Moessbauer spectrometry - Analytical Chemistry (ACS Publications)

Mossbauer Spectrometry 1. R. DeVoe and 1. 1. Spiikerman, National Bureau o f Standards, Washington, D. C.

T

supplements our previous review ( I S d ) , and it is recommended that the reader refer to our previous review since nomenclature and terminology are the same. Emphasis here is given to the applications which have expanded to a considerable extent in certain areas. A11 of the applications t o specific compounds have been entered in tabular form similar to the previous review. n7e have modified the format from last time so that a section on techniques for analyzing a Mossbauer spectrum could be included. With the exception of a few references in the text only articles published in 1966 and 1967 are included. It is recognized that the review does not contain all of the published work for this time period. I t is particularly evident that references which appeared in the literature in late 1967 have been omitted. Certain other omissions have been made; for example, me have not included any references to abstracts of manuscripts or talks-e.g., Bulletin of the American Physical Society. In addition, we have excluded references that were not available at NBS or readily obtainable from the Library of Congress. Without question the most comprehensive compilation of references and data is that provided by Muir, Ando, and Coogan (32s). The Mossbauer spectrometry group a t the National Bureau of Standards has a computerized compilation that is similar to that of Muir. An NBS Technical Note is scheduled to be printed annually containing general information currently published about papers, but cataloging spectral parameters. The major advantage of this compilation will be its minimum lead time. Mossbauer spectrometry is probably one of the most reviewed subjects. In the last two years several good reviews on applications in specific areas of study have been published (26, S4, 35, 104, HIS REVIEW

12SJ ISS, 169, 191, 1923, 195, 200, 101, 204, 223, 224, 257, 292, s14, 518, 524, 375, 39.4, 400, .422, 427, 429, 441, 500).

It is most fortunate to have these reviews available, as it can be expected that activity in these fields will increase. SPECTROPHOTOMETRIC TECHNIQUE

Two years ago the principles of the method were described. This time it is only necessary to amplify those areas that have received the most attention.

472 R

ANALYTICAL CHEMISTRY

In addition, certain promising areas of future interest will be outlined. 1. Preparation of Sources. Considerable understanding has been obtained (mostly through trial and error in the laboratory) about the factors t h a t must be controlled in order to make a good source of “recoilless” radiation. A “good” source can be defined as one which has a long halflife (few hours), few high energy precursor gamma rays, and a high fraction of recoilless emission (and radiation which is unsplit by hyperfine interaction). In order to obtain a single line source it is necessary that the radioisotope be in a highly symmetric lattice site. To obtain a source with a large recoil free fraction, a high effective Debye temperature is required (%‘) (S20, 358) which is related to the Debye temperature by the expression (see previous review 1.34).

this interference (recoil implantation). The nuclei, excited by the Coulomb interaction, recoil from the surface of the target onto a catcher foil. This foil acts as the lattice for the recoiling nucleus which then emits the Mossbauer gamma ray (4%). Cse of the recoil implantation technique has resulted in several new Mossbauer isotopes (see Table I, 4S6). Another method used successfully has utilized the observation of the Mossbauer effect following a nuclear reaction (78, 166) (see Table I). Radiation damage was extremely small in these experiments, and excellent spectra were obtained. 2. Absorbers. Little new information is presented in the literature about practical problems of mounting a material in the spectrometer. Attention to thickness corrections has been appreciable (see below). With one notable exception, uniformity of thickeo’ = eo ( ~ ~ ~ ~ ~ / ~(1) ~ ~ ness, ~ ) l / etc., has2 not been of great concern where JI,,,, Mhostrepresents the atomic (SI 5 ) . mass of the source atom and host (or 3. Detectors. The quality of a Mossbauer spectrum is often deterlattice) atom, respectively. Another mined by the type of detector used. factor to be considered for producing For gamma rays of energy below 20 good sources is the mode of decay to keV, the proportional counter gives the produce the nuclear energy level that best resolution with satisfactory effiexhibits recoilless emission. Charge ciency. The solid-state detector can states on the atom produced by precuralso be used, but it is worthwhile only in sor emissions such as p+, p-, or electron special cases where high energy resolucapture must be neutralized and the tion is required. A 90% Kr, 10% methatom must be in a stable lattice position ane filling gas for a 2-inch diameter before the Mossbauer transition takes proportional counter gives the best place. This means that conducting results for mFe Mossbauer spectrometry metals invariably make a good matrix. because the Kr provides good detection Another factor that is not related to the Mossbauer effect is the electronic efficiency (60%), and the X-ray absorption edge is slightly less than the 14.4self-absorption of the radiation by the keV 57Fe gamma-ray energy. Sealed matrix of the source. Care must be counters are relatively short-lived, partaken to avoid such effects. ticularly a t high counting rates. The There are a variety of sources availuse of P-10 gas (90% Ar-lO% CHh) flow able and the selection of source can be counter eliminates this problem; they dictated by the type of absorbers-e.g., have excellent resolution, but their effitheir chemical shift-which are to be ciency is much lower than sealed investigated. counters (15% for a 2-inch diameter Suitable sources have been found for counter). only a limited number of radioisotopes. Above 20 keV, a thin NaI(T1) scinSeveral new techniques using acceleratillation crystal is generally used. If tors or reactors have been described pulse height resolution is a problem, (see Table I). the solid-state lithium-drifted silicon The most promising technique is Coulomb excitation (see Table I) (110), detector should be used. A resolution of 1 keV can easily be obtained and the where a Van de Graff accelerator is used efficiency is excellent in this range. to generate the Mossbauer radiation by If the Mossbauer energy level is bombarding a thin foil of the isotope of highly converted, it is possible to make interest with p, n, a or 1 6 0 particles. a detector that significantly increases The background radiation is generally the efficiency of the spectrometer. A high in these experiments, but recent detector can be fabricated which is modification in the apparatus reduces

~

~~

Table 1.

Application of MSssbauer Spectrometry to Chemistry

Compilation of Publications for 1966 and 1967 Energy of Mossbauer gamma ray 1 and 2, respectively, in keV C Y Internal conversion coefficient K = Ka:p X-ray energy in keV = Magnetic moment of excited and ground state producing Mossbauer gamma ray 1, ple1plP respectively, in nuclear magnetons (nm) = Electric quadrupole moment of excited and ground state producing Mossbauer &le, &I, gamma ray 1, respectively, in barns (b = 1 0 - 2 4 cm2). [Nuclear data taken from reference number (323)] Abbreviations: EFG = electric field gradient AE, = electric quadrupole splitting = asymmetry parameter (428) 8s = chemical shift € = magnitude of effect (428) 60 = Debye temperature AR/R = fractional nuclear radius change where excited to ground state = ( A R ) and radius of ground state = R H = effective magnetic field a t the nucleus * = indicates that chemical shift of iron compounds was referenced to sodium nitroprusside

El E2

Mossbauer nuclides 67Fe( - l / ~ ) E = 14.4 keV

= =

Subject or material studied Nuclear parameters

a

= 9

Types Lifetime of excited state FeSiFe. 6H20 K shell fluorescence yield

K

= 6 . 5 keV

Observation of effect

pd

=

&.

-0.154nm

(Wk)

Source preparation

= +0.09024 nm

Alloys

Fe-Pd

= +0.285 b

Alloys

Fe-AI, Fe-Ti Fe-Cr Fe-Cu Fe-Ge, Fe-Sn Fe-In Fe-110 Fe-Ah, Fe-Cr-Ti Fe-Ni Fe-Pd Fe-IZh Fe-Si Fe-Sn Fe-Se Fe-Tm Fe-S'

Carbides

Doped materials

Co-FeSi V-Si-Fe, Mo-Cr-Fe Fe-Co-V Martensite Cementite Corundum In-Sb, Ga-Sb Fe Ngo Mn-Au

Ni-metal NiO, &In0 SrTi03

Remarks 97.7 + 0 . 2 n s Qe = +0.2 b Wk = 0.322 z!z 0.029 136-keS' line Diffusion into Zn, Mo, Sn, A1 Diffusion into Cu, Fe, and Pd Compared with a magnetic susceptibility Two sites

...

(116, 117, 246, (171, 476) 596)

Paramagnetic phase and ferromag- (171, 390) netic, a: iron precipitate AE,, CS e

Short range order H us "K Phase transitions Two sites, AE,, CS Disordered cubic' lattice H = 0 a t low temperature, CS AEq

Fine particles H us. yo carbon Quantitative application Two sites Effect of external magnetic field e measured 0.08 to 1" K polarization of radiation observed AEq-crystal field antiferro- and ferromagnetic properties Comparison with NMR H us. O K H us. O K. Metal or FeS+ AE,, CS*

(3711 (474) (277) (197) (182, 166, 602) (206)

($44, 391) (L86) (i9) (161)

(212) (7)

= 554 kOe, 78" K. H >10-2yc= precipitated CoCll 193) = 1.03 i 0.03

Alloys

Au-Fe

pCs=

Effect of Dressure

Au-Cu-Ni Au-Mn Metal Au-V, Au-Cu, Au-Mn, Au-Te

0.56nm =+1.17nm Qg = 1 . 5 b =

pe po

(+3/~)

77.3 keV (+'/e) 3.7 70.4 keV = 10.37nm = +0.145 nm = +0.56 b

= = =

'96Pt ( - 1 / z ) Doped materials Et = 98.9 keV ( - 3 / ~ ) Ez = 129.7 keV ( - 6 / ~ ) 011 = 7.2 plc = -0.65nm pl0 = +0.61 nm Observation of effect g9Ru keV ( + 3 / 2 ) E Compounds K = 19.6 keV = -0.285 nm po = -0.625nm Qe = -0.15 b

(z6#

H

=

0.402 i 0.025 nm 1.29 x 103koe

Ez/Mi = 0. I ARIR = AE,, CS

+

H , ion implantation

Fe, Co, Ni Pt, Be, Cu, I r

Backscatter geometry 99-keV transition used, CS,

RuOz, RUOp, ruthenocene

CS, H

5.5 25.8 keV = +0.76nm = -1.046 nm = -0.07 b

=i

K

=

pa po

Qe

(Continued)

476R

e

GROUPIV, V, VI AND VIIA ELEMENTS A R / R = $3.3 X lo-' f 1 by Metal and oxide conversion, electron measurements from 0 shell Tin halides AR/R > 0 Tin halides ARIR < 0 Halides, oxides, also of Sb AR/R = f 1 . 2 zt 0 . 4 X lo-' Source preparation Barium stannate Compare well with MgzSn Evaluation of E MgPSnand PdaSn source discussed Pd3Sn Very narrow line width

l19Sn ( + l / d Nuclear parameters E = 23.8 keV ( + 3 / ~ ) Ly

(39.2)

(See Is4W)

(+O)

E

ARIR measured

Nuclear parameters


Table I. Application of Mossbauer Spectrometry to Chemistry (Continued)

Mossbauer nuclides

Subject or material studied Alloy

Mineral

Oxides

Halides

Remarks

Types Co-Sn, Ni-Sn, Pd-Sn Pt-Sn, Rh-Sn PtcSn, Ir-Sn cu-Sri Te-Sn Nb-Sn RSna

CS us. atom % Sn (linear) E measured CS us. atom % Sn (nonlinear) E US. ' K. R = La, Ce, Pr, Nd, Sm, and Yb compared with NMR H H US. O K., pc,/po = 0.7 f 0.02 H,conduction electron polarization

Co-Sn Doped Cu, Ag, Au, Mn Arandisite, canfieldite, cassiterite, cylindrite, francheite, herzenbergite, hulsite, ni erite, nordenskofdine, stannite, teallite Tourmaline solid solution Ba-Ti-Sn-0 AE,, partially resolved SnOz Oxides and fluorides Anomalous CS explained by crystal field effects H SnFe garnets Splitting due to inexact composition SnOz Fe spinel Intermediate of reaction, SnC14 Sn(A1H4)4 LiAlH4

+

Binding in vulcanized butyl rubber Comparison with infrared spectra OD, c

Other Organotin compounds Many Halides Sn-CHTX R,SnH,

Hot atom effects Surface absorption

lzlSb ( + 6 / ~ ) Nuclear parameters E = 37.2 keV . . a = 10.6 K = 26.9 keV pa = +3.359nm Q. = -0.75 f 0.09 b Qp = -0.42b lesTe (+'/-A E = 35.6 keV

Hexacoordinate E US, O K. Quantitative conclusions not possible Mossbauer parameters correlated with NMR

Triphenyl tins Phenanthroline complexes with di-n-butyltin dihalide (n-C4Hg)zSnC12 (n-CIHs)zSnO Phenanthryl tins Phenylene and naphthylene oxy-tins Barenes Both Sn and Fe measured (CHa)4Sn?FedCO)la Methyl tins CS,. AE,. SnOz Recoil effect by (n, a) reaction On silica gel Binding energy, OD Tetraneophyltin Steric hindrance Trimethyltin cyanide Anisotropic absorption (Karyagin effect) Oxides and halides Sbd&

Compounds

+*

ARIR = -8.5 3 x 10-4 -0.75 0.09 b H,ion implantation

Q.

Irradiatkn damage causes CS AEp us. K., two sites in NaIOa

a

=

13.3

K pa

= =

28.0 keV +0.65nm

AE, is small AE,

pa

=

- 0.887 nm

H

Q.

= kO.19

+

b

Observation of effect 78Ge ( O/Z) E = 67.0 keV ( + 6 / ~ ) a = 0.23 K = 10 keV p, = -0.88nm Q, = -0.26 b

Metal Metal Metal and oxide

*

= 148 5 kOe pe = 0.74 f 0 . 0 7 nm Specific heat measured

On = 360 "K, Coulomb excitation 0.125 A R / R = +io-3 Lifetime of excited state = 2.33 0 . 2 X 10-Osec e =

*

(Cmtinued)

VOL 40, NO. 5, APRIL 1968

e

477 R

Table

Mossbauer nuclides 1971

E

(+v2) = =

a

K

=

ps pQ

= =

Qo = Q, = 1201

E

57.6 keV ( +7/2) 3.8 29.2 keV 1.96 nm i2.809nm -0.71 b -0.79b

(f'/Z)

01

pa po

Q.

Q,

27.72 keV (+6/*) 5.0 = +2.84nm = f2.617 nm -0.68b = -0.55b

I.

Application of Mossbauer Spectrometry to Chemistry (Continued)

Subject or material studied Nuclear parameters Compounds

Remarks

Types HALOGENS a

0

4

ARin/\Rize

Hot atom effect

KIClz, IC1 H I in frozen solution Te in Te(OH),

CSys. K. Ionic form Recoil form IOB-s

Nuclear parameters

Source of Te in Al

Metal Compounds

Doped iron SnIa Ag120I Tellurium compounds

E = 27.72 i 0.06 keV Mass separated source a = 5.3 rt 0 . 3 H = 1.1 X 108kOe Both Sn and I measured Very narrow line

Compounds

Review

= =

Ref.

NOBLEGASES

83Kr( + 9 / ~ ) E = 9.3 keV a

K p,

Qe Q

(+7/2)

11 12.8 keV -0.97nm = 0.459 rt 0.006 b = +0.27 b

(93)

Use of *aRb as a source (286) Qe/QQ = 1.7 rt 0.02 KrF2 CS, AE,, Qd = 0.459 f 0.006 b A R / R = +4 f 2 10-4 Solid krypton OD L-37' k. (362) Alkali bromide and bromate Some broadening and distortion due (364) to recoil damage

(w

= = =

Hot atom effect

ALKALIMETALS Review

4'K (-4) E = 29.4 keV (-3) LY = 0.35 K = 3.35 keV po = -1.298nm &, = 0.09 b lsaCs ( f 7 / 2 )

E a

K pe pg QD

= 81 keV(fS/2) = 1.63

Demonstration of effect

Metal, halides

Compounds

Cesium halides

32.0 keV = +3.3nm = f2.579nm = -0.003 b

=

General

lslDy (+'/z) Alloys El = 25.6 keV ( -'/-z) E2 = 74:5 keV ( - 8 / ~ ) a1 = 2.5 a2 = 0.65 K = 47.0 keV pla = + 0 . 5 n m Compounds pZs = f 1 . 6 n m p, = -0.455nm &is = +1.75b Q, = + 1 . 8 b l'lE~(+'/z) Compounds E = 21.6 keV (+'/z) a = 29 K = 42.5 keV p, = +2.5nm pQ = +3.464 nm Qe = f 1 . 2 b QQ = +0.95b 1W Comnounds _ h_ (+s/.,> El = 97.4 keV (-s/~) E2 = 103.2 keV (+"/a) ai = 0.41 Hot atom effect a2 = 1.55 K = 42.5 keV pic = +3.2nm p2, = +2.03nm QiQ +2.93b \

478 R

I

, " I


RAREEARTHS Produced by Coulomb excitation Many CS theory discussed Intermetallics Review DyAL, DyFez, DyCos, H DyNis, DyCo2, DyNi2 Mntd -.- -

_I_

-1.2 i 0 . 1 Qb/QI = 0.85 f 0 . 1

Metal Metal Doaed gadolinium D+AI garnet DyFeOs Dysprosium-ethyl sulfate

pe/pQ =

EU203, EuO, EU EuSO~,EuBe

cs

EupOs, EuSO4 EuI garnet Metal EueOr Doped CaFs

Lifetime of excited state 2.14 f 0 . 2 X 10-%ec e US. ' K., OD = 94.6' K. CS us. concentration of Eu

(Cuntinued)

Table 1.

Mijssbauer nuclides


Subject or material studied

1"Er 1"Er (+O) E = 80.6 keV (+2) Q = 7.2 K = 50.2 keV pe = +0.61nm Qe = - 1 . 6 b

Nuclear parameters Compounds

166Gd ( -a/,)

Nuclear parameters

El

Types ErC13.6Hz0 ErAh Metal Metal-single ErFeOs

crystal

Erbium ethyl sulfate GdzOa

60.0 keV (-6/z) 86.5 keV E3 105 keV ff1 7.5 Q 0.49 K 44 KeV p,. -0.564nm fill -0.27nm Qu = + 1 . 3 b E2

= = = = = = = =

I67Gd E = 64 keV


l@Gd ( + O ) E = 79.5 keV (+2) Q = 5.94 K = 43.96 keV


176Hf E = 88.3 keV


180Hf E = 93.3 keV


1"Ho ( - 7 / ~ ) E = 95 keV ( - 9 / 2 ) Q = 3.12 K = 44.9 keV pl = +4.15nm Qu = + 3 b ls9Tb ( + 3 / ~ ) E = 58 keV (+6/2) Q = 10.1 K = 45.5 keV


16gTm(+1/z) E = 8.41 keV (fa/*) Q = 325 K = 51.9 keV ps = +0.6nm pl = -0.23nm Q6 = - 1 . 2 b

Compounds

170Yb E = 84.2 (+2) a = 6.7 K = 53.6 keV fie = $0.668 nm

Compounds

E

=

78.7 keV

174Yb E = 76.5 keV 168

-176yb

**U E Q6 Q

= 45 keV = +11.3 = 625

f0.3 b

(328) (490) (382) (3811

(489) (347) (406) (436) (316)

HfOz, HfF.

Qe(176)/Q.( 180) measured

Metal Metal

Crystal field effect

Ytterbium iron garnet YbPda, YbNi5, YbNIz

Spin relaxation Spin relaxation


Nuclear parameters

f i ~ ,=

1.01 i 0.01 nm

YbCla .6H10

Nuclear parameters Nuclear parameters

2 4 l b

Relaxation effects, H us. K. H measured H = 7.71 f 0.15 X lo3 kOe H = 5.6 f 0.15 X lOakOe Spin relaxation effects Relaxation effects Lifetime of excited state = 0.22 nsec. (Ea) 6 . 3 f 0.4nsec. E,, 1 . 2 i 0.04 nsec. Ea

Ref.

Very narrow line '68Gd(Y, p)'6?Eu

1'lYb ( - 1 / 2 ) Nuclear parameters E1 = 66.7 keV ( Compounds E, = 75.9 keV Q =10 pzs = 1.01 f 0.01 nm pr = +0.5b irayb

Remarks

Oxide

Coulomb excitation

(163,166)

CS, A E &. = +11.3 rrt 0.3 b Coulomb excitation

(443) (893, 367)

ACTINIDES

General

Review

Compounds

Metal, AmFa, Am02


UaOa

(44%

(Continued)


479 R

Table 1.

Mossbauer nuclides


Subject or material studied

23’Np E = 59.5 keV a = 1.07 K = 103.5 keV fie = +2nm go = & 5 n m

Compounds

237NpOn

231Pa


Pa02

E a

K

= 84.2 keV = 2.8 =

B

= 0.0045

104.2 keV

sensitive to either the conversion electron or the emitted X-ray but not the gamma rays in the energy range of the Mossbauer gamma ray (333). The counting rate is much lower in this case, and therefore stronger sources can be used with an overall decrease in data acquisition time. 4. Doppler Drives. I n the decade since hfossbauer’s discovery, the Doppler drive has changed considerably from mechanical drives and from electromechanical drives that tinie-modulate the wave forms of motion as input to pulse height analyzers (75, 102, 108, 275, 4G8). Most drives are electromechanical and are of two types, constant velocity and constant acceleration (GO, 424, 478). The system using constant velocity has a scaler-timer which measures the counts from the detector at a given velocity. Often these systems are programmed to cycle at a given velocity until a preset number of counts is collected. The programmer then changes the velocity setting and repeats the process. Such a system can be used with the multiscaler mode of a multichannel pulse height analyzer (33, 272, 279, 319, 480). For constant acceleration drive the velocity function can be either a sawtooth wave form or a triangular wave form (85, 102, 215, 383, 494) with a single or double parabolic displacement (260, 360, 501). The triangular wave form with velocity sweep will result in two mirror imaged spectra on the multichannel analyzer. The synchronization of the analyzer and the drive in the time-averaging mode is extremely important (107, 319). If a wave-form generator is used, both the analyzer and drive must be synchronized. A simpler approach is to use the analyzer as a wave-form generator as described in the previous articles (134, 135, 425). This idea has subsequently appeared in later reports (5, 69,337,359). I n the special case where a stationary source and absorber are required, modulation of a single crystal, from which the radiation is diffracted, can be used 480 R

Remarks

Types

*


(343). This method can also be used to obtain polarized sources when the radiation is reflected at the Bragg angle. Several new techniques using conventional spectrometers have been developed, and are important for specific applications (4, 57). A derivative Mossbauer spectrometer (70, 7 1 ) , based upon ideas used in the electron spin resonance modulating technique, is very satisfactory for the determination of small changes in peak position (for example, detection of small changes in chemical shift with temperature or pressure). Another interesting technique is that of simultaneous collection of separate spectra with two different materials on the same Doppler drive by using subgroups of channels‘in a multiscaling analyzer (399). This procedure increases the precision of measurement of spectral parameters by normalizing transients in the drive-e.g., by using a standard t s . unknown. 5. Cryostats. Many Mossbauer isotopes require low temperature t o observe the effect and, in many cases, a variation in temperature is necessary to interpret the hlossbauer spectrum (408,see below). Several cryostats have been described for cooled absorber only, or for both cooled source and absorber (352, 495). 6. Magnetic Fields. As in the case of temperature studies, the application of external magnetic fields is extremely useful for spectral interpretation. Weak magnetic fields (1 kG) are easy to apply and to align with a permanent magnet. Large fields (50-100 kG) require more elaborate equipment and care must be taken to provide proper shielding and alignment. While several laboratories have installed this equipment, no references on this subject were found in the recent literature. 7. Massbauer Nuclear Fluorescence Scattering. Although transmission geometry is generally used, fluorescence scattering has been observed a n d has the great advantage that very thick, bulk samples can be

measured (378, 499). Since the 57Fe Mossbauer level has a large internal conversion coefficient (9.5) it is possible to detect the 6.3-keV X-ray radiation and the 8-keV conversion electrons. Figure 1 shows the nuclear fluorescence scattering spectrum of a cast iron, Standard Reference Material 1174, obtained by detecting the 6.3-keV X-rays. Because the 122-keV precursor gamma ray also produces a 6.3-keV X-ray by electronic fluorescence, the background level is significant, and there is little advantage in detecting the 6.3keV X-ray in preference to the 14.4keV energy. Detection of the short range 8-keV conversion electrons would give only the Nossbauer spectrum of atoms near the surface of the material. d very good presentation of the scattering technique appears in a report by Debrunner and Frauenfelder (126). In addition to this work, calculations on optimum geometry are presented in reference (227). Another paper describes conversion electron coefficient measurements by a scattering technique (17 9 ) . 8. Precision and Accuracy. It is desirable t o have equipment t h a t measures with satisfactory reproducibility before evaluation of systematic errors is made. I n t h e case of Mossbauer spectrometry we are concerned with the reproducibility of peak position and peak area (or height in some instances). Reproducibility of peak position is particularly useful because of the necessity of measuring small changes in chemical shift with temperature or pressure. The variation in peak position can result from extraneous motion in the Doppler drive, excessive width of the Mossbauer absorption peak, and the random process of radioactive decay (counting statistics). I t is possible with a good spectrometer and known line shape of absorption peak in the spectrum to limit the random error in peak position to that due only to counting statistics (373, 428). In a transmission spectrum we ob-

t PP

+ +

+

@

s ++

Q +

"a++

+s

t

s

*+st @t

B

%

t

0

t

+


481

R

serve a count due to the background radiation. This background comes from the Mossbauer gamma ray emitted with some recoil ( B ) and frcm electronic interaction-e.g., Compton scattering, etc.-between high energy gamma rays from the source and matter near the detector and in the absorber (B’). The height of the peak ( H ) is a satisfactory measure of peak area if it can be assumed that the line shape and width are known. Figure 2a indicates these measures on an absorption peak. Figure 2b shows the hypothetical frequency distribution chart for each of the parameters. The variance of the parameters B , B! and H can be determined by a least-squares analysis of the experimental data using known functions for the background and line shape of the absorption peak. These variances arise from counting statistics from spectrometer (Doppler drive) inconsistencies and from improper models in the leastsquares analysis. It is important to note that quite often the major contribution to the variance is that due to counting statistics. When one attempts to describe quantitative efficiency of a Mossbauer spectrometer, the proper terminology must use the absolute magnitude of H , B , and B’ along with the statistical variance of these parameters. The notation, fraction effect ( E ) (134, 237, 638, $09) , expressed in terms of the experimental parameters is

B E =

- (B - H) B

+ B’

=-

B

H

+ B’

(2)

The variance of E can be calculated from the variances of H , B , and B’. We can increase E by reducing B’. For example, this means that we try to eliminate gamma rays in the source that are higher in energy than the Mossbauer gamma ray. This can be done by selecting the proper nuclear reactions. The resolution and, therefore, the selectivity of the detector can be improved. However, care should be taken to assure high efficiency because, if fewer counts for the same period are collected than before, the variance of E will increase. This entire problem can profitably use the concepts of L. A . Currie (118). The problem is one of “detecting” an absorption peak with given variances of the parameters. Qualitatively we can state that the most efficient spectrometer is that which gives the largest “measurable” peak per unit time. The term “lowest measurable” or quantitative value resulting from an analysis is also defined in reference (118). B’ can also be reduced by the use of X-ray absorption filters. I n the case of S7Fe the 6.3-keV X-ray can be filtered with a 5-mil aluminum foil. For tin a 2-mil palladium foil and for iodine a 4-mil indium foil are recommended. A resonant detector (see de-

482 R


v) c

c

3

0

0

I R e l at i v e

Ve I o c i t y

(0)

Counts

(b 1 Figure 2a. Parameters related to per cent effect in MGssbauer spectrum Figure 2b. Frequency distribution of measured parameters scription above) can almost completely eliminate B’. An additional limitation on the efficiency of the spectrometer is the counting rate that can be accepted by the electronic system. Elimination ot B’ allows a greater source strength to be used so that greater precision in the parameters can be obtained per unit time. It is interesting to note that with B’ reduced to a negligible value, very small percentage effects can be measured because the fractional variance of the parameters decreases with increasing total counts collected. (Of course, the time of analysis is increased considerably.) The limit can be determined using the nomenclature of reference (118). The thickness of the absorber affects both the variance of the peak position and B’. Thick absorbers produce line broadening (with deviation from the Lorentzian profile) and excessive beam attenuation. The absorber thickness should be determined from the effective Mossbauer absorber thickness given in Equation 10, reference (134). If this thickness produces gamma-ray attenuation of 37% or more, the counting efficiency will be low, and nonresonant scattering will be significant. The absorber thickness is then determined by this attenuation process (208). The accuracy of the spectral parameters can be evaluated with a spec-

trometer of high precision by designing a series of experiments and observing a shift in peak position and height (or area). Nonlinearity in the Doppler drive can cause significant systematic error in the peak position. The linearity of a spectrometer can be measured by several techniques. The most direct method utilizes the six-line spectrum of a high-purity iron foil. However, great care must be taken in selecting the proper material to perform this calibration (410). A second method employs high frequency acoustic modulation of a source or absorber superimposed upon the relative Doppler velocity (114). The high frequency modulation produces side bands for a single line absorber. The side band separation is a function only of the frequency, while the side band absorption depends on the modulation of the acoustic amplitude. This method provides a continuous check on linearity. The most accurate technique employs an optical interferometer (428). Because this method does not involve the Mossbauer effect, it can be used simultaneously while a spectrum is accumulated, and an error signal can be derived to correct any nonlinearity in the Doppler drive. Geometry of source, absorber, and detector can cause systematic errors by introducing severe distortion into the spectrum via the background. The opti-

mum geometry is entirely determined by the absorber. Theoretically, the best geometry requires the absorber to be half way between the source and detector. This configuration minimizes the scattering (Compton and Rayleigh) produced by the source in the absorber and also minimizes the detection of the scattered Nossbauer radiation from the absorber. However, most Mossbauer energy levels have a large internal conversion factor which reduces the scattered Mossbauer radiation detected by the counter. In practice the absorber should be closer to the detector than to the source. For a moving source geometry, the counting rate will be a function of the source detector distance, and hence a function of the Doppler velocity. A sawtooth velocity wave form will give a parabolic distortion, while the triangular velocity wave form will produce a distorted double parabola. A moving absorber geometry eliminates this problem only in the first order, since nonresonant scattering by the absorber also gives parabolic distortion. Large separation of the source and the detector virtually eliminates this distortion but requires intense sources. Another geometrical arrangement that distorts the line shape and reduces the effective velocity results from the source area and the detector aperture. The Doppler velocity vector ? and the -pray direction make an angle 8,and the effective velocity (V,) is d

?e

=

? cos 8

(3) This velocity error can be several per cent for close geometry (185, 228, 265). Serious systematic errors can result from using the height as an indicator of peak area unless the line width and shape remain constant (499). Corrections for this effect can be measured and applied. Several other factors can affect the accuracy of the measurements, but these can be eliminated by taking “blank” spectra. Most windows in counters contain impurities which give a spectrum. Beryllium, aluminum, and many plastics contain iron and should be carefully examined. 9. Use of Standards in MSssbauer Spectrometry. Many of the above-mentioned systematic errors can be eliminated through the use of appropriate standards. The National Bureau of Standards has certified a single crystal platelet or properly oriented sodium nitroprusside. The distance between the two peaks in this spectrum has been measured with high precision and accuracy (426, 428). For velocity calibration, it is useful to have as a standard, a material such as very pure iron foil whose magnetic dipole interaction produces a multipeaked spectrum. The Sational Bureau of

Standards is considering the calibration of such a standard a t the present time. Quite apart from the problem of systematic errors in the spectral parameters is the problem of reporting chemical shifts. In order to gain some uniformity in reporting chemical shifts of iron compounds, the use of the NBS sodium nitroprusside is recommended. We have indicated by an asterisk in Table I those who have used the KBS standard. It is very important that those who are not reporting chemical shifts of iron compounds with respect to the NBS standard do so for two reasons. First, conversion of chemical shift data from one compound to another is not necessary. Second, it is inadvisable to report chemical shifts with respect to sources or other compounds because the chemical shift may not be representative of the “average” chemical structure. The high reproducibility of the NBS standard has been carefully proven so that the worker can be confident that each laboratory which uses the NBS standard as a reference point can intercompare their data. 10. Spectrum Resolution Technique. The fact that the line width is a significant fraction of the band width over which the resonance absorption is observed requires t h a t measurements sometimes be made to within 0.001 of a linewidth. This can only be achieved with the aid of machine digital computation. Furthermore, complex hyperfine interactions, or nonequivalent lattice positions of Mossbauer nuclides, can result in a very complex spectrum with partially overlapping lines (258). Very few programs are listed in the literature, but it can be assumed that all of the major laboratories doing Mossbauer spectrometry have them. Several computer programs are now available which can extract the Ptlossbauer parameters from the spectra. These programs can be grouped into three types. a. Computation of Mossbauer spectra from theoretical considerations. These spectra assist in providing classification of the types of interactions present, particularly in the case of mixed quadrupole and magnetic dipole interactions (106, 146, 178, 289). b. Computer curve fitting, using a linear combination of Lorentzian line profiles, without constraints on linewidth, amplitude, and line positions. Since this requires three independent parameters for each absorption line, this procedure is limited to about 12 peaks per spectrum, for most computer storage capacities (95). c. Computer curve fitting with restraints. This greatly reduces the number of independent parameters, but requires an a priori knowledge about the sample. This is about the only means to resolve 5’Fe spectra with

magnetic hyperfine interactions and with several nonequivalent lattice positions. Using the known ratio of the magnetic moment of the excited to the ground state, assuming all peaks have equal line width, and using the theoretical nuclear transition probabilities causes an iterative least-squares analysis to converge rapidly. The curve fitting programs are based upon a least-squares procedure which requires a linear function of the independent variable and hence, a linearization of the Lorentzian profile [ L ( x ) ] ,

with amplitude A , half width r, and position of the absorption peak, p . Linearization is performed by replacing the parameters with an initial value plus a correction term and then by expanding them into a Taylor series. ANALYSIS OF A MOSSBAUER SPECTRUM

In the previous review the basic phenomena of the hyperfine interaction were described. In addition, some examples were given of the various interactions in iron compounds. In this section an attempt is made to provide a systematic procedure for identifying and sorting out the components of a complex Mossbauer spectrum. The least-squares mathematical techniques provide a method for resolving a complex spectrum into a series of peaks giving their position and area. However, the challenging task is the assignment of these peaks to groups that result from a specific hyperfine interaction caused by a specific structure. It is not possible to be comprehensive in a few paragraphs, but procedures will be described that outline the method of attack. It is perhaps obvious that any of the facts deduced from the designed experiments reinforce each other by a feedback mechanism. For example, if some information is available about the electric field gradient tensor, this information can be used to reduce the number of degrees of freedom in the least-squares analysis as described in a previous section. In the description that follows, general examples of common electronic states in iron and tin compounds will be used. No intermetallic compounds or alloys will be described because of the added complexity due to their structure. pure electric quadrupole interaction (EQI) produces two peaks for iron and tin, three for nickel, five for iodine, and seven for tellurium. Several papers have described the pertinent theory VOL 40, NO. 5, APRIL 1968

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(28,106,199,224,230). A pure internal magnetic dipole interaction (MDI) produces six peaks for iron (239, 240, 448, 464, 479, 488, 488). Combinations of electric quadrupole and magnetic dipole interactions are often observed. Several theoretical discussions have appeared (130, 174, 273, 282, 477). Because of the superposition of the many peaks and other effects, one observes considerable difference in the peak intensities. In addition, peak asymmetry that is produced by mixed quadrupole and magnetic dipole interaction can be due to relaxation effects (68, 123, 124, 177, 211, 274, 344, 346, 353, 361, 465). These effects are the result of the interaction of the fluctuating magnetic field produced by atomic electrons with the nuclear llossbauer levels (59, 350). The field fluctuation rate is controlled by spin-spin and/or spin-lattice interactions, and the peak asymmetry is a function of the relaxation rate. If the relaxation rate is fast enough the apparent observed field is zero. For those compounds that produce a single peak, magnetic relaxation can produce peak broadening. In addition, diffusion in a nonideal crystal causes broadening of peak (286, 287). To complicate matters somewhat further, asymmetric peak intensities in a polycrystalline material can be caused by a crystal orientation dependence of the Debye-Waller factor. For a single crystal, the peak asymmetry is a function of the crystal orientation with respect to the direction of the Mossbauer radiation. The chemical shift is another effect that can be observed in a Mossbauer spectrum (40, 284). Quite often it is necessary to evaluate those peaks produced by electric quadrupole and magnetic dipole interaction before a centroid or position of the degenerate level can be used t o express the chemical shift. Considerable information in certain spectra can be derived from measuring the fraction of effect or the Debye-Waller factor (257,854). It can be readily understood that direct interpretation of a single Mossbauer spectrum without further experimentation is usually impossible. In fact, it is always true that data from other spectroscopies such as microwave spectroscopies, infrared] magnetic susceptibility, etc., are required to provide assistance with the proper interpretation of the spectrum. There are a number of experiments that can be designed to assist in separating the various interactions described above. Temperature Change. Measuring the Mossbauer spectrum as a function of temperature provides much information and should be performed in almost every instance for both magnetic and quadrupole interactions. An example of the utility of temperature variation for magnetic spectra is

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the study of the behavior of the internal magnetic field near the Curie (Ned) temperature of a ferromagnetic (antiferromagnetic) compound or alloy. Variation of a quadrupolar spectrum with temperature often reflects a change in Boltamann population of atomic energy levels. For instance, significant temperature dependence is usually observed for high spin de iron because the additional electron above the half-full d shell is free to Boltamann populate the d levels. I n contrast high spin d5 iron exhibits little if any temperature dependence since the d shell is half full. The two relaxation effects (spin-spin] and spin-lattice) cannot be distinguished by temperature change. The asymmetry increases with decreasing temperature for spin-spin relaxation, but the relationship is unpredictable for spin-lattice relaxation. Temperature dependence of chemical shift is not particularly significant from the standpoint of determining interactions. The value of the chemical shift can be very helpful in determining the structure under study. Many publications (see Table I) contain catalogs of chemical shifts and the clustering of specific electronic configurations around definitive regions of chemical shift provides useful information. The anisotropy in the Debye-Waller factor approaches zero as the temperature is decreased. However, it is difficult to distinguish this temperature effect from certain of the spin-lattice relaxation effects. This can be accomplished by molecular dilution. The structure is then isolated from the lattice and the spin-lattice interaction is removed. This dilution procedure is often not a simple task. Sometimes dilute substitution in a lattice of similar type is possible. Some work has been done using solvation of the molecule (without interaction) and then freezing the solution t o take the spectrum. Occasionally one can observe a preferred orientation of a polycrystalline sample caused by simple preferential packing (due to crystal shape) in the absorber mount. This will cause an asymmetric EQI. In fact, measurement of such asymmetry as a function of angle of incidence to the gamma ray provides data about the sign of the electric field gradient in the compound. Finally, the use of an external weak magnetic field (1 kG) to polarize the source results in population of only certain levels in the absorber (196,417). This results in decreasing the complexity of the spectrum particularly in those cases where the M D I occurs with two separate structures in the lattice. It is also possible to apply a large magnetic field (50-100 kG) to a compound with predominant EQI that will allow measurement of the electric field gradient tensor.

APPLICATIONS

All of the applications are itemized in Table I. There is a noticeable increase in the number of applications on iron and tin compounds, and a lack of applications with other elements. Several new isotopes have been found, primarily with the assistance of the Coulomb scattering technique. An interesting acceleration in the study of pressure effects is noted (126, 127, 178, 502,803). These experiments require very great care in their design to be assured that the expected compression of the lattice is being achieved. Some interesting theoretical papers have appeared on the problem of residual charge states produced by nuclear reactions prior to the decay of the Mossbauer level (166, 271, 340, 342). Some effort has been made to correlate the Mossbauer parameters of tin compounds. Although considerable difficulty has occurred particularly in the assignment of AR/R (see Table I) some interesting progress has recently been demonstrated (111, 188, 190, 222, 504). Another interesting study is the effect of small particle size on the Mossbauer spectral parameters (6, 65, 285, 295, 532, 339, 404, 462). Several new applications that were not described in the previous review are the study of surface absorption (82, 109,110,143,470)and the measurement of intermediate compounds produced during chemical reactions (Table I.) It would be improper not to mention the possibility of measuring quantitatively the presence of known structures in a material. The present authors have recently reviewed work that demonstrates the feasibility of measuring relative concentration of oxidation states. It still remains to be demonstrated if the problems outlined in the last review article can be resolved satisfactorily to allow direct quantitative measurement of a specific structure. SUMMARY

It may be of interest to attempt to generalize about the place Mossbauer spectrometry appears to be taking in the total complex of spectrometries which allows deductions about chemical structure to be made. Mossbauer spectrometry is, of course, closest to the microwave spectrometries. In particular, it often competes most closely with KMR. In the case where well defined hyperfine levels exist-e.g., with most iron compounds-the much higher precision of S M R is superior to the Mossbauer method (455). However, when there is considerable spread in the levels, Mossbauer spectrometry is very valuable in assigning appropriate frequency regions for NMR study. Of course, for measuring electric quadrupole interaction,

Mossbauer spectrometry becomes unique if the spin state of the ground level is and that of the Mossbauer level is greater than '/z. There is little question but that those working in fields of Mossbauer spectrometry have much to learn from the microwave spectroscopists about the pertinent hyperfine interactions, and increasing efforts have been made to understand the relationships between these closely related fields. I t is notable that only a limited number of papers have been published on a wide variety of applications to many areas in science, from surface absorption to the measurement of nuclear parameters. Development of these ideas probably is slowed by a lack of elements to which this spectrometry can be conveniently applied. It is undoubtedly the task of both the radiochemist and physicist to remedy this situation. Recent developments in radioisotopic sources and the recoil implantation technique may provide the stimulation for expanding the method to other elements. Fortunately, the importance of iron chemistry particularly in metallurgy provides much needed impetus for extension of the applications. Improvement in instrumentation, particularly in radiation detection systems will also provide increasing interest in this unique spectrometry. ACKNOWLEDGMENT

We could not have produced this compilation of references within the time schedule imposed upon ourselves without the much appreciated assistance of Robert Boreni, who operates the computerized information retrieval system, and Miriam Oland who carefully typed the entire manuscript. LITERATURE CITED

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Moessbauer spectrometry - Analytical Chemistry (ACS Publications)

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