Phase Transitions High-pressure phase transitions in ...

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Phase Transitions

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High-pressure phase transitions in transition metal carbides XC (X = Ti, Zr, Hf, V, Nb, Ta): a first-principle study Anurag Srivastavaa; Mamta Chauhana; R. K. Singhb a Advanced Material Research Laboratory, ABV-Indian Institute of Information Technology & Management, Gwalior 474010, M.P., India b School of Basic Sciences, ITM University, Gurgaon, Haryana 122017, India Online publication date: 13 December 2010

To cite this Article Srivastava, Anurag , Chauhan, Mamta and Singh, R. K.(2011) 'High-pressure phase transitions in

transition metal carbides XC (X = Ti, Zr, Hf, V, Nb, Ta): a first-principle study', Phase Transitions, 84: 1, 58 — 66 To link to this Article: DOI: 10.1080/01411594.2010.509644 URL: http://dx.doi.org/10.1080/01411594.2010.509644

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Phase Transitions Vol. 84, No. 1, January 2011, 58–66

High-pressure phase transitions in transition metal carbides XC (X ^ Ti, Zr, Hf, V, Nb, Ta): a first-principle study Anurag Srivastavaa*, Mamta Chauhana and R.K. Singhb a

Advanced Material Research Laboratory, ABV-Indian Institute of Information Technology & Management, Gwalior 474010, M.P., India; bSchool of Basic Sciences, ITM University, Gurgaon, Haryana 122017, India

Downloaded By: [Srivastava, Anurag] At: 10:19 15 December 2010

(Received 30 May 2010; final version received 16 July 2010) First-principle density functional approach has been applied to study the B1!B2 structural phase transition in transition metal carbides (TMCs) (XC; X ¼ Ti, Zr, Hf, V, Nb, and Ta) under the application of pressure. The computations have been performed using ground state total energy calculation approach of the system. The study computes the stability of structure as a function of pressure in original rocksalt (B1) and hypothetical CsCl (B2)-type phases using generalized gradient approximation with Perdew–Burke–Ernzerhof-type parametrization and local density approximation with Ceperley–Alder-type parametrization as exchange correlation functional and observed that the vanadium carbide is found to be the most stable amongst all the carbides taken into consideration. Pressure of more than 400 GPa transforms the original B1-type phase of these carbides to a B2-type phase. We have also calculated the ground state properties, such as lattice constant (a), bulk modulus (B0), and pressure derivative of bulk modulus (B00 ) of TMCs. Keywords: phase transition; transition metal carbides; high pressure; first principle; rocksalt; CsCl

1. Introduction Technological advancements have increased the need for new kinds of materials for industries such as electronics, petroleum, and aerospace. Advanced transition-metal ceramics are the compounds with at least one transition d-metallic element and one of the five non-metallic elements (boron, carbon, nitrogen, oxygen, and sulfur). These advanced ceramic materials of transition metals, due to their various remarkable characteristics, such as high melting temperature, extreme hardness, electrical resistivity, magnetic susceptibility, superconductivity, and chemical resistance, have become very important in the field of material science. Due to an extremely high melting point, these materials are called refractory materials. Due to the unusual combination of thermo mechanical properties, the carbides of transition d-metals of groups IVB and VB are of great scientific and technological interest [1,2]. On the one hand, these materials have high melting points and are of high hardness, comparable to diamond, properties typical to covalent materials; on the other hand, these *Corresponding author. Email: [email protected] ISSN 0141–1594 print/ISSN 1029–0338 online ß 2011 Taylor & Francis DOI: 10.1080/01411594.2010.509644 http://www.informaworld.com


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59

are brittle, show metallic luster and metallic conductivity, and few of them are superconducting in nature with a very high transition temperature Tc (Tc ¼ 11.1 K for NbC and 10.35 K for TaC) [3]. Blaha et al. [4] revealed that there is some charge transfer in refractory compounds which provides metallic as well as ionic-type bonding in addition to the covalent bonding in these materials. This unusual bonding nature is responsible for the unique properties of transition metal carbides (TMCs). Being ultra hard in nature, these materials are widely used in high-speed steel cutting tools. Advances in accurate theoretical modeling have made possible the computation of structural properties of various crystals and their structural phase transition under high compression, which has created new possibilities for studying the hard materials. For example, theoretical predictions of hard structures [5,6] have led to a number of experimental efforts [7] to synthesize super-hard materials. As the super-hard materials are used under extreme conditions of temperature and pressure, it becomes very interesting to study their behavior under high pressure. Theoretically, a number of ab initio electronic structure calculations [8–15] have been done on transition d-metal carbides in the original NaCl-type structure describing their band structure and bonding mechanism. The cohesive properties of 3d, 4d, and 5d TMCs were discussed by Haglund et al. [16,17] by using the linear muffin tin orbital (LMTO) method. However, not many reports are available on the study of these materials under high compression. However, Ahuja et al. [18] using the FPLMTO method have predicted NaCl (B1) to CsCl (B2)-type phase transitions in TiC, TiN, and TiO; whereas, recently Singh et al. [19] reported phase transition in NbC and ZrC through model calculation. The elastic properties of polycrystalline HfC0.967, NbC0.964, TaC0.994, and WC1.007 were determined at 23 C, and the data were corrected to theoretical density by Brown et al. [20] some time ago. First-principle electronic structure and positron-state calculations for transition-metal carbides and nitrides were performed and the positron affinities and lifetimes were determined by Puska et al. [21]. A mechanism to enhance the hardness in multilayer coatings was proposed by Hugosson et al. [22] using the technologically important hard TMCs as prototypes whereby they have demonstrated, through firstprinciples calculations, that by suitable alloying the energy difference between several competing structures can be tuned. A review shows that less efforts have been made on understanding the high pressure structural behavior of these materials and, looking to the technological importance of these materials, we thought it is pertinent to explore the possibility of analyzing the pressure-induced B1 to B2-type structural phase transitions in TMCs (XC; X ¼ Ti, Zr, Hf,V, Nb, and Ta). The success of first-principle methods in explaining the high-pressure properties of materials using variety of codes based on density functional theory has also prompted us for the present computation. For computing pressure-induced phase transition in TMCs we have used the SIESTA code [23] based on density functional theory. Besides the structural phase transitions, this study also includes the ground state properties, such as lattice parameter (a), bulk modulus (B0), and pressure derivative of bulk modulus (B00 ) of TMCs.

2. Computational details: a brief In the present calculation, a first-principle pseudopotential approach has been used within the framework of density functional theory [24]. The exchange-correlation energy is calculated by both the local density approximation (LDA) with Ceperley–Alder (CA) [25]

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A. Srivastava et al.

3. Results and discussion In order to calculate the ground state properties total energy is calculated by the self-consistent run of Kohn Sham equations [27]. The total energies are calculated at various volumes to find the minimum energy point. The volume at which the total energy becomes minimum is considered to be the equilibrium volume of the crystal. For calculating the equilibrium lattice constant and other ground state properties, such as bulk modulus and pressure derivative of bulk modulus, the computed total energies at different volumes are fitted to Murnaghan’s equation of state [28] in both the rocksalt (B1) and CsCl (B2)-type phases of TMCs. Stability analysis, ground state properties, and high-pressure phase transition of different TMCs are discussed in the following sections.

3.1. Stability and ground state properties Using the LDA and GGA schemes the total energies have been computed for the whole series of above-mentioned TMCs. The computed total energies of 4B and 5B transition metal compounds in the NaCl-type phase have been shown in Figure 1(a) and (b) and it is observed that in the 4B series TiC with lowest energy can be considered as the most stable, whereas in the 5B series, VC with lowest energy claimed to be the most stable one.

(b) –220

(a) –220 GGA

LDA

–240 Energy (eV)

–240 Energy (eV)


type parametrization and the generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE)-[26] type parametrization. Metal atoms occupy the (0, 0, 0) site while carbon atoms occupy the (0.5, 0.5, 0.05) site in both the B1 and B2-type structures of these materials. The pseudopotential used in the present calculation is norm conserving in a non-relativistic form. We have used the SIESTA code for the calculations that are suitable for electronic structure calculations and ab initio molecular dynamics simulations of molecules and solids [23]. Double zeta basis set is used for atomic orbitals of valence shell for the calculations. In the self-consistent run for all the above-mentioned TMCs Pulay algorithm is used with a diagonal mixing weight of 0.03 for iterations and the mesh cut-off energy of 200 Ry is chosen in both the B1 and B2-type phases of these TMCs. A k-grid of 7 7 7(343) is used for TiC, HfC, and TaC in the whole irreducible Brillouin zone, whereas for ZrC, VC and NbC a k-grid of 8 8 8(512) is used as obtained by convergence test for these compounds with an energy difference of 25 meV.

–260 –280 –300 –320

–260 –280 –300 –320

–340

–340 TiC

ZrC

HfC VC Crystal

NbC TaC

TiC

HfC

VC NbC Crystal

Figure 1. Total energy of TMCs using the (a) LDA scheme and (b) GGA scheme.

TaC

61

Phase Transitions

Table 1. Lattice constant (a), bulk Modulus (B0), pressure derivative of bulk modulus (B00 ), and phase transition pressure (PT) of TMCs. a(A˚) Crystal TiC

Present


Experimental others

ZrC

Present Experimental others

HfC


VC


NbC


TaC


B1

B2 a

B00

B 0 (GPa) B1 a

B2

B1

B2

PT (GPa)

284.48 226.91b – –

3.239 3.438b – –

2.610 2.901b – –

691 a 709b – 490e

3.020a – 3.773j

326.07 306.32b – 267d 270e 220f 390g 310h 281.24a – 250k

247.59a – –

3.442a – –

2.114a – –

525a – 98j

2.984a 2.943b – –

310.33a 314.31b – 260k

233.04a 236.84b – –

2.908a 2.984b – –

2.594a 2.650b – –

485a 494b – –

2.670a 2.623b – –

330.83a 358.57b – 321d

279.65a 302.47b – –

3.195a 3.238b – –

2.772a 2.802b –

807a 813b – –

2.899a 2.867b – 3.696j

356.61a 360.17b – 335k

321.65a 325.05b – –

2.946a 2.949b – –

2.387a 2.431b – –

559a 538b – 85j

2.892a 2.854b – –

391.28a 401.37b – 360k

345.23a 352.64b – –

3.038a 3.141b – –

2.509a 2.554b – –

641a 660b – –

4.270 4.218b 4.328c 4.38d

2.721 2.706b – –

4.666a 4.698c 4.687i 4.700j 4.64k 4.687a 4.629b 4.640c 4.641i 4.57k 4.174a 4.107b 4.166c 4.182l 4.22d 4.556a 4.518b 4.470c 4.592j 4.470m 4.44k 4.539a 4.477b 4.456c 4.454m 4.456i 4.39k

a

a

a

a

Notes: aPresent GGA result; bpresent LDA result; creference [2]; dreference [13]; eLDA study in reference [18]. fGGA study in reference [18]; greference [30]; hreference [31]; ireference [14]; jreference [19]; kreference [15];. lreference [29]; mreference [3].

However in the whole series, VC which has the lower energy in comparison to TiC defends it as the most stable amongst all the TMCs. The calculated ground state properties, such as lattice parameters, bulk modulus, and pressure derivatives of bulk modulus for both the B1 and B2-type phases of TMCs, obtained by fitting the data of total energies for different unit cell volumes to Murnaghan’s equation of state, are summarized and compared with other reported theoretical and experimental values in Table 1. In the case of the original B1-type phase of TMCs, all these parameters are in close match with the values reported by other workers, experimentally [2] and theoretically [3,13–15,18,19,29–31]. In the case of

62



Figure 2. Enthalpy as a function of pressure for TiC using the (a) GGA scheme and (b) LDA scheme.

Figure 3. Enthalpy as a function of pressure for HfC using the (a) GGA scheme and (b) LDA scheme.

the B2-type phase, the computed lattice parameters of ZrC and NbC find the theoretical counterparts for comparison, whereas for TiC, VC, HfC and TaC the present findings could not be compared due to the lack of reported data. The case is similar with their bulk modulus and pressure derivatives, where our calculated values could not get any counterpart for validation and have probably been reported for the first time.

3.2. High-pressure phase transition TMCs (XC; X ¼ Ti, Zr, Hf, V, Nb and Ta) under ambient conditions crystallize in the NaCl-type phase and are found to undergo a structural phase transition to a hypothetical CsCl-type phase under compression. To determine the phase transition pressures, the enthalpy (H ) (i.e. Gibbs free energy at T ¼ 0 K in which entropy is ignored) of TMCs is calculated at various pressures. The pressure at which the difference in enthalpies of both the competitive phases becomes zero (i.e. HB1 HB2 ¼ 0) is called phase transition pressure (PT). The plot of calculated enthalpies (H ¼ E þ PV ) at various pressures for different carbides taken into consideration are given in Figures 2–7. Below the transition pressure, enthalpy of the B1-type phase is lower than that of the B2-type phase, while above the transition pressure enthalpy of the B2-type phase is lower than that of the B1-type phase. Thus, below the transition pressure the B1-type phase is considered to be stable, and above

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Figure 4. Enthalpy as a function of pressure for VC using the (a) GGA scheme and (b) LDA scheme.

Figure 5. Enthalpy as a function of pressure for NbC using the (a) GGA scheme and (b) LDA scheme.

Figure 6. Enthalpy as a function of pressure for TaC using the (a) GGA scheme and (b) LDA scheme.

PT it is the B2-type phase that becomes stable. The present computed transition pressures for TMCs using the LDA and GGA schemes in the framework of SIESTA code have been compared with other reported values and found that in the case of TiC the values are bit higher than the data reported by Ahuja et al. [18]. This difference in the two observations might be due to the difference in approaches used by the researchers, as Ahuja et al. have used the full potential approach and this study uses the pseudopotential approach. In another model calculation [19], the reported values of transition pressure for NbC and ZrC

64



Figure 7. Enthalpy as a function of pressure for ZrC, using the GGA scheme.

are much less as compared to our calculated values for these materials. For other materials, we are probably the first to report the B1 to B2 phase transitions under high compression. In the case of HfC, VC, and TaC, the results could not be compared due to unavailability of any reported data. Comparative results of transition pressures for the whole series of TMCs are given in Table 1. In most of the TMC compounds, the calculated transition pressures are very high. The study of phase transition and ground state properties has been done by using both the LDA and GGA schemes and concluded that, like other reports, here too, GGA is giving better results than LDA.

4. Conclusion In view of the findings reported in the above sections of this article, we can conclude that this study for the stability analysis, ground state properties, and studying the structural phase transition by using the SIESTA code is in good agreement with the other reported studies, particularly in the case of ground state properties. Unavailability of data on phase transition in TMCs defends the present observations as the first by using ab initio methods and needs validation through experimental and theoretical results. We are sure that these findings will certainly stimulate work in this area and may work as input data for a number of researchers interested in understanding the behavior of TMCs under high pressure.

Acknowledgement The authors gratefully acknowledge the DRDO for providing financial support for the research. One of the authors, Mamta Chauhan, is grateful to DRDO for providing JRF.

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