Download Ta alloys, studied by X-ray diffraction and molecular dynamics

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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.
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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
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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. Kränzlin for support with
XRD, M.J. Süess for TEM sample preparation and analysis and
A. Kuronen for helpful discussions about the MD simulations.
Discussions with A.S. Sologubenko are appreciated. Support by
the Nonmetallic Inorganic Materials Group (EDX) and the Laboratory for Multifunctional Materials (XRD) is gratefully
acknowledged. Film deposition was carried out at the FIRST Center for Micro- and Nanoscience; TEM experiments were done at
the Scientific Center for Optical and Electron Microscopy (ScopeM) at ETH Zurich. This work was financed by SNF grant no.
200021_135137.
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C.M. Müller et al. / Acta Materialia 82 (2015) 51–63
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