APPLIED PHYSICS LETTERS 93, 171905 共2008兲
The partitioning and site preference of rhenium or ruthenium in model
nickel-based superalloys: An atom-probe tomographic and first-principles
study
Yang Zhou,1,a兲 Zugang Mao,1,b兲 Christopher Booth-Morrison,1 and David N. Seidman1,2,c兲
1
Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive,
Evanston, Illinois 60208-3108, USA
2
Northwestern University Center for Atom-Probe Tomography (NUCAPT), 2220 Campus Drive, Evanston,
Illinois 60208-3108, USA
共Received 22 July 2008; accepted 22 September 2008; published online 28 October 2008兲
The partitioning behavior and sublattice site preference of Re or Ru in the Ni3Al 共L12兲 ␥⬘precipitates of model Ni–Al–Cr alloys are investigated by atom-probe tomography 共APT兲 and
first-principles calculations. Rhenium and Ru are experimentally observed to partition to the
␥共fcc兲-phase, which is consistent with the smaller values of the ␥-matrix Re and Ru substitutional
formation energies determined by first-principles calculations. APT measurements of the
␥⬘-precipitate composition indicate that Re and Ru occupy the Al sublattice sites of the Ni3Al 共L12兲
phase. The preferential site substitution of Re and Ru at Al sublattice sites is confirmed by
first-principles calculations. © 2008 American Institute of Physics. 关DOI: 10.1063/1.2998654兴
Nickel-based superalloys, which are widely used in landbased and aerospace turbine engines, have been studied extensively due to their incomparable high temperature
strength and resistance to creep and oxidation. These alloys
owe their extraordinary high temperature mechanical properties to strengthening of the ␥共fcc兲 matrix by coherent, elastically hard ␥⬘共L12兲-precipitates. Refractory element additions such as Re, Ta, or W improve ␥⬘-precipitate stability by
decreasing the coarsening kinetics of the ␥⬘-phase, while simultaneously providing solid-solution strengthening.1 At
temperatures above 1273 K, however, localized supersaturations of Re and W can lead to the precipitation of refractoryrich topologically close-packed 共TCP兲 phases.2–6 These TCP
phases are deleterious to the mechanical properties of commercial superalloys because they consume refractory additions, reducing both solid-solution and precipitation
strengthening.4,6 Ruthenium is added to modern nickel superalloys to inhibit the formation of TCP phases, thereby extending the creep capability of single-crystal superalloys to
higher temperatures.2,7,8 The mechanisms by which Ru suppresses TCP phase formation have been the subject of some
debate, although the effect of Ru on the ␥ / ␥⬘ partitioning of
other refractory elements, particularly Re, has been identified
as playing a major role.2,9,10
We investigate the partitioning and site substitution behavior of Re or Ru in Ni–Al–Cr model superalloys aged at
1073 K, employing both atom-probe tomography 共APT兲 and
first-principles calculations. Three alloys, Ni-10.0 Al-8.5 Cr,
Ni-10.0 Al-8.5 Cr-2.0 Re, and Ni-10.0 Al-8.5 Cr-2.0 Ru
at. %, were chill cast in a 19 mm diameter copper mold to
form polycrystalline master ingots. The ingots were homogenized at 1573 K for 20 h, then solutionized in the ␥-phase
field at 1503 K for 3 h and water quenched. Ingot sections
were aged at 1073 K under flowing argon for 256 h, then
water quenched, and microtip specimens were prepared for
a兲
Electronic mail: [email protected].
Electronic mail: [email protected].
c兲
Electronic mail: [email protected].
b兲
0003-6951/2008/93共17兲/171905/3/$23.00
study by APT. Pulsed-laser APT data collection was performed at an evaporation rate of 0.04 ions pulse−1, a specimen temperature of 40.0⫾ 0.3 K, a pulse energy of
0.6 nJ pulse−1, a pulse repetition rate of 200 kHz, and a
gauge pressure of ⬍6.7⫻ 10−8 Pa. APT data were visualized
and analyzed with the IVAS™ 3.0 software program 共Imago
Scientific Instruments兲. We note that the details of the phase
decomposition of the model alloys studied herein are provided elsewhere, and that the alloys do not contain TCP
phases.11–14
First-principles calculations were performed using the
plane wave pseudopotential total energy method with localdensity approximations,15 as implemented in the Vienna ab
initio simulation package.16,17 Projector augmented-wave
pseudopotentials18 were employed with an energy cutoff of
300 eV for plane waves in the 8 ⫻ 8 ⫻ 8 Monkhorst–Pack
k-point grids, and were found to give convergent results. The
calculated lattice parameter of the relaxed Ni3Al 共L12兲 structure was determined to be 0.348 nm, in good agreement with
the room temperature experimental value of 0.357 nm.1
A spheroidal ␥⬘-precipitate from the Ni–Al–Cr–Ru alloy
aged at 1073 K for 256 h is visualized by APT 共Fig. 1兲;
similar reconstructions are available for the Ni–Al–Cr–Re
alloy in the work of Yoon et al.12 In both alloys, Al is observed to partition strongly to the ␥⬘ phase, while Cr and the
refractory additions, Re or Ru, partition to the ␥-matrix. The
concentration profiles across the ␥ / ␥⬘ interface of the Ni–
Al–Cr–Re and Ni–Al–Cr–Ru alloys, as measured by the
proximity histogram method,19 are displayed in Fig. 2. The
partitioning ratio, defined as the concentration of an element
in the ␥⬘-phase divided by the concentration of the same
element in the ␥-phase, is calculated to quantify the partitioning behavior of an element. Rhenium and Ru were found
to partition to the ␥-phase, in agreement with previous
studies,20–22 with partitioning ratios of 0.37⫾ 0.03 and
0.37⫾ 0.07, respectively.
The energetic driving force for the partitioning of Re or
Ru to the ␥-matrix was determined by first-principles calculations in a system of 12⫻ 2 ⫻ 2 unit cells 共192 atoms兲 con-
93, 171905-1
© 2008 American Institute of Physics
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
171905-2
Appl. Phys. Lett. 93, 171905 共2008兲
Zhou et al.
Substitutional Formation
-1
Energy (eV atom )
-matrix
1.0
0.5
0.0
-0.5
0.8
0.6
0.4
0.2
0.0
-0.2
'-precipitate
Re substitution
Ni site
Al site
Ru substitution
Ni site
Al site
-1.0
-0.5
0.0
0.5
1.0
Distance from /' Interface (nm)
FIG. 1. LEAP tomographic reconstruction of a spheroidal ␥⬘-precipitate in a
model Ni-10.0 Al-8.5 Cr-2.0 Ru at. % alloy aged at 1073 K for 256 h. The
elements that partition to the ␥共fcc兲-matrix, Cr and Ru atoms, are shown in
white, while Al atoms, which partition to the ␥⬘ - 共L12兲 precipitates, are
shown in black; Ni atoms are omitted for clarity.
structed along the 具100典 direction. The supercell was divided
by a 兵100其 interface, and the two halves of the supercell were
occupied by the ␥-Ni and ␥⬘-Ni3Al phases, respectively. Every Ni atom on the ␥-Ni side of the interface was treated as
a potential substitutional site for the Re or Ru atoms, while
on the Ni3Al side, the Ni and Al sublattice sites were treated
as separate substitutional sites. To ensure coherency of the
兵100其 ␥ / ␥⬘ interface, the structures on either side of the interface were relaxed within the constraints of the Ni3Al crystal structure. The substitutional formation energies of Re or
Ru as a function of distance from the 兵100其 interface were
calculated employing
tot
+ n M ␮ M 兲 − 共Etot + nZ␮Z兲兴/nZ ,
EZ→M = 关共EZ,precipitate
共1兲
tot
EZ→Ni = 关共EZ,matrix
+ nNi␮Ni兲 − 共Etot + nZ␮Z兲兴/nZ ,
共2兲
tot
where M is Ni or Al, Z is Ru or Re, E is the total energy
tot
tot
and EZ,matrix
are the total enprior to substitution, EZ,precipitate
ergies when elements Z partition to the precipitate or matrix
Concentration (at.%)
-matrix
16
12
8
10
8
6
80
78
76
2
1
-10
'-precipitate
Ni-Al-Cr-Re
Al
Ni-Al-Cr-Re
Ni-Al-Cr-Ru
Ni-Al-Cr-Ru
Cr
FIG. 3. The substitutional formation energies of Re and Ru atoms as a
function of distance from the ␥共fcc兲 / ␥⬘共L12兲 heterophase interface from
first-principles calculations for a ␥共Ni兲 / ␥⬘共Ni3Al兲 system.
phase, respectively, and nZ is the number of Z atoms. The
chemical potentials per atom of the pure bulk elements ␮i are
calculated by assuming the same cell symmetry and are determined to be −6.538, −4.195, −10.512, and
−13.682 eV atom−1 for Ni, Al, Re, and Ru, respectively. The
calculated substitutional formation energies of Re and Ru are
smaller in the ␥-matrix than in the ␥⬘-precipitate 共Fig. 3兲,
providing the energetic driving force for the partitioning of
Re and Ru in the ␥-phase. It is noted that the addition of Re
and Ru leads to an increase in the total energy of the L12
crystal structure.
Table I summarizes the ␥⬘-phase compositions of the
three alloys studied herein for samples aged at 1073 K for
256 h. The sum of the ␥⬘-precipitate concentrations of Al, Cr,
and Re or Ru is ⬃25 at. % for the investigated alloys, indicating that the four solute elements substitute preferentially
to the Al sublattice sites of the Ni3Al structure.
The site preference of Re or Ru is studied by firstprinciples calculations by substituting one Re or Ru atom at
one of the Ni or Al sublattice sites in the Ni3Al superlattice,
resulting in four substitutional structures: 共NixRe1−x兲3Al,
Ni3共AlyRe1−y兲, 共NixRu1−x兲3Al, and Ni3共AlyRu1−y兲. A threedimensional periodic supercell with 2 ⫻ 2 ⫻ 2 unit cells was
constructed for the substitutional energy calculations, and the
total energies of the cells converged to 2 ⫻ 10−5 eV atom−1,
while residual forces converged to 0.005 eV nm−1. Table II
lists the calculated total energies of the relaxed structures,
Etot, and the site substitutional energies, EZ→Ni and EZ→Al,
which are defined as
tot
tot
+ nNi␮Ni兲 − 共ENi
EZ→Ni = 关共E共Ni
Al + nZ␮Z兲兴/nZ , 共3兲
1−xZx兲Al
Ni
3
TABLE I. The experimental compositions of the ␥⬘ - 共L12兲 precipitates of
the Ni-10.0 Al-8.5 Cr, Ni-10.0 Al-8.5 Cr-2.0 Ru, and Ni-10.0 Al-8.5 Cr-2.0
Re at. % alloys aged at 1073 K for 256 h.
Re/Ru
-5
0
5
Distance from /' interface (nm)
10
FIG. 2. Nickel, Al, Cr, and Re 共Ru兲 concentration profiles across the ␥ / ␥⬘
heterophase interface for alloys Ni-10.0 Al-8.5 Cr-2.0 Re and Ni-10.0 Al-8.5
Cr-2.0 Ru at. %, both aged at 1073 K for 256 h.
Alloy
Ni 共at. %兲
Al 共at. %兲
Cr 共at. %兲
Ni–Al–Cr
75.69⫾ 0.28 18.06⫾ 0.30 6.24⫾ 0.20
Ni–Al–Cr–Ru 75.71⫾ 0.29 18.06⫾ 0.26 5.36⫾ 0.15
Ni–Al–Cr–Re 75.61⫾ 0.16 17.57⫾ 0.30 5.95⫾ 0.32
Ru or Re 共at. %兲
¯
0.87⫾ 0.06
0.86⫾ 0.17
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171905-3
Appl. Phys. Lett. 93, 171905 共2008兲
Zhou et al.
TABLE II. Total and site substitutional energies determined by firstprinciples calculations. 共For this calculation, x = 0.042 and y = 0.125, and Z
= Re or Ru.兲
Ni3Al
共NixRe1−x兲3Al
Ni3共AlyRe1−y兲
共NixRu1−x兲3Al
Ni3共AlyRu1−y兲
Etot
共eV兲
EZ→Ni,Al
共eV atom−1兲
−206.587
−212.494
−215.282
−209.621
−212.200
¯
1.237
0.792
0.940
0.705
This research was supported by the National Science
Foundation 共NSF兲 under Grant No. DMR-0804610. APT
measurements were performed at the Northwestern University Center for Atom-Probe Tomography 共NUCAPT兲. Research assistant Professor D. Isheim is kindly thanked for
managing NUCAPT. The LEAP® tomograph was purchased
with funding from the NSF-MRI 共Grant No. DMR 0420532,
Dr. C. Bouldin, grant officer兲 and ONR-DURIP 共Grant Nos.
N00014-0400798 and N00014-0610539, Dr. J. Christodoulou, grant officer兲. We thank Dr. R. D. Noebe of the NASA
Glenn Research Center for alloy preparation.
tot
tot
EZ→Al = 关共ENi
共Al1−yZy兲 + nAl␮Al兲 − 共ENi Al + nZ␮Z兲兴/nZ .
3
3
共4兲
The site substitutional energies of Re or Ru are significantly
smaller at the Al sublattice sites than at the Ni sites 共Table
II兲, confirming that these refractory additions prefer to occupy the Al sublattice sites of the Ni3Al structure. A study of
the Ru ␥⬘-precipitate site substitution in a ternary Ni–Al–Ru
alloy, employing the atomic site location by channeling enhanced microanalysis technique, showed that Ru is five times
more likely to occupy the Al sublattice sites, in qualitative
agreement with the first-principles results determined
above.23 We note that a previous study employing methods
similar to those used herein showed that Ta also occupies the
Al sublattice sites of the ␥⬘-phase.24
The average atomic displacements and forces at the first
nearest-neighbor distance associated with the local strains
and stresses resulting from the site substitution of Re or Ru
at the Ni or Al sublattice sites are displayed in Table III. The
average atomic displacements and forces are found to be
smaller for substitution of Re or Ru at the Al sublattice sites,
providing supporting evidence that the refractory additions
prefer to occupy the Al sublattice sites.
To conclude, Re and Ru partition strongly to the
␥-matrix phase in model Ni–Al–Cr alloys because the values
of the site substitutional energies of the refractory additions
are smaller in the ␥-phase than in the ␥⬘-phase. Additionally,
the APT experimental results and first-principles calculations
TABLE III. Average atomic forces and displacements at the first nearestneighbor distance from first-principles calculations for four site substitutional structures.
共NixRe1−x兲3Al
Ni3共AlyRe1−y兲
共NixRu1−x兲3Al
Ni3共AlyRu1−y兲
demonstrate that Re and Ru substitute preferentially at the Al
sublattice sites in the Ni3Al 共L12兲 structure.
Average atomic force
共eV Å−1兲
Average atomic displacement
共Å兲
0.0874
0.0196
0.0354
0.0104
0.3650
0.0966
0.1109
0.0655
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1
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