Crystal Structures and Chemical Bonding of Magnesium Carbide at

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Crystal Structures and Chemical Bonding of Magnesium Carbide at High Pressure Hanyu Liu, Guoying Gao, Yinwei Li, Jian Hao, and John S Tse J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b07862 • Publication Date (Web): 16 Sep 2015 Downloaded from http://pubs.acs.org on September 21, 2015

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The Journal of Physical Chemistry

Crystal Structures and Chemical Bonding of Magnesium Carbide at High Pressure Hanyu Liu1, Guoying Gao2, Yinwei Li1,3, Jian Hao3 and John S. Tse1,4*

1

Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E2, Canada

2

State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China

3

School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China

4

State key laboratory of Superhard materials, Jilin University, Changchun, 130012, China

1

ACS Paragon Plus Environment


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Abstract Recent studies of magnesium carbides (Mg-C) system under pressure were motivated by the successful high-pressure and high-temperature synthesis of Mg2C and Mg2C3. Here, we systematically investigate the high pressure structures and chemical bonding of the Mg2C, Mg2C3 and MgC2 system using swarm optimization technique in combination with first-principles electronic structure methodology. The structural evolution with pressure of the Mg-C systems clearly shows a systematic trend with progressive increase of electron donation from the Mg to C. To accommodate the electrons, the C valence sp orbitals rebybridized continually and adopted different modes of chemical bonding. We demonstrated that the evolution of the electronic and crystal structures can be explained from a Zintl-Klemen charge-transfer concept. Therefore, at sufficiently high pressure metallic MgC2 and Mg2C transformed to semiconductors, while Mg2C3 undergoes an insulator-metal transition. The present results established the richness of carbon bonding of different stoichiometries under high pressure.

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Introduction Metal Carbides have been studied intensively due to the technological importance of their physiochemical properties.1-3 Magnesium compounds containing Mg-C and C-C bonds are quite fascinating in both fundamental science and synthetic perspectives. Moreover, the nature of the Mg-C chemical bond is of fundamental relevant to polar organometallic compounds and to the understanding of the covalent/ionic nature of carbanions. It is well known that carbon can form a variety of s-p hybrid orbitals (sp, sp2 and sp3) and, as a result, forming different structural motifs. On the other hand, charge transfer between Mg and C could induce phase transition at high pressures due to the electronegativity difference between Mg and C. The ambient-pressure chemistry of the Mg-C system has been studied quite thoroughly.4 Under normal temperature and pressure conditions, magnesium forms acetylide-like carbide, MgC2,5 which is similar to all other alkaline earth metals. Mg also forms Mg2C3 containing the unique [C=C=C]4- group.6 Recently, Kurakevych et. al.1 presented evidence on the formation of a third carbide of magnesium, namely Mg2C. This compound is found to have a face-center cubic (FCC) space group from in-situ X-ray diffraction between 15-30 GPa and at temperatures 1775-2275 K.1 When this compound is quenched to normal conditions, it was found that the structure contains novel C4- methanide anions. A previous theoretical work systematically studies the crystal structures of Mg2C at high pressures.7 The prediction of high pressure polymorphs has been a subject of topical interest. However, detail and systematic investigation on the evolution of the structures based on well-established 3



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chemical bonding concept have been scare. Here, we performed an extensive structural search on MgC2, Mg2C3, and Mg2C up to 300 GPa using the particle swarm optimization technique in combination with first-principles electronic structure methodology.

As will be reported below, a systematic trend in the local binding of

the carbon is observed.

We showed that these changes can be explained by the

simple Zintl-Klemen model based on the increase of electrons being transferred from Mg to C with increasing pressure. We believe this concept is general and is applicable to explain the structures reported in several recent studies on the high pressure hydrides of alkali and alkaline8-13 and perhaps other binary compounds14, 15.

Results and discussions At low pressure, MgC2 partition into graphite sheets and magnesium, similar to the structure of MgB2. At 1 GPa, the most stable structure of MgC2 is consisted of alternate graphene and Mg layers in the P-6m2 space group [Fig. 1] with only one type of C-C bond of 1.42 Å in the hexagonal layer. The Mg atoms are situated in the middle of alternate hexagonal carbon rings.

This structure is not too surprising as

carbon is stable in the graphitic form under ambient conditions. The calculated formation enthalpies of MgC2 show the recently found MgC2 structure is not the most stable structure. This point will be discussed later. At ~3.9 GPa, a P-1 structure becomes stable and this structure is consisted of two pentagonal carbon rings are linked through a C-C bond of 1.41 Å. At 20 GPa, this structure has three different C-C of 1.41, 1.47 and 1.51 Å for the bridging C atoms. This structure was stable up to 29 4


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GPa followed by the transformation to a C2/m structure at higher pressure. The latter structure is constructed from 1D chain of fused benzene rings running along the b axis. At 50 GPa, there are two different C-C bond-lengths of 1.44 and 1.46 Å. Above 70 GPa, the MgC2 adopted a new P-3m1 structure. This structure is composed of a planar network of Mg atoms and 2D puckered carbon layers in which the carbon atoms are arranged in the boat conformation similar to cubic diamond. This sequence of transformation can be explained from the consideration on the efficient number of electron that can be transferred from Mg to C atoms. At low pressure C atoms prefer to be sp2 hybridized with a graphene layer structure. In view of the electronegativity difference, carbon can accept electrons from Mg. As the pressure is increased, more electrons are transferred from the Mg 3s orbital to the carbon atoms.

The extra electrons occupying antibonding π* orbitals and weaken the

aromaticity of the graphene and the carbon atoms then preferred to form fused pentagon rings linked by edge-sharing of common double C=C bonds. At even higher compression, more electrons are transferred and the sp2 bonding network eventually transformed to sp3. Each carbon atoms now bonded to 3 adjacent atoms with an electron occupying in the remaining sp3 hybrid orbital and localize in the interstitials between the now buckled layers. These structural transformations are promoted by external PV work (where H=E+PV, H, E, P and V are enthalpy, total energy, pressure and volume, respectively.) To quantify the bonding description, Bader charges of Mg and C atoms at different pressures were calculated [Table I]. The results show unambiguously increased charge transfer from Mg to C. At pressure higher than 50 5



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GPa the Mg almost lost (1.63e) all of the valence electrons. Analogous to MgB2, it is expected that the low-pressure P-6m2 MgC2 is a metal due to the alternate graphene and Mg layered structure. Band structure calculations confirm this expectation [Fig. 2]. The higher pressure phases P-1 and C2/m structures are also found to be metallic. In comparison, the band structure shows the P-3m1 structure is an insulator with an indirect band gap of 0.8 eV at 100 GPa. The result is not surprising as the Bader charge calculations already show the electron transfer from Mg to C increased abruptly from 0.37e to 1.62e accompanying the C2/m → P-3m1

phase transition and the latter structure becomes more polar. The computed

electron charge difference of the four high-pressure phases for MgC2 compared in Fig. 2. To accommodate the electrons from Mg and to alleviate the repulsive interaction the sp2 mixed with an empty 2p orbital transforming to sp3 and changed from a metal to an insulator. For Mg2C3, structure search successfully reproduced the Pnnm and C2/m (C2/m–1)3 structures observed at low pressure (Fig. 3) as the lowest energy structures. The agreement between experiment and theory validated the computational scheme and the choice of parameters. Above 39 GPa, Mg2C3 adopted a C2/m structure (labeled as C2/m-2 structure). Instead of the [C=C=C]4- units found at low pressure the carbon atoms form polymeric 2D chains in the new high pressure structure. At 50 GPa, 4 different C-C bond-lengths (1.42, 1.47, 1.50, 1.55 Angstrom) are found in the C2/m-2 structure. At 89 GPa, Mg2C3 underwent another phase transition into a P21/m structure. This structure is similar to the P-3m1 structure of MgC2 with the formation 6


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of single bonded buckled C-C rings. Both Pnnm and C2/m-1 Mg2C3 were found to be insulators [Fig. 4]. This is reasonable as both structures are consisted of C3- anionic units. Once again we resorted to the Bader charges to elucidate the chemical bonding (Table 1). Even at very low pressure, the Mg atoms have already lost 1.67e to the C3 untis. The calculated electron charge difference in the Pnnm and C2/m-1 structures show the two terminus C atoms in the C3 units accepted these electrons from Mg. In principle, a linear C3 unit can accommodate two 2e from Mg and put them into the nonbonding orbital that has high orbital contribution from the two terminal C without severely affect the C-C-C bonds. At higher pressure, as the C3 units are pushed closer, it is preferable for the negatively charged C3 units to link (bond) in order to delocalize the excess electrons to gain overall stability.

This is observed at the C2/m-1 to C2/m-2 transition. Moreover, the

band structure of C2/m-2 indicates it is a metallic phase with a sign of electron delocalized along the C-C chains. At even higher pressure, the C2/m-2 chains started to buckled. As in the case of MgC2, to alleviate electron repulsion at high compression, C rehybridized to sp3 placing some electrons into the interstitial sites. This is found in the P21/m structure which is the most stable above 89 GPa. At low pressure, similar to Mg2C3, the stable Mg2C structure is consisted of C3 units. This structure motif is again due to significant charge transfer from Mg to C and in which the occurrence of C3 anionic units are more preferable. The C-C bond-length in the [C=C=C]4- unit is 1.33 Angstrom at ambient pressure. Unlike Mg2C3, at high pressure a face center cubic (fcc) phase with the Fm-3m space group with Mg and C 7



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forming a dense packed solid is found. In this Mg-rich compound, a lot more electron are available from Mg, consequently, the C3 units can no longer be stabilized and dissociated into carbon anions.

The reason being, in principle, each carbon anion

can accept 4 electrons to fulfill the octet. The formation of a cubic structure can be understood from the calculations of the Bader atomic volumes. As expected the negative carbide are spatially much more diffuse and having a larger volume of 23 A3 as compared to the Mg2+ cation of 6 A3. The large volume difference favours a fcc closet pack structure as NaCl. At 40 GPa the fcc phase transforms into a Pnma structure (Fig. 5). In this structure, there are 5 C atoms and 6 Mg atoms around each Mg atom and 7 Mg atoms around each C atom at 100 GPa. The Pnma structure is stable over a very broad pressure range as no new structure was found up to 300 GPa, the highest pressure studied here. On the other hand, above 250 GPa, a new P63/mmc structure becomes energetically competitive as the Pnma structure.

The very similar

formation enthalpies may indicate both structures could coexist above 250 GPa. Charge difference shows Mg atoms in the high pressure phases of Mg2C are almost fully ionized and ionic C4- and Mg2+ are formed as clearly seen in the charge difference plots [Fig. 6].

The band structures show they are insulators with band

gaps close to 2 eV. Finally, the thermodynamic and dynamic stabilities of Mg2C, Mg2C3 and MgC2 are examined from the formation enthalpies in the pressure range 1-300 GPa and phonon band structures. The results on the energetics are summarized in Fig. 7. The formation enthalpy of MgCx was calculated using the fractional representation Mg(1-x)Cx 8


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Crystal Structures and Chemical Bonding of Magnesium Carbide at

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