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 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 ðX= 2DtÞ¼1 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. s 2 / m D

(b) Diffusion coefficient, coefficient, Diffusion

Fig. 3 Arrhenius plot of diffusion coefficients of carbon in niobium. Fig. 4 Examples of penetration profiles for diffusion of carbon in molybdenum at 1271 and 1376 K. because the grain size is much larger than the length of concentration profiles. The diffusion coefficients calculated from the slopes in Figs. 1 and 2 are listed in Table 1. The studying the decarburization kinetics. The results of Schmidt Arrhenius plots of diffusion coefficient of carbon in niobium and Carlson6) by diffusion couple method and those of are shown in Fig. 3. The figure also shows experimental Nakonechnikov et al.4) and Son et al.5) by 14C tracer method results obtained by earlier workers.4­7) As seen in Fig. 3, the appear consistent. Our own results match satisfactorily with diffusion coefficients obtained by us are somewhat higher those of Nakonechnikov et al. at lower temperatures. The than those of earlier workers but fairly consistent within differences go up marginally with the increase in temper- themselves. The temperature dependence of diffusion ature. The overall differences do not amount to more than coefficients determined in course of the present investigation 10%. can be expressed by the following equation D=m2 s1 ¼ 2:2 105 expð176 kJ mol1=RTÞ: ð5Þ 3.2 Diffusion of carbon in molybdenum Figures 4, 5 and 6 show the concentration profiles of 14C It is important to note here more than one technique have in molybdenum. The plot of {1 ¹ C(X)/2C0} versus X shows been employed by different workers as shown in Table 2. D0 a linear relationship at all temperatures. Then, influence of and Q are the preexponential factor and the activation energy grain boundary diffusion on the measured diffusion coef- in the Arrhenius relation. Their results are plotted along with ficient is negligible because of the same reason as described our own data in the Fig. 3. Smallest diffusion coefficient above. The diffusion coefficients calculated from the slopes are those reported by Hörz and Lindenmaier7) obtained by in Figs. 4, 5 and 6 are listed in Table 3. The Arrhenius plots Diffusion of Carbon in Niobium and Molybdenum 1789

(a) (a) 0.95 1515 K 1669 K

0.90 o 0.80

1 - C/2C 0.70

0.60

0.50 0123456789 X / 10-4 m (b) 0.95 (b) 1469 K

0.90 o 0.80

1 - C/2C 0.70

0.60

0.50 0123456789 X / 10-4 m (c) 0.95 Fig. 6 Examples of penetration profiles for diffusion of carbon in 1419 K molybdenum at 1569 and 1669 K. 0.90 Table 3 Diffusion coefficient of carbon in molybdenum. o ¹ 0.80 Temperature/K Diffusion time/s Diffusion coefficient/m2 s 1 1669 9.00 © 102 4.90 © 10¹11 1 - C/2C 0.70 1669 9.00 © 102 4.71 © 10¹11 0.60 1569 7.20 © 103 2.60 © 10¹11 © 3 © ¹11 0.50 1569 7.20 10 3.08 10 0123456789 1515 2.05 © 104 1.18 © 10¹11 -4 X / 10 m 1515 2.05 © 104 1.24 © 10¹11 ¹ Fig. 5 Examples of penetration profiles for diffusion of carbon in 1469 5.76 © 104 3.57 © 10 12 molybdenum at 1419, 1469 and 1515 K. 1469 5.76 © 104 6.09 © 10¹12 1419 1.48 © 105 3.10 © 10¹12 1419 1.48 © 105 2.76 © 10¹12 1376 1.73 © 105 7.04 © 10¹13 of diffusion coefficient of carbon in molybdenum are shown 1376 1.73 © 105 3.20 © 10¹13 in Fig. 7. This figure also includes the experimental results of 1271 8.73 © 105 2.84 © 10¹14 previous workers.4,9,11­14) The temperature dependence of the 1271 8.73 © 105 6.12 © 10¹14 diffusion coefficients determined in the course of present investigation below 1515 K is expressed by the following equation D=m2 s1 ¼ 2:2 105 expð367 kJ mol1=RTÞ: ð6Þ hydrocarbons, oxygen and nitrogen in the annealing atmospheres. The large distribution in the magnitudes of preexponential (4) In most of the cases, there is a paucity of data points in factors and the activation energies reported by different the diffusivity plots. In view of this, determination of a authors listed in Table 4 is truly surprising. The preexponen- truly representative of preexponential factor and tial factors range from 7.3 © 10¹11 to 4.0 © 10¹6 m¹2 s¹1. activation energy is difficult. The activation energies range from 73 to 382 kJ mol¹1. This Above 1540 K, the temperature dependence of diffusion variation could be attributed to the following factors: coefficients obtained by Schmidt and Carlson,12) Kunze and (1) The differences in the techniques used for measure- Reichelt11) and Lorang and Langeron14) are consistent with ments by different authors. the present work. On the other hand the Arrhenius plot (2) Variations in the impurity level and contents of the obtained by Rudman9) and Nakonechnikov et al.4) are little specimens used by different authors. lower than above results. However, the results of Lesage (3) Because of the high reactivity of molybdenum, the and Huntz13) are significantly lower than all other authors results could also be influenced by the presence of yielding very high activation energy. Present results below 1790 J. Imai, O. Taguchi, G. P. Tiwari and Y. Iijima

Table 4 Previous data on diffusion of carbon in molybdenum.

Temperature D Q Authors 0 Method /K /m2 s¹1 /kJ mol¹1 Schnitzel (1964) 300­673 7.3 © 10¹11 73 internal friction Nakonechnikov 1473­1873 2.0 © 10¹6 172 14C tracer et al. (1966) Rudman (1967) 1783­2243 3.4 © 10¹6 172 carburization Shchelkonogov 293­673 2.8 © 10¹8 167 internal friction et al. (1968) Kunze and Reichelt 1508­2033 4.0 © 10¹6 164 decarburization (1970) Schmidt and Carlson 2163­2593 3.3 © 10¹6 153 diffusion couple (1976) Lesage and Huntz 1079­1513 4.16 © 10¹8 382 14C tracer (1976) Lorang and 1533­2283 1.04 © 10¹6 139 decarburization Langeron (1978)

D=m2 s1 ¼ 2:2 106 expð152 kJ mol1=RTÞ: ð7Þ

In case of molybdenum, there is break in diffusivity plot. Hence, we must have two different expressions for low and Fig. 7 Arrhenius plot of diffusion coefficients of carbon in molybdenum. high temperature regions. Prior to this, we would like to discuss the results of Lesage and Huntz.13) These data obtained through decarburization technique are smaller than 1515 K are similar to that of Lesage and Huntz13) in one our results in the overlapping temperature region by more respect. There is break in the diffusivity plots suggestive of than an order of magnitude. The specimen employed by a bimodal diffusion behavior indicating that the diffusion Lesage and Huntz13) contained 300 mass ppm of carbon and parameters may be different in different temperature regions. therefore contained a fine dispersion of carbides. Some of these precipitates may not contain carbon in full stoichio- 4. Discussion metric ratio. This kind of precipitates may interfere with flux of diffusing carbon atoms by trapping them. Such a In a situation when we are faced with more one expression phenomenon can lead to low apparent diffusivity. Thus when for diffusion coefficient, it is imperative to find an expression diffusing species is chemically reactive in nature, a strict which represents, as closely as possible, the parameters control on the composition of the matrix is essential. The defining the process of diffusion under consideration. The solubility of carbon in molybdenum has been measured by choice becomes easier if the diffusion coefficients covering Gebhardt et al.17) and by Rudman.9) The temperature five to six decades of diffusion coefficients over extended dependence of the solubility Cs (mass ppm) is expressed by temperature ranges are available.16) As seen in the Tables 2 Gebhardt et al.17) as and 4, the temperature range of most measurements does not ln Cs ¼ 15:64 2:075 104=T ð8Þ exceed 500 K. In case of niobium, Powers and Doyle3) have pointed out that the internal friction peak observed by Wert2) and by Rudman9) as 8) is due to oxygen atoms. Schnizel has obtained very small ln Cs ¼ 16:78 2:29 104=T: ð9Þ activation energy for carbon diffusion in molybdenum by internal friction measurements. This is probably caused by Thus, the carbide precipitates in the specimen containing the fact that broad internal friction peaks observed sometimes 300 mass ppm of carbon dissolve above 2088 K (eq. (8)) or arise from the interactions between oxygen, nitrogen and 2067 K (eq. (9)). Therefore, if Lesage and Hunts13) extended carbon atoms. It is not easy to identify the intrinsic peak the temperature range of measurements above the precip- caused by carbon diffusion. Hence, the diffusion data itation temperature, the observable diffusion coefficients are obtained by internal friction measurements are excluded. consistent with the diffusivity data at higher temperatures. As In case of niobium, if disregard the results of Hörz seen in Fig. 7, if the Arrhenius line obtained by Lesage and and Lindenmaier,7) the present results along with those of Hunts13) is extended to higher temperature, it crosses the Nakonechnikov et al.4) Son et al.5) and Schmidt and Arrhenius lines obtained by Scmidt and Carlson,12) Lorang Carlson6) constitute a consistent set of data. There is a good and Langeron14) and Kunze and Reichelt11) at about 2000 K, degree of consistency at low and high temperature region and which is near to the carbide dissolving temperature estimated variations in the middle range are restricted to a few percent as above. On the other hand, Kunze and Reichelt11) used the points only. A least mean square fit giving equal weight to all molybdenum specimen containing 130 at ppm of carbon. data points may yield a truly representative expression to Hence, the precipitation temperature of carbide in the characterize the diffusion of carbon in niobium as follows: specimen is estimated to be 1613 K (eq. (8)) or 1635 K Diffusion of Carbon in Niobium and Molybdenum 1791

(eq. (9)). These temperatures are close to 1618 K, from where 5. Conclusions downward deviation from Arrhenius line begins in exper- imental results reported by Kunze and Reichelt.11) Further- The diffusion coefficient of carbon in niobium observed by more, the activation energy observed below 1515 K by the the present experiments is consistent with those of previous present experiment is 367 kJ mol¹1 which is close value to authors. The experimental data on diffusion of carbon in 382 kJ mol¹1 observed by Lesage and Hunts.13) This suggests molybdenum by previous authors and the present work are that the same diffusion mechanism is operative on the both analyzed in view of carbon content in the specimens. The cases. The bending temperature of the Arrhenius line of the significant influence of carbide precipitates on diffusion of present results is 1563 K. Therefore, the solubility of carbon carbon in molybdenum is emphasized. Tracer diffusion studies in the present specimen can be estimated to be 10.6 mass ppm in high purity materials are needed to establish true coefficients (eq. (8)) or 8.4 mass ppm (eq. (9)). This is consistent with the of carbon, nitrogen and other metalloids in metallic systems. value of 10 mass ppm observed by Suezawa and Kimura18) in “low carbon molybdenum rod” supplied by Climax REFERENCES Molybdenum Company. As mentioned earlier, the temper- ature dependence of the diffusion coefficients of carbon 1) Creep-resistant steels, ed. by F. Abe, T.-U. Kern and R. Viswanathan, in molybdenum can be represented by combining the (Woodhead Publishing Limited, Cambridge, 2008). experimental results obtained above 1540 K by Schmidt 2) C. A. Wert: J. Appl. Phys. 21 (1950) 1196. 12) 11) 3) R. W. Powers and M. V. Doyle: J. Appl. Phys. 30 (1959) 514. and Carlson, Kunze and Reichelt and Lorang and 4) A. I. Nakonechnikov, L. V. Pavlinov and V. N. Bykov: Phys. Met. 14) Langeron including the present results as follows: Metallogr. 22 (1966) 73. D=m2 s1 ¼ 5:2 106 expð163 kJ mol1=RTÞð10Þ 5) P. Son, S. Ihara, M. Miyake and T. Sano: J. Japan Inst. Metals 31 (1967) 998. It is important to emphasize here that there exists a paucity 6) F. A. Schmidt and O. N. Carlson: J. Less Common Met. 26 (1972) 247. fi 7) G. Hörz and K. Lindenmaier: Z. Metallk. 63 (1972) 240. of data of suf cient precision on the diffusion of metalloids in 8) R. H. Schnitzel: Trans. Met. Soc. AIME 230 (1964) 609. metals. On the other hand, for the diffusion of substitutional 9) S. Rudman: Trans. Met. Soc. AIME 239 (1967) 1949. solutes in metallic systems good quality data on a wide 10) V. Ya. Shchelkonogov, L. N. Aleksandrov, V. A. Piterimov and V. S. ranging system are available.19) The situation is complicated Mordyuk: Phys. Met. Metallogr. 25 (1968) 68. by two main reasons. As evident from the Table 2 and 4, a 11) J. Kunze and W. Reichelt: J. Less Common Met. 20 (1970) 327. 12) F. A. Schmidt and O. N. Carlson: Met. Mater. Trans. A 7 (1976) 127. wide variety of techniques have been employed and the 13) B. Lesage and A. M. Huntz: Memo. Sci. Rev. Met. Janvier (1976) 19. results from different techniques are inconsistent with each 14) G. Lorang and J. P. Langeron: High Temp. High Press. 10 (1978) 165. other. We need radioactive tracer diffusion coefficient 15) P. L. Gruzin: Dokl. Akad. Nauk. SSSR 86 (1952) 289. measurements over extended temperature ranges so that the 16) S. J. Rothman: Diffusion in Crystalline Solids, ed. by G. M. Murch and ­ curvature in the diffusivity plots can be delineated and A. S. Nowick, (Academic Press, Inc., Orland, 1984) pp. 1 61. fi 17) E. Gebhardt, E. Fromm and U. Roy: Z. Metallk. 57 (1966) 732. identi ed. Because of the reactive nature of metalloids, it is 18) M. Suezawa and H. Kimura: Philos. Mag. 28 (1973) 901. also essential to use only high purity materials in such 19) Diffusion in Solid Metals and Alloys, Landort-Börnstein, New Series, studies. Group 3, Vol. 26, ed. by H. Mehrer, (Springer, Berlin, 1990).