Interdiffusion in the Ni–Mo system

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Scripta Materialia 62 (2010) 621–624 www.elsevier.com/locate/scriptamat

Interdiffusion in the Ni–Mo system V.D. Divya, S.S.K. Balam, U. Ramamurty and A. Paul* Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India Received 6 December 2009; accepted 7 January 2010 Available online 11 January 2010

The interdiffusion coefficient in Ni(Mo) solid solution, impurity diffusion of Mo in Ni, average interdiffusion coefficient of the NiMo–r phase and activation energies for diffusion in solid solution and in the r phase of the Ni–Mo binary system are evaluated through the diffusion couple approach. These results are utilized to identify the possible diffusion mechanism. Low activation energy in the r phase indicates a grain-boundary-controlled diffusion process. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Diffusion; Intermetallics; TCP phase

Nickel-based superalloys are used extensively in jet engines and land-based gas turbines because of their superior strength, creep resistance, fracture toughness and excellent phase stability. Significant amounts of refractory elements, such as Mo, W, Re and Ru, are added to enhance the creep resistance in current generation single or polycrystalline superalloys [1–3]. However, these elements can lead to the formation of topologically close-packed (TCP) phases, such as r, l and Laves phases, due to the combination of high temperature and/or stress during service. Typically, these phases tend to be brittle in nature and hence suppression of their formation is desirable [4–7]. This, in turn, requires a thorough understanding of their formation kinetics. Among various possible combinations, the Ni–Mo system is of importance as it promotes the formation of r phase. Despite the fact that diffusion plays an important role in the growth of TCP phases, only few studies have focused on diffusion in this system [8–13]. Davin et al. [8,9] reported that the activation energy remains invariant with respect to the composition in Ni(Mo) solid solution. Heijwegen and Reick [10] and Karunaratne and Reed [11] found that the interdiffusion coefficient and the activation energy do not vary significantly with the composition. However, their studies were limited to the two compositions of 85 and 95 at.% Ni. While these authors also conducted Kirkendall marker experiments using W wire and ZrO2 oxide particles to study the relative mobilities of the species,

* Corresponding author. E-mail: [email protected]

problems such as W reacting with the alloy system and non-reliability in determining the position of the ZrO2 particles complicated the interpretation of the experimental data. Also, the calculated diffusion parameters in the NiMo–r phase suffer from high scatter in the experimental results. Lanam and Heckel [12] calculated the average interdiffusion coefficient in the solid solution, whereas Chou and Link [13] also studied interdiffusion in this system and calculated the parabolic growth constants of the phases. However, it should be pointed out that the relation used to calculate the parabolic growth constant developed in systems with a planar interface cannot be used directly in the systems considered by Chou and Link, which are cylindrical in geometry. In a diffusion couple with cylindrical geometry, unlike a diffusion couple with a planar interface, the interfacial area changes continuously with time. It is thus apparent that further detailed diffusion study is required in this system. In this work, diffusion couple experiments were conducted to determine the diffusion parameters and the activation energy for diffusion in Ni(Mo) solid solution. Foils of Ni (1 mm thickness) and Mo (0.25 mm thickness) with 99.95 wt.% purity supplied by Alfa Aesar, USA were used as the starting materials. Pieces of approximately 7  7 mm2 cross-section were cut from the foils. The bonding faces of the couple halves were ground and then fine polished with 0.25 lm alumina slurry. The polished surfaces were cleaned ultrasonically in ethanol and dried in hot air. The bonding halves were then clamped in a special fixture with the minimum pressure required to allow good contact between the

1359-6462/$ - see front matter Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2010.01.008

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V. D. Divya et al. / Scripta Materialia 62 (2010) 621–624

bonding surfaces. Experiments were conducted in vacuum (106 mbar) in the temperature range of 1050– 1225 °C for 9 h. To check the parabolic growth of the product phase, one set of experiments was conducted at 1050 °C for different annealing times in the range of 9–49 h. The temperature was controlled within ±2 °C. Prior to annealing, particles of titanium dioxide (TiO2) are introduced as the Kirkendall markers at the bonding interface. The oxide powder, with a particle size of around 1 lm, was dispersed in acetone and then applied onto the bonding surfaces before joining. After standard metallographic preparation, cross-sections of annealed diffusion couples were examined in a scanning electron microscope (SEM). Compositional profiles of the interdiffusion zone were determined with an energy-dispersive X-ray spectrometer attached to the SEM. The position of the Kirkendall marker plane was monitored by the presence of an X-ray peak of Ti. Figure 1a shows a micrograph of the interdiffusion zone that developed due to annealing at 1150 °C. Figure 1b shows the corresponding composition profile. It can be seen that only one intermetallic phase, r, grows in the interdiffusion zone [14]. Further, TiO2 particles are found close to the Ni(Mo)/r interface in the Ni(Mo) solid solution part. From the composition analysis, we noted that the solubility limit of Mo in Ni increases with temperature. This can be substantiated from the phase diagram in Ref. [14]. The marker plane is found at

Ni

Ni (ss)

NiMo ( σ phase)

Mo

Composition (Mo at.%)

Mo

Measur ed Aver age

100 80

NiMo (σ phase)

60 40 20

Ni(ss)

Ni

0

10

2

ðDxr Þ ð1Þ 2t At 1050 °C, k p = 6.35  1016 m2 s1. Further, the activation energy, Q (J mol1), for the parabolic growth is determined from the Arrhenius equation,   Q k p ¼ k 0p exp  ð2Þ RT kp ¼

where k 0p (m2 s1) is the pre-exponential factor, R (J mol1 K1) is the gas constant and T is the temperature (K). The Arrhenius plot of the parabolic growth constant is shown in Figure 2, which yields a value of 57.8 kJ mol1 for Q. Note that k p is not a material constant but depends on the end member compositions in a particular diffusion couple. It is thus important to calculate the diffusion parameters, which are materials constants. It can be seen in Figure 1b that the solubility limit of Mo in Ni in the Ni(Mo) solid solution part is reasonably high and it is possible to determine the variation of ~ with respect to composition interdiffusion coefficient, D, following [15]     Z 1 Z x V m dx Y 1Y    ~ DðY Þ ¼ ð1  Y Þ dx þ Y dx 2t dY Vm 1 V m x ð3Þ

K

0

different compositions and temperatures, as listed in Table 1. To check the parabolic nature of the growth of the r phase, experiments were conducted for different annealing times in the range of 9–49 h, first at 1050 °C. The parabolic growth constant, k p , is related to the layer thickness of the r phase, Dxr , and the annealing time, t, according to

20

30

40

50

60

70

Distance (μm)

Figure 1. (a) Back-scattered electron image of the interdiffusion zone developed in the Mo/Ni diffusion couple annealed at 1150 °C for 9 h. K indicates the position of the Kirkendall marker plane. The unaffected Ni end member is far away from the Ni(Mo) part shown in the micrograph. (b) The corresponding composition profile measured, with the average considered for the calculations.

where x is the position parameter. Y is the Sauer–Freise N N variable [16], which is expressed as N þi Ni , where N i is the i i mole fraction of component i. The superscripts + and  refer to the mole fraction at the unreacted left-hand (x ¼ 1) and right-hand (x ¼ þ1) ends of the couple, respectively, and V m is the molar volume. The variation of molar volume with composition is calculated from the lattice parameter data available in the literature [17]. The interdiffusion data calculated in Ni(Mo) is presented in Figure 3a. It can be seen that the change in interdiffusion coefficient with composition is minor. ~ is calculated using the The activation energy, Q, for D equation   ~ ¼D ~ 0 exp  Q D ð4Þ RT ~0 The variations in Q and the pre-exponential factor D with composition are shown in Figure 3b, together with the data available in the literature [8–10]. It can be seen that the values do not change with the composition. The same trend was found by Karunaratne and Reed [11], which further indicates that there is not much difference in the vacancy concentration at different compositions in the Ni(Mo) solid solution part. At the position of the marker plane, the ratio of intrinsic diffusion coefficients can be estimated with the aid of the following equation [18]:

V. D. Divya et al. / Scripta Materialia 62 (2010) 621–624

623

Table 1. The compositions of the Kirkendall marker position found at different annealing temperatures are listed along with the diffusion parameters calculated. Temperature (°C) 1050 1100 1150 1200 1225

DNi (m2 s1)

DNi/DMo

Composition (at.% Mo) 20.45 21.78 22.41 23.66 25.00

-14

10

8.27  1016 1.89  1015 5.23  1015 1.04  1014 1.59  1014

2.35  10 4.92  1015 8.15  1015 1.30  1014 1.72  1014

2.84 2.60 1.56 1.25 1.08

10 10

DMo (m2 s1)

15

-13

Ni(Mo) solid solution

-13

~

-15

6.6

6.8

7.0

7.2 -4

7.4

10 7.6

-14

10

-15

10

-16

D (m /s)

2

~ Q (K p )= 57.8 kJ/mol

10

10

~

2

2

Dav (m /s)

k P (m /s)

Q (Dav)= 81 kJ/mol

1050C 1100C 1150C 1200C 1225C

-14

0

5

10

15

20

25

30

Composition (Mo at.%)

-1

1/Tx10 (K )

R1

ð1Y Þ  Y Nþ dx Ni 1 V m dx  N Ni xK Vm R xK Y R 1 ð1Y þ  N Mo 1 V m dx þ N Mo xK V m Þ dx

# ð5Þ

where V Ni and V Mo are the partial molar volumes of the species at the Kirkendall marker plane. As mentioned earlier, the solubility limits of Mo in Ni increases with temperature. This results in the markers being at different compositions for different temperatures. From the knowledge of the ratio of diffusivities, we can determine the intrinsic diffusion coefficients of the species with the ~ following help of already calculated values of D ~ ¼ C Ni V Ni DMo þ C Mo V Mo DNi D

ð6Þ

Here C Ni and C Mo are the concentrations of elements Ni and Mo, respectively. The calculated values of DNi and DMo are listed in Table 1. If we consider that the ratio of diffusivities at a particular composition does not change much with the change in temperature, then it Ni can be stated that DDMo decreases with the increase in Mo composition. This indicates a change in jump frequency with the change in composition. ~ with the change in composition The variation in D can be used to estimate the impurity diffusion coefficient of Mo in Ni, DMoðNiÞ . The interdiffusion coefficient in a binary A–B system is related to the impurity diffusion coefficient of elements following [19]:   cDT s NB NA ~ ð7Þ D ¼ UAB ðDAðBÞ Þ ðDBðAÞ Þ exp  RT where A and B are the elements in A–B binary system, UAB ¼ d ln aA =d ln N A is the thermodynamic factor, aA is the activity of element A, DAðBÞ and DBðAÞ are the

250 Pr esent Pr esent Ref. [8,9] Ref. [8,9] Ref. [10] Ref. [10]

200 -3

2

R xK

log Do (m /s)

DNi V Ni ¼ DMo V Mo

"

Q (kJ/mol)

300

Figure 2. The Arrhenius plot of the parabolic growth constant kp and ~ av of the r phase. D

-4 -5 -6 3

6

9

12

15

18

21

24

Composition (Mo at.%)

~ at different temperatures with the change in Mo Figure 3. (a) D composition in the Ni(Mo) solid solution. (b) The variation of activation energy and pre-exponential factor with the change in Mo composition in Ni(Mo) solid solution calculated in this work is compared with the data reported in the literature.

impurity diffusion coefficients of A in B and B in A, respectively, DTs is the difference between the solidus temperature and the linear variation between the melting points of A and B, and c is the structure dependent ~ at Mo = 0 at.% coefficient. The extrapolated value of D gives DMoðNiÞ :DMoðNiÞ is plotted with respect to Arrhenius equation in Figure 4 and the activation energy for diffusion is found to be 238.75 kJ mol1. The value calculated in this study is found to be around 40 kJ mol1 less than the value found by Karunaratne and Reed [11] and Ugaste and Pimenov [20]. The change in composition is small in the r phase and ~ However, if one first hence it is difficult to calculate D. ~ int , then calculates the integrated diffusion coefficient, D it is possible to determine the average interdiffusion ~ av following coefficient D

V. D. Divya et al. / Scripta Materialia 62 (2010) 621–624 10

-13

10

-14

10

-15

boundary and lattice diffusion. The exact contributions of the different mechanisms are difficult to determine, because the grain size changes continuously with time. However, the activation energy calculated indicates that it is the diffusion process that actually controls the growth of the phases. The relatively low activation energy in the r phase indicates that it is a grain-boundary-diffusion-controlled process. It should also be pointed out that different phases can grow by different diffusion mechanisms, depending on the grain size in the phase of particular interest. For example, relatively ~ in the Ni(Mo) sohigh values of activation energy for D lid solution part indicate that the diffusion in this part mainly occurs by lattice diffusion.

2

DMo(Ni) (m /s)

624

QMo(Ni) = 238.75 kJ/mol

6.6

6.8

7.0

7.2 -4

7.4

7.6

-1

1/Tx10 (K )

Figure 4. DMo(Ni) at different temperatures with respect to the Arrhenius relation.

~ ~ av ¼ Dint ¼ D DN rB

R N 00B N 0B

~ B DdN

ð8Þ

DN rB

where DN rB ¼ N 00B  N 0B is the composition range of the r ~ int of the r phase can be calculated following phase. D 2

r  þ r ~ r ¼ ðN B  N B Þ ðN B  N B Þ ðDxr Þ D int 2t Nþ  N B "B Z x1r b þ r Dxr N B  N B Vm þ ðN B  N  B Þ dx þ   2t N B  N B 1 V m  Z þ1 b N rB  N  Vm þ B  ðN  N B Þ dx þ þ NB  N Vm B x2r B

ð9Þ

where N rB is the average composition, V rm is the molar volume and Dxr ¼ x2r  x1r is the thickness of the r ~ av calculated at different temperatures are plotphase. D ted in Figure 2. The activation energy for diffusion is found to be 81 kJ mol1, which is much lower than the activation energy calculated by Heijwegen and Reick [10]; however, they did not report the diffusion data points and also mentioned that there was a high experimental error. We measured the apparent diffusion coefficient, which includes contributions from both grain

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