High-Pressure and High-Temperature Stability of Antifluorite Mg2C by

Article pubs.acs.org/JPCC

High-Pressure and High-Temperature Stability of Antifluorite Mg2C by in Situ X‑ray Diffraction and ab Initio Calculations Oleksandr O. Kurakevych* and Yann Le Godec IMPMC, UPMC Sorbonne Universités, UMR CNRS 7590, Muséum National d’Histoire Naturelle, IRD UMR 206, 75005 Paris, France

Timothy A. Strobel and Duck Young Kim Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015, United States

Wilson A. Crichton and Jérémy Guignard ESRF, 6 rue Jules Horowitz, 38043 Grenoble, France S Supporting Information *

ABSTRACT: The high-pressure and high-temperature formation and stability of recently discovered magnesium carbide Mg2C were studied by in situ X-ray diffraction up to 20 GPa and 1550 K. The insights into the thermodynamics of Mg2C under extreme conditions, and its metastability at 0.1 MPa and 300 K, were provided by ab initio calculations of total energies and phonon density of states as a function of pressure. We illustrate how the compound found occasionally in high-pressure experiments could be systematically predicted and discovered in a time-saving way. Similar theoretical approaches can be useful for prediction of synthesis conditions and recovery of new solids.

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INTRODUCTION

Magnesium and carbon do not directly form thermodynamically stable alloys or compounds at ambient pressure, although metastable MgC26 and Mg2C37 are accessible by some chemical routes.8,9 Previous reports have suggested thermodynamically stable Mg-C compounds at high pressure,10 but information on their crystal structures and compositions remains ambiguous. Thus, the phase diagrams of the binary Mg-C system at both ambient11,12 and high pressure conditions10,11,13 are highly unconstrained. At the same time, the eutectic nature of the MgC phase diagram at low concentrations of carbon (e1 at ∼12 at. % C, 1255 K) at 7.7 GPa has been established by optical microscopy and DSC experiments.10 While pressures below 10 GPa remain of principal interest for hydrocarbon transformation/storage14,15 and for diamond growth,13 higher pressures represent a promising domain for the discovery of challenging carbon-based materials, such as ionic semiconductors,16 superhard sp3 and/or sp2 carbon networks intercalated with Mg (clathrates,17 doped polymerized fullerenes,18 etc.), and even novel types of “polymeric” carbides

Synthesis of new binary chemical compounds is, in some aspects, an even more challenging and difficult task as compared with the search for advanced known materials and often requires sophisticated chemical approaches and new control parameters for synthesis, e.g., high pressure.1 Carbon compounds, although intensively studied for more than half a century, still remain a major center of scientific and technological attention.2 Modern design of new materials is often based on challenging theoretical predictions, allowing not only the optimization of composition and crystal structure at given thermodynamic conditions3 but also improvement of specific materials properties.4 However, some important limitations remain for refractory solids, for which the transformations start mainly at very high temperatures, and one cannot easily obtain the reliable ab initio data. A large number of predicted thermodynamic parameters often leads to an important accumulation of errors and a strong deviation of theoretical equilibria from experimental data.5 In this paper, we show how to resolve this problem by combining experimental data with ab initio calculations using the magnesium-carbon system as an example. © 2014 American Chemical Society

Received: January 29, 2014 Revised: March 20, 2014 Published: March 21, 2014 8128

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Figure 1. Mg2C stability under extreme p−T conditions. (a) A sequence of in situ X-ray powder diffraction patterns of Mg-C sample, taken during compression to 18 GPa (at 300 K), heating to 1550 K (at ∼18 GPa), and subsequent isothermal decompression (at ∼1550 K). The formation of Mg2C was observed at ∼1500 K during heating at 18 GPa after the Mg-C interaction above 1400 K. At 1550 K, Mg2C decomposes at the pressure of ∼11 GPa. Symbols represent the reflection lines of Mg (∇), MgO (●), Mg2C (▼), glassy carbon (*), Mg2C3 (×), and artifact (+). (b) Isopleth section (identical for 33−50 at. % C range) of tentative p−T phase diagram of Mg2C. The stability line of Mg2C was drawn using our in situ data at 1550 K and the 0 K value predicted by ab initio calculations (stability compared to Mg−diamond mixture). The melting temperatures of Mg2C and Mg2C3 were estimated using the Lindemann model combined with ab ibitio calculations of the Debye temperature under pressure (○). Solid symbols correspond to the in situ observations of Mg2C stability (●) and its decomposition into Mg2C3 phase (▲), while half-open symbols represent the same compounds observed in recovery experiments.

with one-dimensional carbon chains.19 Many such phases have been suggested and studied using ab initio methods; however, these calculations are often limited to 0 K. At the same time, the real phase transitions, if they occur, often require very high temperatures (>1500 K) to overcome kinetic barriers. Thus, knowledge of the Mg-C phase diagram at extreme p−T conditions is of high importance for the design of new advanced materials, but it cannot be constructed in a traditional theoretical approach because neither thermodynamic potentials nor melting points are known, especially for proposed hypothetical phases. Mg2C antifluorite carbide was hypothesized in 1993 by Corkill and Cohen16 and recently obtained by Kurakevych et al.20 at high-pressure conditions. The compound forms from the elements at pressures above 15 GPa and takes on the antifluorite structure (cubic system, space group Fm3̅m, lattice parameter a = 5.4480 Å). Mg2C is also fully recoverable to ambient conditions.20 This compound is unique in the sense that carbon is stabilized in a rare C4− ionic state. In this paper, we report in situ measurements of Mg2C stability at high pressure and high temperature using X-ray diffraction (XRD) with synchrotron radiation. Ab initio calculations of the phonon dispersion and density of states (PhDOS) have allowed us to understand the dynamical stability at ambient conditions (metastability in a thermodynamic sense), as well as to evaluate the thermophysical properties of Mg2C and to construct the equilibrium Mg-C phase diagram.

heating. A sequence of XRD patterns was obtained at the ID06 beamline of the ESRF using a newly installed large-volume press, which has enabled a large amount (1−3 mm3) of the light-element samples to obtain good quality powder diffraction patterns under pressures at least up to 20 GPa (the experimental details are described in the Supporting Information). Pressure and temperature were estimated using the p−V−T equations of state of Mg and MgO (Table S1, Supporting Information).21,22

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RESULTS AND DISCUSSION The in situ X-ray diffraction patterns at 18(1) GPa indicate that the Mg lines disappeared at ∼1400(50) K, below the melting temperature of pure magnesium that can be estimated as 1600−1850 K at 18 GPa21,23 (Figure 1a). This can be explained by its interaction with glassy carbon (Figure 1a). However, the formation of well-crystallized Mg2C was observed only at temperatures above 1500(50) K. After all magnesium was transformed into Mg2C, the isothermal decompression at ∼1550(50) K was performed. At pressures below ∼11(1) GPa, new reflections were observed, indicating that Mg2C is stable only above this pressure at 1550(50) K (Figure 1b). The new phase formed on decompression is a high-pressure polymorph of Mg2C3 that will be described elsewhere. By combining the observations of in situ stability above 11 GPa at 1550K with previous ab initio predictions of 0 K thermodynamic stability (as compared to pure elements) above 15 GPa by calculation, we can draw an isopleth (constantcomposition) p−T section (identical at least in the 33−50 at. % C range) that gives the lower-pressure boundary of Mg2C thermodynamic stability (Figure 1b). If decompression is performed at 300 K, the Mg2C phase may be recovered at

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EXPERIMENTAL METHODS To observe the in situ formation and stability of Mg2C at high pressures and high temperatures, a mixture of Mg and glassy carbon was compressed to 18 GPa and probed by XRD during 8129

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Figure 2. Lattice dynamics of Mg2C by ab initio calculations. (a) Phonon dispersion curves of Mg2C at 0.1 MPa and −16 GPa (solid and dashed curves, respectively). Absence of imaginary modes at ambient pressure (negative ω2) is indicative of dynamic stability of the phase. Only at −16 GPa, such a mode appears and crosses the zero frequencies near X and K points (the lowest acoustic phonon modes at both pressures are represented by thick curves). (b) Phonon density of states (PhDOS) of Mg2C, obtained by integration of phonon dispersion curves at 0.1 MPa (solid line) and 15 GPa (dashed line). Inset shows the corresponding cv values at these pressures. Although the pressure shift of PhDOS is significant, the cv values are not much influenced.

The observed metastability at ambient conditions may be understood by examining phonon dispersion relations. Dynamic instabilities appear when imaginary frequencies are observed in the phonon dispersion spectrum (ω2 < 0 for at least one of the modes), and in this case, the phase becomes unstable and undergoes structural transition into a more favorable form. To examine the dynamic stability, phonon calculations were performed based on density functional perturbation theory41 implemented in Quantum Espresso.42 Calculations predict that, at 0.1 MPa, and at pressures at least up to 75 GPa, no such modes appear and the antifluorite structure remains stable (solid lines in Figure 2a). Only at negative pressures (< −16 GPa), the “imaginary frequencies” of the lowest acoustic phonon mode appear near the X and K points (thick dashed lines in Figure 2a) and the structure becomes unstable even at low temperatures. At ambient pressure, Mg2C remains metastable for a long time and may be easily recovered (Figure 1b). To render Mg2C unstable, one needs high temperatures (noticeably above 300 K, Figure 1b), where the atomic mobility increases due to diffusion and the compound decomposes. The products of decomposition at 0.1 MPa are, most probably, carbon and a magnesium sesquicarbide or magnesium. In addition to dynamic stability, it is also interesting to examine the elastic stability of Mg2C through application of the Born criterion.43,44 Mechanical stability of cubic crystals requires the following relationships between elastic constants: C11 > 0, C11 − C12 > 0 (tetragonal shear stability), C11 + 2C12 > 0 (bulk stability), and C44 > 0 (shear stability). It is easy to see that elastic constants obtained by ab initio calculations satisfy these criteria (C11 = 269 GPa, C12 = 20 GPa, C11 − C12 = 249 GPa, C11 + 2C12 = 309 GPa, and C44 = 106 GPa).45 Thus, Mg2C remains mechanically stable at atmospheric pressure. The final step in understanding the HPHT stability of antifluorite magnesium carbide was achieved by construction of the equilibrium T−x diagram at 15 GPa (demonstration of thermodynamic stability). The Gibbs thermodynamic potential was estimated at HPHT conditions using a combination of ab initio energies and PhDOS calculations, and with experimental equation of state data. After integration of phonon dispersion

ambient conditions and remains metastable at least for months under an inert argon atmosphere. The upper-T boundary for the Mg2C stability is defined by the melting temperature (later in the paper, we will show that, at 15 GPa, the melting is congruent) that has been established using a Lindemann model24 combined with ab initio calculations of the Debye temperature (Figures S1 and S2, equation S6, Supporting Information). Figure 1b also indicates the tentative upper temperature limit of solid carbide(s) existence at lower pressures, estimated by connecting the Lindemann’s melting temperature of Mg2C3 (low-pressure metastable phase)7 and the cross point of melting/stability of Mg2C. The negative slope obtained suggests that atomic volumes Vsol(Mg2C3) > Vliq(Mg2C3), contrary to Vsol(Mg2C) < Vliq(Mg2C), which is well in agreement with the available density data (Figure S3, Supporting Information). At high enough temperature, the deviation of observed transformations from thermodynamic equilibria tends to zero in both soft ionic and harder covalent compounds. At low temperatures, remarkable reverse-transition hysteresis may arise, especially in the case of light-element solids with rigid covalent networks, such as diamond-like25,26 and boron-rich27 ones. This phenomenon favors the recovery of a number of metastable high-pressure materials.28,29 The metastability is less pronounced in the case of more soft covalent bonds in heavier elements but still may occur. For example, high-pressure Si allotropes are unstable, but some intermediate phases may be recovered,30 as well as some high-pressure Si clathrates.31 Recovery of metastable, predominantly ionic HP compounds of transition metals (e.g., high-pressure rock-salt ZnO)32 is also rarely predictable. The main factors that determine metastable phase recovery could be low/moderate temperatures,32,33 timescale,34,35 nanostructuring,32,33 presence of isostructural compounds,36,37 alloying,38,39 time−p−T sample history,40 etc. In the case of highly ionic compounds of nontransition light metals, this phenomenon is not common, and in this respect, Mg2C remains quite unique.20 The recovery of this phase is reproducible and, contrary to rock-salt ZnO, is not sensitive to time and grain-size scales. 8130

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Figure 3. Thermophysical properties of Mg2C and Mg-C phase diagram at 15 GPa. (a) Thermal expansion α = (∂ ln V/∂T)p and heat capacity cp (atomic value) of Mg2C (solid lines correspond to 0.1 MPa and dashed lines to 20 GPa) obtained using calculated cv, Grueneisen parameter γ, and bulk modulus B. (b) Equilibrium phase diagram of Mg-C system at 15 GPa (solid lines and curves) containing congruently melting antifluorite Mg2C compound, which forms eutectic equilibrium with Mg (quasi-degenerated e2) and with diamond (e3). At pressures above 15 GPa, Mg2C of antifluorite structure with a C4− anion is stable in a wide x−T domain (∃ T: 0 < x < 0.6, and ∃ x: 0 < T < 2430 K). Two rectangular areas bound the x−T domains of experimental observations at 15 GPa (ex situ study of multianvil samples): Mg2C can be recovered at x < 0.6 at. fraction of C. The dashed curves and line represent the metastable Mg-C liquidus and solidus, respectively.

curves (Figure 2a), the PhDOS of Mg2C was used to estimate cv at ambient pressure and 15 GPa (Figure 2b; equation S1, Supporting Information). At both pressures, cv values are only slightly different and do not have much influence on the strong pressure dependencies of α and cp (equations S2 and S3, Supporting Information). The study of PhDOS with pressure allowed us to establish the evolution of the Debye temperature, θD, and Grueneisen parameter, γ, with pressure (Figure S1, Supporting Information). θD takes on a value of 654 K at ambient pressure, while γ = 1.5 decreases with pressure with a characteristic value of V (dγ/dV) = +1.65. Next, the p−V−T equation of state, thermal expansion α, and bulk modulus B of Mg2C (Figure 3a; equation S2, Supporting Information) were estimated using the calculated cv and γ values. The inset of Figure 3a compares experimental and theoretical p−V−T points. Calculated values up to 20 GPa and 2000 K fit well the theoretical p−V−T equation of state proposed in ref 46 (Figure S4, equation S5, Supporting Information). The good agreement between experimental and ab initio HPHT equations of state provides an estimation of the specific heat capacity, cp, of Mg2C (Figure 3a; equation S3, Supporting Information), lying between corresponding values for magnesium and diamond. The atomic enthalpy of formation (as compared to hcp Mg and diamond) for Mg2C (ambient pressure) was estimated by ab initio calculations as ΔHf0K = +19.3 kJ mol−1. Changes in the Gibbs potential with pressure were taken into account using procedures described elsewhere.47,48 The Gibbs thermodynamic potential for the Mg-C liquid phase was calculated using the irregular solution approximation (six-parameter model, equation S8, Supporting Information). The interaction parameters of the irregular solution model that satisfy the eutectic condition at 7.7 GPa (∼12 at. % C, 1255 K)5 were found to be ΔVmix = 0, ΔHmix = 20x2(1 − x) kJ mol−1 and ΔSmix = 10x(1 − x)(x − 0.5) J mol−1 K−1. Figure 3b shows the T−x phase diagram at 15 GPa that represents the combination of experimental and ab initio

thermophysical data discussed above, suggesting only the antifluorite compound. This diagram is compatible with our in situ observations of phase transformations in the Mg-C system at pressures above 15 GPa: e.g., at 18 GPa, even in an excess of carbon (2C:1Mg), only one Mg-rich compound forms, viz., Mg2C (Figure 1a). To confirm the congruent melting of Mg2C under such conditions (15 GPa, 2500 K) would be a challenging task for future study of Mg2C under extreme conditions. According to our ex situ observations in the experiments below 15 GPa, the new Mg-C phase(s) appear(s) in the carbon-rich systems, in addition to Mg2C, whereas, in the stoichiometric mixture (1C:2Mg), only the antifluorite compound forms. Therefore, the phase diagram should be more complicated and requires additional studies outside the scope of this work. In our 9 GPa ex situ experiments, Mg2C was not recovered at any Mg concentration. In Figure 3b, we also indicate the concentration zone of Mg2C formation. It is interesting to note that no formation of Mg2C was observed in ex situ experiments at 15 GPa when the carbon concentration was above 60 at. % C, even at temperatures up to 1975 K (Figure 3b). This is due to the formation of high-pressure carbides of other compositions, e.g., Mg2C3 (not reflected on the phase diagram), although, at ∼18 GPa, Mg2C forms even at 66 at. % C and no other carbides were observed.

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CONCLUSIONS Finally, the combination of in situ probing, standard thermophysical and ab initio data allowed us to explain the p−T−x domains of dynamical, mechanical, and thermodynamic stabilities of Mg2C with an antifluorite structure. At 15 GPa and above, it has a wide domain of thermodynamic stability and should melt congruently. Mg2C forms from the elements at pressures ∼ 15 GPa, most probably by solid-state interaction. After formation, it can be recovered (fast quench to 300 K and subsequent decompression) and remains metastable at ambient conditions at least for months. During high-temperature 8131

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decompression (1550 K), the phase becomes unstable at pressures below 11 GPa. The high-temperature instability at lower pressures is due to the thermal diffusion and subsequent phase segregation, whereas the low-temperature metastability is due to the “stability” of vibrational modes and mechanical stability of the crystal structure. One can also conclude that high pressure plays an important role in the stabilization of the C4− anion in the antifluorite structure: the only known isostructural compound Be2C (stable at ambient pressure) is highly covalent in comparison.20

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ASSOCIATED CONTENT

S Supporting Information *

Details of high-pressure and synchrotron radiation experiments, ab initio calculations, and thermodynamic analysis. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +33 1 44 27 44 56. E-mail: oleksandr.kurakevych@ impmc.jussieu.fr. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank K. Cherednichenko for assistance in synchrotron XRD measurements. This work was supported by DARPA under ARO contract numbers W911NF-11-1-0300 and W31P4Q-13-1-0005 (TAS and OOK) and by the Energy Frontier Research in Extreme Environments Center (EFree) under award number DE-SG0001057 (DYK). In situ experiments were performed on the ID06 beamline at the European Synchrotron Radiation Facility (ESRF), Grenoble, France.

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