Pib Para Ciencia Y Tecnlogia

A methodfor measurement the Debye-Walier factor f of
M. Capaccioli “, L. Cianchi b.*, F. Del Giallo b, P Moretti b, E Pieralli b, G. Spina *
Rcccivcd 6 January 1995: revised form tueiti
24 March 1995

Abstract An extended discussion is presented of the absolute absorption area method ( AAAM) for measuring the Debye-Wailer factor / of Mbssbauer isotopes, the line widths of which are muchgreater than that of “Fe. The problems arising from the determination of the absorption area and of the baseline am thoroughly examined by means of a theotelical analysis of the shape of the absorption spectrum. The “‘ELI in EBCO is used to illustrate the pmposed method.

1. lntroducthm The accurate measurement of the Bebye-W3)ler f3ctor f &ssbaucr spectra is relevant for the absolute mean square:!isplacement evaluation of the resonant nuclei. We shall descri t 2 a method for single Lorentzian Mtissbauer line compounds based on the absolute absorption area method ( AAAM ). Compared to the relative area method. no hy por?ests IS RquilBd regarding the Iattic;: dynam;cs. For an exhaustive review o! ihe various published melhods for evaluating f, we refer to Kolk [ I 1. In any case, for theAAAM. the ama values of the absotption spectra must be measured. O’Connor [ 231 points out that the effnr in the ama comes mainly from the eva!uation of the baseline. In order to m&me the related error, for iron, he uses a set of measurmnents taken for several “0~ values. The total counts vemus u- are measured, reported as a function of I/uand linearly fitted. The zero intercept and the slope of thefitted tine make it possible to evaluate the ama and the baseline. The drawback is that u- N 300/;, must be used: for iron, this means ulu = 30 mm/s. Therefore, the implementing of O’Connor’s method can be difficult or impossible for isotopes having line widths greater than that of -Fe. For example, the natural tine width f. of ‘s’Eu is about 0.67 mm/s. so that 3OOr. 5 200 mm/s. The use of suchvelocities creates experimental problems, particularly in the case of low-temperature measurmnents. in which the soume movement may be limited by additional mechanical constmints. Neverheless, a simple fitting of the spectrum cannot give correct baseline and area values without knowledge of the spectrum wing trend. We intend to show tha& even in the
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presence of strong non-linearabsorption,the spectrum wings (i.e. the pottion of spectrum at a distance of mom than gfn horn the resonance, with g of the order of several units) can be considered, with low error, as Lorentzian lines having a 2fr, width. This then ahows a determination of the spectrum area using a fitting procedure.

2. Lhe

sbapc theory

Let us consider a simple transmission M6ssbauer spectrum and call 6 therelative I.S.. f the half-height line width, N(u) the counting rate corresponding to velocity U. and N(m) the rate for souse and absorber completely out of rescnmnce. Indicating with Na the counting rate due to all noise sources, function E(U). which represents the shape of rhe absorption spechum, takes the form: E(U) _ N(m) N(w) -N(u) - Na .

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014-583X195/3tRSO@1995EtaicrsfiaressDI0l68.S83X(95)00500-5

B.V. Ailti@bnxved

filling EC = &a/c tk Doppler shift due to the velocity I’ of a sotme emitting 7~ rays of energy f%. F can be written as:

x {I -e+hS(E-&J-a)]}

dE.

(2)

where 1. = IY,CT,.& is the absottxer thickness, n. the number of resonant nuclei per unit area, and ~a the maximum mscsonant cross-section. As a consequence of small untesolved hyperlir.e intenctions, theabsorber and source line widths f, and r, are both greater than the natural one f.. The functions S(EZ&r,) and L(EEs - &. rS),centered at G and 15 rrspertively; represent the energy abcnrption cross-section dependence and the normalized source cmission spectrum. Integrating Eq. (2) versus u (in units f.). we obtain the area A of the line that is independent of the source charactcristks. except...