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PRECISION PHASE ANALYSIS
A. Bläsius, U. Gonser
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, suppl&ment au no 12, Tome 37, Dtkembre 1976, page C6-397
PRECISION PHASE ANALYSIS
A. BLASIUS and U. GONSERUniversitat des Saarlandes, Fachbereich Angewandte Physik D-6600 Saarbriicken, Germany
RBsumB. - La haute prkcision dans la determination des limites dans des diagrammes de phase obtenus h l'aide de l'effet Mossbauer sera demontree dans le cas de la solubilite du Fe dans le Ti
a une tempkature se situant entre 585 "C et 810 OC.
Abstract.
-
The high precision in the determination of boundaries in phase diagrams obtainableby Mossbauer spectroscopy will be demonstrated for the case of the solubility of Fe in Ti in the temperature range of 585-810 "C.
In the phase analysis of a multi-phase alloy by this spectroscopy it is required that the phases containing resonance atoms can be distinguished by the difference of at least one Mossbauer parameter (monopole, dipole, quadrupole interaction). The solubility of the resonance atoms in the various phases in an alloy system will determine the distribution. This distri- bution has to be considered in the analysis in which one correlates the fraction of a spectral component with the fraction of a particular phase applying the lever relationship.
Let us consider the binary system AB in which one component, for instance A, contains a certain abun- dance of a resonance isotope. An alloy with an original composition Co decomposes at temperature T I in the two phases a and
P
with atomic concentrations Ca and Cp as shown in figure 1. The number of primitive cells Ma and Mg - each primitive cell contains oneThe constitution diagram indicating the phases Ax By
atom - is given by the well-known lever relation- ship [2].
Similarly, one may apply the lever relationship at temperature T,. The number of primitive cells (Me and M p ) multiplied by the respective solubility Ca and Cp in the a and phase is proportional to the corresponding spectral intensity I, and Ip in the thin absorber approximation and the assumption is made that the effective Debye-Waller factor is isotropic and the same for both phases
W T1
5
+ 4 lr w a w I I- 2existing at various temperatures can be regarded as a guideline in physical metallurgy. The termphases is not restricted to crystallographic phases ; order-disorder phases' and magnetic phases should also be included.
1,
Thus, the determination and knowledge of phase dia- grams, particularly the simple binary systems, are of great significance in this field. Frequently, Mossbauer spectroscopy has been used in the analysis of phases. The method is usually considered as relatively coarse, allowing determinations with an accuracy in the order of a few percent. However, there are cases, particularly in physical metallurgy, where the accuracy can be increased by several orders of magnitude and a, phase A
=P to C t B
analysis is possible with a precision of
-
0.001' at.%.
AX By al OL2This will be demonstrated through the quantitative C O N C E N T R A T I O N IN A T %
determination of the solubility of Fe in Ti. Comparable FIG. 1. - Schematic phase diagram demonstrating the lever accuracy has been obtained for the solubility of rslationship. Symbols see text.
Fe in A1 [I].
I
P a * P - - - t - - - - - - - - L - - - . - - _ - - L L L L L L - ? I I I, 1 , I I IC6L398
Thus,
The ratio I,/Ia is measured by Mossbauer spectroscopy. If Cg is not known from the phase diagram one catl obtain it by two measurements with different originaI concentrations Co (1) and Co (2) and using eq. (3)' again. If C, is very small, that is C, % C,, one can still
Fe T I
A t o m i c p e r c e n t T I
FIG. 2.
-
Fe-Ti phase diagram from ref. [3].- 1 0 +1
V E L O C I T Y IN M M l S
FIG. 3. -Room temperature Mossbauer spectra of Ti-Fe
alloys annealed at 585 "C. Zero velocity corresponds to the
isomer shift of a-Fe.
obtain an intensity ratio of the two spectral compo- nents of approximately the same magnitude by choos- ing a Co close to the a-phase boundary. In this case the number of primitive cells of a might be greater than by many orders of magnitude (Ma $ MB), however, the absolute amount of resonance atoms is rather evenly distributed between the two phases. Under this condition this method is nearly independent of the effective (resonance) thickness because both phases will influence the resonance absorption in a similar fashion. The phase diagram of Ti-Fe [3] is shown in figure 2. The various phases have been analysed by Mossbauer spectroscopy 14, 51. Of interest here is the Ti-rich a-phase on the right side. According to Hansen- Anderko the solubility of Fe in hexagonal Ti is smaller than 0.2 at
%.
This a-phase is for concentra- tions > 0.2 at%
Fe in equilibrium with the ,!?-phase above 580 OC and below the eutectic line with the intermetallic compound FeTi. Titanium of highest purity containing 0.29, 0.20 and 0.08 at%
Fe5'Solid solubility limits of Fe in Ti at various temperatures
Annealing Specimen com-
temperature (OC) position at( %)
- - 0.29 585 0.20 0.08 0.29 650 0.20 0.08 0.29 700 0.20 0.08 0.29 810 0.20 0.08 Value of 1~11, - 6.238 4.250 1.033 5.071 3.299 0.981 2.849 2.643 0 2.866 1.863 0 Solubility limit of Fe in Ti (at
z)
- 0.041 f 0.006 0.039 2 0.003 0.040 f 0.004 0.049 f 0.007 0.047 f 0.008 0.041 & 0.004 0.077 f 0.006 0.056 f 0.004 A t o m ~ c p e r c e n t I r o nFIG. 4. - a-phase boundary of Ti-rich Fe alloys. and
dashed line from ref. [6]. Our results by Mossbauer analysis
PRECISION PHASE ANALYSIS C6-399
(Fe enriched) were annealed at 585,650,700 and 810 OC for about one week and subsequently quenched. Addi- tional annealing of one week produces no changes in the spectra. Mossbauer spectra from the 585 OC anneal run are shown in figure 3. The two phases (a and P) can be identified by the characteristic hyperfine pattern : the a-phase exhibits a single line while the P-phase shows a quadrupole splitting [4, 51. The relative line intensities of the a and the /3 phases reflect sensitively, the distribution of the small absolute amount of iron atoms in the two phases. In table I
the temperature dependent intensity ratios and the boundary of the a-phase, C,, are given. The C, values obtained at one temperature from a set of original concentrations - C, = 0.29, 0.20 and 0.08 - should
be the same and might be considered as a check of this method of analysis. The precision is reflected in the evaluation of the error in C, which is smaller than 811 000 at
% at all temperatures, as shown in the last
column of table I. From these data the boundary of the a-phase in the Ti-Fe system can be drawn as shown in figure 4. The magnitude of the solubility of Fe in @-Ti is in agreement with measurements by Raub et al. [6], represented by the dashed line, but the temperature dependence of the solubility disagrees.Acknowledgements. - The support by the Deutsche
Forschungsgemeinschaft and the discussions with Dr. F. E. Fujita and Dr. M. Ron are gratefully acknowledged.
References
[I] NISHIO, M., NASU, S., MURAKAMI, Y., N@pon-Kinzoku- [4] RUPP, G., 2. Phys. 230 (1970) 265.
Gakkai-shi 34 (1970) 1173 (in Japanese).
[5] STUPEL, M. M., RON, M., WEISS, B. Z., J. Physique Colloq. 35
[2] HAASEN, P., Physikalische Metallkunde (Springer-Verlag)
1974. (1974) C 6-483.
[3] HANSEN, M., ANDERKO, K., Constitution of Binary Alloys 161 RAUB, E., RAUB, Ch. J., ROSCHEL, E., J. Less-Common Metals
