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Diffusion of Carbon in Niobium and Molybdenum

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Diffusion of Carbon in Niobium and Molybdenum Materials Transactions, Vol. 55, No. 12 (2014) pp. 1786 to 1791 ©2014 The Japan Institute of Metals and Materials Diffusion of Carbon in Niobium and Molybdenum Jun-ichi Imai1, Osamu Taguchi2,+, Gyanendra Prasad Tiwari3 and Yoshiaki Iijima1 1Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan 2Department of Materials Science and Engineering, Miyagi National College of Technology, Natori 981-1239, Japan 3Department of Information Technology, Ramrao Adik Institute of Technology, Vidya Nagri, Nerul, Navi Mumbai 400709, India Diffusion coefficients of carbon in niobium and molybdenum have been determined by the residual activity method with radioactive tracer 14C in the temperature ranges between 1168 and 1567 K for niobium and between 1271 and 1669 K for molybdenum. The temperature dependences of the diffusion coefficient of carbon in niobium and molybdenum are expressed by D/m2 s¹1 = 2.2 © 10¹6 exp(¹152 kJ mol¹1/ RT) and D/m2 s¹1 = 5.2 © 10¹6 exp(¹163 kJ mol¹1/RT), respectively. Since the solubility of carbon in molybdenum is very small, the diffusion of carbon in molybdenum is strongly influenced by carbide precipitation at lower temperatures. [doi:10.2320/matertrans.M2014277] (Received July 31, 2014; Accepted September 30, 2014; Published November 8, 2014) Keywords: carbon diffusion, niobium, molybdenum, carbon solubility, precipitate effect 1. Introduction 2. Experimental Procedure Iron, nickel and cobalt based superalloys appear to have 2.1 Material achieved full potential in relation to their use as structural Niobium metal rod arc-melted and machined to 12.5 mm in materials for corrosive environments as well as high diameter was supplied by Materials Research Corporation, temperatures.1) The strength of these alloys comes partly USA. Main impurities, in mass ppm, shown by chemical from solid solution strengthening and partly from precip- analysis are C-40, O-20, N < 5, Ti < 30, Fe-20, Si-25, Cr-30 itation hardening. For applications at temperatures higher and Ta-250. To induce grain growth, as received rod was than 1200 K and under intense radiations encountered in fast annealed by an electron beam heating at 2173 K for two and fusion reactors, precipitation hardening loses its sheen as hours under a vacuum of 1 © 10¹5 Pa. The resultant grain the source of strengthening for the matrix. Titanium and size was about 4 mm. The rod was cut to make 7 mm thick zirconium are ruled out because of phase transformation and disc specimens. One of the flat faces of the discs was high diffusion rates. Hence, niobium, vanadium, tantalum metallographically polished followed by electropolishing in a and molybdenum are the available choices as suitable H2SO4 solution containing 10% HF. materials for structural components of fast and fusion Six mm diameter “low carbon molybdenum rod” was reactors. The combination of high melting point and high obtained from Climax Molybdenum Company, USA. Ac- strength possessed by these metals enhances their usefulness cording to the supplier, maximum nominal impurities, in in severe environments. However, these metals show high mass ppm, are as follows: C-50, N-20, O-15, Si-80, Fe-80 propensity to absorb interstitials like carbon, nitrogen and and Ni-20. Three such rods were melted together by an oxygen. Because of its tendency to form carbides, carbon electron beam heating to produce a rod of ten mm diameter. has a profound influence on the mechanical properties of The grain size was about 3­4 mm. These rods were sliced to transition elements. In view of this, knowledge of the six mm thick disc specimens. One of the flat faces of the disc diffusion properties of carbon assumes great significance. In was metallographically polished and finished with electro- the present paper, we present results of the radioactive tracer polishing in a 10% H2SO4 solution. diffusion in niobium and molybdenum. It may be mentioned here that the previous studies of diffusion of carbon in 2.2 Radioactive tracer niobium were carried out during the years 1950­1972.2­7) Radioisotope 14C(¢-ray 156 MeV, half-life 5730 years) Similarly, the diffusion of carbon in molybdenum was was supplied in the form of fine carbon particles of less than studied in the years 1964­1978.4,8­14) This is first reported one µm diameter by The Radiochemical Centre, Amersham, investigation of carbon diffusion in these metals after more UK having a relative activity of 3.3 TBq/kg. A few drops of 14 than three decades. It is also pertinent to recall here many the suspension of the particle of C in CCl4 were put on the of the earlier investigations were performed via indirect flat and polished surface of the specimen with the help of a technique without the use of 14C radioactive tracer. The micropipette and dried in air. object of the present article is to present new data on the diffusion of carbon in pure niobium and molybdenum 2.3 Diffusion annealing matrices and make a comparative study of present results The sealed specimens in evacuated quartz tubes were with the earlier ones. diffusion annealed at temperatures between 1168 and 1567 K for varying periods from 8.40 © 103 to 3.46 © 105 seconds +Present address: Professor Emeritus, Miyagi National College of for niobium. The annealing temperatures for molybdenum Technology. Corresponding author, E-mail: [email protected] ranged from 1271 to 1669 K and the corresponding annealing Diffusion of Carbon in Niobium and Molybdenum 1787 periods varied from 9.00 © 102 to 8.73 © 105 s. All the (a) temperatures were controlled within «2 K. After the diffusion annealing, the cylindrical surface of the specimen was machined in a precision lathe to reduce the diameter by about 1.8 mm in order to eliminate the possible contribution of surface diffusion to diffusion inside specimen matrix. 2.4 Concentration profiling The flat surface of the specimen was removed successively through grinding. The thickness of each layer after grinding ranged from 5­50 µm which was estimated from weight loss (b) measured in a precision balance, surface area of the specimen and density of niobium or molybdenum as the case may be. Residual activity of the specimen after each grinding was counted in a windowless Q-gas flow counter having 2³ geometry. The background of the counter was 20­30 cpm. To reduce statistical uncertainty of the counting, Q-gas flowed for 2 min before the beginning of 5 min counting. 2.5 Analysis of the data For one dimensional diffusion of a tracer from a thin film into a sufficiently long rod analyzed by the residual activity (c) method,15) the solution of Fick’s second law is given by dIn ®In À ¼ const:CðXnÞð1Þ dXn Here ® is the absorption coefficient (in m¹1) of the matrix 14 for ¢ radiation from radioisotope C, In is the surface activity (in counts per set time) after a thickness Xn is removed from the original surface. C(Xn) is the concentration of radio- active tracer in the matrix at a distance Xn from the original ® 14 ¢ ¹1 surface. The values of for C -ray are 140000 m and fi ¹1 Fig. 1 Examples of penetration pro les for diffusion of carbon in niobium 170000 m for niobium and molybdenum, respectively. As a at 1168, 1269 and 1369 K. result, the value of the parameter ®In/(¹dIn/dXn) º 100 for all the cases, so the term dIn/dXn in eq. (1) can be neglected without introducing any significant error. Thus, C(Xn)is ’ proportional to In. The solution of Fick s law for an (a) instantaneous source of thin film geometry diffusing unidirectionally through the lattice is given by pffiffiffiffiffiffiffiffiffi CðX; tÞ¼M=2 ³Dt expðX2=4DtÞ: ð2Þ o Here M denotes the total mass of the diffusing substance at X = 0 and at time t = 0. When the surface concentration is 1 - C/2C maintained constant through the period of diffusion, eq. (2) is transformed as below: pffiffiffiffiffiffi 0.50 CðX; tÞ¼C0 erfcðX=2 DtÞ; ð3Þ where C0 is the constant concentration at the surface defined (b) by X = 0. If ¯(X) represents the probability function for normal Gaussian distribution, eq. (3) is transformed to pffiffiffiffiffiffiffiffi ÈðX= 2DtÞ¼1 À CðXÞ=2Co ð4Þ 3. Results 3.1 Diffusion of carbon in niobium Figures 1 and 2 show the concentration profiles of 14C in niobium. The plot of {1 ¹ C(X)/2C0} versus X shows a linear relationship at all temperatures. Here, influence of Fig. 2 Examples of penetration profiles for diffusion of carbon in niobium grain boundary diffusion on the diffusion profile is negligible at 1478 and 1567 K. 1788 J. Imai, O. Taguchi, G. P. Tiwari and Y. Iijima Table 1 Diffusion coefficient of carbon in niobium. Table 2 Previous data on diffusion of carbon in niobium. / / fi / 2 ¹1 Temperature K Diffusion time s Diffusion coef cient m s Temperature 2 ¹1 ¹1 Authors D0/m s Q/kJ mol Method ¹ range/K 1567 8.40 © 103 3.55 © 10 11 ¹6 1567 8.40 © 103 2.59 © 10¹11 Wert (1950) 323­413 1.5 © 10 113 internal friction © 4 © ¹11 Powers and Doyle 1478 2.47 10 1.23 10 403­503 4 © 10¹7 138 internal friction 1478 2.47 © 104 1.32 © 10¹11 (1959) ¹ Nakonechnikov 1369 8.64 © 104 4.12 © 10 12 1373­1673 9.3 © 10¹7 146 14C tracer et al. (1966) 1369 8.64 © 104 4.60 © 10¹12 Son et al. (1967) 1203­2073 3.3 © 10¹6 159 14C tracer 1269 1.07 © 105 1.16 © 10¹12 Schmidt and Carlson © 5 © ¹13 2173­2573 2.6 © 10¹6 158 diffusion couple 1269 1.07 10 9.83 10 (1972) 1168 3.46 © 105 2.58 © 10¹13 Hoerz and ¹6 5 ¹13 1873­2393 1.8 © 10 159 decarburization 1168 3.46 © 10 3.52 © 10 Lindenmaier (1972) (a) 1376 K -1 Nakonechnikov et al.
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