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CrMo composition-modulated films
Scripta Materialia 51 (2004) 119–124 www.actamat-journals.com
Diffusion in Ni/CrMo composition-modulated films Alan F. Jankowski *, Cheng K. Saw Lawrence Livermore National Laboratory, Chemistry and Materials Science, P.O. Box 808, L-352, Livermore, CA 94551-9900, USA Received 17 November 2003; received in revised form 30 March 2004; accepted 30 March 2004
Abstract The diffusivity in a Ni–Cr–Mo alloy is determined using a composition-modulated structure of alternating Ni and Cr–Mo layers. The decay of the composition modulation is measured using X-ray diffraction and analyzed through the microscopic theory of diffusion. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Diffusion; Multilayers; Alloy; Composition-modulation
1. Introduction The behavior of the Ni–Cr–Mo alloy system has been studied extensively at high temperatures [1–5]. Aging effects on the microstructure are known in this alloy system, as e.g. heterogeneous precipitation. The stability of the Ni–22wt.%Cr–13wt.%Mo corrosion-resistant alloy at low temperature can be made by an extrapolation from high-temperature data. As an alternative, a direct assessment of stability at temperatures below 800 K is made possible by measuring the interdiffusion of alternating Ni and Cr–Mo layers. An isothermal anneal temperature of 760 K is selected as this temperature is less than the 800 K lower bound that’s normally associated with direct observation of intermetallic phase formation in the Ni–22wt.%Cr–13wt.%Mo, i.e. Ni2 (Cr, Mo) alloy [1,4,5]. There is significant interest for the use of this alloy as a containment vessel for the long-term storage of high-level radioactive materials at temperatures below 500 K [5]. The use of composition-modulated materials, such as multilayers, is a proven method to examine the interdiffusion of materials in samples at low temperatures [6–8]. X-ray diffraction is used to measure the changes in the composition profile that result from the anneal treatments [6–8,12]. The diffusion kinetics are quantified by analyzing the decay of the nanometer-scaled composition fluctuation using the *
Corresponding author. Tel.: +1-9254232519; fax: +1-9254220049. E-mail address: [email protected] (A.F. Jankowski).
microscopic theory of diffusion [6,9–12]. In this study, three Ni/CrMo samples, each of a different composition wavelength are used to determine the corresponding B ) using the microscopic interdiffusivity coefficient (D theory of diffusion. The DB values are then fit as functions of the composition wavelength to determine the [12]. macroscopic diffusion coefficient (D)
2. Experimental Method 2.1. Sample preparation The synthesis of the composition-modulated structures enables an initial study of solid-solution kinetics at low temperature in the Ni–22wt.%Cr–13wt.%Mo alloy. The Ni/CrMo multilayer films are prepared by planar magnetron sputter deposition. The deposition chamber is cryogenically pumped to a base pressure of 1.6 · 105 Pa. Three deposition sources are equally spaced 10 cm beneath the substrate platen. An argon gas pressure of 0.67 Pa, at a mass flow rate of 0.42 cm3 s1 , is used to sputter the 6.3 cm diameter targets. The magnetron sources are operated at 260–300 V discharges in the dc mode with 100–134 W forward power. These sputter deposition parameters used for the working gas pressure, source-to-substrate separation, and discharge voltage produce sputtered neutrals that are in a nearthermalized condition when arriving at the substrate [13,14].
1359-6462/$ - see front matter 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2004.03.045
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Table 1 Interdiffusivity parameters of Ni/CrMo multilayers Composition wavelength dNi=CrMo (nm)
Layers N
Normalized satellite intensity as a function of time I i ðtÞ ½I B ðtÞ1 104 i ðt ¼ 0Þ
+1
)1
+1
)1
+1
Amplification factor 2RðkÞ (105 s1 )
0.129 1.286 38.83
0.138 0.229 13.50
0.068 0.148 5.285
0.018 0.191 9.549
0.016 0.112 4.979
)3.28 ± 0.21 3.60 )3.01 ± 0.18 1.58 )2.64 ± 0.04 0.60
i ðt ¼ 2Þ
Rate
X-ray
)1
3.27 4.76 7.90
3.29 ± 0.08 300 4.99 ± 0.17 200 8.10 ± 0.14 120
3.094 2.775 0.174 17.76 18.87 1.703 211.1 288.5 67.44
+1
)1
i ðt ¼ 8Þ
The substrate passes sequentially over each of the targets. Two of the targets are Ni (0.99994 purity) and the third is a composite target comprised of Mo and Cr pieces (0.9994 purity). For the source-to-substrate distance and the sputter gas parameters used in these depositions, a 2:1 ratio of the Cr to Mo area in the composite target yields a Cr0:65 Mo0:35 film composition, as verified using energy dispersive spectroscopy (EDS) measurements. To approximate the alloy composition of Ni0:665 (Cr–Mo)0:335 in the deposited film, the number of atomic planes of Ni to number of atomic planes of Cr– Mo is held constant at a ratio of 5:3. EDS analysis of the multilayers confirms a film composition of 64–67 at.% Ni. The instantaneous deposition rates are calibrated to the applied target power using 6 MHz quartz crystal microbalances. The deposition rates range from 4.5 · 104 to 5.0 · 104 nm W1 s1 . To change the composition wavelength (dNi=CrMo ), the frequency (x) of the substrate table rotation is varied along with the total number (N ) of layer pairs to yield a constant film thickness (N dNi=CrMo ) of 1.0 lm. The measurements of dNi=CrMo based on deposition rates are listed in Table 1. Sapphire wafers that are 0.50 mm thick are used for the substrates. The temperature of the substrate table remains at 302–319 K during the sputter deposition process. 2.2. Heat treatments The stability of the multilayer is assessed using isothermal anneal treatments to progressively homogenize the artificial composition modulation. The samples are placed in a quartz tube with an inert atmosphere of flowing Argon gas, and annealed using a Lindberge furnace. The samples are heated to a temperature (T ) of 760 ± 12 K at a rate of 0.33 K s1 , held at the anneal temperature for a period of time (t), and subsequently cooled to below 400 K at a rate greater than 2 K s1 . The multilayer samples are successively removed from the furnace hot zone at the time intervals 2, 8, and 20 h. 2.3. X-ray diffraction The Ni/CrMo multilayer films are characterized using a powder diffractometer with Cu Ka X-ray radiation.
i ðt ¼ 20Þ
Dispersion relation B2 ðhÞ (nm2 )
Interdiffu B 1020 sion D (cm2 s1 ) 4.56 ± 0.30 9.53 ± 0.57 22.0 ± 0.33
The diffractometer is equipped with an analyzing monochromator and is operated in the h/2h mode. The high-angle diffraction scans reveal the long-range and short-range ordering of the multilayer. The Bragg reflections indicate the film texture whereas the satellite peaks of increasing order (i) reflect the composition modulation in the growth direction. Reference values of the interplanar d-spacing and 2h position of Ni(1 1 1), Cr(1 1 0), and Mo(1 1 0) are 0.2034 nm at 44.51, 0.2040 nm at 44.37, and 0.2225 nm at 40.51, respectively [15]. Each sample is measured in the as-deposited condition (t ¼ 0) and after the anneal treatment.
3. Analysis method A quantification of the interdiffusivity is determined by analyzing the decay of the composition fluctuation (or static concentration wave) using the microscopic theory of diffusion [9–12]. The advantage of the discrete theory in comparison to the continuous theory is that it can be applied to describe ordering, spinodal decomposition, and artificially introduced composition modulation in disordered solutions where the behavior at short wavelengths is of interest. The wavelength, i.e. the layer pair spacing or repeat periodicity, of the composition fluctuation (dNi=CrMo ) is calculated from the separation of the satellites about the Ni/CrMo superlattice reflection in the h/2h diffraction scans. The satellite peaks arise as a consequence of the difference in scattering intensity that results from the composition modulation along the growth direction of the film. An asymmetry in the satellite spectrum is the result of widely different scattering factors and atom sizes of the modulated solid solution [16]. In a symmetric case, the component layers have nearly equivalent scattering factors, densities, and atomic weights [6,8,15]. The intensity of the satellites for the Ni/CrMo multilayer samples should be approximately symmetric. The peak intensity of the satellite I i ðtÞ for each order ðiÞ of reflection is normalized to the Bragg reflection I B ðtÞ. The decrease in I i ðtÞ for the annealed samples from the as-deposited condition of I i ð0Þ indicates a progressive homogenization of the composition fluctuation with time (t) [6,9,11]. The satellite intensities are proportional to the square of the composition profile
A.F. Jankowski, C.K. Saw / Scripta Materialia 51 (2004) 119–124
amplitude. The relative decay in satellite intensity determines the amplification factor RðkÞ, as previously reported [9–11], according to the expression lnfI i ðtÞ ½I i ð0Þ1 g ¼ 2RðkÞ t:
ð2Þ
The dispersion relationship B2 ðhÞ for face-centeredcubic (fcc) growth along the [1 0 0] or [1 1 1] is given by Khachaturyan [11] 2 B2 ðhÞ ¼ 2f1 cosð2phÞg dðhklÞ ;
ð3Þ
where dðhklÞ is the (hkl) interplanar spacing of the Bragg reflection, h ¼ dðhklÞ ðdNi=CrMo Þ
1
ð4Þ
and dNi=CrMo ¼ 2p k 1 :
ð7Þ where Fe ðhÞ is the Fourier transform of the elastic strain energy of the distorted lattice, f 00 is the second derivative with respect to composition of the Helmholtz free energy per unit volume, l is the order of the polynomial, and Kl are the gradient-energy coefficients. In the long wavelength approximation, B2 ðhÞ equals k 2 . Also, f 00 and Kl are identical with those expressions appearing in the continuous theories [17–19] or the discrete theory [20]. Thus, Eq. (7) describes a general polynomial B with B2 ðhÞ that has a behavior for the variation of D An expansion of the diffusion coefficient defined as D. series expression in Eq. (7) yields B ¼ D ½1 þ K 0 B2 ðhÞ þ K 0 B4 ðhÞ þ K 0 B6 ðhÞ þ ; D 1 2 3 ð8Þ 1
B versus where Kl0 equals 2Kl ½f 00 þ Fe ðhÞ . A plot of D 2 B ðhÞ fitted with a polynomial curve determines the diffusion coefficient D.
ð5Þ
Similarly, derivation of the dispersion relationship B2 ðhÞ for body-centered-cubic (bcc) growth along the [1 0 0] or [1 1 0] is again expressed by Eq. (3). However, for [1 1 1] bcc growth the dispersion relationship is given by [11] 2 B2 ðhÞ ¼ 2f1 cos3 ð2phÞg f3dðhklÞ g1 :
is related to [6,12]. Therefore, the diffusion coefficient D the interdiffusivity coefficient DB by the expression [12] n o B ¼ D 1 þ Fe ðhÞ ðf 00 Þ1 þ 2ðf 00 Þ1 R½Kl B2l ðhÞ ; D
ð1Þ
Typically, the decay of the first-order satellites below and/or above the Bragg reflection (i ¼ 1; þ1) are used in the computation of the amplification factor RðkÞ [6,12]. The RðkÞ is related to the generalized interdiffu B through the dispersion relationship B2 ðkÞ as sivity D [11] B: RðkÞ ¼ B2 ðkÞ D
121
ð6Þ
The structural dependency of the interdiffusivity coeffi B is seen in the dispersion relationship that cient(s) D accounts for the multilayer periodicity and growth orientation. can be derived from The bulk diffusion coefficient (D) the interdiffusivity coefficient(s) DB . Typically, the bulk is measured using a macroscopic diffusion coefficient (D) diffusion couple. It’s customary to assume that there is a and T 1 over a wide linear relationship between ln D range of temperatures. The bulk diffusion coefficient (D) represents the long wavelength approximation of the B . A curvilinear fit to the interdiffusivity coefficient D B with variation of the interdiffusivity coefficient D the dispersion relationship B2 ðhÞ yields the bulk diffusion coefficient at B2 ðhÞ equal to zero. That is, a multilayer with an infinite composition wavelength is the equivalent of a macroscopic diffusion couple. Although it may first appear at long repeat periodicities (dNi=CrMo ) B will decrease linearly with B2 ðhÞ or perhaps inthat D versely proportional to B2 ðhÞ, it has been observed that use of a higher-order polynomial relationship fits the B with B2 ðhÞ [6]. Only the higher-order behavior of D polynomial expression can account for the behavior of B with B2 ðhÞ at very short composition wavelengths D
4. Experimental results and analysis The X-ray diffraction scans for the Ni/CrMo multilayer samples (no. 918, 919, and 920) are shown (in Fig. 1a–c) in the as-deposited condition (t ¼ 0) and after anneal intervals (t) of 2, 8, and 20 h. The average multilayer-pair spacing dNi=CrMo computed from the diffraction scans of the as-deposited samples are listed in Table 1. The t ¼ 0 values of dNi=CrMo are in agreement with the microbalance rate measurements. A Bragg reflection for the multilayer coating is found at 44.10 (2h) with an interplanar d-spacing of 0.2052 ± 0.0004 nm. The 0.2052 nm d-spacing is nearly equivalent to that for Cr(1 1 0), and rests between the Ni(1 1 1) and Mo(1 1 0) values, suggesting a (1 1 1)fcc-(1 1 0)bcc superlattice growth. The 0.2052 nm superlattice d-spacing is only 0.7% less than the 0.2068 nm d-spacing measured along (1 1 1) for the Ni(Cr,Mo) solid solution [21]. The change in separation between the superlattice reflection and the satellite peaks indicates a change in the dNi=CrMo after each anneal treatment. The diffraction measurements indicate an increase in dNi=CrMo of up to 3% after 2–8 h and an increase of up to 9% after the 20 h anneal treatment at 760 K. An additional Bragg reflection at 44.45 (2h) on the high-angle side of the superlattice peak appears after the anneal treatments. This location corresponds with the Ni(1 1 1) and Cr(1 1 0) reflections and may indicate some relaxation of the superlattice. Also, note the appearance and slow growth of a very diffuse reflection at 39.6 (2h) in Fig. 1a–c as a
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Fig. 1. The X-ray diffraction patterns for sample (a) no. 918, (b) no. 919, and (c) no. 920 are plots of the logarithmic peak-intensity versus 2h position that reveal changes in the Ni/CrMo superlattice reflections after anneal treatments at 760 K.
result of the anneal treatments. The corresponding dspacing of 0.227 nm can be fitted to a Ni2 (Cr,Mo) intermetallic phase. The 0.227 nm d-spacing fits the (0 0 2) Bragg reflection of the tetragonal r-phase with lattice parameters a ¼ 0:880 nm and c ¼ 0:454 nm, as well as the (0 0 4) Bragg reflection of the orthorhombic P-phase with lattice parameters a ¼ 1:698 nm, b ¼ 0:475 nm, and c ¼ 0:907 nm [5,22]. The possibility of forming an intermetallic at 760 K in the present findings is consistent with an interpretation as deduced from changes in the (1 1 1) d-spacing of long-range ordering for the Ni(Cr,Mo) solid solution below 800 K [21]. However, the diffuse peak at 39.6 (2h) appears statistically insignificant (at less than one part in 106 ) with respect to the intensity of the superlattice Bragg reflection. Thus, a statistical analysis of the kinetics for intermetallic formation is not in competition with homogenization of the concentration wave. The amplification factor RðkÞ for each multilayer is determined from Eq. (1). Data for the decay of the sa1 tellite peak intensity I i ðtÞ ½I B ðtÞ (shown in Fig. 1a–c) are concisely listed in Table 1 with the corresponding time (t in hours) of the anneal treatment. The method to determine the diffraction peak intensities is standard. Each peak is determined using Gaussian(s) fitted to the background intensity. The satellite peak intensities (i ¼ 2, i ¼ 1, i ¼ þ1, and i ¼ þ2) decrease with the
time of the anneal treatment. A rapid non-linear decay of the satellite intensity is initially found after the 2 h anneal treatment. This result is typical for short annealing times and has been attributed to several factors including recrystallization and grain growth that drive the early stages of annealing as well as the nonlinearity of the diffusion equation [6,23]. The RðkÞ value is mathematically determined using a standard linear regression fit to quantify the numerical variation in 1 lnfI i ðtÞ ½I i ð0Þ g with time for t P 2 h. The fitting procedure introduces a statistical error for RðkÞ that is listed in Table 1. Next, the dispersion relationship B2 ðhÞ is quantified for both (1 1 1) fcc and (1 1 0) bcc growth as B is given by Eq. (3). The generalized interdiffusivity D 2 then computed from RðkÞ and B ðhÞ using Eq. (2). The B are listed in Table 1. A values for RðkÞ, B2 ðhÞ, and D B versus B2 ðhÞ is shown in Fig. 2. The data plot of the D points of Fig. 2 are fitted to a (l ¼ 2) second-order polynomial expansion of Eq. (8) resulting in the following expression B ¼ D ½1 0:616B2 ðhÞ þ 0:104B4 ðhÞ: D
ð9Þ
The curve fit (shown in Fig. 2) to the Ni/CrMo data of expressed by Eq. (9) yields a diffusion coefficient D (3.28 ± 0.13) · 1019 cm2 s1 for the Ni–CrMo system at 760 K. A higher-order fit for Eq. (8) cannot be justified since there are only three composition wavelengths.
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123
5. Discussion and Summary
B versus the dispersion Fig. 2. A plot of the interdiffusivity coefficient D relationship B2 ðhÞ for the Ni/CrMo multilayer samples.
for the Ni/CrMo system at 760 K is The value of D consistent with and intermediate to values extrapolated from high temperatures (shown is Fig. 3) for tracer isotopes in Ni diffusion couples. Since it is customary to assume that there is a linear relationship between ln D and T 1 over a wide range of temperatures, the diffusion Þ at temperature T can be described by coefficient DðT the expression Þ ¼ Do eðQ=RT Þ ; DðT
ð10Þ
where Q is the activation energy for diffusion and R is the universal gas constant of 2 kcal mol1 . Using the Monma et al. results [24] for the diffusion of Cr51 in Ni over the temperature range of 1373–1643 K, an extrapolated value of 2.76 · 1019 cm2 s1 is computed Þ at 760 K noting that Q equals 65.1 kcal mol1 for DðT and Do equals 1.1 cm2 s1 . Similarly from the Borisev et al. results [25] for the diffusion of Mo99 in Ni over the temperature range of 1173–1473 K, an extrapolated Þ value of 4.29 · 1018 cm2 s1 is computed at 760 K DðT noting an activation energy Q of 51.0 kcal mol1 and a Do value equal to 1.6 · 103 cm2 s1 .
is plotted as a Fig. 3. The variation of the diffusion coefficient D function of temperature for Cr51 and Mo99 isotope diffusion in Ni along with the present result for the Ni/CrMo multilayer at 760 K.
The microscopic theory of diffusion is now used in the present analysis to treat a pseudo-epitaxial system as a surrogate for a single-phase structure that is typically used in the conventional application. This approach is feasible since the formalism for the dispersion relationship as expressed in Eq. (3) does not differentiate between a fcc (1 0 0), fcc (1 1 1), bcc (1 0 0) or bcc (1 1 0) structure. The single Bragg reflection observed in Fig. 1a–c for the multilayer is consistent with a (1 1 1) fcc Ni and (1 1 0) bcc Cr0:65 Mo0:35 growth variation of these structures. Thus, additional characterization of microstructure beyond the diffraction results is not required at present for the diffusion analysis since a single equation for the dispersion B2 ðhÞ is sufficient to determine the diffusion coefficient for the Ni/CrMo multilayer. Although the topic for a separate detailed presentation, preliminary transmission electron microscopy examination confirms the (1 1 1) fcc and (1 1 0) bcc growth of the Ni/CrMo multilayers. Electron diffraction patterns taken from sample no. 920 in plan view reveal a Kurdjumov–Sachs relationship, as was previously seen for Au/Nb multilayers [26]. A single-phase structure was observed for Au/Nb multilayer composition wavelengths less than 3 nm. The analysis method used at present is appropriate for assessing diffusion in crystalline multilayer structures with well-defined growth orientations [27]. When the high-angle X-ray reflections are not present, as is the case for amorphous multilayer structures, then the grazing angle satellites can be used to determine the diffusion coefficients [28–31]. Use of the grazing angle B of satellites for determining the interdiffusivities D textured-crystalline multilayer materials would not appear rigorous as this approach will omit the crystallographic reference required to determine both the dispersion relationship B2 ðkÞ and amplification factor RðkÞ as seen in Eq. (2). In other words, the use of an amorphous multilayer analysis will eliminate the crystallographic information present at high angle, that is crystallographic orientation and normalization to Bragg peak intensity. The amorphous derivation cannot account for the effects of anisotropy in crystalline structure diffusivity. In summary, the value for the diffusion coefficient D in Ni2 (Cr,Mo) is computed from Ni/CrMo multilayers as the long wavelength equivalent to a macroscopic diffusion couple. The decay rate of the artificially deposited, short-range order is measured by the X-ray diffraction technique and analyzed using the microscopic theory of diffusion. The diffusion coefficient is fit to the variation of the interdiffusion coefficients with the dispersion relationship for three sputter-deposited Ni/ CrMo multilayers, each of a different composition is wavelength. The macroscopic diffusion coefficient D
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found to be 3.28 · 1019 cm2 s1 for Ni2 (Cr,Mo) at 760 K. This value is consistent with an extrapolation of high-temperature tracer diffusion data.
Acknowledgements The authors thank Dr. Patrice Turchi for his thoughtful review of the manuscript. This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under contract No. W-7405Eng-48. References [1] Leonard RB. Corrosion 1969;25:222. [2] Hodge FG. Corrosion 1973;29:375. [3] Raghavan M, Berkowitz BJ, Scanlon JC. Metall Mater Trans A 1982;13:979. [4] Tawancy HM, Herchenroeder RB, Asphahani AI. J Metals 1983; 35:37. [5] Summers TSE, Wall MA, Kumar M, Matthews SJ, Rebak RB. In: Wronkiewicz DJ, Lee JH, editors. Scientific basis for nuclear waste management XXII. Mater Res Soc Symp Proc, vol. 556. Warrendale, PA: Materials Research Society; 1999. p. 919–26. [6] Tsakalakos T. Thins Solid Films 1981;86:79. [7] Jankowski AF, Tsakalakos T. J Appl Phys 1985;57:1835. [8] Jankowski AF, Sedillo EM, Hayes JP. Jpn J Appl Phys 1994;33: 5019.
[9] Khachaturyan AG. Prog Mater Sci 1978;22:1. [10] Cook HE, de Fontaine D, Hilliard JE. Acta Metall 1969;17:765. [11] Khachaturyan AG. Theory of structural transformations in solids. New York: John Wiley and Sons; 1983. pp. 128–36. [12] Jankowski AF, Tsakalakos T. Metall Trans A 1989;20:357. [13] Somekh RE. J Vac Sci Technol A 1984;2:1285. [14] Westwood WD. Mater Res Soc Bull 1988;13(12):46. [15] Cullity BD. Elements of X-ray diffraction. Reading, MA: Addison-Wesley; 1978. p. 512–21. [16] Moss SC. In: Cohen JB, Hilliard JE, editors. Local atomic arrangements studied by X-ray diffraction. New York, NY: Gordon and Breach Science; 1966. p. 114–5. [17] Cahn JW. Acta Metall 1961;9:795. [18] Cahn JW. Acta Metall 1962;10:179. [19] Cahn JW, Hilliard JE. J Chem Phys 1958;28:958. [20] Cook HE, Hilliard JE. J Appl Phys 1969;40:2191. [21] Karmazin L. Mater Sci Eng 1982;54:247. [22] Villars P, Calvert LC. In: Pearson’s handbook of crystallographic data for intermetallic phases (Vol 1). Metals Park, OH: American Society for Metals; 1985. [23] Tsakalakos T. Scripta Metall 1986;20:471. [24] Monma K, Suto H, Oikawa H. J Japan Inst Metals 1964;28: 188. [25] Borisev EV, Gruzin PL, Zemskii SV. Zashch Pokryt Metal 1968;2: 104. [26] Jankowski AF, Perry PL. Thin Solid Films 1990;193/194:799–806. [27] Greer AL, Spaepen F. In: Chang LL, Giessen BC, editors. Synthetic modulated structure materials. New York, NY: Academic Press; 1985. p. 419–86. [28] Spaepen F. Mater Sci Eng 1988;97:403–8. [29] Ross CA, Wu DT, Goldman LM, Spaepen F. J Appl Phys 1992; 72:2773–80. [30] Spaepen F. J Magn Magn Mater 1996;156:407–10. [31] Wang W-H, Bai HY, Wang WK. J Appl Phys 1999;86:4262–6.
Diffusion in Ni/CrMo composition-modulated films Alan F. Jankowski *, Cheng K. Saw Lawrence Livermore National Laboratory, Chemistry and Materials Science, P.O. Box 808, L-352, Livermore, CA 94551-9900, USA Received 17 November 2003; received in revised form 30 March 2004; accepted 30 March 2004
Abstract The diffusivity in a Ni–Cr–Mo alloy is determined using a composition-modulated structure of alternating Ni and Cr–Mo layers. The decay of the composition modulation is measured using X-ray diffraction and analyzed through the microscopic theory of diffusion. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Diffusion; Multilayers; Alloy; Composition-modulation
1. Introduction The behavior of the Ni–Cr–Mo alloy system has been studied extensively at high temperatures [1–5]. Aging effects on the microstructure are known in this alloy system, as e.g. heterogeneous precipitation. The stability of the Ni–22wt.%Cr–13wt.%Mo corrosion-resistant alloy at low temperature can be made by an extrapolation from high-temperature data. As an alternative, a direct assessment of stability at temperatures below 800 K is made possible by measuring the interdiffusion of alternating Ni and Cr–Mo layers. An isothermal anneal temperature of 760 K is selected as this temperature is less than the 800 K lower bound that’s normally associated with direct observation of intermetallic phase formation in the Ni–22wt.%Cr–13wt.%Mo, i.e. Ni2 (Cr, Mo) alloy [1,4,5]. There is significant interest for the use of this alloy as a containment vessel for the long-term storage of high-level radioactive materials at temperatures below 500 K [5]. The use of composition-modulated materials, such as multilayers, is a proven method to examine the interdiffusion of materials in samples at low temperatures [6–8]. X-ray diffraction is used to measure the changes in the composition profile that result from the anneal treatments [6–8,12]. The diffusion kinetics are quantified by analyzing the decay of the nanometer-scaled composition fluctuation using the *
Corresponding author. Tel.: +1-9254232519; fax: +1-9254220049. E-mail address: [email protected] (A.F. Jankowski).
microscopic theory of diffusion [6,9–12]. In this study, three Ni/CrMo samples, each of a different composition wavelength are used to determine the corresponding B ) using the microscopic interdiffusivity coefficient (D theory of diffusion. The DB values are then fit as functions of the composition wavelength to determine the [12]. macroscopic diffusion coefficient (D)
2. Experimental Method 2.1. Sample preparation The synthesis of the composition-modulated structures enables an initial study of solid-solution kinetics at low temperature in the Ni–22wt.%Cr–13wt.%Mo alloy. The Ni/CrMo multilayer films are prepared by planar magnetron sputter deposition. The deposition chamber is cryogenically pumped to a base pressure of 1.6 · 105 Pa. Three deposition sources are equally spaced 10 cm beneath the substrate platen. An argon gas pressure of 0.67 Pa, at a mass flow rate of 0.42 cm3 s1 , is used to sputter the 6.3 cm diameter targets. The magnetron sources are operated at 260–300 V discharges in the dc mode with 100–134 W forward power. These sputter deposition parameters used for the working gas pressure, source-to-substrate separation, and discharge voltage produce sputtered neutrals that are in a nearthermalized condition when arriving at the substrate [13,14].
1359-6462/$ - see front matter 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2004.03.045
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A.F. Jankowski, C.K. Saw / Scripta Materialia 51 (2004) 119–124
Table 1 Interdiffusivity parameters of Ni/CrMo multilayers Composition wavelength dNi=CrMo (nm)
Layers N
Normalized satellite intensity as a function of time I i ðtÞ ½I B ðtÞ1 104 i ðt ¼ 0Þ
+1
)1
+1
)1
+1
Amplification factor 2RðkÞ (105 s1 )
0.129 1.286 38.83
0.138 0.229 13.50
0.068 0.148 5.285
0.018 0.191 9.549
0.016 0.112 4.979
)3.28 ± 0.21 3.60 )3.01 ± 0.18 1.58 )2.64 ± 0.04 0.60
i ðt ¼ 2Þ
Rate
X-ray
)1
3.27 4.76 7.90
3.29 ± 0.08 300 4.99 ± 0.17 200 8.10 ± 0.14 120
3.094 2.775 0.174 17.76 18.87 1.703 211.1 288.5 67.44
+1
)1
i ðt ¼ 8Þ
The substrate passes sequentially over each of the targets. Two of the targets are Ni (0.99994 purity) and the third is a composite target comprised of Mo and Cr pieces (0.9994 purity). For the source-to-substrate distance and the sputter gas parameters used in these depositions, a 2:1 ratio of the Cr to Mo area in the composite target yields a Cr0:65 Mo0:35 film composition, as verified using energy dispersive spectroscopy (EDS) measurements. To approximate the alloy composition of Ni0:665 (Cr–Mo)0:335 in the deposited film, the number of atomic planes of Ni to number of atomic planes of Cr– Mo is held constant at a ratio of 5:3. EDS analysis of the multilayers confirms a film composition of 64–67 at.% Ni. The instantaneous deposition rates are calibrated to the applied target power using 6 MHz quartz crystal microbalances. The deposition rates range from 4.5 · 104 to 5.0 · 104 nm W1 s1 . To change the composition wavelength (dNi=CrMo ), the frequency (x) of the substrate table rotation is varied along with the total number (N ) of layer pairs to yield a constant film thickness (N dNi=CrMo ) of 1.0 lm. The measurements of dNi=CrMo based on deposition rates are listed in Table 1. Sapphire wafers that are 0.50 mm thick are used for the substrates. The temperature of the substrate table remains at 302–319 K during the sputter deposition process. 2.2. Heat treatments The stability of the multilayer is assessed using isothermal anneal treatments to progressively homogenize the artificial composition modulation. The samples are placed in a quartz tube with an inert atmosphere of flowing Argon gas, and annealed using a Lindberge furnace. The samples are heated to a temperature (T ) of 760 ± 12 K at a rate of 0.33 K s1 , held at the anneal temperature for a period of time (t), and subsequently cooled to below 400 K at a rate greater than 2 K s1 . The multilayer samples are successively removed from the furnace hot zone at the time intervals 2, 8, and 20 h. 2.3. X-ray diffraction The Ni/CrMo multilayer films are characterized using a powder diffractometer with Cu Ka X-ray radiation.
i ðt ¼ 20Þ
Dispersion relation B2 ðhÞ (nm2 )
Interdiffu B 1020 sion D (cm2 s1 ) 4.56 ± 0.30 9.53 ± 0.57 22.0 ± 0.33
The diffractometer is equipped with an analyzing monochromator and is operated in the h/2h mode. The high-angle diffraction scans reveal the long-range and short-range ordering of the multilayer. The Bragg reflections indicate the film texture whereas the satellite peaks of increasing order (i) reflect the composition modulation in the growth direction. Reference values of the interplanar d-spacing and 2h position of Ni(1 1 1), Cr(1 1 0), and Mo(1 1 0) are 0.2034 nm at 44.51, 0.2040 nm at 44.37, and 0.2225 nm at 40.51, respectively [15]. Each sample is measured in the as-deposited condition (t ¼ 0) and after the anneal treatment.
3. Analysis method A quantification of the interdiffusivity is determined by analyzing the decay of the composition fluctuation (or static concentration wave) using the microscopic theory of diffusion [9–12]. The advantage of the discrete theory in comparison to the continuous theory is that it can be applied to describe ordering, spinodal decomposition, and artificially introduced composition modulation in disordered solutions where the behavior at short wavelengths is of interest. The wavelength, i.e. the layer pair spacing or repeat periodicity, of the composition fluctuation (dNi=CrMo ) is calculated from the separation of the satellites about the Ni/CrMo superlattice reflection in the h/2h diffraction scans. The satellite peaks arise as a consequence of the difference in scattering intensity that results from the composition modulation along the growth direction of the film. An asymmetry in the satellite spectrum is the result of widely different scattering factors and atom sizes of the modulated solid solution [16]. In a symmetric case, the component layers have nearly equivalent scattering factors, densities, and atomic weights [6,8,15]. The intensity of the satellites for the Ni/CrMo multilayer samples should be approximately symmetric. The peak intensity of the satellite I i ðtÞ for each order ðiÞ of reflection is normalized to the Bragg reflection I B ðtÞ. The decrease in I i ðtÞ for the annealed samples from the as-deposited condition of I i ð0Þ indicates a progressive homogenization of the composition fluctuation with time (t) [6,9,11]. The satellite intensities are proportional to the square of the composition profile
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amplitude. The relative decay in satellite intensity determines the amplification factor RðkÞ, as previously reported [9–11], according to the expression lnfI i ðtÞ ½I i ð0Þ1 g ¼ 2RðkÞ t:
ð2Þ
The dispersion relationship B2 ðhÞ for face-centeredcubic (fcc) growth along the [1 0 0] or [1 1 1] is given by Khachaturyan [11] 2 B2 ðhÞ ¼ 2f1 cosð2phÞg dðhklÞ ;
ð3Þ
where dðhklÞ is the (hkl) interplanar spacing of the Bragg reflection, h ¼ dðhklÞ ðdNi=CrMo Þ
1
ð4Þ
and dNi=CrMo ¼ 2p k 1 :
ð7Þ where Fe ðhÞ is the Fourier transform of the elastic strain energy of the distorted lattice, f 00 is the second derivative with respect to composition of the Helmholtz free energy per unit volume, l is the order of the polynomial, and Kl are the gradient-energy coefficients. In the long wavelength approximation, B2 ðhÞ equals k 2 . Also, f 00 and Kl are identical with those expressions appearing in the continuous theories [17–19] or the discrete theory [20]. Thus, Eq. (7) describes a general polynomial B with B2 ðhÞ that has a behavior for the variation of D An expansion of the diffusion coefficient defined as D. series expression in Eq. (7) yields B ¼ D ½1 þ K 0 B2 ðhÞ þ K 0 B4 ðhÞ þ K 0 B6 ðhÞ þ ; D 1 2 3 ð8Þ 1
B versus where Kl0 equals 2Kl ½f 00 þ Fe ðhÞ . A plot of D 2 B ðhÞ fitted with a polynomial curve determines the diffusion coefficient D.
ð5Þ
Similarly, derivation of the dispersion relationship B2 ðhÞ for body-centered-cubic (bcc) growth along the [1 0 0] or [1 1 0] is again expressed by Eq. (3). However, for [1 1 1] bcc growth the dispersion relationship is given by [11] 2 B2 ðhÞ ¼ 2f1 cos3 ð2phÞg f3dðhklÞ g1 :
is related to [6,12]. Therefore, the diffusion coefficient D the interdiffusivity coefficient DB by the expression [12] n o B ¼ D 1 þ Fe ðhÞ ðf 00 Þ1 þ 2ðf 00 Þ1 R½Kl B2l ðhÞ ; D
ð1Þ
Typically, the decay of the first-order satellites below and/or above the Bragg reflection (i ¼ 1; þ1) are used in the computation of the amplification factor RðkÞ [6,12]. The RðkÞ is related to the generalized interdiffu B through the dispersion relationship B2 ðkÞ as sivity D [11] B: RðkÞ ¼ B2 ðkÞ D
121
ð6Þ
The structural dependency of the interdiffusivity coeffi B is seen in the dispersion relationship that cient(s) D accounts for the multilayer periodicity and growth orientation. can be derived from The bulk diffusion coefficient (D) the interdiffusivity coefficient(s) DB . Typically, the bulk is measured using a macroscopic diffusion coefficient (D) diffusion couple. It’s customary to assume that there is a and T 1 over a wide linear relationship between ln D range of temperatures. The bulk diffusion coefficient (D) represents the long wavelength approximation of the B . A curvilinear fit to the interdiffusivity coefficient D B with variation of the interdiffusivity coefficient D the dispersion relationship B2 ðhÞ yields the bulk diffusion coefficient at B2 ðhÞ equal to zero. That is, a multilayer with an infinite composition wavelength is the equivalent of a macroscopic diffusion couple. Although it may first appear at long repeat periodicities (dNi=CrMo ) B will decrease linearly with B2 ðhÞ or perhaps inthat D versely proportional to B2 ðhÞ, it has been observed that use of a higher-order polynomial relationship fits the B with B2 ðhÞ [6]. Only the higher-order behavior of D polynomial expression can account for the behavior of B with B2 ðhÞ at very short composition wavelengths D
4. Experimental results and analysis The X-ray diffraction scans for the Ni/CrMo multilayer samples (no. 918, 919, and 920) are shown (in Fig. 1a–c) in the as-deposited condition (t ¼ 0) and after anneal intervals (t) of 2, 8, and 20 h. The average multilayer-pair spacing dNi=CrMo computed from the diffraction scans of the as-deposited samples are listed in Table 1. The t ¼ 0 values of dNi=CrMo are in agreement with the microbalance rate measurements. A Bragg reflection for the multilayer coating is found at 44.10 (2h) with an interplanar d-spacing of 0.2052 ± 0.0004 nm. The 0.2052 nm d-spacing is nearly equivalent to that for Cr(1 1 0), and rests between the Ni(1 1 1) and Mo(1 1 0) values, suggesting a (1 1 1)fcc-(1 1 0)bcc superlattice growth. The 0.2052 nm superlattice d-spacing is only 0.7% less than the 0.2068 nm d-spacing measured along (1 1 1) for the Ni(Cr,Mo) solid solution [21]. The change in separation between the superlattice reflection and the satellite peaks indicates a change in the dNi=CrMo after each anneal treatment. The diffraction measurements indicate an increase in dNi=CrMo of up to 3% after 2–8 h and an increase of up to 9% after the 20 h anneal treatment at 760 K. An additional Bragg reflection at 44.45 (2h) on the high-angle side of the superlattice peak appears after the anneal treatments. This location corresponds with the Ni(1 1 1) and Cr(1 1 0) reflections and may indicate some relaxation of the superlattice. Also, note the appearance and slow growth of a very diffuse reflection at 39.6 (2h) in Fig. 1a–c as a
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Fig. 1. The X-ray diffraction patterns for sample (a) no. 918, (b) no. 919, and (c) no. 920 are plots of the logarithmic peak-intensity versus 2h position that reveal changes in the Ni/CrMo superlattice reflections after anneal treatments at 760 K.
result of the anneal treatments. The corresponding dspacing of 0.227 nm can be fitted to a Ni2 (Cr,Mo) intermetallic phase. The 0.227 nm d-spacing fits the (0 0 2) Bragg reflection of the tetragonal r-phase with lattice parameters a ¼ 0:880 nm and c ¼ 0:454 nm, as well as the (0 0 4) Bragg reflection of the orthorhombic P-phase with lattice parameters a ¼ 1:698 nm, b ¼ 0:475 nm, and c ¼ 0:907 nm [5,22]. The possibility of forming an intermetallic at 760 K in the present findings is consistent with an interpretation as deduced from changes in the (1 1 1) d-spacing of long-range ordering for the Ni(Cr,Mo) solid solution below 800 K [21]. However, the diffuse peak at 39.6 (2h) appears statistically insignificant (at less than one part in 106 ) with respect to the intensity of the superlattice Bragg reflection. Thus, a statistical analysis of the kinetics for intermetallic formation is not in competition with homogenization of the concentration wave. The amplification factor RðkÞ for each multilayer is determined from Eq. (1). Data for the decay of the sa1 tellite peak intensity I i ðtÞ ½I B ðtÞ (shown in Fig. 1a–c) are concisely listed in Table 1 with the corresponding time (t in hours) of the anneal treatment. The method to determine the diffraction peak intensities is standard. Each peak is determined using Gaussian(s) fitted to the background intensity. The satellite peak intensities (i ¼ 2, i ¼ 1, i ¼ þ1, and i ¼ þ2) decrease with the
time of the anneal treatment. A rapid non-linear decay of the satellite intensity is initially found after the 2 h anneal treatment. This result is typical for short annealing times and has been attributed to several factors including recrystallization and grain growth that drive the early stages of annealing as well as the nonlinearity of the diffusion equation [6,23]. The RðkÞ value is mathematically determined using a standard linear regression fit to quantify the numerical variation in 1 lnfI i ðtÞ ½I i ð0Þ g with time for t P 2 h. The fitting procedure introduces a statistical error for RðkÞ that is listed in Table 1. Next, the dispersion relationship B2 ðhÞ is quantified for both (1 1 1) fcc and (1 1 0) bcc growth as B is given by Eq. (3). The generalized interdiffusivity D 2 then computed from RðkÞ and B ðhÞ using Eq. (2). The B are listed in Table 1. A values for RðkÞ, B2 ðhÞ, and D B versus B2 ðhÞ is shown in Fig. 2. The data plot of the D points of Fig. 2 are fitted to a (l ¼ 2) second-order polynomial expansion of Eq. (8) resulting in the following expression B ¼ D ½1 0:616B2 ðhÞ þ 0:104B4 ðhÞ: D
ð9Þ
The curve fit (shown in Fig. 2) to the Ni/CrMo data of expressed by Eq. (9) yields a diffusion coefficient D (3.28 ± 0.13) · 1019 cm2 s1 for the Ni–CrMo system at 760 K. A higher-order fit for Eq. (8) cannot be justified since there are only three composition wavelengths.
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123
5. Discussion and Summary
B versus the dispersion Fig. 2. A plot of the interdiffusivity coefficient D relationship B2 ðhÞ for the Ni/CrMo multilayer samples.
for the Ni/CrMo system at 760 K is The value of D consistent with and intermediate to values extrapolated from high temperatures (shown is Fig. 3) for tracer isotopes in Ni diffusion couples. Since it is customary to assume that there is a linear relationship between ln D and T 1 over a wide range of temperatures, the diffusion Þ at temperature T can be described by coefficient DðT the expression Þ ¼ Do eðQ=RT Þ ; DðT
ð10Þ
where Q is the activation energy for diffusion and R is the universal gas constant of 2 kcal mol1 . Using the Monma et al. results [24] for the diffusion of Cr51 in Ni over the temperature range of 1373–1643 K, an extrapolated value of 2.76 · 1019 cm2 s1 is computed Þ at 760 K noting that Q equals 65.1 kcal mol1 for DðT and Do equals 1.1 cm2 s1 . Similarly from the Borisev et al. results [25] for the diffusion of Mo99 in Ni over the temperature range of 1173–1473 K, an extrapolated Þ value of 4.29 · 1018 cm2 s1 is computed at 760 K DðT noting an activation energy Q of 51.0 kcal mol1 and a Do value equal to 1.6 · 103 cm2 s1 .
is plotted as a Fig. 3. The variation of the diffusion coefficient D function of temperature for Cr51 and Mo99 isotope diffusion in Ni along with the present result for the Ni/CrMo multilayer at 760 K.
The microscopic theory of diffusion is now used in the present analysis to treat a pseudo-epitaxial system as a surrogate for a single-phase structure that is typically used in the conventional application. This approach is feasible since the formalism for the dispersion relationship as expressed in Eq. (3) does not differentiate between a fcc (1 0 0), fcc (1 1 1), bcc (1 0 0) or bcc (1 1 0) structure. The single Bragg reflection observed in Fig. 1a–c for the multilayer is consistent with a (1 1 1) fcc Ni and (1 1 0) bcc Cr0:65 Mo0:35 growth variation of these structures. Thus, additional characterization of microstructure beyond the diffraction results is not required at present for the diffusion analysis since a single equation for the dispersion B2 ðhÞ is sufficient to determine the diffusion coefficient for the Ni/CrMo multilayer. Although the topic for a separate detailed presentation, preliminary transmission electron microscopy examination confirms the (1 1 1) fcc and (1 1 0) bcc growth of the Ni/CrMo multilayers. Electron diffraction patterns taken from sample no. 920 in plan view reveal a Kurdjumov–Sachs relationship, as was previously seen for Au/Nb multilayers [26]. A single-phase structure was observed for Au/Nb multilayer composition wavelengths less than 3 nm. The analysis method used at present is appropriate for assessing diffusion in crystalline multilayer structures with well-defined growth orientations [27]. When the high-angle X-ray reflections are not present, as is the case for amorphous multilayer structures, then the grazing angle satellites can be used to determine the diffusion coefficients [28–31]. Use of the grazing angle B of satellites for determining the interdiffusivities D textured-crystalline multilayer materials would not appear rigorous as this approach will omit the crystallographic reference required to determine both the dispersion relationship B2 ðkÞ and amplification factor RðkÞ as seen in Eq. (2). In other words, the use of an amorphous multilayer analysis will eliminate the crystallographic information present at high angle, that is crystallographic orientation and normalization to Bragg peak intensity. The amorphous derivation cannot account for the effects of anisotropy in crystalline structure diffusivity. In summary, the value for the diffusion coefficient D in Ni2 (Cr,Mo) is computed from Ni/CrMo multilayers as the long wavelength equivalent to a macroscopic diffusion couple. The decay rate of the artificially deposited, short-range order is measured by the X-ray diffraction technique and analyzed using the microscopic theory of diffusion. The diffusion coefficient is fit to the variation of the interdiffusion coefficients with the dispersion relationship for three sputter-deposited Ni/ CrMo multilayers, each of a different composition is wavelength. The macroscopic diffusion coefficient D
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found to be 3.28 · 1019 cm2 s1 for Ni2 (Cr,Mo) at 760 K. This value is consistent with an extrapolation of high-temperature tracer diffusion data.
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