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A Diffraction Study of Diffusion in the Mo-Cr System

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2656 TECHNICAL NOTES Vol. 32, pp. 2656-2659. J. Phys. Chem. Solids A diffraction study of diffusion in the Mo-Cr system (Received 29 December 1970) A DIFFRACTION method for studying interdiffusion in powder compacts was first proposed by D u w e z and Jordon[l], and later put on a quantitative basis by Rudman[2] and applied to the C u - N i system by Fisher and Rudman[3] and also be Heckel[4]. Diffraction method has also been applied to analyze diffusion under one dimensional conditions [5,
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  2656 TECHNICAL NOTES J. Phys. Chem. Solids Vol. 32, pp. 2656-2659. A diffraction study of diffusion in the Mo-Crsystem (Received 29 December 1970) A DIFFRACTION method for studying inter-diffusion in powder compacts was first pro-posed by Duwez and Jordon[l], and later puton a quantitative basis by Rudman[2] andapplied to the Cu-Ni system by Fisherand Rudman[3] and also be Heckel[4].Diffraction method has also been applied toanalyze diffusion under one dimensional con-ditions [5, 6]. The present work is concernedwith an application of the Rudman-Duwezmethod to a b.c.c, system. Specifically, Mo-Crsystem was chosen for this purpose as infor-mation relating to interdiffusion in this systemis rather scanty and also somewhat conflicting:Pines and Smushkov[5] and Gruzin et al. [7] have reported parameters characterizingthe diffusion of Cr in Mo (see Table 1; asummary of their original Russian paper ap-pears in the Chemical Abstracts [6]). Prolosh-kin and Sidunova[8] and Arzhanyi andVolkova[9] from experiments with diffusion Table 1. Average diffusion parameters forb.c.c, binary systems System Do (cm2/sec) Q (k cal./mole) Ref.Mo-Cr 2.9 ã 10 a 61.4 This workMo-Cr 2-7 ã 10 a 58.0 7Mo-Cr 7.5 ã 10 -~ 84.0 5Mo-Ti l'0 x 10 a 66-0 12Mo-Cb I-0 ã 10+a 137 12Cb-V 5.0 x 10 2 68 0 12 couples, on the other hand, have concludedthat Mo and Cr do not form a continuousseries of solid solutions and postulated theexistence of an intermediate phase contraryto other works on this system[10]. The diffrac-tion method for studying interdiffusion issuited to systems with complete range of solidsolubility and our preliminary measurementswere concerned with this question. We how-ever failed to detect any intermediate phase orany other deviations from complete solidsolubility in Mo-50%Cr powder compactsfollowing successive diffusion anneals at1050 or 1200~For the diffusion runs, samples were pre-pared by mixing thoroughly high purity + 325mesh size Mo and Cr powders in equiatomicproportions. The mixture was compressedinto 1 in. dia. billet forms under 35,000 psipressure and given diffusion anneals at 1050and 1200~ for times ranging from 50 to 1600min under continuous flow of argon. Follow-ing each annealing treatment the sample sur-face was gound on 400 and 600 grit papers toremove any oxidized surface layer. The smalldegree of cold work introduced in this processwas relieved by a short anneal (15 min) at alower temperature (800~ (In a separate runit was established that no measureable diffu-sion occurred at this temperature even afterannealing for 1600 min. Following the strainanneal the sample was lightly ground andetched before making the diffraction runs.These consisted of recording the (200)diffraction profiles of Cr and Mo in a singlecontinuous run following each diffusionanneal. Filtered Mo Ka radiation was usedand the peaks were scanned at 0.2~ coun-ter velocity in a 0 -- 20 scanning diffractometerequipped with a scintillation counter. Follow-ing Rudman[2], each measured profile wascorrected for instrumental broadening and theremainder of the broadening attributed tocomposition fluctuation in the sample. Thecorrected profile f(20) may then be shown tobe related to N(c), the number of unit cellsof composition c in the sample by the equa-tion [2] N(c) = Q(c)f(20) (1)where Q (c) = [kA-'vd' (c)dK~t (c)] X[cfMo+(1--c)fc~ -2,  TECHNICAL NOTES 2657 20 is the scattering angle, c is the atom frac- 1.0tion Mo in the sample, dakt(c) is the (hkl) _.......~_...~ interplanar spacing which is a function of c, d'(c) =d(dhkz)/dc, v is the volume of the 0.8unit cell, A is the absorption factor, the f's ......represent the atomic scattering factors for Crand Mo corrected for anomalous dispersion 0.6and k is a constant. The lattice parameters for /t~.~i__- ~ ...................the Mo-Cr system, was taken from the work ~ I,, ----of Goldschmidt and Brand[1 1] which gives a o.4 ~~i,---~600linear variation between 3.145 ,~, for Mo to ~ ~---t=so2.880 ,~, for Cr from which d' (c) was com- . --t=120puted. In order to obtain the concentration- 0.2penetration profile, Rudman[2] defines a oparameter x, equivalent to the penetration ;, parameter used in conventional diffusion o.o '0'.4 '' 016'' '0~' ' '1.0 studies, in terms of N(c) 0.2 X ~-Fig. 1. Fraction Mo (c) as a function of the penetrationparameter (x) for Mo-Cr powder samples interdiffusedat 1200~ for the indicted times (t) in minutes. Using equations (1) and (2), the measured (200)Mo-Cr diffraction profile after each diffu-sion anneal was reduced to a c-x profile. Theresults for the 1200~ diffusion runs are shownin Fig. 1. Similar curves were obtained for the1050~ anneals. The concentration penetra-tion curves (Fig. 1) have the expected shapesexcept near the regions x ~ 0, 1 where thereis a tendency for the curves to round off.Straight line extrapolations shown by thedashed lines in Fig. 1, however, appear morereasonable as it is unlikely to have a few isola-ted regions of pure metals in the sample norinstantaneous contamination of all metalsat the earliest possible annealing time, as therounding-off of the c-x curves would seem toindicate. Similar behavior has also been re-ported for the Cu-Ni system by Fisher andRudman[3] who considered it as an artifactarising from the approximate nature of theinstrumental broadening correction. It ispossible to derive from these curves the timevariationof the degree of interdiffusionwhich is defined by the ratio (mt/m| where mt is the net mass transfer across the inter-face between the components at time t andmoo is the same quantity at infinite time [2, 3]. mt is given by an integration over the c-x profile: mt = ~ct~.,=o~ x' dc (3) JO where x'= 0 defines the srcinal interfacebetween the components. The variation of (mt/m=) with time is shown in Fig. 2 for thetwo interdiffusion temperatures used in thisstudy. Assuming an Arrhenius type tempera-ture dependence for m t, an average activationenergy Q for interdiffusion in the Mo-Crsystem may be derived from this data; theresult is listed in Table 1.In addition to Q, it is also possible toderive information about the average D andhence Do from the c-x profiles (Fig. 1) bypostulating a specific model for diffusion.From the works on the Cu-Ni system itappears that the concentric sphere model [3, 4]is perhaps the most appropriate one for de-scribing interdiffusion in powder compacts.The validity of this model in the present workwas determined by metallographic examina-  2658 TECHNICAL NOTES 0.7....-~. 0.6 E E -40.5 Z 0.4 _z 0.3= 0.2 0.1 2o0 c I I I 0 10 20 30 40t /2 (min.) Fig. 2. Degree of interdiffusion as a function of (time)89 during annealing of Mo-Crpowder compacts at 1050 and 1200~ respectively. tions which revealed, quite early in the pro-cess, roughly spherical Cr rich regions in thesample surrounded by Mo rich material; thispattern continued until the entire Cr-rich corehad been consumed. (A micrograph of thesample after 75 min at 1050~ is shown inFig. 3.)Adopting this model and with appropriateboundary conditions[3], the diffusion equa-tion may be solved for c(x) for different valuesof D and t. By comparing these curves withthe experimental c(x) curves a value of D isfound which gives the best fit between the twosets for a given temperature. The results ob-tained in this manner are listed in Table 1along with the Do and Q values for severalother b.c.c, systems taken from the literature[12]. It is seen that the Q value for the Mo-Cr system follows the same, generally highertrend found for other b.c.c, systems whilethe Do values do not seem to show much cor-relation; the X-ray values and that of Gruzin et al.[7], however, are in good agreement.The X-ray analysis yields only the averagediffusion parameters, corresponding to diffu-sion in a concentrated solution. It is possible,however, to draw some qualitative conclusionsregarding the relative diffusivities of the twocomponents. For example, the c-x profiles(Fig. 1) show that after 50min at 1200~no pure Mo is left in the sample while con-siderable Cr remains. This faster contamina-tion of Mo by Cr may be indicative of a higherintrinsic diffiusivity for Cr compared to Mo,a result which is expected to hold especiallyin concentrated solutions. Second, we notethat despite the high interdiffusion tempera-tures used and the high Q value found in thepresent work indicating the dominance ofvolume diffusion, it is unlikely that somesurface diffusion is not involved in the sinter-ing of the powder compacts. In fact, the quickencircling of one metal by the other mentionedabove does indicate the importance of surfacediffusion during the early stages of annealing.However, the overall rate controlling processin achieving homogenization is volume diffu-sion and this is what the composition profilesand the Do and Q values derived from thediffraction data represent.  Fig. 3. Photomicrograph of Mo-Cr powder compact after inter-diffusion at 1050~ for 75 min. Cr rich and Mo rich regions are inlight and dark contrasts respectively. Mag. approx. 170x. [Facing page 2658]

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