PHASE ANALYSIS IN METALS AND ALLOYS BY MÖSSBAUER SPECTROSCOPY

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PHASE ANALYSIS IN METALS AND ALLOYS BY MÖSSBAUER SPECTROSCOPY

S. Nasu, U. Gonser, A. Bläsius, F. Fujita

To cite this version:

S. Nasu, U. Gonser, A. Bläsius, F. Fujita. PHASE ANALYSIS IN METALS AND ALLOYS BY MÖSSBAUER SPECTROSCOPY. Journal de Physique Colloques, 1979, 40 (C2), pp.C2-619-C2-620.

�10.1051/jphyscol:19792215�. �jpa-00218595�

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JOURNAL DE PHYSlQUE Colloque C2, supplt!ment au n o 3, Tome 40, mars 1979, page C2-619

PHASE A N A L Y S I S I N METALS AND ALLOYS BY MOSSBAUER SPECTROSCOTY

S. Nasu, U. Gonser, A. Blisius and F.E. Fujita*

Fachbereich Angewandte Physik, U n i v e r s i t i f t d e s Saartandes, 6600 Saarbriicken, Cemnmzy.

* ~ a c u ~ t ~ of Engineering Science, Osaka U n i v e r s i t y , Osaka, Japan

Rlsu&.- Des limites de solubilitl ont lt6 calculles pour les trSs petites concentrations par une m6thode numlrique de simulation fond6e sur les int6grales de transmission. A partir des r6sultats obtenus pour la solubilit6 du fer dans le titane et dans l'aluminium des paramstres thermodynami- ques ont ltl calcul6s.

Abstract.- A numerical simulation method using transmission integrals has been applied in the de- termination of phase boundaries in extremly small concentration ranges. From experimental results of Ti-dilute-Fe and Al-dilute-Fe alloys the solid solubilities and thermodynamical parameters were deduced.

Precise information on phase diagrams is im- portant in physical metallurgy. The analysis of su- perposed spectra makes it possible to obtain the distribution of resonance atoms among various phases provided the phases are distinguishable by at least one of the hyperfine parameters.

; Figure 1 shows a typical " ~ e transmission spectrum at room temperature obtained from an aluminium foil containing about 190 ppm " ~ e . The rela- tively large single-line component represents "Fe dissolved into the aluminium matrix (a-phase) while the other three lines are due to the intermetallic compound A1l3Fek (usually called 0-phase, in this paper called 6-phase for convenience) / I / .

-1 0 1

VELOCITY IN MMIS

Fig. I : Typical " ~ e assbauer spectrum obtained from a dilute alloy of Fe in Al. Dotted lines are results from least-square fit using the sum of Lo- rentz functions. Velocity scale is relative to a-Fe at room temperature.

Using the lever relationship as suggested previously /2,3/, the concentration of the a-phase C, is given by

C, = Co

(CB

-

^{Co) n6/na}⁺^CB^'

where C is the original composition of the specimen, C is the Fe concentration in the 6-phase and n In

6 6 a

the ratio of the number of 5 7 ~ e atoms in the phases.

This equation is valid not only for phases in equilibrium but also for any kind of distribution of resonance atoms. In certain cases, such as the deter- mination of solid solubilities in metals in extremely small concentration ranges, this method can be applied with high accuracy.

For ~gssbauer transmission spectra, under the assumptions of (I) absence of polarization, (2) ne- gligible self-absorption in the source and (3) Lo- rentzian line shape for source and absorber, the velocity dependent counting rate p(v) is given by

with fan,uo

(ra21b)

fg"*ao(

rg2 1 ' )

=

&

( E - E ~ ) ~ + ra2/,, + ( E - E ~ ) ~ + rg2/,,

Here N represents the Mgssbauer radiation and

Nb

the back-ground. fa and f6 are the appropriate Gssbauer fractions. Quite common in this type of analysis is the use of the thin-absorber approxima- tion or of the Bessel's function expression for non- overlapping lines. For a well overlapped spectrum like that of figure 1, both of these approximations lead to errors, and so we have resorted to a compu- ter simulation method based on equation (2). Using proper values for uo, n + n f

If

,r ,r ,r

a 6'6 a s a ~ ' ~ o and

Nb

and a set of assumed values for n In

B

a* we calculate a set of artificial transmission spectra.

wefit each of these spectra with ordinary Lorentz functions and use the results to calculate the area ratio A /A of these Lorentzian lines for each value

B a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792215

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C2-620 ^JOURNAL^DE^PHYSIQUE of nB/na. Next we fit the actual experimental spec-

trum with a similar set of Lorentz functions and calculate the ratio of A /A which we then compare

0 3

with the simulation results to obtain the correct value of nB/na

.

Utilizing this method and equation 2) we determined the solid solubility of Fe in tita- nium and in aluminium. Similar work in both alloy systems was performed previously by ~Zssbauer spectroscopy /2,3/. Figures 2 and 3 show the equilibrium phase boundaries found for the two systems, and also shown are the same data plotted in a form suitable for determining the changes in excess thermodynamical quantities.

-

HANSEN .RS8

---

~ h / k - 8 3 0 0 K AS/ k- 2 5 RAUB et a1 1967

I I I I

10 1 to" 1 o - ~

Fe CONCENTRATION ( a t %I

bS4/k- 0 LL HULTGREN et al 1963 A H ~ : ~ - ~ o ~ K

.. , 1

-

C ^-10

0 9 1 0 11 1 2

1 0 0 0 I T I K - ' 1

Fig. 2 : Phase boundary and the excess thermodynamical quantities for the T-Fe alloy system. White circles are results from the present investigation and black dots are results from reference /5/.

In each case, the slope of the straight line is the relative excess enthalpy change Ah/k, and the value of the y-intercept at 1/T = 0 is the relative excess entropy change, AS/k. The values obtained for the Ti-Fe system were Ah/k = 8300 K and ASlk = 2.5,

a6 a 0

using AH /k= 508 K and AS /k = 0.44 for pure Ti /4/. For the A1-Fe alloy system, the values of Ah/k and AS/k were determined as 8400 K and 0.9, respec-

- Ah/k- EL00 K AS /k- 0 9 EDGAR. 19L9

'

⁰⁰³I ⁰⁰²^I ⁰⁰¹^I

^'I

⁰ Fe CONCENTRATION (at %I

Fig. 3 : Phase boundary and the excess thermodynamical quantities for the A1-Fe alloy system. White circles are results from present investigation and black dots are from reference /6/.

Acknowledgements.- This work was supported by the DFG. Discussions with Pr. R.S. Preston are gratefully acknowledged.

References

/I/ Nasu, S., Gonser, U., Proc. 5th Int. Conf.

Gssbauer Spectroscopy, Bratislava (1973) 311.

/2/ Nishio, M., Nasu, S., Murakami, Y., J. Japan Inst. Metals

2

(1970) 1173.

/3/ Blssius, A., Gonser,U., J. Physique Colloq.

2

(1976) C6-397.

141 Hultgren, R., Orr, R.L., Anderson, P.D., Kelley, K.K., "Selected values of thermodynamic proper- ties of metals and alloys", (J. Wiley, New Yor),l 1963, p. 287.

/5/ Raub, E., Raub, Ch. J., Rsschel, E., Compton, V.B., Geballe, T.H., Matthias, B.T., J. Less- Common Metals

12

(1967) 36.

/6/ Edgar, J.K., Trans. AIME

180

(1949) 225.

tively. Very large relative enthalpy changes agree with very small solid solubilities in these alloy systems.