Local Atomic Structure of a High-Entropy Alloy: An X-Ray

and Neutron Scattering Study

WEI GUO, WOJCIECH DMOWSKI, JI-YONG NOH, PHILIP RACK, PETER K. LIAW,
and TAKESHI EGAMI

By using high-energy synchrotron X-ray and neutron scattering, the local structure of a ternary
high-entropy alloy Zr1/3Nb1/3Hf1/3 is characterized by means of pair distribution function
(PDF) analysis. Results show that this alloy is a body center cubic (b.c.c.) phase in both bulk
sample and in a thin film ~1.5 lm thick. The PDFs obtained from X-ray diffraction and neutron
diffraction agree well with each other. The measured PDFs differ from the calculated PDF,
particularly in the peak shape of the first two peaks, indicating local lattice distortion due to
different atomic sizes in the solid solution.

DOI: 10.1007/s11661-012-1474-0
 The Minerals, Metals & Materials Society and ASM International 2012

I. INTRODUCTION II. EXPERIMENTS

HIGH-ENTROPY alloys (HEA) have attracted As a test case to study the local structure of HEAs, we
much research interest in recent years.[1,2] These alloys selected a ZrNbHf alloy, containing only three elements
usually contain 5 to 13 elements with nearly equi-molar to simplify sample preparation and data analysis. A thin
ratio. They have attractive mechanical properties and film sample was sputtered on an amorphous silica wafer
engineering potential as high temperature radiation 0.5-mm thick. The thickness of the thin film was about
damage materials.[1,3] In many cases, these alloys possess 1.5 lm. The sample was examined using high-energy
single phase b.c.c. or f.c.c. structures.[1–4] Occupation of synchrotron X-ray in a transmission mode; the incident
the same crystallographic sites by atoms with different X-ray wavelength was 0.12488 Å. A Mar3450 area
sizes in the solid solution makes the lattice locally detector was employed to record the diffraction patterns
distorted, and this local distortion effect is a vital on beamline ID6-C, Advanced Photon Source, Argonne
strengthening mechanism in the single phase HEAs.[5] National Laboratory, IL. In addition, a blank wafer of
Therefore, investigation of local lattice distortion is silica was measured and used as a background during
crucial to the understanding of the strengthening effect. data analysis. A bulk sample of Zr1/3Nb1/3Hf1/3 was
Long-range lattice distortions (strain fields) can be casted in an argon atmosphere using an arc melter with
determined from broadening of the Bragg peaks, but the Ti getter. The sample was then sliced into small
the local atomic level lattice distortion does not broaden cubes of the size of 0.5 9 0.5 9 0.5 mm3 using an
the Bragg peak. In this paper, we use the pair distribu- electrical discharge machine. This was necessary in order
tion function (PDF) method, by which the real space to randomize crystal orientation and remove texture.
distribution of atoms in the lattice can be determined. The cubes were sealed in a vanadium container and
The PDF represents the distribution of inter-atomic time-of-flight neutron diffraction was performed on the
distances. Lattice distortion will influence the peak high intensity powder diffractometer (HIPD) at Los
position and width which can be directly observed in the Alamos National Laboratory, NM. The data were
PDF.[6] In this work, information on both the total and collected for 14 hours using eight detector banks at
local structures is extracted from high-energy synchro- different angles. In addition, background and the
tron X-ray and neutron diffraction using the PDF diffraction from a vanadium standard and the sample
analysis. container were measured. The data were processed using
pdfgetN package[7] to obtain the PDF.

WEI GUO and JI-YONG NOH, Graduate Research Assistants, III. RESULTS AND DISCUSSION
WOJCIECH DMOWSKI, Research Associate Professor, PHILIP
RACK and PETER K. LIAW, Professors, are with the Department of Figure 1 shows the X-ray diffraction pattern obtained
Materials Science and Engineering, University of Tennessee, Knoxville, for the Zr1/3Nb1/3Hf1/3 thin film. The continuous rings
TN 37996. Contact e-mail: pliaw@utk.edu TAKESHI EGAMI,
Professor, is with the Joint Institute for Neutron Sciences, Department indicate that the grains in the thin film are very fine.
of Materials Science and Engineering, University of Tennessee, However, since the thickness is only ~1.5 lm, the
Knoxville, and also with the Department of Physics and Astronomy, amount of grains in the X-ray beam is limited. Conse-
University of Tennessee and also with the Oak Ridge National quently, the intensity along the rings is not uniform,
Laboratory, Oak Ridge, TN 37831.
Manuscript submitted April 13, 2012.
suggesting that texture developed during sputtering. For
Article published online November 7, 2012 example, the arrows mark uneven intensities in the first

1994—VOLUME 44A, MAY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

inner ring corresponding to the (110) plane. The
azimuthally integrated intensity is plotted in the
Figure 2(a). The peak positions can be indexed with the
b.c.c. pattern indicating that this thin film is composed of
a body center cubic phase. Figure 2(b) shows the neutron
diffraction pattern of the bulk sample. The pattern can be
well fitted to a b.c.c. phase using GSAS package.[8] It is
observed that besides the major b.c.c. solid solution, some
minor scattering peaks are observed (indicated by an
arrow). However, the intensity of these peaks is very
small, indicating a low content of the secondary phase.
The calculated lattice parameters from the X-ray data on
the thin film and from the fitted neutron data of bulk
sample are 3.4869 and 3.4898 Å, respectively, and are
identical within error.
Figure 3(a) shows the X-ray structure function S(Q)
of the thin film sputtered on the silica wafer. Because the
thickness of the silica substrate is about several hundred
times that of the thin film, the scattering intensity is
dominated by the substrate. Consequently, the obtained
S(Q) is noisy, particularly in the high Q region. Several
exposures (10 to 12) were performed to improve
statistics and extract intensity originating from the film. Fig. 1—Diffracted ring pattern of the ZrNbHf thin film. The contin-
Figure 3(b) presents the S(Q) obtained from the bulk uous rings indicate fine grain microstructure and the high intensity
sample using neutron scattering. The average grain size regions arrowed in the first ring indicate preferred orientation.
is smaller in the thin film resulting in broader peaks. The
reduced PDF G(r) is obtained through Fourier trans- atomic size differences. The calculation assumes that the
formation of S(Q): lattice symmetry is body-centered cubic with all equiv-
alent atomic sizes. However, in reality, the lattice should
Z1 be locally distorted due to the size difference among the
2
GðrÞ ¼ Q½SðQÞ  1 sinðQrÞdQ; ½1 Zr, Nb, and Hf atoms (the metallic radii of Zr, Hf, and
p Nb are 1.60, 1.59, and 1.46 Å, respectively). Thermal
0
factors determined by the Reitveld analysis, u = 0.017,
where r is the inter-atomic distance and Q is the scattering are indeed larger than what is expected for phonon
vector. For both X-rays and neutron data, the Q range for amplitude by nearly an order of magnitude, reflecting
Fourier transformation was limited to 20 Å1. Figure 4 the atomic level disorder. For the range r > 4 Å, the
shows the PDFs for the thin film obtained from the X-ray PDFs calculated using these thermal factors agree well
diffraction and for the bulk Zr1/3Nb1/3Hf1/3 samples from with the experimental PDFs, particularly for the neu-
the neutron scattering data. The first peak position agrees tron PDF. Also, the agreement is not bad for the first
well for both of the two plots, but the intensity varies peak. However, they significantly disagree for the
slightly due to different scattering powers of each element. second PDF peak. In the experimental PDFs, the
The X-ray PDF shows obvious noise due to the limited second peak is so broad that it is not even resolved.
statistics. The neutron data do not exhibit a preferred grain The first peak simply reflects the size differences, but the
orientation even though the grains are coarse in the bulk strong broadening of the second peak implies that
sample. This is also confirmed in GSAS refinement in locally, the lattice becomes distorted away from the
Figure 2(b). b.c.c. structure. There are only eight nearest neighbors
The model PDF for b.c.c. Zr1/3Nb1/3Hf1/3 calculated in the b.c.c. structure, but local packing allows up to 12
using PDFgui[9] is also shown in Figure 5. In the nearest neighbors as in the f.c.c. lattice. So, when the
calculation, we used the lattice parameter obtained local lattice is distorted, some of the second neighbors
from the Rietveld refinement of the neutron scattering can become the nearest neighbors, blurring the distinc-
intensities. The model PDF generally agrees with the tion between the first and second nearest neighbors.
neutron data except for some details. In the neutron Figure 6 shows the first two peaks of the radial
PDF, the first peak position is at 3.08 Å, which distribution function (RDF), RðrÞ ¼ 4pr2 q0 gðrÞ, of the
corresponds to the Zr-Nb/Hf-Nb inter-atomic distances. Zr1/3Nb1/3Hf1/3 sample. The width of the second peak
The second peak at 3.48 Å corresponding to the lattice (0.59 Å FWHM) is significantly wider than that of the
constant is clearly resolved in the calculated PDF, but first peak (0.30 Å FWHM), indicating strong distortion
merges with the first peak in the neutron PDF. The of the second neighbor shell. The coordination number
PDFs agree well with each other for distances r greater NC can be obtained by calculating the area under RDF
than 4.55 Å. The peak positions in the neutron and peaks. The total value of NC for the first and second peaks
calculated PDF are shown in Table I. of the Zr1/3Nb1/3Hf1/3 sample is 15.5, while the first and
The difference between the experimental and the second nearest neighbors in b.c.c. lattice, as illustrated in
calculated PDF in the short range originates from the two Gaussian peaks, are 8 and 6, respectively. The

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, MAY 2013—1995

 (a) (b)

Fig. 2—(a) The diffraction pattern shows body center cubic phase in the thin film sample. (b) The neutron diffraction peaks show a b.c.c. phase
and minor phase (diffuse scattering is indicated with arrow).

(a) (b)

Fig. 3—The scattering factor of the thin film obtained from the X-ray diffraction (a) and the bulk sample from neutron scattering (b).

10 12
10 Neutron
X-ray 8
8 Calc 10
Neutron 6
6 diff. 8
4
4
2 6
2
G(r)

Diff.
G(r)

0 4
0

-2 -2
2
-4 -4
0
-6 -6

-8 -2
-8
2 4 6 8 10 12 14
-10 -4
r ( Å) 2 4 6 8 10 12 14 16 18 20
r (Å)
Fig. 4—The pair distribution function of the thin film obtained from
X-ray diffraction and the bulk sample from neutron scattering. Note Fig. 5—The PDFs obtained from the neutron and the calculation
that the fluctuation in the valley between the first and second peak agree well. The difference in the first two peaks (see arrow) origi-
of the X-ray data originates from noise (as indicated with arrows). nates from the size difference of the atoms in the lattice, which
makes the second peak shadowed by the first peak in the neutron
data.

1996—VOLUME 44A, MAY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

 Table I. A Comparison of the Peak Positions in the Calcu- measured and calculated PDFs is particularly significant
lated and Neutron PDFs for the second peak of the PDF. This implies that the
local structure of this alloy is strongly distorted away
Calculated 3.02 3.48 4.93 5.84 6.97 7.71
Neutron 3.08 — 4.94 5.80 6.96 7.74 from the average b.c.c. structure.
Note that the difference in the greater r region is small because the
atomic size difference affects the local lattice distortion.

ACKNOWLEDGMENTS
The authors would like to thank D. Robinson for help
at the ID-6 beamline setup and A. Llobet for the experi-
ments conducted on the HIPD beamline of the Lujan
Neutron Scattering Center at thw Los Alamos National
Laboratory. Use of the Advanced Photon Source is sup-
ported by the U.S. Department of Energy (DOE), Office
of Science, under Contract No. DE-AC02-06CH11357.
The Lujan Center of the Los Alamos National Labora-
tory is funded by the US Department of Energy, Office
of Science, Office of Basic Energy Science, under contract
No. DE-AC52-06NA25396. This project was supported
by the Department of Energy EPSCoR Implementation
award, DE-FG02-08ER46528.

Fig. 6—The first and second peaks of the RDF for the Zr1/3Nb1/3
Hf1/3 alloy. A fitted peak originates from two Gaussian peaks,
reflecting the two nearest neighbor shells in b.c.c. lattice.

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