Precision and interlaboratory reproducibility of ...MBr-rNoe, Densy DyA,n Department of Earth, Atmospheric, qnd Planetary Sciences Massachusetts Institute of Technology Cambridge,

American Mineralogist, Volume 69, pages 1127-1 144, 1984

Precision and interlaboratory reproducibility of measurementsof the Miissbauer effect in minerals

MBr-rNoe, Densy DyA,n

Department of Earth, Atmospheric, qnd Planetary SciencesMassachusetts Institute of Technology

Cambridge, Massachusetts 02139

Abstract

Although the technique of Mcissbauer spectroscopy is now 25-years old and widely used,little empirical work has been done to determine its accuracy in measurements on minerals.To solve this deficiency, two mineral standards (a grunerite and an almandine/andraditegarnet mix) have been selected. Precision of the technique was measured through fivedifferent sets of experiments seeking to analyze the reproducibility of measurements on asingle sample mount, on several identical mounts of the same sample, and on a set ofmounts with different sample concentrations, run times, and background counts. The twomineral standards were analyzed by other scientists at seven different laboratories; theirdata were also fit by the MIT program. The standard deviation of multiple measurementson the MIT apparatus is better than 0.016 mm./sec for isomer shift, 0.060 mm/sec or betterfor quadrupole splitting, and l.02Vo on individual peak area data. The standard deviation ofinterlaboratory measurements on the same minerals is slightly better because only ideal runconditions were used: 0.006 mm/sec for isomer shift, 0.023 mm/sec for quadrupole splitting,and l.44Vo on individual peak area data. Probable errors on different aliquots of the samesample are approximately +0.02 mm/sec for isomer shift and quadrupole splittings, and-rl.sVo on area data for well-resolved peaks.

Introduction

Since 1967, over 814 papers have been published in thegeological literature which apply the Mcissbauer effect in57Fe to interpretations of mineral crystal chemistry (Fig.l). Numerous other papers have made reference to Mciss-bauer measurements for Fe3*lFe2+ determinations orstructural Fe site occupancy information, to the extentthat the technique has become one of the many common-ly used analytical tools available to geochemists andmineralogists.

However, the technique of Mrissbauer spectroscopy isstill relatively young; Rudolph Mossbauer published hisfirst papers only 26-years ago (Mcissbauer, 1958). In thefirst l0-15 years after Mcissbauer's discovery, M<issbauerspectrometers were literally home-built from scratch inchemistry, physics, and mineralogy laboratories aroundthe world, with a wide array of geometries, standards,and electronic configurations. Because the experimentalapparatus and methodology for Mcissbauer work werecustomized for each lab, there was little consistency inthe type of source used or the method by which spectraldata were processed. By the 1970's, commercial Mciss-bauer apparatus became widely available, but manyworkers continued to maintain and update their originalequipment. Today each Mdssbauer laboratory has its

0003-004)v84lltt2-1r27$02.00 tt27

own distinctive experimental apparatus, computing facili-ty, and philosophy for recording, measuring, and report-ing its results (for example, Mitrofanov et al., 1977;Graham et al.. 1977:. LeFever. 19791 and Fultz andMorris. 1978).

Over the years there have been some attempts tostandardize the type of calibration procedures (Herber,1971) and the method of reporting results (Zuckerman etaI.,1972); these have been received with varying degreesof success. The predominant trend has been for each lab(and subsequent generations of graduate students andcolleagues) to develop its own philosophy on optimiza-tion of experimental technique and curve-fitting. A fewattempts at interlaboratory standardization (e.g., Minaiand Tominaga, 1982) or comparison of Fe3+/Fe2* ratiosagainst wet chemistry (Whipple, 1973 and 1974; Bancroftet al., 1977) have given inconsistent results, althoughagreement between different Mcissbauer labs is consis-tently better than between Mossbauer and wet chemicallabs.

Fortunately, several workers in the field have devotedgreat effort toward a statistical evaluation of the tech-nique. The literature prescribes the optimal sample con-centration and thickness (Hafemeister and Shera, 1966;Ure and Flinn, 1971; Shenoy et al., 1974), the relativemerits of fitting techniques (Lin and Preston, 1974),

tt28

1964 t"tt*"rtt1o,","ot"tt 1976 leTe

Fig. 1. Publications with MossBAUER as a keyword from theGeoref Database, search performed August, 1982.

methodology for quantitative site population estimates(Bancroft, 1967; 196911970), and even a unique criterionfor evaluating Mcissbauer curve flts (Ruby, 1973). BothLaw (1973) and Dollase (1975) have given thorough,excellent reviews of the statistical limitations of thetechnique.

However, the practical problems of the technique haverarely been published. While it may be useful to know theoptimal iron concentration for a Mossbauer experiment,it is perhaps far more important to the worker with, say, alimited quantity of lunar sample to know how far he candeviate from the ideal value and still have worthwhileresults. Is it really necessary to weigh all samples outcarefully? A similar problem involves the duration of theexperiment. In these days of careful cost monitoring,what is the minimum length of run-time for which optimalresults can be obtained? Finally, it may sometimes be-come necessary to compare or tabulate the Mcissbauerresults of Lab A with Lab B. How valid are suchcomparisons?

Five years and 94 Mossbauer spectra ago, this studywas undertaken to resolve these many questions. Theresults reported here represent empirical guidelines forM<issbauer spectroscopy labs based on experimental, nottheoretical, calculations. Data on two minerals designat-ed as standards are tabulated for each of seven Moss-bauer labs which ran them. The conclusions reached hererepresent a realistic overview of the state of the art ofmineralogical applications of M<issbauer spectroscopy.

BackgroundSince the subject of statistical limitations of Mcissbauer

spectroscopy has been covered elsewhere in great detail, areplicate discussion will be passed over. There are a number ofbooks and articles which give a general background on thetheory and applications of the Mcissbauer effect; a partial listmight include Fluck, 1967; Wertheim, 1967; Spijkerman, 1968;Greenwood, 1970; Greenwood and Gibb, l97l; Bancroft, 1973;and Marfunin, 1979. Two handbooks from the Mdssbauer EfectData Center (1984a and b) give thorough summaries ofboth data

DYAR: PRECISION AND REPRODUCIBILITY OF MOSSBAUER MEASUREMENTS

o

o

o!Et

2

and references on mineralogical studies. However, for thepresentation of experimental results which follows, it is useful toreview briefly the major parameters by which Mcissbauer spectraare evaluated:

Isomer Shift, IS or 6, (also called chemical shift in somepapers) arises from the difference in s-electron density at thenuclei of the radioactive source and the absorbing iron nuclei inthe sample or absorber (Fig. 2). For example, Fe57 in Pd (formed

by electron capture from 57Co) emitting nuclear gamma rays toFe57 in a Pd absorber gives rise to zero isomer shift' But whenFe57 is in a different chemical environment from that of theemitter, the resultant difference of s-electron density at thenucleus produces a finite 6. Isomer shift is afected by oxidationstate, coordination number, spin state of iron atoms, and ligand-type coordinated to iron cations, and may be augmented by asecond-order Doppler shift, which is temperature dependent'Since isomer shift depends heavily on a calibration standard, it isoften deceptive to compare values from various publishedpapers. In this paper, all values will be cited with respect to themid-point of the metallic a-iron foil spectrum, by applying thefollowing adjustments to the values reported for alternativestandards, as suggested by the Mcissbauer Effect Data Center(Gettys and Stevens, l98l): Cr, -0.154; stainless steel, -0.09;

Rh; +0.106; Pd, +0.177; and Cu, +0.225 (figures quoted forisomer shift values in mm/sec relative to o-Fe).

Quadrupole Splitting, QS or A, arises from an electric fieldgradient (EFG) at the nucleus, which produces two or moreenergy levels when nuclear charge distributions are non-spherical (i.e., I = l). Both electronic structure of the Fe atomand the arrangement of the ligands around it contribute to theEFG. Asymmetry of the (localized) electronic configurationdominates the symmetry of the ligand environment, such thatany departures from "perfect" cubic symmetry will cause theabsorbing ion to experience a different electronic environment,

M O S S T A U E N P A I A M E T C N 3

7 7 - r . r .

;

t t /sEc

Fig. 2. Graphical representation of Mcissbauer parameters,shown on an energy level diagram and a typical (in this case,olivine) spectrum.

FF

. . .2

F $

which changes the quadrupole splitting (see Fig. 2). QS alsodepends on iron valency, spin state and relative site ordering;Figure 3 shows a plot of IS vs. QS for common minerals. Notethat these data are for oxygen environments only; non-oxygenenvironments, such as sulfides, tend to follow similar trends withsomewhat different parameters. The relationship seen in Figure 3arises from the dependence of QS on the radial expectationfunction (r-')tr, and shows how the shielding by d electronsafects IS.

The Linewidth, f , of a Mrissbauer line is generally taken to bethe sum of the natural source and absorber linewidths;experimentally, this is the full width at half peak height of theMdssbauer peak. It can be defined theoretically as the linewidtharising from the Heisenburg Uncertainty Principle:

. _ t h . l n 21 . , - -

trtz

In a Mossbauer experiment the natural linewidth observable canbe defined as:

w" = 2ch ' ln2

Ey tuz

where h is hl2at E" is the energy of the gamma transition, and t172is the halflife of the excited nuclear level (Stevens, l98la). For57Fe the theoretical value of fo, as calculated from "lifetimedata," is 0.1940(3) mm/sec (Stevens, l98lb).

The best Mrissbauer source materials are those which emit amonochromatic line with a width close to the theoretical valueand have a substantial recoil free fraction; 5tco in pt (0.22 nmlsec) and Pd and Rh (0.23 mm/sec) are commonly used. Thelinewidth of a metallic iron spectrum when measured with suchsources gives a "lower limit" for experimentally-determinedlinewidths of approximately 0.24 mm/sec; the added widthbetween theory and experiment is probably due to nearest

lt29

neighbor interactions and defects, residual mechanicalvibrations, and the "cosine smearing efect" (Spiikerman et al.,1965) which can broaden and shift the line. In crystallinesilicates, which come close to the lower limit, Fe2* peaks rangefrom 0.27-0.28 mm/sec, while Fe3* peaks (0.28-0.35 mm/sec)are often slightly broader (Bancroft, 1973). Deviations fromthese values may result from several causes: next nearestneighbor effects, electronic relaxation (Morup and Both, 1975),thickness distortion (Ruby, 1973), and multiple, superposedpeaks (Whipple, l98l).

It is also instructive to review the statistical parameterscommonly used to evaluate Mdssbauer fits. Chi-squared (x'z) isgenerally defined as

Chi-squared : r, : N + i ( ""iu;Jitt')'

where N is the number of points to be fitted, n is the number ofparameters to be fitted (N - n is sometimes referred to as thenumber of degrees offreedom), Yc(I) are the calculated valuesfor the curve, and Yn(I) are the data points. The optimum valuefor 12 is one; or one times the number of degrees offreedom aspresented here. 12 can be said to represent the likelihood that thecalculated curve represents the data within its errors (note theVy"(t) term ln the expression, which approximates thestandard deviation of each point). However, good values of 12can be very misleading because they may represent fits withlarge error bars on the data. To get around this problem, astatistical parameter was needed which had the capability tonormalize the data with respect to the number of counts in theexperiment. The parameter of Misfit was derived by Ruby (1973)to provide a comparative goodness-of-fit criterion which couldevaluate diferent spectra inespective of the magnitude of theirbaselines. Misfit is defined bv two other criteria:

DYAR: PRECISION AND REPRODI]CIBILITY OF MOSSBAUER MEASUREMENTS

which is the distance between the calculated and theexperimental results (discrepancy of the fit); and

Distance. ": i [( ""lu;li")'-

signar, S = i [(*'3u-,1i")'

'1,

-t- I l .

J

o

E Ic

FE

o

E o.sIoo

Fig. 3. Plot of isomer shift versus quadrupole splitting forcommon minerals, based on commonly accepted values (RogerBums, personal communication).

which measures the difference between the experimental dataYp(I) and the baseline Yo. Misfit, defined as the ratio D/S, isoptimal when it is close to zero; i.e., a Misfit value close to zerois essentially the same as a chi-squared close to one.

Misfit is an extremely useful parameter in Mossbauerexperiments because it is sensitive to more than the magnitude ofthe baseline. The numerator, D, is similar to 12 in that it dealswith the difference between the calculated curve and theexperimental results. However, the denominator, S, is areflection of (and directly proportional to) the duration andcounting rate of the experiment, the number of channels over

3( mm /scc)O U A D R U P O L E S P L I T T I N G , A

[-----ii!lrorrro| - ' . 1

.rcurt_l

l 130

which a peak is observed, and the square ofthe observed effect.These characteristics enable the experimenter who calculatesMisfit to separate the efects of pure counting statistics (like X'z)from the actual experimental errors of the experiment (which willbe discussed at length). Derivations and further information(including several examples) on Misfit use can be found in Ruby697j.

For the purposes of this study it is also useful to describe thebasic statistical terms which will be used to compare differentresults. The mean is defined as an arithmetic average or the sumof all the observations divided by the number of observations. Itis usually represented by the symbol X.

The variance gives an averaged squared deviation from themean. It can be used effectively for comparisons; its square root,the standard deviation, is even more useful because it is in theunits of the measurements of the data.

In this study, the sample variance, s2, is computed using

) x , 2 - n x 2

s 2 = t : t

'n - l

where X; is the observation, X is the sample mean, and n is thenumber of observations. Standard deviation. or s. is defined asthe square root of s2. Groups of data having the largest s or s2values will have the greatest spread among the values of thedifferent measurements. A complete explanation can be found instatistics texts (e.g., Spiegel, I 961 ; Davis, I 973 ; or Taylor, I 982).

Finally, for completeness it is useful to briefly describe atypical experimental set-up, as shown in Figure 4. The source ofnuclear gamma rays (commonly 57Co in a Pd or Rh matrix for FeMdssbauer spectroscopy) is attached to an oscillator (or to bothends of an oscillator, as pictured). The doppler velocity of thesource is varied by (generally) a linear motor; commonly used"constant acceleration" drives sweep linearly through a range ofvelocities from negative (as the source moves away from thespectrometer) to positive speeds. The resultant velocity/timeprofile has a characteristic zig-zag pattern.

The recoil-free gamma rays which are emitted from the sourcespan an array of energies of 14.4+0.001 keV (Stevens, l98lb).

Fig. 4. Schematic of a typical Mossbauer apparatus, showinggamma rays generated by the source mounted on the oscillator,passing through the sample, and being detected, gated,processed, and finally stored in a multichannel analyzer. Datamay then be processed by computer.


They pass through the sample, where they may be absorbed by57Fe isotopes having comparable nuclear energy levelseparations. Some of the gamma rays pass unabsorbed(depending on sample thickness and density) through the sample,to be registered on a detector. The pulses recorded by thedetector pass through a pre-amplifier, linear amplifier, and alinear gate (or single channel analyzer) to select the l4'4 keVenergy range. Counts are stored as they are received in eachchannel in turn of a 256, 512, or 1024 channel (common

increments) multi-channel analyzer. The isomer shift zero isstandardized (usually) against the midpoint of an iron foilspectrum; the known positions of the iron foil peaks are used todetermine the number of mm/sec/channel.

Data are accumulated in the multi-channel analyzer for a timeperiod depending on source strength and the relative Feconcentration versus the bulk weight of specimen. Othercal ibrat ion standards, such as sodium nitroprusside(Naz[Fe(CN)sNO] '2HrO) or stainless steel, are sometimesused when a high degree of precision over a smaller velocityrange is desired. Each standard has a distinctive isomer shiftrelative to metallic iron; simple corrections can be used to makecomparisons between experiments using diferent standards.Run time varies from hours to days depending on thejudgment ofthe experimenter. Data in counts per channel (i.e., finite velocityincrement) are then transferred to the computer and processedby any one of a number of curve fitting and/or deconvolutionprograms, ranging in complexity from simple triangle fittingprograms to such complex programs as the Gauss nonlinearregression algorithm of Stone et al. (1971).

Experimental method

This study is divided into two parts: intra- and interlab-oratory comparisons. The intralaboratory work wasaimed at determining the optimum run characteristics forthe experimental apparatus in the Mcissbauer Spectrosco-py Lab at MIT. Once these were defined, the samegrunerite sample was run ten times under identical condi-tions to test precision, and ten aliquots of the samesample were run to test for homogeneity of this standardmineral.

The interlaboratory work was performed voluntarily atseven different labs chosen randomly from twelve. Partic-ipants, institutions, and spectrometers are listed in Tablel. Dr. Wayne Dollase generously ran one of the standardsthree times with different run durations to test his spec-trometer for electronic stability.

Two mineral standards were selected to be used for thisstudy. Standard "R" is a quartz-grunerite schist from theLuce Lake area, Labrador City, Canada. This well-studied sample (Klein, 1964; Klein and Waldbaum, 1967;Bancroft etal.,1967\ was the most iron-rich (95.37oFe2+)grunerite that I could obtain; it is an especially advanta-geous standard because of its high iron content (44.99wt.% FeO), its homogeneity, the simplicity of its spec-trum, and the presence of well-resolved peaks. Wetchemical analyses performed at the Smithsonian Institu-tion show that this sample has less than 0.1%o Fe2O3,which should not be detectible by the Mtissbauer effect'The bulk sample was ground by hand under acetone in an

DYAR: PRECISION AND REPRODUCIBILITY OF MOSSBAUER MEASUREMENTS l l 3 l

Table l . Participants, institutions, and spectrometers ininterlaboratory comparison

Table 2. Compositions of mineral standards

Standa.d "A"Garnet l l l i x**

A l m n d i n e A n d r a d i t eh@sade, Kankel i te-type,constant accelefat ion

Aust ln Science Associatesconstant accelefat ion

iluclear Data fl0660p.ogramable mult ichannela n a l y z e r w i t h i n - h o u s e - b u i l tdr i ve

Elscint MVTm D.ive with CanberraSeries 40 ICA

Ul ssel /Hal de.

s e l f - e d e , H r l d e r d . l v eelectro-mchanlcal lbpplervelocl ty generator, constantaccelefat lon f tA, HalderElectronics, l lunlch counter,anpl ' l f ler, po{er supply: Urtec

hmsade, dr lven by PDP 11/10m l n l c o m p u t e r , d r i v e s i g n a l ,l inear famp, and f lyback

S t a n d a r d " R "Gru neri te*

Hayne A. D,ol laseDepartnent of Edrth .nd Space Sclencesl.Jniversl ty of Cal i fofnia, Los AngelesLos Angeles, CA 90024 USA

Roger G. EurnsDepadrent of Earth and Planetary Sciencesl lassachusetts Inst l tute of TechnologyCambridge, l lA 02139 USA

Ffank E. fhrgginsU.S. Steel Research, i ls #98125 Janlson Lanei b n r o e v i l l e , P A 1 5 1 4 6 U S A

F r l e d r i c h A . S e i f e . tl4 i neral o9l sches Inst i tutK t e l U n i v e r s i t y0lshausenstr. 40, 2300 Xtelfest Gemany

Enver i lu.adLehfstuhl fur BodenkundeTechni sche (hiversl tat l tunchenD-8050 Frel s i ng-8el henstephanIest Gemlny

Georg ArthauerUniversi ty of ihrburgInst i tute of l l lneralogyLahnberge, 3550 Marburgl{est Gemany

Catherine i tCrmonrRese.rch School of Earth sclencesA u t r a l l a n l h t l o n a l U n l v e r s i t yP . 0 . 8 o x 4C.nberra ACT 2600Austral ia

S i 0 2 4 9 . 0 1

T i 0 2 0 . 0 5

A1 203 0 .00

Feo 44 .99

l4n0 0 .37

M g o 3 . 1 7

C a o 0 . 3 1

Na20 0 .04

KZl 0.00

CrZ03

F Z 1 . 0 0

H20* 1 .28

HZ0- 0 .3 I

PZ0S 0 .10

ToTAL: 100.63

3 7 . l 3

0 .06

2 1 . 6 0

31.86

2 . 3 7

5.44

1 . 6 0

0 . 0 1

35.29

0.00

0 . 0 3

2 7 . 7 4

0 . 0 1

0 . 2 6

32.93

0 . 0 3

100.07

* f r o m K l e i n , 1 9 6 4 , p . 9 5 6 . l l i c r o p . o b e a n a l y s i s w a s p e r f o r r e d b y J u n l t o ,D e p t . o f G e o l o g i c a l S c i e n c e s , H a r v a r d U n i v e . s i t y . F e i s r e p o . t e d a s F e o .

* ' G a r n e t s w e r e c r u s h e d b y r c r t a a a n d p e s t l e a n d w e i g h € d i n t o g a r n e t n i r " A "i n t h e p r o p o . t i o n w t . 1 F e 6 6 6 1 6 6 ; 1 s l v t . X F e a l m n d i n e - 0 , 1 8 5 . l l i c r o p r o b ea n a l y s e s o f t h e g a . n e t s w e r e m d e b y K a r e n K i m b a l l o n t h e M I T D e p t . o fE a r t h , A t m o s p h e r i c , a n d P l a n e t a . y S c i e n c e s M i c r o p r o b e . F e i s . e p o . t e d a sF e 0 .

r Spectra Ere fun by 0r. S. J, C.npbel l , thpartMt of Soltd State physics,Research khool of Phjrsical Sclences

l{ote: Each padiclpant {as randmly asslgned a n@ber, .anglng f .on l -7. Torespect the conf ldent ial i ty of the part ' lc lpants, . l l rcferences frmhere on r l l l be to n@bers $lch do mt coffesDond to the order of theI lst above.

agate mortar, a few grains of magnetite were removedwith a hand magnet, and about 80% of the quartz wasremoved by use of a magnetic separator. Approximatelyl0% (by volume) quartz and trace amounts of magnetiteremained in the batch of standard "R" distributed forinterlaboratory comparison.

Standard "A" is a mechanical mixture of two garnets.This mixture was chosen to simulate typical bulk rockMcissbauer measurements, which are commonly per-formed to determine whole rock Fe3*/Fe2+ ratios onsamples containing more than one mineral. Andraditecrystals were hand-picked from Harvard University sam-pIe 87373 from Val Malenco, Italy; almandine crystalsfrom Fort Wrangell, Alaska were selected from the MITTeaching Collection. Each garnet was ground by hand,under acetone, and then weighed into individual aliquotvials in the proportion wt.Vo Fe^nalwt.%o Fe.r- : 0.185.Participants were asked to use all of the standard materialprovided, or to take their sampling from a well-homoge-nized mixture.

Natural mineral standards were chosen in spite ofimpurities and slight structural defects in order to makethe study geochemically (or mineralogically) relevant.Compositions are given in Table 2, and typical fittedMcissbauer spectra are shown in Figures 5 and 6.

Aliquots of each of the two standards were sent to allparticipants. The format of the accompanying question-naire was:

General Infomation Sheet

[F i l ' l th is ou t once fo r your fac l l i t y ]

Ins t i tu t ion where spec t rmeter i s loca ted :

Name and address of person fi l ing th'is report:

Description of mounting procedure (type of-holder, rcuntlng medium'amount o f sample , vo lune o f ho lder , e tc . ) :

Average length of run time:

source mat r ix (57co jn Pd, Rh, e tc . ) :

Source s t rength (n i l l i cu r ies ) :

Distance from sanDle to source:

Type of spectroneter:

Year Durchased:

Nunber of channels stored for each spectrum:

Ca l ib ra t ions w i th respec t to :

Computer used for processing:

Nam o f p rogram used fo r f i t t ing :

Source Prcgran:

Year written/obtai ned :

Author :

curve shaDe used: RUN sHEFr

[Fi1l out one of these for each run, or send your computer printout]

Sample number:

Temperature:

Number o f cons t ra in ts in f ina l f i t :

Type o f cons t ra in ts ( l i s t ) :

Base l ine :

tr32

Shape o f base l i ne :

Anount o f d is to r t ion :Peak Paraneters

Peak # Center Halfwidth Area t Gaussian Height % area

Pos i t ions in m/sec ( i f above ls in te rns o f channe l nunbers)

Peak Center t lalfwidthll i issbauer Data

-

Peaks IS ql

t - 4

2-3

Sta t is t i cs (where app l i cab le )

l l i s f i t :

Ch i -souared:

# degrees of freedom:

The MIT results were calibrated using the midpoint and peakpositions of a 6 ,rm a-Fe foil, 9.99% purity, as supplied by NewEngland Nuclear and as specified by the Numerical DataAdvisory Board of the National Research Council (1971). Peakpositions used were the most recent values supplied by theMrissbauer Effect Data Center: -3.0760, -0.8379, 0.8397, and3.0760 (John G. Stevens, pers. comm., 1984). Dr. Stevens alsopointed out that these values do not depend heavily on theabsolute purity of the a-Fe foil used for calibration; if there isimpurity (usually in the form of C) in the foil, it will produceanother set of six very weak lines in the spectrum which will notatrect the a-Fe lines. Four hour (500,000 count) calibrations ofthe spectrometer were carried out once every thirty days, withmineral measurements performed back-to-back in the interimperiods. Negligible variation in the position of zero velocity orthe velocity gradient of the spectrometer was observed over thethirty day period.

Participants at other laboratories were requested to use similara-Fe foils for calibration to insure consistent results. Theirindividual procedures for calibration were not surveyed;however, subsequent communications have revealed that somelabs may not have used the most current Fe peak positions,causing slight deviations in their results (see Discussion).

ResultsWork done at MIT

The original aim of this study was to reassess theprecision of the Mossbauer technique on a state-of-the-art

Gsrnal Slrndrrd "A" Aln.ndino / Andradltc


Grun.r i ta Standatd "R"

Fig. 6. Fitted Mcissbauer spectrum of standard "R", an iron-rich grunerite amphibole, which was used both as intra- andinterlaboratory standard.

spectrometer at MIT by using a natural mineral standard.This was pursued through five different sets of experi-ments, seeking to analyze the reproducibility of measure-ments on a single sample mount, on several identicalmounts of the same sample, and on a set of mounts withdifferent sample concentrations, run times, and back-ground counts. Considerable effort was made to approachthe analyses in an unbiased fashion; the following resultsare presented in the order in which they were determined.

Effects of sample concentration were first studied byrunning a series of diferent Fe concentration mounts foridentical 24 hour periods, with no control over thenumber of baseline counts (Table 3). I Although a statisti-cal "good fit" was attained for the 20 mg Fe/cm' sample,the predominating trend, as seen in Figures 7a and 7b,was for the best statistics and gamma ray absorbance tooccur at a concentration of 5-7 mg Fe/cm2, at around 2.5million baseline counts.

This conclusion was further tested by holding thenumber of baseline counts constant at I million, andallowing time and sample concentration to vary. Resultsare presented in Table 4. As can be seen in Figures 8a and8b, the optimal concentration necessary to make 12approach 509 and Misfit approach 0 falls at the concentra-tion of 7 mg Fe/cm2.

Effects of run duration and number of backgroundcounts on the statistical parameters of the fits were testedafter the optimum iron concentration (7 mg Fe/cm2) hadbeen determined. Time and the number of baseline counts

I Complete listings offull data for each run (as listed in Tables3J, 12, and l3), including run times; baseline counts; Feconcentrations; individual peak positions, widths, and areas;isomer shifts; quadrupole splittings; and error data can beobtained by ordering Document AM-84-256 from the BusinessOffice, Mineralogical Society of America, 2000 Florida Avenue,N.W., Washington, DC 20009. Please remit $5.00 in advance forthe microfiche.

!

C

a

F

t

E

F

aa

Fig. 5. Fitted Mdssbauer spectrum of standard "A"mixture of almandine and andradite garnet.

I 133

+ @ o + N @ N N@ @ o o o o o o o oo o o o o Q o o F @o o o o o o o o o +o o o o o o o o o oo o o o o o o o o o

t t t l

O O O H O N t s HN O D O @ @ O O

6 - O H O + € E0 6 0 0 0 6 6 0

+ 6 0 N O t s O 6 N O@ @ o o < r o d t s o6 N t s @ O O < + O +

F @o o

@ o d+ N O 6 d O O O N N I O @ Oo 6 N O O O O O d @ t O N do + 6 6 6 * 6 O 6 O J O O 6

d d l o o a

o @ 9N O N O O € O N O @ l O O Oo @ o F o < 6 0 @ + l o o N@ N N F N N t s N t s o l o O t s

N N N N N N N N N N I O O N

N + o + F o o o @ 6 t 3 3 D@ @ o o o o @ o @ @ t o r 6o o r o o H o o o o l o o o

H H I o o d

N a oo @ q o H o o 6 H F I o 6 @o < 6 0 0 0 6 0 6 0 1 o H 6

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+ o dO O i

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to !U L

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I 134

2 2 5 3 3 5 4 1 5

Numbar ot counts x106

Sample Concentrat ion m9 Felcm2

Fig. 7. Plot of number of counts versus 70 transmission (a)and sample concentration versus Misfit (b) for grunerite runsw i thT :24hou rs .

were allowed to vary (Table 5). Results shown in Figures9a and 9b amply demonstrate that short run times (basedon a gamma ray flux strong enough to supply about100,000 background counts/hour) give the most desirablevalues for x2 (close to 509) and Misfit (close to 0). Thisconclusion can be explained by the effects of smallinstrumental problems, such as the cosine smearing fac-tor (Spijkerman et a1., 1965), baseline inconstancies,source problems, nonlinear drives, etc., for which Misfitwas designed to be sensitive. As will be discussed later,these problems are not unique to the MIT apparatus.

Reprodubility of replicate analyses on a single mountwas tested once the optimum run characteristics had beendetermined (Table 6). Peak positions vary from theirrespective means by up to 10.02 mm/sec; widths vary10.02 mm/sec and areas of individual peaks are within-+ | .670. However, isomer shifts are reproducible to with-in -t-0.012 mm/sec, and quadrupole splittings are generallygood to +0.016 mm/sec. These figures can be regarded asa realistic lower limit on the experimental reproducibilityof the Mcissbauer apparatus, as influenced by the MITlab's electronic stability and computer fitting procedures.

A test of the homogeneity of the standard was under-taken to examine the suitability of the grunerite for


!o

Ec

F

SamPlc Concenttat ion mg Felcm2

Fig. 8. Plot of sample concentration versus ;12 (a) and versusMisfit (b) for grunerite runs with one million baseline counts.

interlaboratory calibrations. Results are shown in Table7. Reproducibilities are 10.028 mnr/sec for peak posi-tions. 10.08 mm/sec for widths, +2.07o for areas ofindividual peaks, 10.026 mm/sec for isomer shift, and-+0.11 mm/sec for quadrupole splittings. Although thestatistical variance in the Mossbauer parameters of thedifferent aliquots is at least twice that of measurements onthe same sample (Table 8), their means are almost identi-cal, and the grunerite was deemed suitable for a standard.

I nt e rlaboratory c o mp qris on

Seven laboratories ran the two mineral standards whichwere circulated. Each lab had its own distinctive methodof sample preparation (Table 9); all were careful to weighout the appropriate amount of sample to be used. Runcharacteristics (Table l0) were fairly consistent through-out. As anticipated, each group had its own distinctivefitting procedure (Table 11).

Results of the Mcissbauer experiments are shown inTables 12 and 13. Comparison of variances between theMIT experiments and the corresponding values fromdifferent laboratories for standard "R" shows some inter-esting trends (see Table 8). For peak positions, widths,isomer shifts, and quadrupole splittings, there is onlyslightly more variance between labs than there is on the

Samplr Concentrat ion mq Fezcm2

I 135

@ o o d d o o - o +N N O d O d d O N €o o o o o o o o Q oo o o o o o o o o ao o o o o o o o o o

o o o o o o o o o oI

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@ o o o

@ o Q o d t so o + @ o oo o o o o oo o o o o o

d @ €o o o + H @ l o o 6

@ N 6 < 6 + O O D + l o o 66 4 6 6 O 6 6 6 6 6 1 O O 6

d n l o a d

H o o6 H O @ N N + O O @ l O O Od N O d O O O O O 0 l O O Qo 6 o F F @ @ o @ @ l o o @

N N N N N N N N N N I C O N

O F No o t s d o N N o N o l o o oqqeq eeqq qql qqq

d d l o o i

o o o6 i + O o N o O O O I e O Oo + o o o o o + + € l o o o

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Fig. 9. Plot of time versus x2 (a) and versus Misfit (b) forgrunerite runs where the sample concentration was held constantat7 mg Fe/cm2.

MIT apparatus alone. However, there is considerablyless variance in peak area throughout the MIT experi-ments, especially when the "Different Laboratory" dataset is compared against the most similar MIT data set, "7mg Fe/cm2 with Time Varying." This is probably becausethe MIT data are all fit with identical curve shapes. Totest this hypothesis, raw spectral data were collectedfrom the different labs. Spectra were entered by hand intothe MIT computer, to be processed and fit with the MITcurve-fitting program. The results are shown in Tables 8and 14; as predicted, variance in individual peak areas issomewhat reduced when all spectra are fit to the samecurve shape.

Discussion

Optimization of exp erimental t echnique

It is not surprising that this study found the optimalsample concentration to be 5-7 mg Fe/cmz. However, it isimportant to be reminded that even small deviations fromthat value can produce rather drastic increases in thecorresponding statistics of the eventual fit. Above theoptimal concentration, 12 increases (degrades) very

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Table 8. Standard deviations of Mrissbauer parameters* for standard "R"

fi37

q. s.2-3

Q. s,1-4

t { id th Area I .S . l .S .Peak 2 Peak 3 1-4 2-3

Posi t I onPeak I

Repeated Runs, Same Sanple, Same ibuntIdentical Run Conditions, Different Samples7ng Felcm wlth Time Varylng24 Hour Runs, Counts and Concentratlon Vafying

I l l i l l i on Counts , l ime and Concent ra t ion Vary ingDifferent LaboratorlesDiffercnt Laboratorles, Same Fitt ing Program

0.00740.01690.00770.0140

0.01520.04680.00630.0169

0.01200.024 I

0.25840.62470. 18381.0217

0.00530.01580.00470.0054

0.01310.00580.0050

0.0057 0.0090 0.009s0.0131 0.0598 0.03930.0047 0.0117 0.00870.0122 0.0165 0.0240

0.0140 0.0308 0.02850.005t 0.0225 0.01090.0100 0.0144 0.0126

0.8708l . 14590.9564

0.02260.0142

* t{ote that values for all the different paraneters cannot be directly compared, because standard deylatlon is in the ulrlts of the origlnalmeasurenent (m/sec for all but area, hfi ich is gtvE;-lE-/).

quickly; for example, at 30 mg Fe/cm2 X2 is 1.5 to 2 timeslarger than at7 mg Fe/cm2. The more sensitive parameterof Misfit is also greatly affected by sample concentration.

Similarly, duration of runs is a very critical parameter.Samples which were run for just one million counts seemto give Misfit values closest to zero; above that 12increases by at least l\Vo for every million counts.Shorter runs produce decaying Misfit values. These con-clusions may seem to contradict one of the commonassumptions in counting statistics: the idea that morecounts will produce better X2 values. Unfortunately thisassumption is not true in cases where electronics anddrive systems are involved; for Mcissbauer spectroscopy,more time means a chance for long term electronic drift(due to a combination of instability in the electronics andmechanical instability) to have a greater influence onruns. Use of a laser interferometer (e.g., Cosgrove andCollins, l97l or Otterloo et al., 1983) might partly offsetlong-term instabilities, and thus allow longer runs. How-ever, the addition of an interferometer to the drivemechanism monopolizes one half of the spectrometer,such that only one mineral spectrum (instead of the usualtwo) can be run at a time. Such a loss of productivity is

Table 9. Methods of sample preparation

Pel lets p.essed betreen alunlnm fol l , r l th voluoe adlustrble (3-5 [EFelcmz); s.nple diareter ippror lm.tely 1/2 inch.

At 0" rotatton, s i lp le in plast lc cmprcsi ion holder wlth 1.5 o dl i leters l n p l e h o l e ; s . n p l e d l l u t e d i n ^ 5 0 [ E o f c u b l c b o r o n n l t . l d e : 1 7 0 E ' R ' ,?0 rE 'A' . At 54.7o rotat lon, s i lp les dlspersed ln lucl te (78 69 "R*,110 i lg 'A" to 1000 mg lucl te) ln dlsks of 3.2 d diaretef.

Euehler tr lnsopt lc poder (200 ng) usedâs muntlng redluf i ; 18.6 n9 "R',2 6 . 7 n g ' 4 " , l n l e a d o r a l u n l n u n 1 . 3 m z s a n p l e h o l d e . .

Smples grcund in rgate rcrta. and nlred r l th sugar, munted in 2 d2cyl lndr lcr l plexlglass holders wlth qulnt l t les adjusted to concentrat lonsof 3 ng Felcrz.

S.6ples I l red r l th {arn vasel lne ln polyethylene "c!p" (r f l . t , c l rculardtsi of ^1" dianeter x 3/16" helght). i rnple denstt ! oi 0.16;g 57Felcrzf o r ' R " a n d " A ' .

SMples ground wlth sugaf and acetonc and Mnted ln 5 m thlckplextglass holders f i th l r d ' lameter holes for s i lp le. SmDle held inpl lce by clear cel lo tape. Concentrat lqs .djusted to 7-10 n9 Felqz.

Smple nixed yl th boron nl tr lde pdder, rcunted betxeen tro [Ular dlsks(avefage thlc lnels 0.12 m) and fDunted ln brass sanple holder. Area ofsanple ' 1.43 qz, thlckness of sanple (etcludlng ryl l r disks) , O.5O m;24.69 ng'R": 131.32 n9 8t l ; 30.rc | | |g 'A" . 124.33 rE 8l used.

probably not worth the increase in stability, except incases where major fluctuations are suspected. Therefore,it is generally necessary to strike a compromise betweenhaving a long enough run to accumulate sufficient countsto adequately define the spectrum, and having a shortenough run to avoid electronic drift. On the MIT equip-ment, runs which last I million counts seem to make thebest compromise. That corresponds to about six hoursexposure of a mineral to a 95 mCi source.

When this result was defined, it seemed logical to see ifothers had a similar problem with instability. WayneDollase ran our standard "R" for run times correspond-ing to 2, 4, and 6 million background counts on the UCLAspectrometer. He reported the following results (Dollase,pers. comm., March, 1983):

l. The weighted peak location precision calculatedfrom the least-squares fit is: 0.fi)12 mn/sec, 0.0010 and0.0008 for the 2, 4, and 6 million count spectra, respec-tively. However, the mean reproducibility of the fourpeaks on the three spectra is 0.013 mn/sec and thusisomer shifts and quadrupole splitting probable errors areapproximately -+0.02 mm/sec. This large difference be-tween precision and actual reproducibility is due to asystematic offset of random magnitude (0.01-.02) fromspectrum to spectrum caused by the nature of the elec-tronics and drive systems. Because of this poorer repro-ducibility, one could not expect to see more accuratepeak locations in higher count spectra.

2. Peak width and Lorentzian/Gaussian peak shapefractions show reproducibility of 0.01-0.02 mm/sec andlVo, respectively. Higher background-count spectra areexpected to show slightly broader peaks and slightlygreater Gaussian components due to short term drift butthis effect seems negligible in the case of these threespectra.

3. Area fractions have a mean reproducibility of 0.2%which is probably fortuitous as experience suggests thatprobable errors in area are about lVo for such spectra.Least-squares fitting errors are 0.1-0.2%.

4. The goodness offit indicators reflect the differencesin total background counts. The value of chi-squaredincreases with background count as would be expected

t .

I 138 DYAR: PRECISION AND REPRODUCIBILITY OF MOSSBAUER MEASUREMENTS

Table 10. Run characteristics*

Lab ltumber

AvePage Fun t ime, in hoursSource matri x

Source strength, in nciDistance f rom sample to source,

# channel s

10-16Rh

20in crn 20

1024

^100^9 -11**

512

4 8 4 8 4 4 8Rh Rh Pd Rh

20 30 15 1001 5 7 ? O l 0

to24 !024 256 512

8-23Pd

20-24Rh

35J

255 or 512

r Al l resul ts rcre cal ibrated wi thrt Distances from detector to source

nespect to nEtal l ic i ron.were given as 13.5-19 or .

due to the small systematic inadequacies of the calculatedmodel (as caused by spectrometer nonlinearity and drift,sample saturation, chemical inhomogeneities, etc.).Note, however, that MISFIT decreases to very lowvalues for high background count spectra demonstratingtheir increased quality.

Note that on the UCLA spectrometer, Misfit does notappear to get larger with longer run times. This suggeststhat the UCLA system has much less long term drift.However, two of their 7o Misfit values are an order ofmagnitude higher than the corresponding values observedin the MIT data (see Table l5). Because it yields consis-tently lower Misfit values, the MIT fitting program proba-bly gives better fits over a wide range of backgroundcounts, in spite of long term drift. This point serves tohighlight the uniqueness of each spectrometer set-up andfitting program and to emphasize that each apparatusprobably has its own criteria for optimization.

It is also necessary to consider what the optimal sampleconcentration might be for non-silicates. Results for apyrite and a ferberite (FeWOl) sample are shown inFigures l0 and I l. Sulfur-bearing samples appear to have

Table 11. Fitting procedures used*

l . l loSSFlT program, obtalned in 1974 frm Geophysical Laboratory,t lash' lngton, DC. Runs on PoP l l cmputer uslnq Lorentzian l ine shapes,

a lower optimum concentration around 2 mgFelcm2; thetungsten-bearing ferberite probably requires more samplefor experimental optimization.

Interlaboratory comparison

It is obvious from even a cursory inspection ofTable 8that the variance in M<issbauer parameters is somewhatgreater for the array of different laboratories than formeasurements made at a single lab. Given that thevariation does exist, it is important to consider threequestions: (l) Are the variations significant? (2) What arethe probable causes of this variation? (3) What can bedone to reduce such variation? The answers to thesequestions are of vital importance to both experimentersand users of Mcissbauer data.

The question of significance is fairly easily answered.The different results can be compared rigorously throughuse of common statistical tests. The T test, which is usedto test hypotheses about the equivalency oftwo samples,evaluates the likelihood of mean values falling within asample-based distribution. The F test determines equalityof variances based on the theoretical F distribution of allpossible pairs of sample variances in a random samplingof a normal population (Davis, 1973).

To perform these tests, two populations are needed.Rather than combining all the MIT measurements, one

Fig. 10. Plot of sample concentration versus Misfit for pyritespectra where time was held constant at twelve hours.

AiloSS progfan, or iginal ly frm Carnegie- l le l lon l , t iversi ty (P. Flynne t a l . ) , e x t e n s i v e l y n o d i f i e d f o r u s e b y s u r v e y e d i n s t l t u t l o n . R u n s mESItrTl or PDP-11/34A r l th 28K Mory, f l t t lng 1001 Lorentzian l lnes h a p e s .

I { o E S F I T p r o g r a m , o b t a i n e d f r m 8 , , J . E v a n s , A n n A r b o . , i n 1 9 7 8 , r c d i f i e dby Runge in 1978 and by ihgel in 1982. Runs on Telefunken TR 440c m p u t e r , f i t t i n g L o r e n t z i a n c u r v e s h a p e s .

NoRI{oS program (based on mSFlT, Argonne Nat ' lonal Laboratbry , i thsubrout ines rr i t ten in the Physics Departrent of the surveyedi n s t i t u t i o n ) , r r i t t e n i n 1 9 7 9 b y G . s h e n o y , B . D u n l a p , F . E . f a g n e r , a n dt l . Koch. Runs m CDC Cyber 175 uslng Lorentzlan l ine shapes.

[05FIT progran wrl t ten by the su.yey part ic lpant ln 1970. Runs o lBi l3033, using a Giussian-b.oadened Lorentzlan curve shape.

SToNE progran rr i t ten by A. J. Stone ln 1970, nodif ied for PDP-11/34cmputer by K. Parkin and users at th.e surveyed inst i tut ion. UsesL o r e o t z i a n l i n e s h . p e s .

DCPFIT progran w.i t ten ln 1975 by D, C. Price, Runs m t lnivac l l00/82c m p u t e r f i t t i n g p s e u d o - L o . e n t z i a n l i n e s h a p e s .

r Further infomation on the var lousa u t h o f ; t o p f e s e r v e c o n f i d e n t l a l i t y

f l t t i n g r c u t i n e s i s . v a i l a b l e f r m t h l saefeaenced paDefs are not cl ted here.

mg Fo /cm

I 139

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N @ O N 6 0 0 t s @H o o o @ o o + no 6 @ @ N N N N O

6

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o o o o o o o o o l o o o o

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o o o o o o o o o l o o o 6

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DYAR: PRECISION AND REPRODT]CIBILITY OF MOSSBAUER MEASUREMENTS

Table 14. Mdssbauer spectra fit with one program

Lab llo. Ismer Shi ft(m/sec)

Quadrupol eSpl I tt i ng(rn/sec)

1-4

^ Degrees ofx. Freedoml , t i s f i t

2-31-4

35.5737.0435.5432.06

3s.8735.3737.343t .57

Varlrnce 3.522?Standafdt)evlatlon 1.8768llean 35.8557

12.60 15. 1513. l0 16.7716.95 13.40t4.62 13.87

2.3296 0.9147

1.5263 0.9564t5.829 14. 1857

33 .75 1 .16133.60 1.15335.52 1. 16638.25 1.159

35.38 1.163u . t l 1 . 17832 .31 1 .15033 .94 1 .153

3.5892 0.0000

t.9207 0.006034.6786 1.1579

I2J

4

5* (O)5 ( 2 1 )67

515 499837 487

u06 499779 495

t072 243501 243528 509537 497

16.88 1.38015 .02 13 .3514.60 14.3415 .31 14 .39

1.0761.064r . s2t .072

1.0931.0931 .0711.066

0.0001

0.01001.0749

2.798?.1912.7982.803

?.7602.7302.7882.187

0.0002

0.01442.1901

l .5tt81 . 5 4 11 . 5 4 51 . 5 4 1

1 . 5 1 2l . 5 1 61.5471 . 5 3 3

0.0002

0.0126l .53 t i1

0.0000130.0006250.001060.00u I

0.002050.0006270.0001 1l0.000485

r Drta from lab 5 were orlglnally subm{tted wlth a 2U Gaussian l ine shape cmponent in peak shapes. The ilIT prcgram reflt the same datawlth both 0l and 211 Gaussian conponent. Statistics are cdnputed using only the of, data.

set of data, the 7 mg Fe/cm2 with time and concentrationvaxying data set, were used because those parametersmost closely approximate the conditions of the differentlabs. The T test, which deterrnines equality of means oftwo groups of samples, is defined as:

T :X r - X z

so (l/nr) + (ln)'

where X1 and X2 are the two sample means, nl and n2 arethe number of samples in each sample group, and so isdefined as the square root oft

s l=( n r - l ) s ? + ( n z - l ) s 3

n l + n 2 - 2

Ifthe calculated value of the T test exceeds the selectedvalue of 2.074 for a 2.5% level of significance with 22degrees of freedom (for data column l), then the testimplies that there is little evidence to suggest that themeans are equal.

Similarly, the F test is defined as

where the degrees of freedom eeual n1 -

numerator, and n2 - I for the denominator.

Table 15. Comparison of misfit values on different spectrometers

null hypothesis that the variances are equal will bedisproven when the values for the F test in column 2exceed the critical value of 3.37 for the 2.5% level ofsignificance (see Davis, 1973 or Bevington, 1969).

Results of the statistical evaluation are shown in Table16. Data columns one and two show results for the MITdata versus diferent laboratories' data, all fit with differ-ent programs. The results suggest that mean values forpeak position, isomer shift, and quadrupole splittings aresignificantly different between the two groups. Note thatisomer shift and peak position, which are dependent onfoil calibration and source corrections, show the mostsignificant variation in their mean values. Highest valuesfor variance between the two data sets occurs for areadata, as might be expected from use of diferent fittingprograms and the incorrect assumption made aboutequality of peak areas.

Data columns three and four show results for the sameMIT data compared with the different laboratories' data,all fit with the same program. Means of the two sets are

SamPle Concentration mg Felcm

Fig. ll. Plot of sample concentration versus 12 for ferberitespectra where time was held constant at twelve hours.

s?F = ; ,

si

I for theAgain, the R

x

8|clgroundCounts

UCLASpectrmter

r.ilTSpectrmeter

2 x 1 0 6

4 x 1 0 5

5 x 1 0 6

0.r08 (15)t

0 . r r 1 ( 12 ) l

0.043 (5) t

0.0170 (103)t

0,0601 (83)1

0.0576 (63)t

DYAR: PRECISION AND REPRODI]CIBILITY OF MOSSBAT]ER MEASUREMENTS

Table 16. Statistical tests for variance in different Mrissbauer Darameters

lr4l

Parameter

one Lab ( l l IT ) , same progran,vs. Different Labs, same program

T Test F Test

one Lab (l i l lT), same program,vs. oifferent Labs, same progran

T Test F Test

Peak Pos i t ion , Peak II ld th , Peak 2Area, Peak 3

Isomer Sh i f t , l -4Ismer Sh i f t , 2 -3Quadrupo le Sp l l t t ing ,Quadrupo le Sp l i t t lng ,

5 . 1 4 4 70.68721.0844

5.92354.76062.62322.9057

2.O74 (951 conf idence

3.37 (95 f con f idence

2.2t94L2.282664.5 183

1.23101 . 1 1 7 92.40111.0981

leve l )

leve l )

0 .847 2

5 .45003.86902.30882 . 3 3 8 3

T tes t Ho: !1 = u2

t 1gs1 H^ ; s2 = s2- l 2

1-42-3

27.0980

1.58724.61361 . 5 1 0 92. t I79

> 2 .101 (951 conf ldence leve l )

> 3 .73 (951 conf idence leve l )

T tes t h : u l = !2

F test tto; s2r= s2

f a i l s i f T >

f a i l s i f F >

f a i l s i f T

r a l t s l r I

different only for isomer shift data; variance is significant-ly different only for the area data and one of the isomershift values. These results suggest that use ofa consistentcurve-fitting program among all labs might improve re-producibility to a small degree, especially if the apparentdiscrepancy caused by foil calibrations and source cor-rections could be corrected. If such a universal fittingprogram were to be selected, a logical candidate would beMosspEc (and its many descendents), originally writtenby A. J. Stone at Cambridge and developed extensivelythere by both theoretical and physical chemists (seeStone et al. l97l or Stone et al., 1984). This program isundoubtedly the most widespread M<issbauer fitting pro-gram, due in part to its mention in Bancroft's (1973) book.However, such an improvement would probably not beworth the large amount of time and trouble that would benecessary to implement such a plan.

Next it is useful to discuss the possible causes forimprecision in these data, and to ascertain why theobserved variance for all the samples is as high as it is. Itis convenient to discuss each suspected cause of errorseparately:

Counting statistics are the underlying source of errorfor this type of measurement. However, a simple examplecan be used to show that this type of error is relativelysmall when compared to the overall peak areas that areused to determine Fe3*/Fe2* ratios (Whipple, 1973). In atypical spectrum with one million baseline counts, whereone standard deviation is 1000 and an average peak heightmight be 20,000 counts (2Vo absorption) one standarddeviation is 5Vo ofthe average peak height. Since a peak'sarea may cover 20-30 channels, the area variation ofthepeak due to statistics alone is very small. Furthermore, ithas been shown that errors due to having too fewbackground counts can be minimizedby thorough testingof the individual spectrometer.

Long term drift is also a universal problem in all ofthelabs tested. It may be responsible for a substantial part ofthe error in these measurements. However, it can also be

minimized by individual testing and/or laser interferome-try.

Inhomogeneity in the standards was tested; variance inthese measurements was found to be about the same orworse than the variance between labs. Inhomogeneitymay contribute to the errors in these measurements, but itis difficult to separate its effects from the other sources oferror.

Sample concentration might cause error; as was seen inthe MIT measurements, many of the fit statistics andparameters can change with concentration. However,sample concentration remained essentially constant in theinterlaboratory experiments, so that factor cannot beresponsible for causing imprecision in those measure-ments.

Electronic relaxation may cause differences in peakamplitudes, particularly in ferric iron (Goldanskii andMakarov, 1968). However, there was no evidence ofamplitude diferences in the ferric peaks of the garnetstandard spectrum, showing a lack of relaxation efects.

Peak overlap has been shown by Dollase (1975) to be asource of large uncertainty in M<issbauer measurementswhere peak separation is less than 0.6 times the peakwidth at half peak height. However, this is not the casefor either the grunerite or the garnet standard, both ofwhich have large separations between peaks. In bothmineral standards, a slight overlap between the two lowervelocity peaks may cause the (2) to rob area from thelowest velocity peak (l), causing the observed inequal-ities in the areas of the inside doublets (peak 2 and 3).This problem could be corrected by use of area data froma more fully constrained fit, or by using only the highervelocity peaks of the doublets for area ratios. The latterapproach is favored by the data given here, which gener-ally show less variance in peak position for the two highvelocity peaks.

Real area inequalities in unconstrained fits can affectarea data and resultant Fe3*/Fe2* ratios. Whipple (1973)observed that unequal peak areas may be due to the

t l42

spectrometer drive moving too rapidly through one regionof the spectrum, causing the apparent width of any peaksin that region to decrease. In such cases, it may beimportant to make adjustments to the drive spring, or touse the other half of a doublet for Fe3*/Fe2* calculations.However, in this study all but one of the labs which didunconstrained fits on sample "R" found the lower veloci-ty peak (2) to be 2.30-3.55% larger than its higher velocitymate. Since these results are based on several differentspectrometers, drive maladjustment was probably not acause for this error.

Lack of width constraints has been suggested by Haw-thorne (1983) as a possible source of error. However,since there is so little overlapping of peaks it seemsunlikely that the lack of width constraints could becausing any of the peaks to borrow width from anyothers.

Preferred orientation in the samples can be a majorcause of peak asymmetry and inequality, particularlywith platy minerals. However, all the surveyed labs tookthe precaution of mixing the samples with some sort offiller/coating to remove preferred orientation, so this isprobably not a major source of error either.

Errors in the model, especially how many peaks can befit, could be suspected as a cause of error, especiallysince the grunerite spectrum contains contributions fromFe2* infour sites, leading to the potential of four quadru-pole split doublets. However, Hawthorne (1981), Ban-croft et al. (1967), Hafner and Ghose (1971), and Ghoseand Weidner (1972\ have all shown that three of thosefour doublets overlap almost perfectly in the spectra,indicating that fitting a two doublet spectrum is a justifi-able model for grunerite. The garnet standard is known tobe a mixture of two minerals, each with only one Fe-bearing site; modelling that spectrum with two doublets isprobably not a source of error either.

Fe foil calibration values are a fundamental source oferror because a spot check revealed that all labs do notuse the same values for standard peak position in the ironcalibration spectrum. The values listed above as suppliedby Dr. Stevens should be universally adopted. Lack ofconcensus on which values are preferable may contributeto error in Mrissbauer measurements, if a given labdeviates significantly from the values that others areusing.

Curve-fitting or deconvolution programs are anotherlikely cause of error in these measurements. As discussedabove, there is a small reduction in variance when alllabs' data are fit with the same program. However, use ofa universal curve-fitting program is logistically unfeasi-ble.

This brings us to the third big question for discussion:how can interlaboratory diferences best be reconciled?Since it would surely be a hopeless task to try to agree ona single method for curve-fitting/deconvolution, it seemswise to consider other alternatives.

In neutron activation studies it is common practice to


report results of repeated runs on the same sample, andresults on standard rocks, in each paper. Mass spectro-scopists correct all their values to accepted standards.These standardization procedures are impractical forMcissbauer spectroscopists; the errors in Mcissbauer mea-surements are more complicated than simply adding acertain number to correct for isomer shift or quadrupolesplitting. Nor is it really practical, given the time andenergy involved, to redo repeated runs on standards andon the samples at hand on a consistent basis. However'on an occasional basis it would be helpful to see publishedcomparisons of the individual research lab's results onthe standards compared to the consensus' "mean val-ues. " It would also be helpful if each lab could publish itsown record for repeated measurements on the samemineral standards, if only infrequently. Such steps wouldprobably go a long way toward reinforcing the credibilityand universal acceptance of the Mdssbauer technique asan analytical tool.

Conclusions

From the outset, the goal of this work was to reevaluatethe analytical precision of the technique of Mossbauerspectroscopy. The results of this prolonged study high-light three major conclusions:

l. The standard deviation of measurements on the MITapparatus is better than 0.016 mm/sec for isomer shift,0.060 mm/sec or better for quadrupole splitting data, and1.02%o on area data. These values are for measurementson different aliquots of the same mineral' Repeatedmeasurements on the same sample have considerablybetter statistics.

2. Optimal precision can be achieved only throughcareful measurements involving strict control and thor-ough understanding of the effects of sample concentra-tion, run duration, and baseline counting statistics'

3. The precision of interlaboratory measurements onthe same standards is slightly better than that observedfor only one lab (0.006 mm/sec for LS., 0.023 mm/sec for

Q.S.; l.44Vo on individual peak area data), since only"ideal" run conditions were employed. Mean values forpeak position and isomer shift vary significantly betweenlabs, and the highest statistical variance is observed inindividual peak area data.

These conclusions then yield some answers to thequestions posed earlier in the introduction: samples withsmall Fe concentrations can be run but the statistics maybe affected in the ways predicted in Figures 7 and 8; it ispossible (and in fact, often preferable) to minimize runtimes and still have good results; and it is possible tocompare results between labs, provided a common miner-al standard has also been analyzed.

Acknowledgments

I am deeply indebted to the participants in this survey, whounselfishly contributed their time, data, and comments to thisproject: Wayne A. Dollase, Roger G. Burns, Frank E. Huggins,

DYAR: PRECISION AND REPRODUCIBILITY oF M}SSBAUER MEAST]REMENTS I 143

gamma-resonance spectroscopy. In V. L Goldanskii and R. H.Herber, Eds., Chemical Applications of Mdssbauer Spectros-copy, p. 96-98. Academic Press, New York.

Graham, M. J., Mitchell, D. F., and Phillips, J. R. (1977) AM<issbauer spectrometer system with data processing capabili-ty. Nuclear Instruments and Methods. l4l. 131-135.

Greenwood, N. N. (1970) Mdssbauer spectroscopy. In H. Eyr-ing, D. Henderson, and W. Jost, Eds., Physical Chemistry: AnAdvanced Treatise, p. 633-:707. Academic Press, New York.

Greenwood, N. N. and Gibb, T. C. (1971) The Mrissbauer efiect.In N. N. Greenwood and T. C. Gibb, Eds., Mdssbauer Spec-troscopy, p. l-45. Chapman and Hall, Ltd., London.

Hafemeister, D. W. and Shera, E. B. (1966) Calculation ofMrissbauer absorption areas for thick absorbers. NuclearInstruments and Methods. 41. 133-134.

Hafner, S. S. and Ghose, S. (1971) Iron and magnesium distribu-tion in cummingtonites (Fe,Mg)7SisO2z(OH)r. Zeitschrift fiirKristallographie, 133, 301-326.

Hawthorne, F. C. (l98l) Amphibole spectroscopy. In D. R.Veblen, Ed., Amphiboles and Other Hydrous Pyriboles-Mineralogy, Vol. 9A,, Reviews in Mineralogy, p. 103-139.Mineralogical Society of America, Washington, D. C.

Hawthorne, F. C. (1983) Quantitative characterization of site-occupanices in minerals. American Mineralogist, 68, 287 -306.

Herber, R. H. (1971) On the current status of Mossbauerspectroscopy standard. In I. J. Gruverman, Ed., McissbauerEtrect Methodology 6, p. 3-15. Plenum Press, New York.

Klein, C. (1964) Cummingtonite-grunerite series: a chemical,optical, and X-ray study. American Mineralogist, 49,963-982.

Klein, C. and Waldbaum, D. R. (1967) X-ny crystallographicproperties of the cummingtonite-grunerite series. Journal ofGeology, 75, 379-392.

Law, A. D. (1973) Critical evaluation of 'statistical best fits' toMossbauer spectra. American Mineralogist, 58, 128-t31.

LeFever, H. Th. (1979) A data-acquisition and processing sys-tem for Mdssbauer spectroscopy. Nuclear Instruments andMethods, 166,133-137.

Lin, T. and Preston, R. S. (1974) Comparison of techniques forfolding and unfolding Mossbauer spectra for data analysis. InI. J. Gruverman, C. W. Seidel, and D. K. Dieterly, Eds.,Mossbauer Effect Methodology 9, p.205-223. Plenum Press,New York.

Marfunin, A. S. (1979) Spectroscopy, Luminescence, and Radia-tion Centers in Minerals. Springer, New York.

Minai, Y., and Tominaga, T. (1982) Mrissbauer analysis ofiron(Il) and iron(III) in geological reference materials. Interna-tional Journal ofApplied Radiation and Isotopes, 33, 513-515.

Mitrofanov, K. P., Gor'kov, V. P. and Plotnikova. M. V. (1977)The parameters of M<issbauer spectra taken by means ofresonance detectors. Nuclear Instruments and Methods. 144.263-269.

Morup, S. and Both, E. (1975) Interpretation of Mcissbauerspectra with broadened lines. Nuclear Instruments and Meth-ods. 124. 445-448.

Mrissbauer, R. L. (1958) Kernresonanzfluoreszenz von gamma-strahlung in lrrer. Zeitschrift Fiir Physik, l5l, 124-143.

Mossbauer Effect Data Center (1984a) Mineral: Data Handbook,Asheville, NC, in press.

M6ssbauer Effect Data Center (1984b) Mineral: ReferencesHandbook, Asheville, NC, in press.

National Research Council (1971) Atomic and Molecular proper-ties, Ad Hoc Panel on Mdssbauer Data, "Nomenclature and

Friedrich A. Seifert, Enver Murad, Georg Amthauer, CatherineA. McCammon, and S. J. Campbell. I thank Cornelis Klein fordonation of the grunerite standard, and the Harvard Universityand M.I.T. Museums for the gamets. I also thank Karen Kimballfor the microprobe analyses, and Eugene Jarosewich, JosephNelen, and Daphne Ross of the Department of Mineral Sciences,Smithsonian Institution, for their wet chemical analyses. Adviceand support were kindly provided by Earle Whipple, DianeDyar, Jim Besancon, Harold Andrews, Anne Vaughan, RogerBurns, Virginia Burns, Roger Buck, Carol Handwerker, andJohn Blendell. Suggestions made by George Rossman and ananonymous reviewer contributed greatly to this manuscript.Special thanks goes to Scott Philtips for statistical advice andmathematical wizardry. I gratefully acknowledge the contribu_tion of the Wellesley College Computer Facility for many, manyhours of computer time while I was a student there. Finally, Ithank Chevron Oil Field Research Company, NSF (grant No.EARE0-16163), and NASA (grant No. NSG-7604) for supportover various periods of this long term study, and FrancisDoughty for yet another awesome typingjob.

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Manuscript received, December I, 1983 ;

accepted for publication, July 16, 1984.

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Precision and interlaboratory reproducibility of ...MBr-rNoe, Densy DyA,n Department of Earth, Atmospheric, qnd Planetary Sciences Massachusetts Institute of Technology Cambridge,