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Available online at www.sciencedirect.com ScienceDirect Acta Materialia 82 (2015) 51–63 www.elsevier.com/locate/actamat The as-deposited structure of co-sputtered Cu–Ta alloys, studied by X-ray diffraction and molecular dynamics simulations ⇑ Claudia M. Müller,a Stefan Parviainen,b Flyura Djurabekova,b Kai Nordlundb and Ralph Spolenaka, a b Laboratory for Nanometallurgy, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland Department of Physics and Helsinki Institute of Physics, University of Helsinki, PO Box 43, 00014 Helsinki, Finland Received 24 June 2014; revised 10 August 2014; accepted 14 August 2014 Abstract—In this study a direct comparison between lattice spacings predicted by molecular dynamics (MD) simulations and values measured from sputtered Cu–Ta films by X-ray diffraction (XRD) is reported. The study spans the entire composition range between pure Cu and pure Ta and takes into account all the phases documented for the Cu–Ta system in the literature (i.e. a-Cu, a-Ta, b-Ta as well as X-ray amorphous structures). For both the experiments and the MD simulations the results are compared to the literature and discrepancies are critically discussed. A direct comparison between simulation and experiments shows that the MD simulations reproduce the interatomic distances observed in the experiments accurately over most of the composition range, with the exception of alloys with 15–30 at.% Ta content where the MD simulations show spontaneous amorphization whereas the experiments suggest that Ta-rich particles are formed in face-centered cubic solid-solution phase. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Sputter deposition; Immiscible materials; Thin films; Molecular dynamics 1. Introduction Copper and tantalum differ significantly in their physical properties, especially in their melting point and crystal structure. In equilibrium, copper and tantalum are completely immiscible [1]: their enthalpy of mixing is usually assumed to be + 3 kJ mol–1 (0.03 eV atom–1) [2], although ab initio calculations indicate that it might in fact be considerably larger [3]. Homogeneous alloys of copper and tantalum have been prepared by non-equilibrium methods, such as mechanical alloying [4,5], ion beam assisted methods [6–8] or physical vapor deposition [9–13], e.g. sputtering. The as-deposited structure of co-sputtered Cu–Ta alloys was found to depend on the alloy composition. Generally, for Cu-rich alloys a facecentered cubic (fcc) solid-solution phase is formed, often with (1 1 1) texture. For Ta-rich alloys a solid solution of either a- or b-Ta structure is observed (i.e. body-centered cubic (bcc) or b-uranium structure). For intermediate compositions, a X-ray amorphous phase is formed [9–13]. Both the composition ranges in which the different phases were observed and the structure of the Ta-rich solid-solution phase vary between different publications. With the advances in computational power over the last years, modeling [14], in particular molecular dynamics ⇑ Corresponding author. Tel.: +41 44 632 2590; e-mail: ralph.spolenak @mat.ethz.ch (MD) [15], has become an increasingly important technique in materials science. MD solves the equations of motion of a system of atoms whose interaction is described by an interatomic potential. Depending on the material type, there are different approaches for the potential function. The embedded atom method (EAM) by Baskes and Dawes [16–18] has become the commonly accepted approach for atomistic simulations in metals and alloys. EAM potentials for Cu–Ta have been developed by several groups: Klaver et al. [3,19,20], Heino and Ristolainen [21,22], Francis et al. [23], Li and Adams [24] and Gong et al. [7,25–28]. The EAM method has later been generalized by Mishin et al. [29]; this so-called angular-dependent potential (ADP) method avoids the central-force description of conventional EAM by introducing angular terms into the potential. An ADP-type Cu–Ta potential was developed by Hashibon et al. [30] for the study of surface wetting; it has been used recently to describe structure evolution (segregation) during high-temperature annealing [31]. While the ADP potential is assumed to provide a more accurate description of the directional bonding components present in transition metals compared to the EAM method, it has been reported that the latter still gives reasonable results, even for the non-cubic b-Ta phase [20,32]. All these potentials have one feature in common: they have been applied to various problems such as thin-film growth [3,19,20,23,24], mechanical properties of interfaces [21,22], interface structure [27], solid-state amorphization [25] and wetting [30], but a systematic comparison between experimentally http://dx.doi.org/10.1016/j.actamat.2014.08.066 1359-6462/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. 52 C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 observed and simulated structures over the entire composition range has not been reported so far. In the present study such a comparison is made. The EAM potential of Gong et al. [25] was chosen for this because it has been used most extensively in literature. substrate. The Si-K peak was therefore excluded from the analysis, eliminating the problem of Ta-M and Si-K peak overlap. The Cu-L and Ta-M lines were used for the analysis of the spectra, and Gaussian peak fits and Proza correction were applied. On average, the standard deviation was < 1 at.%; for all samples it was < 3 at.%. 2. Experimental details 2.3. X-ray diffraction 2.1. Film deposition For XRD, a Panalytical XPert Pro MPD spectrometer with a Cu source was used. The Cu LFF HR source was operated at 45 kV and 40 mA in line focus. The instrument is equipped with a HTK-1200 chamber in which the 1 1 cm large sample is placed on a Al2O3 holder. The measurements were carried out using a 0.04 RAD Soller slit, a 1/4 divergence slit, a 1/2 anti-scatter slit and a 10 mm beam mask in the incident beam path. The diffracted beam path consisted of an X’Celerator detector in scanning mode (active length 2.122 mm) with a 5 mm anti-scatter slit, 0.04 RAD Soller slit and a Ni filter. The measurements were conducted as 2h-x scans with a scan range of 10°–90° 2h, a step size of 0.0167° and with 150 s counting time at x = 5° (the offset was introduced to avoid the substrate peak at 69°). No background subtraction, Ka2 elimination or other processing was used; the spectra were directly fitted in Origin (Pearson VII). The Cu–Ta thin films were co-sputtered on 380 lm thick 3 inch p-type Si(100) wafer substrates (Si-Mat Silicon Materials). The substrates were used as received and featured a 50 nm SiO2 and a 50 nm SiNx barrier layer on top. Materials for sputtering were 99.99% pure. The films were deposited using a PVD Products magnetron sputtering device in which the magnetrons were arranged in a confocal manner directly opposite to each other. The target surfaces (3 inch diameter) were tilted by 35° with respect to the substrate surface and the throw distance was 5 inches. All samples were sputtered with 5 mTorr of Ar and the Ar flow during sputtering was kept at 10 sccm. The base pressure was maintained at around 107 Torr. The deposition took place at room temperature with the substrate rotating at 20–30 rpm. The substrate temperature was recorded before and after deposition and the machine was allowed to cool down between depositions in order to prevent substrate temperatures in excess of 50 °C. The power settings of the two sources were varied to change the alloy composition. The minimum film thickness achieved was 450 nm, the maximum thickness was 1300 nm. The sputter rate varied between 0.3 and 0.72 nm s–1, depending on the alloy composition. The 65 samples investigated in this study were sputtered over the course of three years in six different sessions. 2.2. Basic characterization of sputtered Cu–Ta films For thickness analysis, a thick line was painted on a 2 2 cm large piece of glass with a transparency pen, then the film was deposited on the sample (simultaneously with the deposition of the wafer samples for energy-dispersive X-ray spectroscopy (EDX) and X-ray diffraction (XRD) analysis). After deposition the glass sample was submerged in ethanol for 2 min and the film was stripped by swiping over the marked area with a cotton swab. A Dektak XT Advanced surface step profiler was used for thickness measurements. The thickness of the samples was measured at 10 different positions along the edge of the remaining film. The standard deviation per sample was < 2 nm, which translates to a standard deviation of the deposition rate of < 0.02 nm s–1. The alloy composition was measured using a Zeiss LEO 1530 scanning electron microscope with a Thermo Scientific NanoTrace EDX detector. The microscope was operated at 5 kV in high-current mode at 11 mm working distance (take-off angle 35°), using the 60 lm aperture. For each 1 1 cm large sample 10 area measurements of 250 lm 250 lm and 60 s time per measurement were carried out. Simulations using the Casino 2.48 software [33] indicate that the penetration depth of the electrons under the chosen operating conditions is < 100 nm in both pure Cu and Ta. Since all the sputtered films were at least 450 nm thick, it is assumed that the film thickness was large enough to exclude penetration of the beam into the 2.4. Transmission electron microscopy For transmission electron microscopy (TEM) sample preparation a small piece of the wafer sample was cut in two parts and glued face-to-face with two-component epoxy glue (Gatan G1 (601.07270)). Using the same epoxy glue, the sample was embedded into a brass tube with 3 mm outer diameter. Curing was done on a hot plate at 125 °C. The tube was cut into 300 lm thick disks using a diamond wire saw (Well 5237) before the disks were manually thinned and polished on grinding paper (600 and 4000 grit, respectively) to a thickness of 100 lm. They were then dimple ground with a Fischione 200 dimple grinder and in a final step the sample was polished using a precision ion beam polishing machine (Gatan 691 PIPS) equipped with an upgrade for low-voltage milling. The milling protocol was set for fast milling at 3–5 kV until a hole formed in the center of the sample, followed by a voltage cascade featuring shorter steps at lower voltage (down to 1 kV) in order to minimize ion-milling damage. The samples were analyzed in a 300 kV FEI Tecnai F30 transmission electron microscope. 2.5. Cu–Ta potential The potential was implemented as described by Gong et al. [25], with the exception of a typo in their Eq. (7), which was taken instead as follows: Ka ¼ 4:5f1 þ 4=½2C44 =ðC11 C12 Þ 0:1g: ð1Þ Smoothening of both the electron density function f(r) and the potential U(r) were carried out as described by Guellil and Adams [34]. 2.6. Potential validation In order to check if the potential was implemented correctly the equilibrium lattice distance a0, cohesive energy C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 Ecoh, vacancy formation energy Evf, bulk modulus B and elastic constants C11, C12, C44 were determined for pure Cu and a-Ta—once using LAMMPS [35,36] and once using PARCAS [37,38]. The cohesive energy Ecoh of the structures was calculated from the potential energy Epot at 0 K (after shape equilibration using Berendsen pressure scaling [39]) and the number of atoms N of the structures as follows: Epot Ecoh ¼ : ð2Þ N The enthalpy of mixing is calculated from the alloy content cCu and cTa and the cohesive energies of the alloy Cu Ta Ealloy coh and of pure Cu Ecoh and pure Ta Ecoh as follows: Cu Ta DH mix ¼ Ealloy coh ½cCu E coh þ cTa E coh : ð3Þ 53 adaptive common neighbor analysis (CNA) [41]. Theoretical XRD spectra of the structures were calculated with the procedure described by He et al. [42], using the Debye scattering formula: I¼ N X XX sin 2psrjk f 2j þ f jf k ; 2psrjk j k–j j ð4Þ where fj is the scattering factor of atom j (taken from the International Tables for Crystallography, Vol. C [43]), rjk is the distance between atoms j and k, and s = 2sinh/k is the scattering vector (the wavelength k was assumed to be Cu-Ka1, i.e. 1.541874 Å). 3. Results 2.7. MD simulations 3.1. Potential validation Three different starting lattices were prepared: an a-Cu (fcc) lattice of 30 30 30 unit cells, an a-Ta (bcc) lattice of 30 30 30 unit cells and a b-Ta (b-uranium) lattice of 10 10 20 unit cells. This resulted in cuboids of 10 nm edge length. Solid-solution alloys were prepared from the starting lattices by randomly exchanging lattice atoms. The MD simulations were carried out using the PARCAS MD code [37,38], using periodic boundary conditions and a time step of 0.5 fs. The material cuboids were equilibrated at 300 K for 1 ns using Berendsen pressure scaling [39] with the time constant set to 100 fs. The structures were then run at 0 K for 5 ps under Berendsen pressure scaling to measure the cohesive energy. As a second option, amorphous structures were prepared by subjecting the bcc and fcc cubes to a melt-quenching procedure. The cubes were kept at 4000 K for 5 ps, then quenched with the rate of 0.5 K fs–1 to 0 K. After this, the resulting structure was equilibrated at 300 K for 5 ps under Berendsen pressure scaling. The structures were also run at 0 K for 5 ps under Berendsen pressure scaling to measure the cohesive energy. To mimic experimentally observed composition fluctuations in the samples, an amorphous structure obtained by melt quenching a bcc cube with equiatomic composition was taken and was divided into layers of 1.2 nm thickness. The concentration within each layer was adjusted to a desired value. As can be seen from Table 1, the equilibrium lattice distance a0, cohesive energy Ecoh, vacancy formation energy Evf, the bulk modulus B, and the elastic constants C11, C12 and C44 determined for pure Cu and Ta were in agreement between LAMMPS and PARCAS, with the exception of C44 whose determination in PARCAS was less reliable, most likely due to insufficient relaxation prior to executing the tensile test procedure that was used to determine the elastic properties. It can be seen that the current implementation of the potential is in reasonable agreement with the values given in the original paper by Gong et al. [25], though there are large discrepancies for the elastic constants. This study aims primarily at predicting lattice parameters. Since the lattice constants and cohesive energies are in good agreement with the values reported for the original potential it is believed that the current implementation of the potential can give meaningful results in this context. To check the Cu–Ta part of the potential the enthalpy of mixing was determined (Eq. (3)). Fig. 1 shows the DHmix values obtained for alloys of different concentrations and structures. No significant difference can be observed for ETa coh with bcc (Fig. 1a) and b-Ta structure (Fig. 1b). DHmix for the random Cu–50 at.% Ta alloy is of the order of 0.20–0.25 eV atom–1; for an ordered B2 structure a value of 0.23 eV atom–1 was obtained. Using the Ecoh values given by Gong et al. [25] in their paper a value of 0.21 eV atom–1 would be expected for this structure, which is also in agreement with other literature results [3]. It is concluded that the present implementation of the potential does give 2.8. Characterization of simulation data The structures obtained from the MD simulations were visualized with Ovito [40], which was also used to carry out Table 1. Potential validation for pure Cu and a-Ta using two different MD codes (PARCAS and LAMMPS). For comparison, the literature values and original values of the cohesive energy Ecoh, the equilibrium lattice distance a0, the vacancy formation energy Evf, the bulk modulus B, and the elastic constants C11, C12 and C44 (taken from Ref. [25]) are shown. Cu Ecoh [eV] a0 [Å] Evf [eV] B [Mbar] C11 [Mbar] C12 [Mbar] C44 [Mbar] a-Ta Literature Gong et al. PARCAS LAMMPS Literature Gong et al. PARCAS LAMMPS 3.54 3.615 1.3 0.861 1.7 1.225 0.758 3.54 3.6149 1.2999 0.9224 1.7021 1.2238 0.7577 3.547 3.6108 1.3081 1.04 1.34 0.86 0.61 3.537 3.6108 1.3 1.0309 1.35 0.87 0.76 8.089 3.3026 2.18 1.203 2.66 1.58 0.87 8.0892 3.3026 2.18 1.211 2.66 1.58 0.87 8.0855 3.316 2.0305 1.3 2.01 0.95 0.63 8.0862 3.3163 1.918 1.306 2.0166 0.9513 0.8717 54 C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 Figure 1. The enthalpy of mixing DHmix for alloys of different composition and either fcc, bcc, b-Ta or amorphous structure; The enthalpy of mixing was calculated according to Eq. (3), assuming a-Cu (fcc) structure for pure Cu and either (a) a-Ta (bcc) structure or (b) b-Ta structure for pure Ta. results in accord with the original publication, despite the discrepancies in the elastic properties that were observed. 3.2. MD simulations Crystalline alloy structures were formed by randomly exchanging atoms in perfect fcc, bcc and b-Ta lattices. The resulting structures were then equilibrated for 1 ns with Berendsen pressure scaling; the initial temperature was set to 300 K. Fig. 2a–c shows the temperature evolution during equilibration for the fcc, bcc and b-Ta lattices, respectively. It can be seen that the temperature does stabilize within the 1 ns equilibration time, the value at which it stabilizes depends on the alloy composition; for better illustration, the average temperature during equilibration was plotted as a function of alloy composition and structure (Fig. 2d). Amorphous structures were prepared from fcc and bcc initial lattices by a melt-quenching procedure; they were subsequently equilibrated for 5 ps. The equilibration time was kept short to prevent crystallization of the structures. Fig. 3a and b shows the temperature evolution during the equilibration for amorphous structures prepared from fcc and bcc initial lattices, respectively. In the following it is assumed that the fcc initial structure is a suitable approach for alloys with < 50 at.% Ta, content, whereas the bcc and b-Ta structure should be suitable for alloys with > 50 at.% Ta content. Fig. 2d hence shows that for the amorphous structures prepared from both the fcc and bcc lattices as well as for the crystalline bcc and b-Ta structures the temperature of the alloys equilibrates at values of below 500 K within their applicable composition range. In contrast to this, the crystalline fcc alloys of < 50 at.% Ta content are heating up considerably, with a maximum value of 1066 K for Cu–50 at.% Ta. Fig. 4 shows the time evolution of sample dimensions (length X, width Y and height Z) normalized by the initial values for the crystalline fcc alloys. Initially, the sample dimensions are equal for all three directions (i.e. Xi = Yi = Zi). During annealing an asymmetry of the sample size evolves: along one direction the sample dimension decreases, whereas it increases in the other two directions. It is completely arbitrary along which one of the originally equivalent directions the contraction takes place. To avoid unnecessary confusion the curves in Fig. 4 are thus shown per alloy concentration and are not further distinguished according to the sample dimensions. It can be seen that for alloys with 0–35 at.% Ta no or only minor asymmetry of the sample dimensions is observed after the equilibration (Fig. 4a). A profound asymmetry of the sample dimensions is observed for alloys with 40–65 at.% Ta (Fig. 4b) and again no asymmetry of the sample dimensions is found for alloys with 70–100 at.% Ta (Fig. 4c). Fig. 4d summarizes these results by plotting an equivalent lattice constant aeq obtained from the final (i.e. after equilibration) size along X, Y and Z direction, based on the number of unit cells present in each of these directions in the initial lattice. This procedure allows direct comparison with the data obtained by Gong et al. [25]. Gong et al. reported on the equivalent lattice constant after 0.1 ns of equilibration, but since Fig. 4a–c shows that the sample dimensions were stable after this point in the present simulations it is believed that the comparison with the values obtained for 1 ns equilibration is justified. It can be seen from Fig. 4d that the tendency shown in the literature data is reproduced. The equivalent lattice constant aeq has no meaning if phase transformation has occurred; a phase transformation is, for example, indicated by an asymmetry of aeq in the X, Y and Z directions that were equivalent in the initial lattice structure, but might not be equivalent directions in the newly formed phase. The results in Fig. 4d therefore suggest that a non-fcc structured phase is formed in initially fcc structured alloys with 50–65 at.% Ta during the 1 ns equilibration. No significant sample dimension asymmetry was found for the bcc and b-Ta structures; these results are not shown here for the sake of brevity. XRD spectra were calculated from the equilibrated structures and are shown in Fig. 5 for the fcc initial structure. In general, the peaks shift towards the smaller angles for higher Ta content. Fig. 5a shows the XRD spectra of alloys with 0–40 at.% Ta. It can be seen that the sample spontaneously amorphizes when the Ta content reaches 15 at.%. With further increase of the Ta content the broad amorphous peak also shifts towards the smaller angles. Then, at 40 at.% Ta content, a crystalline phase is formed. Fig. 5b shows that the reflections from this phase become stronger with increasing Ta content and shift towards smaller 2h values. Finally, for >75 at.% Ta the initial fcc structure is retained (Fig. 5c). The nature of the crystalline C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 55 Figure 2. Temperature evolution during 1 ns equilibration of random solid-solution Cu–Ta alloys of (a) fcc, (b) bcc and (c) b-Ta initial structure at constant pressure. It can be seen that the temperature stabilizes in most cases. (d) For better illustration the average temperature during the equilibration is plotted against the Ta content for the different lattice structures. Figure 3. Temperature evolution during 5 ps equilibration at constant pressure of amorphous Cu–Ta alloys that were prepared by a melt-quenching approach from (a) fcc and (b) bcc initial structure. The temperature stabilizes in most cases. The average temperatures are plotted in Fig. 2d for comparison with the crystalline alloys. phases was determined using CNA available in Ovito. Fig. 5d shows an example for the alloy with 50 at.% Ta; the phase that is formed upon equilibration was identified as a bcc structure, indicating that the phase transformation is of displacive (martensitic) nature. Fig. 6 shows the calculated XRD spectra for bcc (Fig. 6a) and b-Ta (Fig. 6b) lattices after equilibration for 1 ns, and for the amorphous structures prepared from fcc (Fig. 6c) and bcc (Fig. 6d) lattices after equilibration for 5 ps. The bcc initial structure (Fig. 6a) seems to remain stable in the range of 10–100 at.% Ta, although the peaks shift towards higher 2h angles and have less intensity for lower Ta content. For 5 at.% Ta an amorphous phase is observed. For 0 at.% Ta the bcc structure is retained. For the b-Ta structure (Fig. 6b) the typical b-Ta peaks are observed for 50–100 at.% Ta (with the peaks losing intensity and 56 C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 Figure 4. Evolution of the sample dimensions X, Y and Z normalized by the starting values Xi = Yi = Zi (cubic sample geometry) during 1 ns equilibration of Cu–Ta alloys with initial fcc structure. (a) For alloys with 0–35 at.% Ta no/only minor asymmetry of the sample dimensions is observed after the equilibration. (b) A large asymmetry of the sample dimensions is observed for alloys with 40–65 at.% Ta. (c) No asymmetry of the sample dimensions is found for alloys with 70–100 at.% Ta. (d) By dividing the sample dimensions by the initial number of unit cells present in each direction an equivalent lattice constant aeq can be obtained. This parameter is compared to literature results by Gong et al. [25]. shifting to higher 2h values for lower Ta content). Below 50 at.% Ta the peak fine-structure is lost and an amorphous phase is observed. The broad peak continues to lose intensity and shifts towards higher 2h for lower Ta content. Analogous to the bcc case, the b-Ta structure is retained in the 0 at.% Ta simulation. XRD spectra for the meltquenched fcc lattice (Fig. 6c) show a broad amorphous peak that shifts to lower 2h values for larger Ta content. For 75 at.% Ta content and above the initial fcc structure is retained. For the melt-quenched bcc structures an amorphous phase is observed for < 90 at.% Ta; the peak position shifts to higher 2h with lower Ta content. The bcc phase is observed for Ta concentrations of 90 at.% and higher. 3.3. Characterization of sputtered samples The 65 samples investigated in this study were sputtered over the course of three years in six different sessions. Fig. 7a shows the variation of sample composition with deposition parameters (i.e. the power applied to the individual targets). It can be seen that there is considerable variation, even within the same sputter session. This is attributed to cross-contamination between the sources (i.e. “poisoning” of the Cu target with Ta when the Cu target is operated at low power) and is also visible in the observed spread of the deposition rate (Fig. 7b). Despite these problems in accurately depositing samples of a predefined composition and thickness, the crystal structure as a function of composition was fully reproducible. Fig. 7c shows characteristic examples of XRD spectra measured for Cu–Ta alloys of different compositions. It can be seen that for Cu-rich alloys a fcc structure with (1 1 1) texture is formed; for Ta-rich alloys a b-Ta structure with (0 0 2) texture is formed. In between there is a composition range (30–70 at.% Ta) where X-ray amorphous structures are formed. A wide coexistence range of the b-Ta phase and the amorphous phase was observed, whereas no such coexistence was found between the fcc phase and the amorphous phase. The pure Ta film consisted primarily of b-Ta with (0 0 2) texture but also contained a small amount of a-Ta (not visible in Fig. 7c due to the axis scaling). 3.4. Resolution limit of XRD The samples in this study were deposited from two sources onto a rotating substrate. Despite the high rotation speed of the substrate they were found to consist of fine layers parallel to the film–substrate interface (Fig. 8a). The layer periodicity klayer was found to correspond to the ratio between the deposition rate per minute and the substrate rotation speed in rpm. A separate study in which the layered structures are analyzed by 3-D atom probe tomography is underway; preliminary results C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 57 Figure 5. XRD spectra calculated from crystalline random solid-solution Cu–Ta alloys with initial fcc structure after equilibration at constant pressure for 1 ns. (a) The initial fcc structure is retained up to 10 at.% Ta content, then a spontaneous amorphization occurs. (b) Between 45 and 65 at.% Ta content a phase transformation into bcc structure occurs. (c) For Ta content of 70 at.% or more the initial fcc structure is retained. (d) Adaptive common neighbor analysis (CNA) data of the Cu–50 at.% Ta structure illustrates the fcc to bcc phase transformation in support of (b). confirm that the fluctuations observed by TEM are of chemical nature. It has been shown by Michaelsen [44] that it is impossible to distinguish very fine (i.e. with wavelengths in the nanometer range) layered structures of two materials from a homogeneous mixture with the same composition by conventional h-2h XRD measurements. Fig. 8b shows calculated spectra for three different structures of amorphous Cu–50 at.% Ta. Almost no difference is seen between the homogeneous structure and the layered structures. For comparison, an experimental spectrum is shown (the spectra have been scaled such that the maximum intensity coincides). It follows that the comparison of the experimental data for nanostructured samples with the MD results for homogeneous samples remains a valid approach as long as the wavelength of the multilayers is below 2 nm, which was the case due to the high rotation speed used in the depositions. 3.5. As-deposited structure—comparison between literature, experiments and simulations Fig. 9a shows the out-of-plane lattice spacings d determined from the peaks in the experimental XRD spectra (filled symbols). It can be seen that there is excellent reproducibility of the crystal structure as a function of composition. For comparison, the lattice spacings reported in the work of Kim et al. [11] are shown (black double crosses). The results obtained in this study agree reasonably well with the literature results for low and high Ta contents, but for the intermediate, amorphous range there are large deviations. In order to allow direct comparison between the MD results and the experimental results the out-of-plane lattice spacings obtained from the simulated spectra (i.e. from Figs. 5 and 6) are plotted as empty symbols. Only the peaks that were also present in the actual, textured samples were evaluated. To ease comparison, the fcc, bcc and b-Ta phases are only shown for < 50 at.% Ta and > 50 at.% Ta, respectively; the same is valid for the amorphous structures although there a small overlap region between 40 and 60 at.% Ta was allowed. A significant deviation between the simulation results and the experiments is observed for pure Ta in the b-Ta phase. While the agreement is excellent for the amorphous phase, there is disagreement for the fcc phase, particularly in the composition range where spontaneous amorphization of the fcc phase occurs in the simulations (i.e. 15–35 at.% Ta). Fig. 9b shows the full width at half maximum (FWHM) of the experimental and calculated XRD spectra. The FWHM values determined from the crystalline phases in the calculated spectra are not indicative and merely represent the sample size. Good agreement is observed for the amorphous structures, with the best agreement in the Ta-rich range. 58 C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 Figure 6. Top: XRD spectra calculated from crystalline random solid-solution Cu–Ta alloys of (a) bcc and (b) b-Ta initial structure after equilibration at constant pressure for 1 ns. The insets show the unit cell of the original lattice structure. Bottom: XRD spectra calculated from amorphous Cu–Ta structures that were prepared by a melt-quenching approach from (c) fcc and (d) bcc initial structure, after equilibration at constant pressure for 5 ps. The insets show a subvolume of the Cu–50 at.% Ta data. 4. Discussion 4.1. Comparison with the literature 4.1.1. Experiments The current results (Fig. 7c) show good qualitative agreement with the most recent experimental work on Cu–Ta by Asami et al. [9], who used a comparable deposition rate (0.1 nm s–1) as in the present case (Fig. 7b). The only discrepancy was that Asami et al. [9] obtained pure Ta in a-Ta structure, whereas in the current study the bTa structure was observed; this might be attributed to the different sputtering techniques used (RF sputtering vs. DC sputtering). In a previous study, Kim et al. [11] provided quantitative data for the lattice spacing, allowing a more direct comparison of the literature data with the current data (Fig. 9a). Both datasets show that the Cu (111) lattice spacing is initially increasing with higher Ta content. Then, above 10 at.% Ta content, the lattice spacing remains constant with increasing Ta content. This indicates that a solid-solution fcc Cu–Ta phase is first formed, and upon saturation (at 10 at.% Ta content) excess Ta crystallizes in small particles within this phase and/or at grain boundaries. Such particles could not be detected by XRD because both their size and volume fraction are very small, but they could be observed in TEM. MD simulations at elevated temperatures carried out by Frolov et al. [31] predict the formation of Ta particles in a solid-solution Cu–6.5 at.% Ta alloy, hence supporting this hypothesis. In the literature, the amorphous range in the Cu–Ta system was reported as 22–69 at.% Ta [9], 39–96 at.% Ta [10] and 44–91 at.% Ta [11]; in this study the amorphous range was 30–70 at.% Ta, which falls within the spread of the literature values. Compared to the work of Kim et al. [11], the lower boundary of the amorphous range was at much lower Ta content. This is illustrated by the large deviation between literature results and current results in the range of 30–45 at.% Ta (Fig. 9a). A possible explanation for this could be the layered structure of our samples (Fig. 8a). Kim et al. [11] used a Cu target with Ta insets and were thus sputtering from only one source—hence layer formation can be effectively excluded in their case. The layered structure in the current samples could delay crystallization and grain growth of the Cu-rich phase by placing diffusion barriers of Ta-rich phase within the sample. This would explain why more crystallization, and consequently a higher value for the lower boundary of the amorphous range, was observed by Kim et al. [11]. Alternatively, it could be an effect of the smaller deposition rate used in the current work compared to the work by Kim et al. [11], although one would rather expect the opposite effect to occur in this case (i.e. less crystalline samples for higher deposition rates). To give a value for the upper boundary of the amorphous range is difficult in the present case due to the considerable coexistence range between what was assumed to be the amorphous phase and the crystalline b-Ta phase. In Fig. 9a it can also be seen that the lattice spacings C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 59 Figure 7. (a) Variation of sample composition (Cu and Ta content CCu and CTa) as a function of the deposition conditions (sputter powers PCu and PTa); it can be seen that there are considerable variations even within the same deposition session. (b) Variation of the deposition rate as a function of the deposition conditions. (c) Characteristic experimental XRD spectra of sputter deposited Cu–Ta samples of different compositions. For Cu-rich alloys a fcc structure with (1 1 1) texture is formed, for Ta-rich alloys a b-Ta structure with (0 0 2) texture is formed. In the range of 30–70 at.% Ta Xray amorphous structures are formed. Figure 8. (a) TEM image of a Cu–54 at.% Ta sample that is characteristic for samples deposited in this work; due to the deposition method the samples consist of very fine layers. (b) Conventional h–2h XRD measurements cannot distinguish between a homogeneous sample and a sample consisting of very thin layers, as is shown here on the example of theoretical spectra calculated for a homogeneously amorphous Cu–50 at.% Ta structure and layered structures with different layer composition and 1.2 nm wavelength. For comparison, an experimental XRD spectrum is shown. determined for the minority phase in alloys with 70–90 at.% Ta could be consistent with both an amorphous phase or nanocrystalline a-Ta. The latter was observed as a minority phase in the pure Ta film. TEM experiments would thus be necessary to identify the true nature of the minority phase and to accurately determine the upper boundary of the 60 C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 Figure 9. (a) Out-of-plane lattice spacings d that were measured in the current experiments (filled symbols) and reported in the literature [11] (black double crosses) are shown in comparison to the values determined from the MD simulations (empty symbols). (b) Comparison between the full width at half maximum (FWHM) values observed in the experiments (filled symbols) and the values determined from the XRD spectra calculated from the structures obtained by the MD simulations (empty symbols). amorphous range. Literature on Ta-rich Cu–Ta alloys is very scarce and to the authors’ knowledge no TEM data on the microstructure of these alloys is available. In contrast to the present work, Kim et al. [11] have not observed any crystalline phases in Ta-rich alloys. As Asami et al. [9] have pointed out, the deposition rate in the study by Kim et al. [11] could have been up to 8 nm s–1 (in the present study, values as low as 0.3 nm s–1 were customary for Ta-rich alloys, e.g. Fig. 7b). The higher deposition rate could have promoted the formation of amorphous alloys and explain the discrepancy between our results and those of Kim et al. [11]. 4.1.2. MD simulations It can be seen in Table 1 that the elastic properties of the EAM potential implemented in this study deviate considerably from the values reported for the original potential by Gong et al. [25]. However, since all the other properties and the enthalpy of mixing of the potential were within reasonable agreement to the original potential, our version of the potential can still be used for simulations that are not concerned with elastic properties, as was the case in this work. The most notable feature of Gong et al.’s [25] Cu–Ta EAM potential is the spontaneous amorphization found to occur in fcc structures with 30–50 at.% Ta content. Spontaneous amorphization of Cu-rich Cu–Ta alloys is not unique to this potential; it has also been reported by Francis et al. [23] for their Cu–Ta EAM potential. In the current study, spontaneous amorphization was observed in fcc structures with 15–35 at.% Ta content. The discrepancy between the current results and the original study could be caused by the fact that Gong et al. [25] used the Parrinello–Rahman (NPT) pressure scheme, whereas the current study uses the Berendsen barostat. In the latter the shape of the unit cell remains fixed, whereas it can change in the Parrinello-Rahman method. Gong et al. [25] stated that the amorphization process occurs in two stages: after 0.1 ns equilibration time a fast, martensitic transformation into an orthorhombic crystal structure occurs, followed by the actual amorphization. The martensitic transformation was not observed for < 25 at.% Ta content, and the entire process was discussed based solely on the example of a Cu–30 at.% Ta alloy. Despite running the simulation twice with different initial velocities assigned to the atoms we could not reproduce the findings of Gong et al. [25] for the Cu–30 at.% Ta case. It can be seen in Fig. 4d that the data of Gong et al. [25] is otherwise in qualitative agreement with the current results, with the sole exception of this specific alloy composition. We found the martensitic phase transformation described by Gong et al. [25] to take place exclusively for 40–65 at.% Ta content, and no subsequent amorphization was found for these samples within the 1 ns time interval. The current results indicate that the fcc to bcc phase transformation occurs via a tetragonal lattice deformation (Bain path [45]). Such a displacive phase transformation occurs on a relatively short timescale, which makes it possible to observe it in MD simulations. CNA shows that for 40 at.% Ta content the resulting structure contains an equal amount of amorphous phase and crystalline phase with bcc structure (also visible in the XRD spectrum in Fig. 5a, where it seems that there is an overlap of two peaks), whereas for 45–65 at.% the phase transformation appears to be complete (e.g. Fig. 5d). The initial work by Gong et al. [25] was dealing exclusively with Cu–Ta alloys of up to 50 at.% with fcc initial structure; the current study spans the entire composition range and takes into account all the relevant crystal lattices (fcc, bcc and b-uranium) as well as amorphous structures, in an attempt to give a more complete picture of the Cu– Ta system. As can be seen from the XRD spectra in Figs. 5 and 6, a number of phases are observed which would be considered unphysical under the chosen boundary conditions. That Ta-rich alloys in fcc structure and pure Cu in bcc structure are still observed in the simulations is caused by two factors: (i) there is an artificial stiffness term introduced in the Ta part of the potential, otherwise Ta-rich alloys would transform into fcc structure as the EAM formalism demands for closest-packed structures—using fcc structured Ta as a starting lattice circumvents this stiffness term; (ii) even if the MD simulations are carried out at elevated temperature it is typically not possible to observe second-order phase transformations (except for displacive C.M. Müller et al. / Acta Materialia 82 (2015) 51–63 ones), within the timeframe of the simulation. It is interesting to note that there is no spontaneous amorphization taking place in bcc or b-Ta starting lattices within the relevant composition range of 50–100 at.% Ta content. Formally, the EAM method should not be expected to give accurate results for the b-Ta phase, but nevertheless there are literature reports claiming to have obtained reasonable results [20,32]. Mishin and Lozovoi [46] determined by ab initio calculations that the cohesive energy of b-Ta is by 0.041 eV lower than the cohesive energy of a-Ta. However, Li and Adams [24] report a value of DEcoh = 0.024 eV from DFT simulations and DEcoh = 0.076 eV from MD simulations using their EAM potential. We find DEcoh = 0.061 eV, which lies within the spread of the reported values. 4.2. Comparison between experiments and MD simulations The most obvious difference between the experimental results and the simulation results in Fig. 9a is observed for alloys with 10–30 at.% Ta content. These films are believed to consist of a crystalline Cu–Ta phase with fcc structure and of small Ta particles distributed within that phase. Frolov et al. [31] have observed the formation of Ta clusters in their MD simulations at high temperatures (750–1000 K) after equilibration for 10 ns and more. Even then clusters were only formed when there was a preexisting enrichment of Ta near the grain boundaries in the polycrystal [31]. As the temperature, equilibration time and defect density in the current work is much lower, particle formation is unlikely to occur during the timeframe of the simulation. The amorphous phase observed in the MD simulations within this concentration range could thus be a metastable phase, which decomposes into two crystalline phases after a sufficiently long holding time, probably not accessible with MD simulations. Within the amorphous range good agreement is observed between the MD simulations and the experiment. The small deviation in lattice constant d can be explained by the fact that the theoretical spectra were calculated using the Cu-Ka1 line for the wavelength, whereas in the experimental data the wavelength was slightly larger due to the presence of the Cu-Ka2 line. It seems that the amorphous structures prepared by melt quenching in MD are suitable to represent the experimental samples from the viewpoint of XRD, though it should be noted that the XRD method does not allow any conclusions to be drawn on the actual microstructure of the samples (Fig. 8b). In the coexistence range of 70–90 at.% Ta the experimental d values of the minority phase lie between the values for the bcc phase and the amorphous phase obtained from the simulations (Fig. 9a). This indicates that the minority phase is either an amorphous phase or nanocrystalline aTa. The FWHM values shown in Fig. 9b rather point to the crystalline phase, but TEM experiments are needed to prove this statement. It is important to note that the MD simulations are not capable of predicting what microstructures will be observed in as-deposited thin films of a given composition; the MD results presented in Fig. 9 have been filtered to eliminate phases that were not observed in the experiments. However, it was shown that the MD simulations are capable of reproducing interatomic distances observed in the experiments with decent accuracy. Given a proper choice of the initial 61 structure it seems very likely that MD simulations could be used to supplement, for example, an experimental study of microstructure evolution at elevated temperatures. 5. Summary and conclusions The most important findings and conclusions of this study can be summarized as follows: Cu–Ta films have been prepared by magnetron co-sputtering and analyzed by XRD. Excellent reproducibility of the crystal structure as a function of composition was observed: up to 30 at.% Ta content an fcc structure with (1 1 1) texture was formed, for 30–70 at.% Ta X-ray amorphous structures were observed and for Ta-rich alloys a b-Ta structure with (0 0 2) texture was formed. Between 70 and 90 at.% Ta a coexistence range of multiple phases was found. The experimental results (Fig. 7c) show good qualitative agreement with the most recent experimental work on Cu–Ta [9]. In the MD simulations spontaneous amorphization of fcc solid-solution alloys with 15–35 at.% Ta content was observed (Fig. 5a). However, the experimental results suggest that the Cu–Ta films with 10–30 at.% Ta content consist of a crystalline (fcc) Cu–Ta phase with small Ta particles at grain boundaries (Fig. 9a). It is possible that the amorphous phase observed in the simulations is metastable and decomposes into the two crystalline phases in the experiment. The XRD spectra of amorphous structures prepared by the melt-quenching procedure in MD were in good agreement with experimental spectra. It was found that the actual samples are not homogeneous and consist of very fine layers (Fig. 8a), but these cannot be distinguished from a homogeneous mixture with the same composition by conventional h–2h XRD measurements (Fig. 8b) [44]. The MD simulations indicate that the minority phase in the coexistence range of 70–90 at.% Ta could be either an amorphous phase or nanocrystalline a-Ta. The experimental spectra (Fig. 9b) seem to point to the crystalline phase, but no definitive conclusion can be drawn without TEM analysis. The MD simulations cannot predict what microstructures will be observed in as-deposited thin films of a given composition, but can reproduce interatomic distances observed in the experiments rather accurately except for the 15–30 at.% Ta composition range. Acknowledgements C.M. thanks D. Koziej and N. 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