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Deformation induced structural effects in cerium
L. Jerome, G. Mohanty
To cite this version:
L. Jerome, G. Mohanty. Deformation induced structural effects in cerium. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-381-C5-382. �10.1051/jphyscol:19795137�. �jpa-00218923�
JOURNAL DE PHYSIQUE Collogue C 5 , supplement au n° 5, Tome 40, Mai 1979, page C5-381
Deformation induced structural effects in cerium (*)
L. E. Jerome (**) and G. P. Mohanty
University of North Carolina, Charlotte, NC 28223, U.S.A.
Résumé. — Nous avons étudié la substructure et la nature des fautes dans des échantillons de cérium y travaillé à froid, par des méthodes de diffraction de rayons X. Nos résultats indiquent un élargissement anisotrope et une asymétrie des raies de diffraction et seulement un très faible déplacement de leur position, ceci dans le cas de limailles travaillées à froid. Ces résultats peuvent être expliqués en considérant des proportions équivalentes de fautes intrinsèques et extrinsèques ainsi qu'une proportion négligeable de fautes de maclage. Cette interprétation est en accord avec les énergies relatives de ces fautes et avec la cinétique de leur formation.
Abstract. — Cold worked substructure and nature of faulting in y-cerium has been studied using X-ray diffraction methods. The results show anisotropic line broadening and peak asymmetry but only minor peak shifts in cold worked filings. The results can be explained in terms of roughly equal concentrations of extrinsic and intrinsic faults and negligible twin faulting. This interpretation is in accord with the expected relative energies of these faults and kinetics of their formation.
1. Introduction. — Phase transformations and faulting modes in y-cerium (fee form) have been the subjects of a number of X-ray investigations previously. Diffraction peak shift studies of faulting in Ce, however, yield conflicting results because of a number of complicating factors including the high reactivity of this metal, residual stress, texture and recovery effects and possibly also because peak shift effects are small for this metal [1-4]. To overcome some of these difficulties, in the present study, peak shifts as well as broadening and asymmetric effects have been examined using the Fourier method of Stokes [5] and Warren and Averbach [6]. Further, steps have been taken to minimize the extraneous effects referred to above. Three kinds of faults [7]
— intrinsic, extrinsic and twin types — common to fee metals are considered in this work. These faults and their densities, using notations introduced by Warren [8], will be represented by a', a" and /?, respec- tively.
2. Experimental. — A cold worked powder sample was prepared by filing solid y-Ce (99.5 % purity) and separating 200 mesh powder inside a dry box under argon. The screened sample was immediately transferred to an X-ray diffractometer equipped with a vacuum sample chamber. Diffraction measurements were performed under a dynamic vacuum using CuKoe radiation and included all fee (y) powder peaks from (111) through (400).
(*) Part of this work was performed while the authors were associated with the Florida State University.
(**) Present address : 10295 Menhart Lane, Cupertino, CA 95014.
3. Results and discussion. — The peak position results are listed in table I expressed in the customary way as the net shift 8{A 2 6) of adjacent peak pairs in cold worked and annealed powder patterns [6].
(Annealed peak positions were established on the basis of undeformed Ce and Th patterns.) The shifts are very small and their signs are irregular, that is, they do not completely correspond to the predicted shifts for any one of the faults [8, 9]. These measure- ments, repeated on another sample, also yielded similar results. We conclude that 8(A 2 6) for our samples are well within the error limits of the measure- ments. Peak shifts in fee metals are caused by both a' and a" [8, 9]. For any powder reflection, the shifts are of equal magnitude but are in opposite directions, so that peak shift analysis can yield only the net density (a' — a"). The data on Ce indicates :
(a' - a") « 0 .
This result may mean that Ce has a high stacking faulting energy (SFE, y) or that a' « a" which cancels out the peak shift effect. An examination of broaden- ing and symmetry effects suggests later to be the likely possibility. Analysis of peak broadening based on the Stokes [5] corrected cosine coefficients by the Table I. — Net peak shifts 8(A 2 6) for cold worked Ce.
8(A 2 6)
Peak pair Sample 1 Sample 2
111-200 - 0 . 0 2 + 0 . 0 1 200-220 - 0.01 - 0.01
220-311 + 0.04 - 0.02
311-222 + 0 . 0 2 + 0 . 0 7
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19795137
C5-382 L. E. JEROME AND G. P. MOHANTY
Warren-Averbach method [6] yielded effective par- ticle sizes De for the directions [loo] and [Ill]. For general cold worked material with faulting, D, has been shown to have the form [8, 101 :
l/De(l 11) = 1/D
+
[1.5(a1+
a")+ 81 0 .433/ao (1)
1/De(200) = 1/D +
[1.5(a' +
a") +
P]/ao (2)
where a, is the lattice parameter and D is an isotropic particle or dislocation cell size in the material. Eqs. (1) and (2) predict anisotropic De when faulting is present with a limiting ratio of De(l 1 1)/De(200) = 2.3. In practice, a smaller ratio is expected because of the
1/D term. Measured De7s for Ce yield :
which indicates contributions from both faulting and D. A simultaneous solution of Eqs. (1) and (2) yielded the following results :
D = 437
A
; 1.5(a1+
a")+ P = 0.014 .
Incidence of faulting is also indicated from the peak asymmetry effect. Both a" and
P
produce this effect with the same sign for any (hkl) but with magni- tudes in the ratio of 4.5 : 1 [8]. The signs, however, vary with (hkl), positive for (1 11) and negative for (200) and (222). The measured peak shapes entirely conform- ed to this prediction. From an analysis of the peak asymmetry, the following solution for the quantity (4.5 a"+ P) was obtained [lo, 61
A simultaneous solution of the three compound probabilities (a' - a"), [1.5(a'
+
a")+ P]
and (4.5 a"+
P) was next performed with the following results : a' = 0.035, a" = 0.035 andP
= - 0.090.Negative
P
in this type of analysis previously has been taken as indicative of insignificant twin fault-ing [l 1, 121. Accordingly, if we set
P
= 0 and carry through the solution a second time, the following results are obtained :The large error limits are typical of solutions based on small second order diffraction effects. The fact that a' x a" is consistent with the view, based on simple next neighbor bond counting, that the energies of the two are probably not much different [7]. This is substantiated by dislocation node studies which show ye,, x y,, in fcc alloys [13]. Further, it appears that the occurrence of a" along with a' may be more common than generally assumed [14]. The fact that peak shifts for most fcc metals and alloys show (a' - a") > 0 can then be accounted for in two ways : despite the roughly equal y, kinetics considera- tions favor a' formation over a" because of the coope- rative motion of partials required for the latter;
secondly, even with the barrier overcome, it appears that the faulted area encompassed by a" is smaller than a' possibly as a consequence of the relative self-energies of the partials bounding the faults [13].
In comparing the Ce results with those on other fcc metals, we note that many of these are based on peak shift data alone. In several cases, however, where all the three effects (broadening, asymmetry and peak shift) have been studied, analyses of the data show that generally x 0 but al/a" w 5-10 which is in contradiction to the Ce result for which a'/a" w 1.
At room temperature y-Ce, however, is very close to the fcc + dhcp transition temperature [15]. Thus a", which introduces six layers of dhcp material in the fcc stacking, may be energetically more favored than a'. This would promote cooperative motion of partials in a manner analogous to that in a martensitic transformation. Such behavior is suggested by several studies which indicate fcc + dhcp transition may indeed be of martensitic nature [16, 17, 181.
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