Page 1
Discovery of the Ternary Nanolaminated Compound Nb2GeC by a Systematic
Theoretical-Experimental Approach
Per Eklund,1,*Martin Dahlqvist,1Olof Tengstrand,1Lars Hultman,1Jun Lu,1Nils Nedfors,2
Ulf Jansson,2and Johanna Rose ´n1
1Department of Physics, Chemistry, and Biology (IFM), Linko ¨ping University, IFM, 581 83 Linko ¨ping, Sweden
2Department of Materials Chemistry, The A˚ngstro ¨m Laboratory, Uppsala University, Box 538, SE-751 21 Uppsala, Sweden
(Received 2 April 2012; published 17 July 2012)
Since the advent of theoretical materials science some 60 years ago, there has been a drive to predict
and design new materials in silicio. Mathematical optimization procedures to determine phase stability
can be generally applicable to complex ternary or higher-order materials systems where the phase
diagrams of the binary constituents are sufficiently known. Here, we employ a simplex-optimization
procedure to predict new compounds in the ternary Nb-Ge-C system. Our theoretical results show that the
hypothetical Nb2GeC is stable, and excludes all reasonably conceivable competing hypothetical phases.
We verify the existence of the Nb2GeC phase by thin film synthesis using magnetron sputtering. This
hexagonal nanolaminated phase has a and c lattice parameters of ?3:24?A and 12.82 A˚.
DOI: 10.1103/PhysRevLett.109.035502PACS numbers: 61.05.cp, 68.37.Lp, 68.55.Nq
Today’s materials science has yielded an unprecedented
frequency of new material discoveries. New complex ce-
ramics (borides, carbides, nitrides, and oxides) for a wide
range of applications are continuously being synthesized.
Much of this work, however, has historically been per-
formed in a trial-and-error manner, and improved theoreti-
cal input in guidance of experimental work is essential. In
response to this challenge, the last decade has especially
seen a tremendous increase in theoretical predictions of
hypothetical novel materials. Traditionally, the vast major-
ity of studies calculate only the cohesive energy of the
compound itself, which does not give information if the
compound is stable relative to any relevant competing
phases. This approach yields an unknown local energy
minimum in an enormous parameter space, and can very
often yield misleading results. A classic example is the
prediction of the ?-C3N4 phase with Si3N4 structure,
which was suggested to be stable and harder than diamond
[1]. Extensive experiments were performed and some
claimed to have synthesized the ?-C3N4phase, but it has
been presently established that it most likely does not exist
[2–4]. A far better approach is to apply exhaustive data-
mining methods to predict new crystal structures [5–8].
However,their basicpremiseisthatitshouldbeknownthat
a material of a specified chemical composition does exist,
followed by determination of its most likely crystal struc-
ture. Such approaches to predict new phases thus do not
truly reflect on whether hypothetical compounds can be
expected to exist experimentally. Consequently, realistic
stability calculations versus relevant competing phases are
necessary, but when performed they are normally done
ad hoc rather than by a systematic approach. The system-
atic optimization approaches that do exist have mainly
been applied to simulate temperature dependence and re-
action paths in fully known systems (see, e.g., [9,10]).
Here, we apply a linear optimization procedure (based
on the simplex method) in which all known competing
phases as well as hypothetical competing phases based on
neighboring and similar systems are included and the
relative stability of any hypothetical compound can be
calculated relative to the most stable combination of com-
peting phases [11,12]. It should be noted here that the
method makes a substantial simplification in accounting
only for enthalpy terms, not entropy. Nevertheless, our
previous benchmarking confirmed that it gives completely
accurate results for existing phases in a fairly large set of
well-known carbide and nitride systems [12], but the criti-
cal test is whether the method also has predictive power.
As a model system for these general research questions,
we have chosen to study Nb-Ge-C, where no ternary
phases apart from Nb3GeC (inverse perovskite) [13] have
been reported in the peer-reviewed literature. The binary
Nb5Ge3can accommodate a substantial amount of carbon
and is thus more appropriately described as Nb5Ge3Cx.
In many similar materials systems, there are phases
belonging to the class of materials known as Mnþ1AXn
phases (n ¼ 1–3, or ‘‘MAX phases’’), a group of inher-
ently nanolaminated ternary carbides and nitrides (X) of
transition metals (M) interleaved with a group 12–16 ele-
ment (A) [14–19]. Most Mnþ1AXn phases are M2AX
phases (originally called ‘‘H phases’’) and have been
known since the 1960s, while the number of M3AX2and
M4AX3phases is relatively limited (around a dozen). It is
therefore natural to pose the question whether similar
phases could exist in the Nb-Ge-C system. This system is
also particularly interesting as it would be reasonable to
expect superconductivity in a novel Nbnþ1GeCnphase.
Only very few Mnþ1AXnphases are reported to be super-
conductors, but those that are mainly tend to be based on
the binary superconductor NbC [15]. Furthermore, these
PRL 109, 035502 (2012)
PHYSICALREVIEWLETTERS
week ending
20 JULY 2012
0031-9007=12=109(3)=035502(4)035502-1
? 2012 American Physical Society
Page 2
complex layered phases have enabled the synthesis of new
2D transition-metal ‘‘MXene’’ carbides [20].
To this end, we have performed a systematic investiga-
tion of the phase stability of the hypothetical Nb2GeC,
Nb3GeC2, and Nb4GeC3. Figure 1 is a flowchart of the
optimization procedure. The choice of competing phases is
based on known binary phase diagrams [21,22] and the
known and hypothetical ternary phases described above.
No Ge-C phase is known, and the solubility of C in Ge (and
viceversa) is negligible. Included phases are schematically
shown in Fig. 2. It is a nontrivial task to find the set of
phases representing the most competitive ones at a certain
composition. We have therefore used the linear optimiza-
tion procedure introduced in Refs. [11,12], where we con-
firmed that this method accurately reproduces existing and
nonexisting phases in numerous known ternary materials
systems. All calculations are based on density-functional
theory using the projector augmented wave method [23] as
implemented in the Vienna ab initio simulation package
(VASP) [24,25]. The Perdew-Burke-Ernzerhof [26] gener-
alized gradient approximation was used for the exchange
and correlation functional. Reciprocal-space integration
was performed within the Monkhorst-Pack scheme [27]
with a plane-wave cutoff energy of 400 eV. The k-point
sampling has been optimized for each phase to obtain a
total convergence within 0:1 meV=atom for the total en-
ergy. Structural optimizations were performed in terms of
unit-cell volumes, c=a ratio (when necessary), and internal
atomic positions to minimize the total energy for all
phases. Through use of this systematic scheme, we search
for the most competitive combination of competing phases
at a given elemental composition.
Figure 2 is a schematic phase diagram for the ternary
Nb-Ge-C system of known (filled circles) and hypothetical
(open circles) phases included in the phase stability study.
A full list of all ?20 included competing phases
with structural information is provided as Supplemental
Material [28]. The results from total-energy calculations of
all competing phases are presented in Table I, including
optimized structural parameters. Together with the simplex
linear optimization procedure we only find Nb2GeC to be
stable (?HCPof ?0:018 eV=atom) with NbGe2, Nb6C5,
and Nb5Ge3C as the set of most competitive phases.
Our results also show that the hypothetical Nb3GeC2
and Nb4GeC3are not stable. The calculated cell parame-
ters and unit-cell volume of Nb2GeC are a ¼ 3:265?A,
c ¼ 12:655?A, and V ¼ 116:83?A3(58:42?A3=formula
unit), respectively.
FIG. 1 (color online).
linear optimization procedure used in order to identity the set
of most competitive phases with respect to Nbnþ1GeCn.
Schematic flow chart of the simplex
FIG. 2.
system of known (filled circles) and hypothetical (open circles)
phases included in the phase-stability study.
Schematic phase diagram for the ternary Nb-Ge-C
TABLE I.
for Nbnþ1GeCnphases compared to its identified most compet-
ing phases (CP).
Calculated formation enthalpy ?HCPin eV=atom
n?HCP(eV=atom)Competing phases (CP)
1
2
3
?0:018
0.026
0.014
NbGe2, Nb6C5, Nb5Ge3Cx(x ¼ 1)
Nb2GeC, Nb6C5, C
Nb2GeC, Nb6C5, C
PRL 109, 035502 (2012)
PHYSICAL REVIEW LETTERS
week ending
20 JULY 2012
035502-2
Page 3
To test this prediction, we synthesized Nb-Ge-C thin
films by dc magnetron sputtering in ultrahigh vacuum
(base pressure ?1 ? 10?9mbar) onto Al2O3(0001) sub-
strates with an NbCx(111) layer at a substrate temperature
of ?800?C from elemental targets of Nb, Ge, and C in an
argon discharge at a pressure of ?0:5 Pa. For details on the
synthesis process and chamber, the reader is referred to
Refs. [29,30]. The applied power on the sputtering targets
was calibrated from known deposition rates and sputtering
yields toresult inaNb:Ge:Ccompositionof2:1:1.Figure3
is an x-ray diffraction (XRD) ? ? 2? scan showing the
NbCx(111) peak and a set of peaks at 13.83?, 27.87?, and
42.27?. These peaks are consistent with the positions of the
basal-plane 0002, 0004, 0006 peaks of the Nb2GeC phase,
correspondingtoacaxisof12.82A˚.XRDpolefigureswere
performed at the positions of the 0002, 0004, and 10?13
(13.83?, 27.87?, and 38.4?2?) peaks of this structure and
are shown as insets in Fig. 3. The pole figure of the 0004
peak (left inset in Fig. 3) shows diffraction only at the
center (i.e., tilt-angle ? ¼ 0) consistent with basal-plane
orientation. The 0002 pole figure was essentially identical
to the 0004 pole figure, as expected for basal-plane peaks.
The 10?13 pole figure (right inset in Fig. 3) shows a set of
diffraction peaks at ? ¼ 57?, corresponding to the angle
between (000‘) and (10?13) planes in the M2AX structure.
The low-intensity diffraction feature in the center of this
pole figure is due to a minute amount of (10?13)-oriented
grains (barely detectable in the ? ? 2? scans, cf., similar
growth results for Cr2GeC [31]). Further confirmation of
the structure identification was obtained by performing a
pole figure of the 10?16 peak (53.9?), which yielded a set of
diffractionpeaksat? ¼ 37?,theanglebetween(000‘)and
(10?16) planes.
Figure 4 shows a high resolution TEM image of the
Nb2GeC film with the beam aligned along the [11?20]
zone axis, unambiguously showing the layered character-
istic zigzag structure of the M2AX crystal structure
(illustrated in the left side of Fig. 4). These XRD and
TEM results prove that the grown phase is indeed
Nb2GeC with M2AX structure with a c axis of 12.82 A˚.
The a lattice parameter is estimated to be ?3:24?A. The
experimentally determined unit-cell volume of 116:45?A3
(58:23?A3=formula unit) is very close to the predicted
value of 116:83?A3(58:42?A3=formula unit).
Further experiments changing the Ge and C content to
the compositions closer to Nb:Ge:C ¼ 3:1:2 or 4:1:3 did
not result in any Nb3GeC2or Nb4GeC3phases, but rather
Nb2GeC and NbCx, as predicted. We can therefore con-
clude that these higher-order phases do not exist, or at least
will bevery difficult to synthesize, since they are not stable
relative to their competing phases. Nevertheless, all three
Nbnþ1GeCnphases are dynamically stable, i.e., stable
relative to lattice vibrations as evidenced by the fact that
no imaginary phonon frequencies exist in the phonon
spectrum (see Supplemental Material [28]). This further
underscores the importance of realistic phase-stability cal-
culations in any prediction-based approach.
In conclusion, we have demonstrated the existence of
Nb2GeC by a combined systematic theoretical optimiza-
tion procedure and a short set of well-defined experiments.
Our work further explains why related hypothetical ternary
phases (e.g., Nb3GeC2and Nb4GeC3) should not exist, or
FIG. 3 (color online).
an Al2O3(0001) substrate. Insets are pole figures of the 0004
(left) and 10?13 (right) peaks of Nb2GeC.
XRD ?-2? scan of Nb-Ge-C thin film on
FIG. 4 (color online).
Nb2GeC film with the beam aligned along the [11?20] zone axis,
showing the layered characteristic zigzag structure of the M2AX
crystal structure (illustrated to the left of the image).
Blue ðdark grayÞ ¼ Nb, black ¼ C, red ðmedium grayÞ ¼ Ge.
High resolution TEM image of the
PRL 109, 035502 (2012)
PHYSICALREVIEWLETTERS
week ending
20 JULY 2012
035502-3
Page 4
at least why they should bevery difficult to synthesize. The
theoretical method used here is in principle generally
applicable to complex ternary or higher-order materials
systems where at least the phase diagrams of the binary
constituents are sufficiently known. Furthermore, it could
be combined with a data-mining approach to also allow for
the prediction of unknown crystal structures in combina-
tion with realistic phase-stability calculations.
The research leading to these results has received fund-
ing from the European Research Council under the
European Community’s Seventh Framework Programme
(FP7/2007-2013)/ERC Grant agreement No. [258509], the
SwedishResearch Council (V.R.), theSwedishFoundation
for Strategic Research, and the Swedish Agency for
Innovation Systems (VINNOVA) Excellence Center
FunMat. The calculations were carried out using super-
computer resources provided by the Swedish National
Infrastructure for Computing (SNIC) at the National
Supercomputer Center (NSC) and the High Performance
Computing Center North (HPC2N). P.E. and M.D. con-
tributed equally to this work.
*Corresponding author.
perek@ifm.liu.se
[1] A.Y. Liu and M.L. Cohen, Science 245, 841 (1989).
[2] J. Neidhardt and L. Hultman, J. Vac. Sci. Technol. A 25,
633 (2007).
[3] D.M. Teter and R.J. Hemley, Science 271, 53 (1996).
[4] R.B. Kaner, J.J. Gilman, and S.H. Tolbert, Science 308,
1268 (2005).
[5] S.M. Woodley and R. Catlow, Nature Mater. 7, 937
(2008).
[6] G. Ceder, D. Morgan, C. Fischer, K. Tibbetts, and S.
Curtarolo, MRS Bull. 31, 981 (2006).
[7] B. Winkler, C.J. Pickard, V. Milman, and G. Thimm,
Chem. Phys. Lett. 337, 36 (2001).
[8] C. Fischer, K. Tibbetts, D. Morgan, and G. Ceder, Nature
Mater. 5, 641 (2006).
[9] S. Ong, L. Wang, B. Kang, and G. Ceder, Chem. Mater.
20, 1798 (2008)
[10] R. Akbarzadeh, V. Ozolins, and C. Wolverton, Adv. Mater.
19, 3233 (2007).
[11] M. Dahlqvist, B. Alling, I.A. Abrikosov, and J. Rose ´n,
Phys. Rev. B 81, 024111 (2010).
[12] M. Dahlqvist, B. Alling, and J. Rose ´n, Phys. Rev. B 81,
220102 (2010).
[13] K.E. Spear and D.F. Palino, Mater. Res. Bull. 18, 549
(1983).
[14] M.W. Barsoum, Prog. Solid State Chem. 28, 201 (2000).
[15] P. Eklund, M. Beckers, U. Jansson, H. Ho ¨gberg, and L.
Hultman, Thin Solid Films 518, 1851 (2010).
[16] J.Y. Wang and Y.C. Zhou, Annu. Rev. Mater. Res. 39, 415
(2009).
[17] M.W. Barsoum and M. Radovic, Annu. Rev. Mater. Res.
41, 195 (2011).
[18] H.-I. Yoo, M.W. Barsoum, and T. El-Raghy, Nature
(London) 407, 581 (2000).
[19] M.W. Barsoum, T. Zhen, S.R. Kalidindi, M. Radovic, and
A. Murugaiah, Nature Mater. 2, 107 (2003).
[20] M. Naguib, M. Kurtoglu, V. Presser, J. Lu, J. Niu, M.
Heon, L. Hultman, Y. Gogotsi, and M.W. Barsoum, Adv.
Mater. 23, 4248 (2011).
[21] T.B. Massalski, in Binary Alloy Phase Diagrams (ASM
International, Metals Park, Ohio, 1986), Vols. 1 and 2.
[22] H. Okamoto, Phase Diagrams for Binary Alloys (ASM
International, Materials Park, Ohio, 2000).
[23] P.E. Blo ¨chl, Phys. Rev. B 50, 17953 (1994).
[24] G. Kresse and J. Hafner, Phys. Rev. B 48, 13115 (1993).
[25] G. Kresse and J. Hafner, Phys. Rev. B 49, 14251
(1994).
[26] J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett.
77, 3865 (1996).
[27] H.J. Monkhorst and J.D. Pack, Phys. Rev. B 13, 5188
(1976).
[28] See Supplemental Material
supplemental/10.1103/PhysRevLett.109.035502 for a full
list of all 20 included competing phases with structural
information, and phonon calculations.
[29] J. Emmerlich, H. Ho ¨gberg, S. Sasva ´ri, P.O.A˚. Persson, L.
Hultman, J.-P. Palmquist, U. Jansson, J.M. Molina-
Aldareguia, and Z. Cziga ´ny, J. Appl. Phys. 96, 4817
(2004).
[30] J. Frodelius, P. Eklund, M. Beckers, P.O.A˚. Persson, H.
Ho ¨gberg, and L. Hultman, Thin Solid Films 518, 1621
(2010).
[31] P. Eklund, M. Bugnet, V. Mauchamp, S. Dubois, C.
Tromas, J. Jensen, L. Piraux, L. Gence, M. Jaouen, T.
Cabioc’h, Phys. Rev. B 84, 075424 (2011).
athttp://link.aps.org/
PRL 109, 035502 (2012)
PHYSICAL REVIEWLETTERS
week ending
20 JULY 2012
035502-4
Download full-text