High-Pressure Synthesis of Manganese Monocarbide: A Potential

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

High-Pressure Synthesis of Manganese Monocarbide: A Potential Superhard Material A. N. Arpita Aparajita,† N. R. Sanjay Kumar,*,† Sharat Chandra,‡ S. Amirthapandian,‡ N. V. Chandra Shekar,§ and Kalavathi Sridhar† †

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High Pressure Physics Section, Condensed Matter Physics Division, Material Science Group, Indira Gandhi Centre for Atomic Research, ‡Material Physics Division, Material Science Group, Indira Gandhi Centre for Atomic Research, and §Condensed Matter Physics Division, Material Science Group, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam, Tamil Nadu 603102, India ABSTRACT: In this paper, we report for the first time formation of novel manganese monocarbide (MnC) using laser-heated diamond anvil cell (LHDAC). The synthesis was carried out at high pressure−high temperature (HPHT) and subsequently quenched to ambient condition. The formation and reproducibility have been confirmed in the pressure range of 4.7 to 9.2 GPa. Employing contribution of different probes viz.X-ray diffraction (XRD), selected area electron diffraction (SAED), and ab initio electronic structure calculation, the structure of MnC was found to be ZnS type i.e. a cubic lattice with a = 4.4294(2) Å. The bulk modulus has been determined to be 170(5) GPa from in situ high-pressure X-ray diffraction (HPXRD). Hardness of ZnS type MnC is estimated from an empirical relation to be about 40 GPa, making it a potential superhard material.

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INTRODUCTION Transition metal carbides (TMCs) are proven to be promising candidates in the pursuit of new superhard materials.1−3 The key parameters for their hardness are (i) high valence electron density offered by transition metals (TM) and (ii) high covalency extended by carbon. Hence, the design of superhard materials envisages incorporation of high carbon content into a TM lattice, wherein TM has high valency. But, we see that in 4d and 5d TM series, only the elements in groups III to VII form carbides and in the case of 3d series, though all the elements form carbides, the reported TMCs are metal rich (i.e., for TMxCy; x > y).4 The reason behind this lies in the way TMxCy forms. In general, the carbon atoms are considered as interstitials in the TM lattice. When C atoms are inserted, simultaneous weakening of TM-TM bond and formation of TM-C bonds happen. The stability of a particular phase depends on the balance between the strength of TM-C and TM-TM bonds.5 Formation of TM-C bonds and their strength can be understood in terms of overlapping of the electronic states of the respective atoms. This overlapping involves two phenomena: (i) Pauli repulsion, which costs energy; and (ii) hybridization forming bonding and antibonding states. For bonding states, hybridization effect is attractive and compensates for the cost of Pauli repulsion. Naturally, the opposite effect is seen for antibonding states. So, the TM-C bond where only the bonding states are occupied is the strongest.6 In the case of TMCs, the filling of antibonding states increases toward © XXXX American Chemical Society

the latter part of the series, making the respective TM-C bonds weaker. This hinders the inclusion of more carbon and explains the absence of carbon-rich carbide phases for the TM present in the latter part of the series. Nevertheless, high-pressure synthesis has been found to mitigate such issues and highpressure syntheses of Ru2C, Os2C, Re2C, and PtC have been reported.7−10 Also, with the improved kinetics offered by high pressure, many counterintuitive compounds such as Na2He, Na3Cl, and NaCl3 have been synthesized.11,12 Manganese (Mn) has the highest valence number among 3d transition metals. In the binary phase diagram of Mn and C, the phases reported are Mn23C6, Mn5C2, Mn7C3, and Mn3C. The thermodynamic properties of Mn−C compounds have been assessed by Djurovic et al. using CALPHAD (calculation of phases diagram) method and the results for MnCx (x ranging from 0.26 to 1) shows that for MnC the enthalpy of formation is positive.13,14 So, formation of manganese carbide with higher carbon content (x ≥ 1) is unfavorable. As discussed earlier, we can expect the synthesis to be attainable by a high-pressure method. Hence, in this study, our objective was to synthesize a carbon-rich manganese carbide phase by use of LHDAC. Received: July 30, 2018

A

DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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EXPERIMENTAL AND COMPUTATIONAL DETAILS

A Mao-Bell type Diamond Anvil Cell (DAC) was used for pressure generation. For the sample assembly, a stainless steel (SS) gasket was preindented to a thickness of 80 μm and a hole of diameter 250 μm was drilled at the center of the indented region using tungsten carbide drill bit. Mn (cubic, I43m) and carbon powder were taken in the atomic ratio of 1:5 and mixed thoroughly by grinding with addition of alcohol. A pelletized sample of about 150 μm diameter along with ruby chip was loaded in the sample chamber. Argon was loaded using in-house cryogenic loading system.15 Argon functions as the insulation layer between the sample and the diamond anvils, and prevents the graphitization of diamond at high temperature. Ruby works as the pressure callibrant.16 Laser heating was carried out with in-house CO2 laser-based (10.6 μm, 120 W) LHDAC set up.17 The LASER spot size was 30 μm. The pellet was visualized using CCD based imaging system and the heating was done in rastering manner with laser power between 30 and 50% for 45 min at a pressure of 4.7 GPa. The temperature measurement was done by spectroradiometric technique and was found out to be 2000 K.18 The experiment was repeated for two more times to check the reproducibility where the syntheses were done at 9.2 and 5.2 GPa, respectively. HPXRD was carried out in a Debye−Scherrer geometry using an 18 kW rotating anode X-ray generator with Molybdenum target (λ = 0.7107 Å) and a mar-345 image plate detector. The X-ray beam was focused to a spot size of ∼100 μm using an external slit. Diffraction patterns were collected for 2 h at each pressure. Due to mechanical constraint of the DAC the data obtained was limited only up to 2θ = 30°. Hence, XRD on the retrieved sample was carried out only with the piston and meaningful data up to 2θ = 40° could be obtained.8 Transmission electron microscopy (TEM) was carried out for further characterization of the sample. As the sample volume obtained from the high pressure synthesis is of the order of microgram, the conventional sample preparation method for TEM was not possible. Hence, the retrieved sample was sheared between the diamond anvils to make it thin and thereby electron beam transparent. Then, the sample was transferred to the carbon coated copper grid. LIBRA 200FE (Carl Zeiss) high resolution transmission electron microscope (HRTEM) operated at 200 kV was used for selected area electron diffraction (SAED) and imaging. The information limit of the microscope is 0.13 nm. Micro-Raman study was carried out using Renishaw inVia Raman Spectroscope, UK with 514 nm laser excitation. The 2D diffractogram was integrated to 1D XRD pattern (intensity vs 2θ) by using fit2d software.19 The XRD pattern has been indexed using ‘powder diffraction data interpretation and indexing program POWD and PCW program.20 Le Bail fitting has been done using Rietica Rietveld program.21 SAED patterns have been analyzed with ImageJ program. Ab initio electronic structure calculations have been carried out employing density functional theory (DFT). PAW−PBE potential method as implemented in VASP code was used; 20 × 20 × 20 kpoints were considered for computation. Calculations using density functional perturbation theory (DFPT) have been carried out to calculate the phonon dispersion using VASP plane wave code and PHONOPY module.22,23

Figure 1. Ambient X-ray diffraction patterns of the sample before and after laser heating confirming the formation of manganese carbide phase and reproducibility of the result. The peaks for Mn−C are marked by arrows. The star marked peaks are from Mn and the triangle marked peaks are from gasket.

Figure 2. 2D diffractogram of Mn−C after laser heating at 4.7 GPa. The thick bright lines are from SS gasket.

patterns of the phases present in the binary phase diagram of Mn and C system viz. Mn 23 C6 , Mn 3 C, Mn7 C3 , and Mn5C2.13,24−27 The comparison confirmed that a new manganese carbide has formed. Mainly, with the aim of probing more d-spacing, TEM imaging and SAED studies were performed. Figure 3 shows the bright field TEM image of the sample. The particles are agglomerated and we also see some graphene like structure in the image. Figure 4 shows the SAED pattern of the sample. We see some continuous rings and some bright dots forming a ring. The dotted rings are due to the small number of crystallites present in the sample. The dspacings were calculated corresponding to the rings and the same have been marked in the pattern. Table 1 lists down the d-spacings obtained from SAED experiment along with those from ambient XRD of the retrieved sample. The d-spacings for Mn and C have been taken from ICDD PDF no. 00−032− 0637 and PDF no. 00−006−0675, respectively. It can be seen that the sample contains manganese and carbon along with the manganese carbide. Also, a few of the d-

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RESULTS AND DISCUSSION Figure 1 shows the ambient XRD patterns of the sample before laser heating and that after heating at 4.7 and 9.2 GPa. Along with the unreacted Mn Bragg peaks, we can clearly see the appearance of new reflections at 2θ positions 15.99, 18.46, 26.26, 30.86, and 32.25°, which indicates the formation of a manganese carbide phase (Mn−C). In Figure 2, the 2D diffractogram of Mn−C formed after laser heating at 4.7 GPa, is shown. The Mn and Mn−C peaks are marked in the image. The thick bright lines are from SS gaskets. We see from Figure 1 that the observed new reflections are reproducible in pressure range of 4.7 to 9.2 GPa. As a first step toward the phase determination, the XRD pattern of the retrieved sample was compared with the XRD B

DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. List of d-Spacings Obtained from SAED Experiment along with Those from XRDa from SAED

Mnb

Cc

1.02 1.09

1.03 (831) 1.09 (811)

1.07 (311)

1.21 (721)

1.26 (220)

1.51

1.52 (530)

1.81 1.96

1.74 1.81 1.89 2.10

Mn−C from XRD 1.10 1.27 1.33 1.56

(510) (422) (332) (411)

remark from Mn from Mn−C mainly

from Mn−C mainly from Mn only from Mn only

2.06 (111)

a

Figure 3. Bright-field TEM image of the retrieved sample. The area where SAED was performed is marked with a red circle. The lighter part is the image of graphene formed along with manganese carbide during laser heating.

b

2.55

2.57 (222)

3.12

3.15 (220) 3.64 (211)

2.21 2.55

from Mn−C mainly from Mn only

The Miller indices for Mn and C are mentioned in parentheses. ICDD PDF No. 00-032-0637. cPDF No. 00-006-0675.

carried out. It was noticed that the TMCs adopt the stoichiometries M3C4, M4C3, M3C2, M2C, M5C2, and MC, and in general, they adopt cubic or hexagonal close packed structures. Hence, the unit-cell parameters were generated for cubic and hexagonal systems. XRD patterns were simulated with different crystal structures and the obtained lattice parameters. The best match to the experimental XRD pattern was obtained with four cubic crystal structures viz. Ag2O, Nb4C3, NaCl (B1) and ZnS (B3) type crystal structures, and one hexagonal structure, i.e., Al3Ni2 type. The experimentally obtained 2θ and those for the candidate structures are mentioned in Table 2. The corresponding crystal planes are also mentioned. We have carried out ab initio electronic structure calculations to obtain the equilibrium lattice parameters of Mn−C in all the above structures. The experimentally obtained unit cell with Al3Ni2 structure type has a = 4.4209(4) Å and c = 3.4211(6) Å. In the unit cell, there are two types of Mn sites those are 1a(0, 0, 0), 2d(0.333, 0.666, 0.621) and C is at 2d(0.333, 0.666, 0.119). However, the simulated XRD pattern of the computed unit cell with relaxed lattice parameters and atom positions does not reproduce the experimentally observed peak at 26.16° and also the predicted Bragg peaks (002) and (1−21) were not observed in the experimental pattern. Hence, the possibility of the synthesized Mn−C adopting the structure type of Al3Ni2 can be ruled out. The lattice parameter for the cubic lattice types obtained was 4.42(2) Å. In Table 3, we list down the computed equilibrium lattice parameters for all the four cubic candidate structures. It can be seen that for the Ag2O and Nb4C3 prototypes, the computed lattice parameters are not in good agreement with the experimentally obtained lattice parameter value. Hence, those structure types can also be eliminated from further analysis. For B3 structure of manganese monocarbide (MnC), the experimental and computed lattice parameters are in good agreement, whereas for the NaCl type they are not. Hence, it appears that B3 type MnC has formed. A study on 3d transition metal monocarbides to understand the relation between average charge density per molecule (ne)

Figure 4. SAED pattern of the retrieved sample. The d-spacings in Å are marked corresponding to the rings.

spacings obtained from XRD for the carbide are missing in the SAED pattern so is the case with Mn and C. This is because of the unconventional sample preparation method adopted. However, electron diffraction clearly corroborates the observation made in XRD. The Micro-Raman spectroscopy study also showed signal only for graphene and no Raman active modes could be obtained for the synthesized manganese carbide, indicating that maybe the novel phase is metallic in nature. For the crystal structure determination the XRD data was taken into consideration for POWD analysis. To get the plausible candidate structures for the LHDAC synthesized carbide, a survey on the structures adopted by TMCs were C

DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 2. List of 2θ Values Obtained Experimentally and the 2θ Values Obtained for the Candidate Structure Typesa 2θ values of candidate structures experimental 2θ (degree)

Ag2O type

Nb4C3 type

NaCl type

ZnS type

15.99 18.46 26.26 30.86 32.25

15.969 (111) 18.459 (200) 26.221(220) 30.851 (311) 32.259 (222)

15.978(111) 18.469 (200) 26.235 (220) 30.868 (311) 32.277 (222)

15.974 (111) 18.465 (200) 26.229(220) 30.86 (311) 32.269 (222)

16.0(111) 18.464 (200) 26.231 (220) 30.862 (311) 32.271 (222)

Al3Ni2 type 16.014 18.502 26.294 30.872 32.266

(011) (110) (012) (211) (022)

a

The miller indices of the crystal planes are mentioned in bracket.

Table 3. Computed Equilibrium Lattice Parameters for the Cubic Candidate Structures for the Synthesized Mn−C candidate structures Mn2C: prototype, Ag2O; space group, Pn3m (224) Mn4C3: prototype, Nb4C3; space group, Pm3m (221) MnC: prototype: NaCl (B1) space group, Fm3m (225) MnC: prototype, ZnS (B3); space group, F43m (216)

computed lattice parameter (a in Å) 4.083 3.932 4.005 4.290

and the cohesive properties, shows that the cohesive energy is maximum for TiC (ne = 4) and it decreases afterward, reaches a minima for MnC (ne = 5.5) and again increases for higher ne. A complementary trend is seen for the density of states (DOS) wherein Fermi level lies in deep minima of DOS for TiC and moves up toward higher density (less stability) and DOS becomes maximum for MnC. Also, from extrapolation of experimental data and theoretical calculation it is seen that with increasing ne the enthalpy of formation becomes unfavorable after VC.28,29 In the light of the above discussion, ScC, TiC, and VC are designated as stable compounds and are reported to be synthesized by high temperature and mechanochemical methods.30−33 Accordingly, CrC, MnC, FeC, CoC, and NiC are designated as metastable compounds. However, among these metastable compounds synthesis of CrC has been reported to be done by ion implantation and that of FeC by pulsed laser deposition.34,35 It is interesting to note that both the stable and metastable 3d TMCs are reported to adopt NaCl (B1) structure type.34−38 Hence, in spite of the difference in lattice parameter, it becomes pertinent to investigate the dynamic stability of MnC in both B1 and B3 structure types. Figures 5 and 6 show the phonon dispersion plots of MnC in NaCl and ZnS structure types at ambient. The appearance of imaginary modes in the dispersion plots for both B1 and B3 structures at ambient indicates that the structures are dynamically unstable. Nevertheless, as the synthesis has been done at HPHT condition and has been quenched; to study the stability at high pressure and high temperature the phonon dispersion relation has been studied up to 10 GPa (unit cell compression, i.e., high pressure) and −20 GPa (unit cell expansion i.e. high temperature). NaCl type MnC was found out to be dynamically unstable in the whole temperature and pressure range studied. However, ZnS type MnC becomes stable at −20 GPa (high temperature) and stays stable at further high temperatures. Figure 7 shows the phonon dispersion plots for MnC with ZnS type crystal structure at −20 GPa. The lattice parameter corresponding to the −20 GPa is a = 4.436 Å, which is in good agreement with the experimental

Figure 5. Phonon dispersion plot for MnC at ambient in B1 structure type. Appearance of imaginary modes infers dynamical instability of the structure.

Figure 6. Phonon dispersion plot for MnC at ambient in B3 structure type. Appearance of imaginary modes infers dynamical instability of the structure.

lattice parameter, i.e., 4.4294(2) Å. Hence, we conclude that a high temperature phase of MnC has formed which crystallizes in ZnS crystal structure. To cite a parallel, it can be mentioned here that though the first paper on HPHT synthesis of PtC reported an NaCl type structure, later, the study by Qian Li et al. has showed that ZnS type structure is the thermodynamically stable state for PtC.9,39 Figure 8 shows the experimental and simulated XRD patterns for the HPHT synthesized MnC plus Mn. The 2θ regions where the gasket peaks were present were excluded during Le Bail fitting and they appear as blank regions in the figure. In the unit cell of MnC, the Mn atom occupies the 4a (0, 0, 0) position and C occupies the 4c 1 1 1 ( 4 , 4 , 4 ) position, and Mn is tertahedrally bonded to C atoms. D

DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 10. (a) HPXRD patterns of MnC. The MnC peaks are indexed in the ambient pattern and are marked with arrows at high pressures. The star marked peaks are from Mn, triangle marked peaks are from gasket, and unmarked peaks are from argon. (b) EOS fit to P−V data.

Figure 7. Phonon dispersion plot for MnC at −20 GPa in B3 structure type indicating structural stability of the structure at high temperature.

the ambient pattern and have been marked by arrows at high pressure. The peaks from Mn and gasket are also marked. For the lattice parameter determination at high pressure the (111) and (200) peaks were taken into consideration. The averages of the volumes obtained from the two peaks have been plotted against pressure in Figure 10b. By fitting the P−V data to second order Birch−Murnaghan equation of state (BM2 EOS) the bulk modulus (B0) was found out to be 170(5) GPa. However, for monocarbides of Ti and V, bulk moduli are reported to be 235(2) GPa and 302 GPa, respectively.40,41 Elastic stiffness constants were estimated for the high temperature phase by electronic structure calculation. For cubic structure three independent elastic constants viz. C11, C12, C44 are needed. For MnC, C11 = 286.44, C12 = 235.27, and C44 = 127.17. These estimated constants satisfy the Born Criterion showing elastic stability of the phase. The bulk modulus was estimated to be 183 GPa by Voigt−Reuss−-Hill average formula, which is in good agreement with the experimental bulk modulus value. The electronic properties of MnC were investigated and Figure 11 shows the band structure and electronic density of state plots for the high-temperature MnC phase. The finite density of state at the Fermi level tells that MnC is metallic and the d-band of Mn is mainly contributing toward it. The metallic nature possibly could be the reason for not getting Raman active modes from Micro-Raman experiment. Figure 12 shows the electronic charge density plot for MnC in the plane (1−10). The color from blue to red indicates low to high charge density. From the plot, we can see that the charge density between Mn and C is high and contour maps show localization of charge between Mn and C, hence they are covalently bonded. The covalent nature of the Mn−C bond can also be seen from the DOS vs energy plot. The overlapping Mn d band and C p band in the interval of approximately −5 eV to −4 eV and −3 eV to −2 eV indicate strong interaction between the 3d and 2p electrons of Mn and C. However, a partial iconicity of Mn−C bond can also be seen in Figure 12. The high density charge cloud (orange color) around carbon infers a charge transfer from Mn to C. The charge density between Mn and Mn is comparatively low and the distribution is uniform

Figure 8. Le Bail fitting of the experimental XRD pattern with B3 type MnC and Mn structures. The inset shows the unit cell of MnC where Mn (the bigger sphere) is at 4a and C (smaller sphere) at 4c. The blank regions of 2θ in the XRD plot are the regions that were excluded during Le Bail fitting because of the presence of gasket peaks over there.

Figure 9 shows the extended unit cell of MnC representing tetrahedral arrangement. The bulk modulus of the synthesized MnC has been estimated by in situ HPXRD experiments. Figure 10a shows the HPXRD patterns of MnC. The MnC peaks are indexed in

Figure 9. Extended unit cell showing tetrahedral arrangement in MnC in ZnS structure. E

DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX

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To understand the high value estimated, we compare it with the hardness of TiC and VC wherein both of them adopt NaCl structure. For TiC, the Ti−C bond length is 2.162 Å (generated with PCW by crystal structure data from reference46) and the corresponding hardness is 16.4 GPa. Similarly for VC the bond length is 2.08 Å and the hardness is 25.4 GPa.38 If we estimate the hardness of MnC in B1 type structure where the Mn−C bond length is 2.214 Å and the hardness value turns out to be 23.67 GPa. So, we can infer that the high value of hardness is endorsed by the high valence electron density of Mn, the short bond length (1.918 Å) and the tetrahedral arrangement in ZnS type MnC. From the above discussion, it can be asserted that MnC is a superhard material which can be synthesized at a reasonably low pressure of 5 GPa. Hence, can be synthesized in bulk by use of multianvil or belt type apparatus and can have important industrial applications like cubic boron nitride, tungsten carbide, and silicon carbide.

Figure 11. Band structure and electronic density of state plot for MnC

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CONCLUSION MnC has been synthesized for the first time at HPHT conditions by using LHDAC. MnC adopts ZnS type crystal structure, i.e., a cubic lattice with space group F4̅3m (216) and lattice parameter a = 4.4294(2) Å. The bulk modulus (B0) has been found to be 170 (5) GPa. The electronic properties as well as thermodynamic, dynamic and elastic stabilities have been investigated which shows that the obtained MnC phase is a high-temperature phase. The theoretical results are in good agreement with the experimental results. The hardness has been estimated to be 40.9 GPa. This makes MnC a potential superhard material that can be synthesized in bulk at a considerably low pressure of 5 GPa.

Figure 12. Electronic charge density plot for the (1−10) plane of MnC

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AUTHOR INFORMATION

Corresponding Author

*Email: [email protected].

throughout signifying metallic nature of Mn−Mn bond. Similar bonding nature is seen in TiC, VC, NbC, TaC, and WC.42,43 The hardness has been estimated from the crystal structure of MnC by using the empirical formula given by Antoniń Š imůnek.44 The formula estimates hardness reliably for a various class of materials (e.g., SiC, VC, WC) with a good correspondence to experimentally determined hardness value.45 Hardness for a compound with two types of atoms is given as

ORCID

N. R. Sanjay Kumar: 0000-0002-0240-8427 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.N.A.A. thanks the Department of Atomic Energy (DAE) for the fellowship and IGCAR management for the help and support. The authors thank Dr. T.R. Ravindran and Ms. Shradhanjali Sahoo for Raman measurements. We also thank all the HPPS members for the valuable discussion.

C b12s12e−σf2 Ω where C and σ are empirically determined constants with values 1450 and 2.8 respectively. b12 is the number of bonds between atom 1 and atom 2 present in the unit cell. s12 is the strength of the bond between atom 1 and atom 2, which is ee defined as s12 = 1 2 ; where, ei= zi ; zi and Ri are the valence H=

n1n2d12

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Ri

electron number and atomic radius of the atom i respectively and f 2 =

2

( ) . n and n are coordination number of atom e1 − e 2 e1 + e 2

1

REFERENCES

(1) Friedrich, A.; Winkler, B.; Juarez-Arellano, E. A.; Bayarjargal, L. Synthesis of binary transition metal nitrides, carbides and borides from the elements in the laser-heated diamond anvil cell and their structure-property relations. Materials 2011, 4 (10), 1648−1692. (2) Yeung, M. T.; Mohammadi, R.; Kaner, R. B. Ultraincompressible, superhard materials. Annu. Rev. Mater. Res. 2016, 46, 465−485. (3) Mohammadi, R.; Kaner, R. B. Superhard materials. In Encyclopedia of Inorganic and Bioinorganic Chemistry; Wiley, 2011. (4) Toth, L. E. Transition Metal Carbides and Nitrides; Academic Press, 1971. (5) Wang, Q.; German, K. E.; Oganov, A. R.; Dong, H.; Feya, O. D.; Zubavichus, Y. V.; Murzin, V. Y. Explaining stability of transition metal carbides - and why TcC does not exist. RSC Adv. 2016, 6 (20), 16197−16202.

2

1 and 2 respectively. Hence, for MnC with ZnS structure, b12= 16, e1= Z(Mn) Z(C) 7 4 = 1.26 = 5.5555, e2= R(C) = 0.92 = 4.3478, n1 = n2 = R(Mn) 4 (can be seen in Figure 9), d12 = 1.918 Å. So, s12 = 0.16 and f 2 = 0.0148. Thereby, H = 40.9 GPa F

DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Switzerland & National Institute for Materials Science (NIMS): Berlin, Germany; Vtiznau, Switzerland; and Tsukuba, Japan, 2012.

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DOI: 10.1021/acs.inorgchem.8b02148 Inorg. Chem. XXXX, XXX, XXX−XXX