9 at w . 19 KI LY AD . . nit . AMS Y the 2. 7 . . ' 5 . :::. o . . It 2)IS 1. IN .. 2 - Fi- WS . . N RT . * . 22 7 C > Pi1 . . Y UNCLASSIFIED ORNL . D TL r 1. . . . 0 L. AT 30 - 425 Paper to be presented at the symposium on Body-Centered Cubic Materials, Gatlinburg, September 16-18, 1964 ornu P-425 DTIE-S CONF-711 -1 OCT $ 1894 MASTER A SUMMARY OF ORNL WORK ON DIFFUSION IN B-Zr, y, Nb, and Ta* T. S. Lundy, ** J. I. Federer, R. E. Pawel, and F. R. Winslow Metals and Ceramics Division Oak Ridge National Laboratory Oak Ridge, Tennessee -LEGAL NOTICE This report me propered na sa neoount of Crvernment sponsored work. Neither the trutied ut, my , www Mahal A. Mehed my tety or reprown totuuprosodd or implied, we mapect to the way My son, or wted wan n eer at way to them, apparna, mented, we were are lowed in the report may not bring privalsiy owned rightoj en n. Ammo many that there with respect to the w a , e for beingou moved thing from the ma olmuy bonher mother, marmo, mettend, w process Worland in de reports New the theme, permu mody w wall at the conclud" medediny - weten w atu, Mwambayo at wala contracte, to the dont wat or contactar a Outest margin of male moteutter spanna, W www.dante, es war employment with wool wateter. .. *Research sponsored by the U. 8. Atomic Energy Commission under contract with the Union Carbide Corporation. **Speaker. . . ... . . . A SUMMARY OF ORNL WORK ON DIFFUSION IN B.-Zr, V, N., and Ta .. . .. . T. S. Lundy, J. I. Federer, R. E. Pawel, and F. R. Winslow studies on diffusion in body-centered cubic metals. This particular aspect of our diffusion work was started approximately three years ago and is continuing throuch the present time. In all experiments we used radio- active tracer methods combined with mechanical sectioning techniques to determine activity profiles after the specimens had been subjected to isothermal diffusion-annealing treatments. We believe, and I think that some of our results support this belief, that there are good reasons for doubting the validity of diffusion coefficients obtained by indirect means, such as by the surface decrease method. We first became interested in studying diffusion in boc metals when we noted that there was an especially wide disagreement among previous investigators> on the experimental values of Dand Q in the Arrhenius- type equation to describe se.lf-diffusion in B-zirconium. Experimental values of D varied by nearly two orders of magnitude and values of Q XL **** large discrepancies was that the different investigators had used szers . Thus, since the decay spectrum overlaps for these isotopes, the experi- mentally determined values could have been different average values of the diffusion coefficients for the two isotopes, 95zr and 95No. We, there. fore, decided to follow separately the diffusion of both isotopes in order to assess this possible explanation. As for all other experiments to be described in this paper, we chose to study the diffusional properties of zirconium by depositing the 1sotope . . . - - - - - - . - - - .. . -. · of interest onto the flat faces of cylindrical specimens and following the subsequent redistribution of isotope for a given isothermal diffusion anneal by sectioning parallel to the initial plane source and counting the activities associated with the sections. If the thickness of the isotope layer is very small relative to the penetration depths, i.e. if n < 0.1VDt where h is the isotope layer thickness, D is the diffusion coefficient and t is the time of the diffusion anneal, the applicable solution to Fck's second law is: M 2 A(x) wong A(x) = exp. - HERE) VIIDU where A(x) = the specific activity at a distance x from the original isotope layer, and M = the total activity originally deposited on the specimen per unit surface area. Thus, plots of in A(x) versus x? should yield straight lines with slopes equal to -(4Dt) 4. If, on the other hand, the original isotope layer 18 too thick, i.e. If n > 0.1 NDE , plots of in A(x) vs x? would no longer be linear but should be concave downward near x = 0. Fortunately, for all of the experiments reported herein the 1sotope layer could be considered to be a plane source. Possible exceptions are limited to a few of the diffusion experiments at low temperatures in the Ta and No systems where sectioning was accomplished by anodizing and stripping The first slide (ORNL-DWG 64–2074) shows four plots of lin A(x) versus x? for the diffusion of ºno in B-zirconium. Even at a temperature of 882°C, slightly above the cph to bcc transformation temperature, the data awe linear on this kind of a plot. Such behavior 18 generally considered to indicate that atomic trarisport occurs primarily by some volume diffusion mechanism. Using penetration plots such as these, we determined the diffusion coefficients for diffusion of 95No and 95Zx into Zx from about . - - - . - - LOT 850 to 1750°C. The next slide (ORNL- LR-DWG 70182R) shows customary Arrhenius-type plots for describing the temperature dependence of diffusion coefficients for both Zr and ºnb in B-zircon.um. At low temperatures the values of D for the two isotopes differ by about a factor of five with 95 No being the slower diffusing species while at high temperatures the D values become almost the same. The presence of 95No as a contaminant in 95zr would, therefore, always tend to lower the apparent self-diffusion coefficient for B-zirconium. Perhaps the most significant thing about these plots of the data is their marked curvature. If one considers the s.lopes of such plots at specified temperatures to be proportional to the activation energy, Q, of the diffusion process, then Q is found to vary from about 20.5 to 47.0 kcal/mole for 95zr and from about 26.0 to 56.0 kcal/mole for 95. Such a wide variation in the apparent activation energies was completely un- expected; but the presence of this variation does allow easy explanation of previous results on the system 95zr in B-zirconium. Values of D and q obtained by any particular previous investigator simply depended on the temperature range emphasized during his work. Emphasis on the low temperature range resulted in low Do and a values; while emphasis at higher temperatures gave higher Do and Q values. There are several possible explanations for the observed curvature. The first, and because of its simplicity perhaps the best, is that it should not be unexpected that the activation energy for a diffusion process varies with temperature. Arrhenius certainly, made no claim that his equation should be applicable over more than a rather limited temperature interval. In fact, he did not attempt to apply his equation to diffusion data. The application to diffusion data was first made in the early 1920'8.? Its almost universal acceptance as a "Law" was based almost entirely on an empirical, ......... ********* foundation generated by a considerable amount of data gathered over limited temperature ranges. With the advent of accurate tracer methods, deviations from the relationship were found, but were believed to be anomalous. It may be that there actually are good theoretical reasons for the activation energy of volume diffusion to be constant with changing temperature. I feel that the matter will be decided by obtaining precise experimental data over wide temperature intervals. Let us not let the tail wag the dog, but properly invert the process. Now if one continues to subscribe to the idea that the Arrhenius concept must hold over wide temperature intervals for a given diffusion process, there exist other possible explanations for the "non-Arrhenius" behavior of the zirconium data. These include: 1. Wo mechanisms of volume diffusion may occur in this system with one dominating at high temperatures (possibly the vacancy mechanism)and the other at low temperatures (possibly the ring mechanism); 2. there may exist a temperature independent vacancy oonoantration that contributor nimirloantly to low temperature diffusional properties, but has little effect on diffusivities near the melting point; and 3. normal volume diffusion may occur by the vacancy mechanism near the melting point while significant contributions from short-circuiting (along boundaries and dislocation pipes) enhance the apparent volume diffusion coefficients determinei at low temperatures. In the Ta and No system, this last effect has been observed and we are inclined to accept it as the explanation in this case. However, further experiments are obviously in order. After finding curvature in Arrhenius-type plots for diffusion in Bazirconium and explaining apparent discrepancies in previously determined D. and Q values for this system in terms of such curvature, we decided to examine the Arrhenius behavior of other bcc systems. In order to avoid transformation problems, and, therefore, have the opportunity of examining Dover still larger temperature intervals using single crystals of the metal of interest, we then chose to study the self-diffusion of vanadiun. After using one batch of the "Ov isotope (t, n = 16.2 days), we found that work on this system was also being done at the University of Illinois and decided against further duplication of effort. With the few specimens that we did examine, however, we obtained reasonably accurate high-temperature data and from this established that deviations from normal Arrhenius behavior occur for self-diffusion in vanadium. The next slide (ORNL-DWG 64-1712) illustrates a typical penetration plot for a lathe-sectioned vanadium specimen. This slide also illustrates the use of Winslow's computer code in automatic calculation and plotting of diffusion data. The diffusion coefficient, confidence limits, and other pertinent information were plotted automatically. Only the classification and drawing number were put onto this figure by human hands. 2 The next slide (ORNL-DWG 64-1048) summarizes our rather cursory study of this system. The data above 1600°C can be described by: D = 58 exp (-91, 500/RT) cm?/sec. This equation is in reasonable agreement with that obtained in the Illinois work to be reported by Dr. Peart. 2 Our lower-temperature data deviate from this equation, but must be considered to be only qualitative. The points at 1200°c were markedly affected by a specimen reaction with quartz. It seems that silicon lovers the diffusion rate of "ov in vanadium. The next system we examined was that of 9No in niobium. Resnick and Castleman 13 had previously determined diffusion coefficients in this system from about 1600 to 2200°C. Peart, Graham, and Tomlin? obtained five data points between about 1700 and 2330°C. In these works the reported activation energies were 105 and 95 kcal/mole, respectively, and corresponding D values were 12.4 and 1.3 cm/sec. We extended the temperature interval both to higher and particularly to lower temperatures in order to more fully describe the Arrhenius-type behavior. In our study of this system, we used three sectioning techniques-lathe, grinding, and, more recently, anodizing and stripping. 15 The first two of these techniques are rather standard, but the third is not so well known. Sectioning a specimen by this method involves the formation and subsequent mechanical stripping of an anodic film from a flat, electropolished surface. Scotch Brand Magic Tape is used to strip the film and contain it during the counting operation. The newly exposed surface is then ready for repetition of the anodizing and stripping. Thickness of the uniform anodic layer is for all practical purposes a unique function of the applied voltage and for niobium can be varied from about 200Å to 1000 X. Sections less than 100 Å thick have been consecutively removed from single crystal diffusion specimens of tantalum by this method. Penetration plots for 9No in niobium obtained by lathe sectioning techniques are shown in the next slide (ORNL-DWG 64-737). The unit of the abscissa is indicative of the sometimes used procedure of first finding D in mg / sec and then making the appropriate conversion to cm/sec. Typical grinding data are shown in the next slide (ORNL-DWG 647455). Here the abscissa has normal distance units of cm?: Next (ORNL-DWG 64-1126), we see penetration plots obtained by anodizing and stripping a single specimen having both 950o and 182ra as diffusing species. For the 95No the activity dropped about a factor of five in the first micron of sectioning while the 102Ta dropped more rapidly, indicating a smaller diffusion coefficient. Also, note that one micron of the specimen was divided in this case into about twenty sections. If necessary, we could have divided this region into 70 or 80 sections. 18 The next slide (ORNL-DWG 64-7457) summarizes our niobium data. It is especially important that a straight line in this plot of in D versus T-- fits most of the data. Positive deviations from this line can, we believe, be explained by a combination of short-circuit penetration of the isotope and limiting resolution of the sectioning procedures. This point will be more clear when we examine the data for diffusion in tantalum. The equation for this line through the data is: D = 1.94 exp (-98,000/RT) cm? / sec. The values of D. and Q are quite close to those determined by Peart, Graham, and Tomlin. 4 The linearity of this plot over nearly ten orders of magnitude of the diffusion coefficient from 2400 down to about 900°c certainly supports the idea that the activation energy for a given volume diffusion mechanism does not necessarily vary with temperature. Most of the initial experiments that we performed using the anodizing and stripping technique were on the system » No in tantalum. The type of penetration behavior first encountered is illustrated in the next slide . rom the surface and one deeper into the specimen. Values of D determined from the slopes of the curves are considerably different for the two regions. In fact, the presence of multiple regions of diffusion makes one worry whether the usual boundary conditions applied to Fick's law are applicable in this case. We compared values of D computed for both regions of such plots with the data of Gruzin and Meshkovo and concluded that the penetration behavior deeper into the specimen was associated with volume diffusion. Thus, at first thought, it appeared that a near-surface effect similar to that now widely reported for diffusion in aluminum and in silver was responsible for the vastly different near-surface characteristics. This interpretation was incorrect. We should have and now do consider the first region to be character. 1stic of volume diffusion in this system. The enhanced penetration deep into the specimen is caused by atomic migration along short-circuiting paths. To reach this conclusion it was necessary to examine the data in terms of the experimental and analytical procedures, as well as their behavior as a function of several experimental variables. A convincing piece of evidence in this respect is seen when penetration behavior of "No into mono and polycrystalline Ta is compared. The next slide (ORNL-DWG 64-4734) 1llustrates this effect for specimens given identical annealing treatments. The greater relative importance of the second region in the polycrystalline specimen is easily seen, although the slope of the first region tends to approach that for the single crystal at very small penetration distances. Thus, depending upon the sensitivity of the sectioning procedure, the presence of short circuiting paths may contribute significantly to the measured "bulk" diffusion coefficients. Obviously, this effect is most pronounced at low temperatures. A more complete penetration plot is shown in the next slide (ORNL-DWG 64-4735). On this scale, it is apparent that the grain boundary or short-circuit component is not well-described by a straight line on a In a versus x? plot. It probably shouldn't be too surprising to find that it is also not linear when plotted as in a versus x, as predicted by the Fisher analysis for ideal grain-boundary diffusion. This is demonstrated for a different specimen in the next slide (ORNL-DWG 64-5055). The next slide (ORNL-DWG 614-7456) summarizes the data for the diffusion of 9No in tantalum. About nine orders of magnitude of D are included; the temperatures ranged from about 1000 to 2500°C. The points that lie above the straight line may be explained for the most part in terms of the effect of short-circuiting on the volume diffusion portion of the penetration plot. In other words, we did not allow enough diffusion time for the particular section thickness that was chosen. The same reason also explains some of the high points on the similar plot for diffusion in niobium. The equation . for describing these data is: D = 0.36 exp (-100, 400/RT) cm²/sec. One point seems painfully clear. That is, one must be especially careful in interpreting low temperature diffusion data because of the large structure-sensitive contributions to the overall penetration plots. For example, in considering our data for diffusion in Ta, the region of pure lattice diffusion would have been missed entirely, if we could not have characterized the first few tenths of a micron penetration. Even when using single crystals, the contributions of subgrain boundaries and dislocation pipes can be appreciable. In summary, we have measured diffusion coefficients over wide ranges of temperature in B-zirconium, vanadium, niobium, and tantalum. We have found deviations from Arrhenius behavior in all cases. For niobium and tantalum these deviations may be explained in terms of short-circuiting. Similar explanations probably do not hold for diffusion in B-zirconium. Samm en........... em .. adi iletimained analocom ****...*V, W .- * REFERENCES 1. Q. B. Federov and V. D. Gulyakin, Met. 1 Met. Chist. Mot. 1, 170 (1959). 2. 6. Kidson and J. McQura, Can. J. Phys. 39, 1146 (1961). 3. V. 8. Lyashenko, V. N. Bykov, and L. V. Pavlinov, Hz. Motal. Metalloved. 8, 362 (1959). ho D. Volokoff, 8. May, and Y. Adda, Compt. Rond. 251, 2341 (1960). 5. Hr. V. Borisov et al., Metall. 1 Metalloved., D. 196 (1948). * 6. 8. Arrhenius, 2. Physik. Chem. 4, 226 (1889). 7. 5. Dushman and I. Langmuir, Phys. Rev. 20, 113 (1922). 8. C. A. Mackliet, Phys. Rev. 109, 1964 (1958). 9. G. V. Kidson, Can. J. Phys. 41, 1563 (1963). 10. Personal communication from R. F. Peart. 11. F. R. Winslow, A FORTRAN Program for Calculating Diffusion coefficients and Plotting Penetration Curves, ORNL-TM-726 (1963). 12. R. F. Peart, "Vanadium Self-Diffusion," a paper to be presented at the Symposium on Body-Centered Cubic Materials, Gatlinburg, Tenn., Sept. 16-18, 1964. 13. R. Resmick and L. S. Castleman, Trans. AIME 218, 307 (April, 1960). 14. R. F. Peart, D. Graham, and D. H. Tomlin, Acta Met. 10, 519 (May, 1962). 15. R. E. Pawel and T. S. Lundy, J. Appl. Phys. 35, 435 (Feb., 1964). 16. P. L. Gruzin and V. I. Meshkov, Probl. Metalloved. 1 Fiz. Metal. 4, 570 (1955), as cited by N. L. Peterson, Diffusion in Refractory Metals, WADD-60-793 (March, 1961). LIST OF FIGURES 1. (ORNL-DWG 64-1074) Penetration Profileg for Diffusion or » No in B-zirconium at 882,993, 1039, and 1100°c(lathe method). Someone (ORNL, FR-DWG 70182R) Temperature Dopondence of Diffusion of » zr and »NO in Bozirconium. 2. 3. (ORNL-DWG 64-1712) Penetration Profile for the Dirfusion or ºv in Vanadium at 1802°C(lathe method). 4. (ORNL-DWG 64-1048) Temperature Dependence of Diffusion or "oy in Vanadium. 5. 6. (ORNL-DWG 64-737) Penetration Profiles for Diffusion of > NO in Niobium, at 2320 and 2395°c(lathe method). (ORNL-DWG 64-7455) Penetration Frofiles for Diffusion of NO and 182Ta in Niobium at 1607°C(grinding method). (QRNL-DWG 64-1126) Penetration Profiles for Diffusion of NO and 182Ta in Niobium at 1408°C(anodizing and stripping method). (ORNL-DWG 64-7457) Temperature Dependence of Diffusion of » NO in Niobium. 7. 8. 9. (ORNL-DWG 63-483) Penetration Profile for diffusion or%mo in Lantalum at 1170°c(anodizing and stripping method). (ORNL-DWG 64-4734) Penetration Profiles Illustrating Effect of Crystalline Perfection on Diffusion of 95 Nb in Tantalum at 1250 °C (anodizing and stripping method). 11. (ORNL-DWG 64-4735). More Complete Penetration Profiles for Specimens Shown in Fig. 10. ('ORNL-DWG 64-5055) Penetration Profile for Polycrystalline Specimen for comparing Data with Fisher's Model of Grain Boundary Diffusion, (ORNL-DWG 64-7456) Temperature Dependence of Dirfusion of 9sNb and 182Ta.. in Tantalum. . ..... . . 1 . . UNCLASSIFIED ORNL-OWO 64-1074 - - - - - Z-32 2-43 1039°C 882. SPECIFIC ACTIVITY (orbitrory units) Z-25 1100°C 2-29 993°C 10 15 20 . A. temº . . . . . UNCLASSIFIED TEMPERATURE (°C) 1600 2000 9000 900 800 2 x 10-7 DIFFUSION COEFFICIENT (cm2/sec) ... .. .. 1 . 10*10 - ..5 6 7 10*/71•K) . . • ' ) 1 1 -- Temperature Dependence of Dittusion of Zo Body Centered Cubic Zirconium. ti 2 . 9.. - 1 - . , , i . i , ' .. UNCLASSIFIED ORNL-OWO M-1712 V-V, 1802 DEG. C., 18120 SEC. a D= 1.5416E-008 (CM***/SEC.) 90 PCT. CONF. =+ OR + 2.09968-010 C.P.S.) ** SPECIFIC ACTIVITY L N - - - X8 -10% (CM) . "* " . - . UNICI.ASSIFICO ONNL.owo 1-1046 TEMPERATURE (°C) 1400 1000 1600 1200 1000 * : - - : <- - -- 1000 . .• . . DIFFUSION COEFFICIENT (cm/sec) . in .,.* .. : : : : : *: * ;": ; :. . . . 1 10,000/- 10k) . . . . . 3 "* UNCLASSIFIED ORNL-DWG 64 - 737 Ladell SPECIFIC ACTIVITY ( arbitrary units) Nb A-4 2395°C . . - - - - - - - - - Nb B-1 . 2320° C . . 8 20:24 12 16 x? . 10-4 Img²) i < . .... Cra . - . . . . . :... 167 . Al -'- in na , vi nii . . :-, - .... ... ... - - - - . . . . . . . . . . - - - - . - - .. wowa 17 -:: is i i .-: . RELATIVE ACTIVITY (arbitrary units) . Liisi Primici .;*:?!.: -*... ! . . . 1:50 100 lywo).901.: qNg6 150 200 1607 °C Nb-14 "inne Cai, - ;• i. ORNL-DWG 64-7456 UNCLASSIFIED 250 - . UNCLASSIFIED ORNL - OWO 64-1186 Nuo SPECIFIC ACTIVITY (arbitrary units) Nb - 4 1408°C . . . : :. ::. ! 1:20 140 60 . 80 MP. 10'0 comey C # . . .. . 'il : ; . . '. ". .. UNCLASSIFIED ORNL - OWO 64-7457 TEMPERATURE (°C) 16 14 12 , (x102) 20 18 D. 1.94 exp(-98,000/RT), . D (cm2/sec) - - - • LATHE SECTIONING • GRINDING • ANODIZING AND STRIPPING c. . . more mi 5.5 6.5 -a. . 10,000/ (ⓇK) Diffusion of 9Nb in Niobium. . .. . . - S ' - :.:..., : WEMA A77 UNCLASSIFIED ORNL-DWG 63-483 TEMPERATURE: 1170°C TIME: 3.53 hr SLOPE = -1.88 x 10"/cm2 D = 1.04 x 10-15 cm