesmall changes in the imbalance of the spin density and thus in H.If the orbital magnetic moment of the parent atom is non-zero, there is afurther term in equation 3.43 given by eitherHL =- 2PB(r - 3)(L)HI, = -2PB(r-3)(g - 2)(S) or(L)and( Hm2ml 11m>(2) C2and 0are the angular independentand dependent termsarbitrarily nor-malised.(3)Relative intensities observed at 900and 00to the principal axis. Normalisationarbitrary.asm =+2and -2respectively. Therearethussixfinitecoefficients. Thesquares of these normalised to give integral values are also given in Table 3.2and are seen tobe 3 : 2: I : 1 : 2 : 3. These are the theoretical intensity ratiosfor a 57Fe (144-keV) Zeeman spectrum, for example, andhave alreadybeenillustrated in Fig.3.4. Appendix 2 contains data for other spin states.The angular terms are formulated as the radiation probability in a directionoto the principal axis (z axis) ofthe magnetic field or the electric field gradienttensor. The appropriate functions 0(I,m) are listed in Table 3.3. The[Refs. on p. 78]68 I HYPERFINEINTERACTIONSTable 3.3 Direction-dependent probability term 0 (I, m)m=Om= 1m= 21=1tsin20-w + cos20)1=2i sin2200 + cos2 20)( 2 Sin220)-.t sm0+-4-3.52probability in a given direction isthen IF I ;>O. Values of Ffor octahedral Fez+ and FeIllwith tetragonaldistortions and spin-orbit coupling included are given in Figs. 5.5 and 5.6.-500-400-300Fig. 5.6 Calculated values of the reduction factorF for low-spin FellI, derived ina similar way to Fig. 5.5 but using a spin-orbit coupling parameter of), = -300em-1. [Ref. 30, Fig.6]A much simplifiedmodel neglectingspin-orbit coupling will give reason-able approximations provided thatVT> At.S, and is illustrated in Fig. 5.7.Thereductionfactor isthengivenby(1 + e-2E,/kT + e-2E,/kT_ e-E,/kT_ e-E,/kT_ e-CE,+E,)/kT),F = - - - - - - - - - ~ ~ - - ~ ~ - - - - - - -(1 + e-E,/kT + e-E,/kT)For an axial field only (i.e. the level splittings E1 =Ez =Eo) the expressionis1 - e-E./kTF- - , - - - ~ - " " " c ; ; ;- 1 +2e-E,/kTI Ll I willgenerally decreasewith increasing temperature, particularly if thelevel separations are small. Tetragonal or trigonal distortions can be estimatedeasily and may be distinguishedby the opposing signs of the coupling con-stanteZqQ, butrhombicdistortionsandspin-orbitcoupling areharder toassign unambiguously.[Refs. on p. IlOjIxy)Iyz)CI IczRhombicfieldvRAxialfieldVTCUbicfieldVof2102 I s7Fe -INTRODUCTIONTetrahedral Fe2+issimilar to octahedralFeHbut haslittlespin-orbitinteraction. Admixture of metal 4p-electrons is allowed into the T2 levels, butnot into the E levels which produce the electric fieldgradient. The observedIxz)Fig. 5.7A simplified orbital scheme for Fe2+ and FeIIIoctahedral complexes.quadrupole splittings are about 30%smaller than for octahedral Fe2+because ofthe greater covalency effects whichaffect the screeningandradial function terms in Ll. Likewise, the upper limit for FellILl values is alsoexpectedtobesmaller, but thisislesseasytoverify. The'electronhole'reversesthe sign of the coupling constant e2qQ. The introduction of appreci-able covalency does not alter the overall validity of the results, provided thatit is realised that theligand-field parameters used do not now apply to thefree ion, but are 'effective' parameters.Theoretical estimations of the quadrupole splitting in covalent diamagneticcomplexes ofiron with lowformal oxidation states (e.g. Fe(CO)s) aredifficult. The electric field gradient is now generated by the molecular orbitalsofthe complex, and in view ofthe large number oforbitals involved in bondingis difficult to interpret. Consequently in this type of compound the quadrupolesplitting is used semi-empirically as a 'distortion parameter'. Low-lyingexcited levels aregenerally absent so that thereis little temperature depen-dence of Ll in such complexes.5.5 Magnetic InteractionsThe appropriate theory fora t ~ t magnetic hyperfine spectrum was givenin Chapter 3.5. The internal fields found in iron compounds and alloys are oftheorder of several hundredkGand can generateclearlyresolvedsix-linespectra. The ground state magnetic moment, Ill' hasbeen accurately deter-mined to be +0'0903 00007 nuclear magnetons (n.m.) [31]. Recentaccurate[Refs. on p. 110]MAGNETICINTERACTIONS I 103determinations of the ratio/-lei/-lg and thence/-leare given inTable5.4. Asthe nuclear termin equation 3.41 is thus known to high precision, the absolutemagnitude of the internal magnetic fields can be found.Table 5.4 The magnetic moment, fIe, of the 14'41-keV level of 57Fe/Lei /La fLe/Cn.m.) Source of data Reference-1,715 0004 -0,1549 00013 iron metal 1-1'7135 00015 -0'1547 00013 57CO in single-crystal cobalt 2-1'715 0003 -0,1549 00013 ultrasonic splitting of iron 3-1'712 0013 -0,1545 0'0024 rare-earth orthoferrites 41. R. S. Preston, S. S. Hanna, and J. Heberle, Phys. Rev., 1962, 128, 2207.2. G. J. Perlow, C. E. Johnson, and W. Marshall, Phys. Rev., 1965, 140, A875.3. T. E. Cranshaw and P. Reivari, Proc. Phys. Soc.,1967,90,1059.4. M. Eibschutz, S. Shtrikman, and D. Treves, Phys. Rev., 1967, 156, 562.Diagnostic application of the measured values of the hyperfine magneticfield, H,requires a knowledge of the origins of the field. The various termswhich contribute were described in Chapter 3.5, but the particular importanceof each for 57Fe has not yet been outlined. The most significant is the Fermicontact interaction. Inionic complexes where thespin densityisproducedby 3d-polarisation effects onthe internal s-shells, the fieldobserved at lowtemperatures where it has reached the limiting value of the Brillouin functionis of the order of 110 kG for each unpaired3d-electron. This is sometimesreferred to as the 220(Sz) rule. For the Fe3+ ion (3d5) the Fermi term is about550 kG, and is440 kG forthe Fe2+ ion(3d6). It should benotedthat thesign of Hs is negative.The orbital termHLandspin momentHD are more difficult to estimate.For anFe3+ionincubicsymmetry, botharezero, andevenindistortedenvironments they are small. Calculations of these contributions in iX-Fe203have been made [32]. The limiting value of ferric hyperfine fields is thereforeabout 550 kG, and it is difficult to distinguish between two cation sites in thesame sample unless they show significant differences in chemical isomer shiftor quadrupole splitting. By contrast, for ferrous iron, the magnitudes of HLand HD can be of the order of Hs, and the resultant field I H Ican be anywherebetween 0 and 450 kG. As a consequence, compounds where cation random-isation can occur may have large local variations in the ferrous-ion environ-ment; theobserved electric field gradienthasnounique valueandgrossbroadening of the spectrum isobserved. This occurs, for example, in iron-titanium spinel oxides [33].Interpretation of magnetic effects in metals and alloys is difficult because adefiniteelectronicstructure cannotbeeasilyassignedtoindividual atoms,and there may be some unpaired 4s-spin density in the conduction band. The[Refs. on p. 110]104 I 57Fe - INTRODUCTIONfieldisusuallyattributedtotwoeffects, core polarisation and conduction-electron polarisation. Core polarisation is the induction of aresultant spindensity in the inner s-shells by unpaired electrons in the outer electron shells.The 3d-contribution will be similar to that for the discrete cations. Conduc-tion-electron polarisation involves the polarisation ofthe 4s-conductionelectronsby bothexchange interactionwiththe 3d-electronsandmixingwith the 3d-band. The core-polarisation term is believed to be the major onein the3d-magnetic elements, but it isnot proposedtodiscuss the problemfurther here. Examples will be found in Chapter 13.The temperature dependence of a hyperfine field froman Fe3+ spinconfigurationfollows the appropriate spin-onlyS= i Brillouinfunctionasappliedtocooperativemagneticphenomena[34, 35]. Small deviationssometimes occur, but in general Hdecreases with rising temperature, fallingincreasingly rapidly towards zero as the critical temperature (the Curie point)isapproached. Themagneticbehaviourof Fe2+islessregularbecause oftheinfluenceoforbital repopulationas outlinedintheprevious section.Sand L are not easily defined for metals, but as Lis generally quenched andtheBrillouin curvesarenotverysensitivetothetotal spinvalue, thebe-haviour is basically similar.Motional narrowing of magnetic hyperfine interactions by spin relaxation(superparamagnetism) has also been recorded; it results from a reduction inparticlesizeorfrommagneticdilution. Conversely, longspinrelaxationtimes canbe inducedinparamagneticferric compounds byappropriatelowering of thetemperature(spin-lattice) ormagneticdilution (spin-spin),resulting in acomplex magneticspectrum. The I i>Kramers' doublet isoften fully resolved, but the I !> and I t> states tend to contribute to abroad unresolved background. Examples of this behaviour will be found inthe detailed chapters on experimental results which follow.5.6Polarised Radiation StudiesA very useful technique which has recentlybeen developedfor 57Fe work,although its application is more general, is the use of polarised radiation. It isconvenient to discuss the subject here, but the reader is advised to refer to theappropriatesectionsinlaterchaptersfor moredetaileddiscussionof thespectra of some of the materials mentioned. Polarisation of the emitted y-raywas first shown in1960 [36], and can take placebytheStark and Zeemaneffects already familiar in optical polarisation studies [37].Therearetwobasicapproaches, thesimplest of which isto use amag-netically split sourcematrix, such asaniron foil, andtomagnetiseit in afixed direction. With iron foils it is convenient to magnetise perpendicular tothe direction of emission. The emittedradiation is then not monochromaticbut consists ofsix individual components with intensity ratios 3 : 4: 1: 1: 4: 3,[Refs. on p.1101POLARISEDRADIATIONSTUDIES I 105each of which has a definite polarisation. In the case we are considering theII t)and I t) I =f t)transitionshavealinearpolarisationwith the electric vector vibration parallel with respect to the magnetisation,and the I t) , 1-> transitions are similar but perpendicularly polarised.In the event that the Mossbauer absorber is unsplit or is a random poly-crystal, the observed spectrum shows no newfeatures. However, if both sourceandabsorberaredirectionallypolarisedbyamagnetic fieldwhichcanbeinternal in origin or by an electric field such as is associated with the electricfieldgradient tensor inasingle-crystal absorber thepolarisationof eachemission line becomes important.In principle each source emission line will come into resonance with eachline in the absorber, but where the emission spectrum has a high symmetrysuchasiniron foil thereisgenerallyareductioninthenumberof non-coincident components. One important effect in this type of experiment is adramatic variation of line intensity with change in the relative orientation ofthe principal directions in thesource and absorber. Calculation of thelineintensities is difficult, but thedetailedtheoryhas beenoutlined[38, 39].Equation3.53canbesimplifiedtogiveanequationfor theproportionalamplitude probability of a source (MI only) emission line asCfi =oU-j-O 0 1-0 20 3-0Doppler velocityI [mm s")Fig. 6.5Theeffectof pressureontheMossbauerspectrumof KFeF3. [Ref. 9,Fig. 5]interaction canbe neither ferromagneticnor antiferromagnetic at non-zerotemperature.The Mossbauer spectra [17] show only a sharp quadrupole doublet between60 K and the suspected ordering transition at 90 K. This confirms that thereis no long-range order and that the spin relaxation is very fast. Long-rangeorder appears as the temperature is lowered to 50 K (see Fig. 6.6). The changeis accompanied by a crystallographic distortion which lowers the symmetry ofthe crystal. The presence of an asymmetry parameter shows that the fourfoldaxishasbeendestroyed. It isprobablethat theloweredsymmetryallowsmagnetic interaction between Fe2+ layers so that the orderingbecomesthree-dimensional. Thequadrupolesplittingandchemical isomer shift aresimilar to those of FeF2 ,FeCl2Anhydrous iron(Il) chloride has the CdCl2 structure and has been studied indetail inthreeindependent investigations. Onoet 01. [18] foundastrongtemperature dependence in C1 and no significant internal magnetic field[Refs. on p_164]IRONCH) HALIDES I 121 10 kG) down to4 K. This is unusual in viewof the known antiferromagnetictransition at24K, butcouldbeexplainedasachance cancellationintheHs + HL + HDsummation. Later work gave a value of 4 kG for the magnetic

liOK9298 57K969694 L-_"';6,-_..J41:--_l,-2Doppler velocity/(mm s-IlFig. 6.6Mossbauer spectra of a single crystal of Rb2FeF4 oriented with the c axisparallel to the y-ray beam. Note the onset of long-range magnetic ordering below60 K. [Ref. 17, Fig. 2)[Refs. on p. 164]122 I HIGH-SPINIRONCOMPLEXESfield at 42 K. A single-crystal spectrum at room temperature gave an asym-metric doublet intensity and confirmed that eZqQ was positive. The Fez + localsymmetryisclosetoanoctahedron of chlorineatomswithatrigonaldis-tortion parallel tothe crystal c axis. The very small trigonal fieldsplits thet Zg tripletandresultsinalargereductionin ~ fromthelimitingvalueof~ ( I - R)(r- 3). The ground state is a doublet and is145 35 cm-1belowthesinglet level [20] (alsoquotedas 119cm-1[18] and 150cm-1[19]).Belowthe Neel temperaturethereis a small increaseinthe quadrupolesplittingduetoanexchangecoupling termof-2Jx(Sz)Szwherex isthenumber of Fe2+ neighbours and(Sz) is thethermal averageofSz. Thechemical isomer shift of 1093 mm S-1 at 42 Kshould be compared with thatof 148 mm S-1 for FeFz. Using the Danon interpretation(p. 93), this largedecreasesignifies[20]aconsiderable increase incovalencyandaneffectiveconfiguration of 3d64so.1Zas opposed to3d64so.ThechemicalisomershiftsinFeFz, FeClz, FeBrz, andFelz havebeenfound to varylinearly withthe Paulingelectronegativityof the halide [21].A linear relationship between the shift and the low-temperature quadrupolesplitting was alsoclaimedtoexist and toindicate a highdegreeof cova-lent bondingand 3d-delocalisationinthe higher halides. Similar studieson FeClz, FeClz.HzO, FeClz.2HzO, FeClz.4HzO, FeS04.7HzO, andFeSiF6.6HzO showed an approximately linear increase in shift with increasingcoordinationtowater molecules, as well as further correlationwiththequadrupole splitting [22]. However, recent work has questioned the validityof such arguments, and has proposed that the substantial changes in chemicalisomer shift are not so much due to 3d-electron delocalisation as toligand-p -? iron 4s-electron transfer [23]. The chemical isomer shift-quadru-pole splitting relationship is also believed to be fortuitous rather than general.A more recent analysis [24] ofthetemperaturedependence of thequadrupolesplitting in FeClz differs considerably from earlier approaches but uses theargument of considerable 3d-delocalisation. Controversies such as theseillustrate the difficulty in distinguishing the factors influencing the Mossbauerspectrum.Although FeClz is antiferromagnetic in zero applied field, it undergoes aspin-flip transition to a ferromagnetic state in fields of greater than105 kG(the entire antiparallel sublattice reverses spin direction). Spectra of a singlecrystal of FeClz insmall external fieldsdonot show anyseparation of thetwo sublattices because the intrinsic fieldis so small [25].FeClzHzOThe structure of iron(II) chloride monohydrate is unknown but, by analogywith the other hydrates, the local iron environment is likely to be one oxygenatomandfive bridgingchlorideionswhichareunlikelytobeequivalent.This increased distortionaccounts for themuch larger quadrupole splitting[Refs. on p. 164]IRON(II) HALIDES I 123in FeC12.H20than in FeCl2 [26]. The compound is antiferromagnetic at lowtemperatures and the saturation value ofthe internal magnetic field (T~ 0 K)is about 251kG [27].A related complex with stilbene PhCH:CHPh(FeCl2.H20)4, is alsoantiferromagnetic below23 Kand shows a very similar behaviour toFeC12.H20 and FeCl2.2H20 [27]. Temperature-dependence data giveexcited-state levels at 309 cm-iand 618 em-i.FeCI22H20Thecrystal structureofFeCI2.2H20 is known, andthewater moleculesoccupythetrans-positions in thenear-octahedral environment. The a,b,c,FeClz2HzOOceFig. 6.7 The ironenvironmentsinFeClz.2HzO andFeClz.4HzO. Thetwositesin the latter are related by a 1800rotation about the b axis.[Refs. on p. 164)124 I HIGH-SPINIRONCOMPLEXEScrystal axes areshown in relation tothe bonds in Fig. 6.7. The compoundbecomesantiferromagneticbelow23K. Comprehensivemeasurementsonoriented single crystals [28] show that e2qQ is positive and that the principalaxis corresponds closely to thez axis (crystalb axis). The quadrupole tem-peraturedependence isconsistent with an electronicgroundstatewhich ispredominantlyI xy) with anI xz) state at ",520em-I. The combinedquadrupole-magnetic interactions show that the spin axis is in the ac planealong the direction of the short Fe-Cl bond (x axis), and that the asymmetryparameter 'YJ=02. Independentdataobtainedonpolycrystallinepowders[29] confirmtheperpendicularrelationanddirectionsof theelectricfieldgradient tensorandH. Direct lattice-sumcalculations havebeenusedtoestimate the lattice contribution to the electric field gradient [30].FeCI2.4H20The structure of this compound is well characterised (Fig. 6.7);it containsdiscretetrans-octahedral sub-units of Fe(H20)4CI2on twopositions in theunit cellrelatedbyarotation of 1800about thebaxis. Thefirst detailedMossbauerstudyusedorientedsinglecrystals[31]. Theminoraxisof theelectric field gradient is the c axis, the principal axis being in the ab plane eitherparallel orperpendiculartotheCI-Claxis. e2qQispositiveand 'YJ=01........1,';po ;.-I-.: I..46

',1;-- ,/".' .;'f"; '!":I'I".. ii-21-- f )(a) , : ..f. c I.: :,:.. J". ."-.'\. tI,

. 0''-, t:. ..4(b)..' ,,,"''''... /1\ .... ..- .. !.1! . '1 ...:{.:If!:l,.r .o'8.".:,:, I..,I.0'0-8 -6 -4 -2 0 2 4 6 8Velocity/(mm 5'1)Fig. 6.8The Mossbauer spectrum of FeChAH2 0 at 04 Kin (a) a single crystalwith the y-ray beam parallel to the b axis, and (b) in polycrystals. [Ref. 33, Fig. 1][Refs. on p. 164]IRON(II) HALIDES I 125The sign of e2qQ was also shownto be positive by using the applied magneticfield method [32]. The electronic ground state is similar to FeF2 , i.e.099 I x2- y2) + 010 IZ2), and Ingalls[5] has estimated the electronicexcited-state levels to lie at 750 cm-iand 2900 cm-i However, these figuresmay not be accurate in view of direct lattice-sum calculations on FeCI2.4H20whichsuggest that thelatticetermcontributes alargeproportionof theelectric field gradient [30].Thecompoundisantiferromagneticbelow11K, andsingle-crystal andpolycrystal spectra at 04K[33]show that thespin axis and theprincipalelectric field gradient axis are close to each other, the angle being estimatedto be15. The magnetic axis is at 30 to the b axis. Line broadening is seenimmediately below the Neel temperature because the electron spin relaxationtimes are comparable to the nuclear precession time. The effect of state mixingon the line intensities of aquadrupole/magneticspectrum is clearly shownbythiscompound(seeFig. 6.8). Sevenhyperfinecomponentsarevisibleinstead of theusual sixbecausethe2 transitioncontain an appreciableadmixture of other states.Independent data [34] confirm these conclusions, and give a more extensiveinterpretation of the spin ordering. The field at the two iron sites makes anangle of 15 tothe b axis of the crystal, the angle between the two fieldsbeing 30. The principal direction of the electric field gradient is at 40 to theb axis, compared with a value of 45 determined by Zory.J ' ! ! i ! = S ~ TFreeionCubictetrahedralcrystal fieldTetrogono IdistortionSpin-orbitcouplingFig. 6.9Splittingsof the electronic energylevelsof ahigh-spind6ionbythecrystal-field and spin-orbit interaction in FeCI42-. [Ref. 36, Fig. 5][Refs. on p. 164]126 I HIGH-SPINIRONCOMPLEXESFeCI42-, FeBr42-, Fe(NCSe)42-, and Fe(NCS)42-The measurement of asmall distortion in the tetrahedral FeC142-ion wasfirst reported by Gibb and Greenwood [35]. The E level is split by a tetragonaldistortioninthecrystal fieldandthisresultsinamarkedlytemperature-dependent quadrupole splitting as the thermal population of the dx'_Y' anddz.levels changes (see Fig. 6.9). A more extensive investigation [36] has shown ."....... - ..,.( , : ." ,"....." .::I:'....".. (al(dl

\o24. (blt....-r2 \ ' ":I 4 M Y01=- .....IIfC,: \ . , .:: ,::: illc.2t 020' J I , I I I I I I ,-40 -30 -ZO -10 0 10 20 30 40Velocity/lmm 5-11Fig. 6.10Mossbauer spectra of (Me4NhFeC14 at (a) 290 K, (b)195 K,(c) 77 K,and (d) 42 K. [Ref. 36, Fig. 2]the existence of such distortions in the ions FeCV-, FeBr/-, Fe(NCSe)42-,andFe(NCS)42-. Inparticular, (Me4NhFeCI4has been studiedindetailfrom 15 to 363 K. The intensity of the resonance decreases dramatically withtemperature rise as seen in Fig. 6.10. The effective Debye temperature is onlyof the order of 200 Kand reflects theincrease in covalency over the octa-[Refs. on p.164]IRON(n) HALIDES I 127hedral Fe2+ ions which give much more intense spectra. The chemical isomershift showsthetypical second-orderDopplershift behaviourasshowninTable6.1. Covalencyalsoleadstoamuchlowerchemicalisomershiftintetrahedral complexesingeneral. ThisisillustratedinFig. 6.11 inwhichFeIzctahedralFeClz.2HzO; FellrzFeClzCsFeF3FeFzRbzFeF4+15~E +104E""CO >CN->Ph3P >S032-> N02- ~ NH3~ Ph3As~ Ph3Sb. Thequadrupole splittings of the iron(II) pentacyanidesalsomirror the:n;back-donation effect, but thisisnotsoin theequivalentiron(III) complexes because of the non-bonding electron contribution to thefieldgradient in the latter case.[Refs. on p.191]184 I LOW-SPINIRON(H) ANDIRON(m) COMPLEXESThe [Fe(CN)sNOF-and [Fe(CN)sNH3P-anions are converted to high-spiniron(II) configurationsat hightemperatureandpressureinasimilarmanner to the ferro- and ferricyanides [45].The sodiumbis-(tetramethylammonium) hexaazidoferrate(lll) complex,Na(Me4Nh[Fe(N3)6]' which is included in Table 7.4 for convenience, appearsto be similar to the cyanide in its bonding [14].Thealkyl andaryl isocyanidesformmanycomplexeswithironwhichfeature 6-coordination and may contain a variety of other ligands. Those ofthe general type FeLz(CNR)4 may occur as cis- and trans-geometric isomers.These caneasily be distinguished in the Mossbauer spectrumfromtheqlzteqlqlzt------r---ql[FeXsY] cio5-[ FeX4YZ] trano5-[FeX4YZ]Fig. 7.9Chargedistributioninsomesix-coordinatecomplexes usingthepointcharge approximation.quadrupolesplitting. Berrett andFitzsimmonsshowed[46, 47]that if twosimilarligandsarerepresentedaspoint chargesql andqzat anidenticalbond distanceI'fromthe central atom, then the electric fieldgradient andhence the quadrupole splitting for thetrans-eompoundshould be twice thatof thecis-isomerinmagnitudeandoppositeinsign. Similarlythemono-substituted complex should have the same magnitude of electric field gradientas the cis-disubstituted complex but be opposite in sign. These relations can bededuced as follows. For the monosubstituted complex [FeXsY] reference toFig. 7.9 shows that the potential, VA at point A is given byVA= - ~ +-q_l- + 4q1 .(I' - =) (I' -:- =) (I'z +Z2)!d2VA2q2 , 2q, 4ql(r2- 2z2)-;Jz2- - (I' _ =)3 i (;-+--Z)3- (1'2 + ZZ)1-As the point A approaches the origin (i.e. z-+ 0) this becomes2qz 2qlVzz(mono) = 3-- -3= 2 ~I' I'[Refs. on p. 1911SUBSTITUTEDCYANIDES I 185For cis-[FeX4Y2] reference to Fig. 7.9 shows that the potentialVA is given byVA = 2q2 + 2ql(r2+ Z2)! (r2+ Z2)! (r + z) (r - z)-2q2 2qlHence Vzz(cis) = -- +-- = -ur 3r 3=- Vzz(mono)Likewise for trans-[FeX4Y 2], VA is given byVA = __ ++ 4ql(r +z) (r- z) (r2+ Z2)!4q2 4qlHence Vzz(trans) = -- - -- =r 3r 3= -2Vzz(cis)These results, together with those of similar calculations for other octahedralcomplexes, are summarised in Fig. 7.10.These theoretical considerations have been verified experimentally thoughusually for the magnitude of the electric field gradient only. For example [47]S-I)[Fe(CN)(CNEth]CI04017cis-Fe(CNMCNEt)4 029trans-Fe(CNMCNEt)4 059Table7.5Mossbauer parameters for isocyanide complexes at room temperatureCompound

8/(mm S-I) (Fe)Reference/(mms-1) /(mm S-I)[Fe(CNMe)6](H504)2 000 -002 (55) -0,1147[Fe(CNEt)6](CI04)z 000 0'00(55)47[Fe(CNCH2Ph)6](CI04)2 0-00 +