Ordering and mechanical strength in l1 2 cubic titanium trialuminides
- PDF / 267,802 Bytes
- 3 Pages / 598.28 x 778.28 pts Page_size
- 69 Downloads / 277 Views
D.G. MORRIS, Professor, is with the Institute of Structural Metallurgy, University of Neuchatel, 2000 Neuchatel, Switzerland. Manuscript submitted May 17, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
nominal composition AIsXTi2 as AaBbCc alloys. The choice of the composition A71C29 makes a close comparison with the "Mn-high Ti" and "Cr" alloys of Winnicka and Varin t41 possible. For a material of A a C stoichiometry, we can write for the superlattice (Fs) and fundamental (/7/) reflections structure factors Fs = fc - fA and F I = fc + 3fA (fc and fA are the atomic scattering factors for the C and A atoms). Accordingly, the intensity ratio of a superlattice/ fundamental2 peak 2 pair can be expressed as (fc - fA) / ( f c + 3fA) . For A71C29, supposing that all C sites are correctly occupied by C atoms with the excess sitting on A sites (long-range order parameter Sc is maximized), we can write Fs = fc - {(0.71/0.75)fA + (0.04/ 0.75)fc}; that is, approximately 0.95 fc - 0.95fA. Also, Fy = f c + 3{(0.71/0.75)fa + (0.04/0.75)fc}; that is, approximately 1.15fr + 2.85 fA" For titanium trialuminide (fc = fTi andfa = fAl), the result of changing from 25 pct to 29 pct Ti has been to decrease Fs and increase F/, and the apparent intensity ratio Is/I/will be decreased by approximately 15 pct. The analysis of Winnicka and Varin t4] is different and ascribes to each lattice site an occupancy factor (A A and Cc for binary alloys) which changes with composition; n a m e l y , A a = at. pct A/75 and Cc = at. pct C/25. This analysis obviously is incorrect, because it takes no account of the real location of atom species. For A3C, Fs ---- f c C c - f a A a and F / = fcCc + 3fAAA. At stoichiometry, both Cc and A a are unity, and we obtain the same expressions as earlier. For the 71 pct A-29 pct C alloy, we have Fs = fc 29/25 - fa 71/75 (that is, 1.16fc - 0.95 fa) and Ff = f c 29/25 + 3fA 71/75 (that is, 1.16fc + 2.84 fD. In the present case, there will be an increase in the deduced intensity ratio as the composition changes from 25 to 29 pct Ti, since F~ increases even though F / i n creases. The intensity ratio of the highly ordered alloys thus appears to increase by a factor of about 2 due to the increase in Ti content. The important difference between these two analyses is that an experimental intensity ratio will be represented by a high value of order parameter (the first analysis) or by a low value (the second analysis). The values of order parameter presented by Winnicka and Varin 141 accordingly have been corrected using the above analyses, and the modified values are presented in Figure 1. Their data are identified: Mn alloy (Ti = 26.6 pct), Fe alloy (Ti = 27.7 pct), Cr alloy (Ti = 28.3 pct), Cu alloy (Ti = 28.3 pct), and Mn alloy (Ti = 29.3 pct). Kogachi et al. tS] use a different method for determining the degree of order. Their results are included in Figure 1 as Fe alloy (Ti = 25 pct), Ni alloy (Ti = 26 pct), Ag alloy (Ti = 26 pct), and Cu alloy (Ti -= 27 pct). No analysis of the chemical composition was reported, and
Data Loading...
