# Discovery of the Ternary Nanolaminated Compound Nb 2 GeC by a Systematic Theoretical-Experimental Approach

**ABSTRACT** 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 Nb 2 GeC is stable, and excludes all reasonably conceivable competing hypothetical phases. We verify the existence of the Nb 2 GeC 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 Å . 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 -C 3 N 4 phase with Si 3 N 4 structure, which was suggested to be stable and harder than diamond [1]. Extensive experiments were performed and some claimed to have synthesized the -C 3 N 4 phase, 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 basic premise is that it should be known that 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 Nb 3 GeC (inverse perovskite) [13] have been reported in the peer-reviewed literature. The binary Nb 5 Ge 3 can accommodate a substantial amount of carbon and is thus more appropriately described as Nb 5 Ge 3 C x . In many similar materials systems, there are phases belonging to the class of materials known as M nþ1 AX n 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 M nþ1 AX n phases are M 2 AX phases (originally called ''H phases'') and have been known since the 1960s, while the number of M 3 AX 2 and M 4 AX 3 phases 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 Nb nþ1 GeC n phase. Only very few M nþ1 AX n phases are reported to be super-conductors, but those that are mainly tend to be based on the binary superconductor NbC [15]. Furthermore, these

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**ABSTRACT:**We report thermal expansion coefficients of the end members and solid-solution compounds in the Cr2(Alx,Ge1−x)C system. All samples studied were essentially phase-pure Cr2AlxGe1−xC except the Cr2GeC sample, which contained a substantial fraction of Cr5Ge3Cx. X-ray diffraction performed in the 25–800 °C temperature range shows that the in-plane thermal expansion remains essentially constant at about 14 ± 1 × 10−6 K−1 irrespective of Al content. The thermal expansion of the c axis decreases monotonically from 17 ± 1 × 10−6 K−1 for Cr2GeC to ∼12 ± 1 × 10−6 K−1 with increasing Al content. At around the Cr2(Al0.75,Ge0.25)C composition, the thermal expansion coefficients along the two directions are equal; a useful property to minimize thermal residual stresses. This study thus demonstrates that a solid-solution approach is a route for tuning a physical property like the thermal expansion. For completeness, we also include a structure description of the Cr5Ge3Cx phase, which has been reported before but is not well documented. Its space group is P63/mcm and its a and c lattice parameters are 7.14 Å and 4.88 Å, respectively. We also measured the thermal expansion coefficients of the Cr5Ge3Cx phase. They are found to be 16.3 × 10−6 K−1 and 28.4 × 10−6 K−1 along the a and c axes, respectively. Thus, the thermal expansion coefficients of Cr5Ge3Cx are highly anisotropic and considerably larger than those of the Cr2(Alx,Ge1−x)C phases.Journal of the European Ceramic Society 04/2013; 33(4):897–904. · 2.36 Impact Factor

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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.109.035502 PACS 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

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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

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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

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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

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