Ab-initio techniques, VASP and CASTEP, are used to investigate the electronic properties of B2 compounds formed between Ti and group VIII elements - a comparative study

. Cesium-chloride (CsCl) based intermetallic alloys that are formed between Ti and Group VIIIB and IB metals (Fe, Ni, Ru, Rh, Pd, Os Ir, Pt and Au) are currently explored for various potential applications as hydrogen storage, shape memory and biomedical materials. These compounds display excellent structural properties such as high strength due to their stable B2 phase at elevated temperatures. However, when some are subjected to unfavourable conditions such as lower temperature they become unstable and undergo a phase transition to low symmetry phases. In this work, we conducted a detailed comparative study using both VASP and CASTEP codes to carry out the first-principles calculations. Phase stability and martensitic phase transition were evaluated from the enthalpies of formation, the density of states as well as the phonon dispersion curves. There was no frequency gap observed on phonons density of states (PHDOS) spectra of the investigated compounds containing noble transition metals due to higher d-orbital electron filling.


Introduction
Titanium (Ti) is the most useful engineering material in the production of components for various applications ranging from biomedical, aerospace and automotive industries [1,2]. This is due to its high strength-to-weight ratio and resistance to corrosion which renders it attractive and ideal [1].
In addition, Ti-based intermetallic compounds are promising materials for hightemperature applications as structural (heat and corrosion resistance) or non-structural materials (electronic devices, superconductors, etc.) [1,3,4,5]. These compounds consist of tighter chemical bonds as compared to pure components, hence they have higher elastic stiffness and melting temperatures [6]. Titanium belongs to Group IV, while Iron (Fe), Nickel (Ni), Ruthenium (Ru), Rhodium (Rh), Palladium (Pd), Osmium (Os), Iridium (Ir), Platinum (Pt) and Gold (Au) belongs to Group VIIB -IB of the transition metals that are located in the d-block of the periodic table of elements, and their valence d-electrons give the transition metals (TM) and their compounds a rich variety of characteristics. The d-electron filling increases from the left to the right of the periodic table due to metal-metal d-d orbital hybridization which eventually enhances ductility [7].
The above-mentioned Group IV transition metals form Cesium-Chloride (CsCl) intermetallic compounds with Group VIIIB and IB transition metals due to limited mutual solubility during solidification [8,9]. These compounds crystallize congruently from liquid to an ordered B2 which is a high-temperature austenite phase at compositions close to 50:50 atomic percentage (at. %). Due to their high melting points, some of these compounds (such as Ti50Ru50, Ti50Os50 and Ti50Fe50) are mostly referred to as refractory intermetallics [8,9,10]. Typically, most of these B2 compounds become unstable and undergo martensitic transformation to crystal structures of lower symmetry at lower temperatures [1,11,12].
Currently, the CsCl-type titanium intermetallic compounds are one of the largest groups of the ordered-structure compounds that have received immense attention as potential structural engineering materials due to their high oxidation resistance, and excellent hightemperature strength. Furthermore, this class of materials have proven to possess the most attractive shape memory properties and potential to store hydrogen [10,13,14,15]. In most Ti-based equiatomic compositions, the B2 phase is a high-temperature phase that undergoes martensitic phase transition on cooling to orthorhombic, tetragonal and monoclinic intermetallic, regarded as the low-temperature phases [1]. This difference in the lowtemperature crystal structures results in shape memory alloys (SMAs) with different properties. SMAs found use in various applications such as in automotive, aerospace, eyeglasses, and sensors as well as in biomedical implants such as guided wires, stents and braces [1,16].
Previous density functional theory (DFT) studies that investigated the influence of electronic structure on martensitic transformation (MT) of binary Ti-based CsCl compounds focused only on the density of states (DOS) [8,9]. In this study, VASP and CASTEP were employed to investigate the origin of the MT mechanism of the Ti-based CsCl compounds on the basis of phase stability and electronic structure (density of states and phonon dispersion curves).

Computational methods
This work was carried out using two DFT-based codes, the Vienna Ab Initio Simulation Package (VASP) [17] and Cambridge Serial Total Energy Package (CASTEP) [18,19], with the projector augmented wave (PAW) [19]. To draw a better comparison, the electron exchange and correlation were described by the Perdew-Burke-Ernzerhof (PBE) functional of the generalized gradient approximation (GGA) [20,21] in both techniques. Similarly, the energy cut-off of 650 eV and the k-points of 13×13×13 were found to be sufficient to converge the total energy of the investigated B2 compounds.

Structural and thermodynamic properties
where, represent the total energy of the B2 compound, and represent the elemental total energies of Ti and TM in their ground-state crystal structures. For a compound to be stable, the enthalpy (also known as the heat of formation) must have the lowest negative (ΔHF<0) value, else unstable at 0 K if it has a positive value [35]. Fig. 2 graphically represent the heats of formation obtained from all the investigated B2 compounds. In general, the formation enthalpies of the B2 compounds were found to be negative (ΔHF<0) for results obtained from CASTEP and VASP codes, demonstrating consistency in predicting the thermodynamic stability of B2 crystals. Using CASTEP code, the Ti50Ir50 and Ti50Au50 compounds were found to be the most (-0.913 eV/atom) and least (-0.368 eV/atom) thermodynamically stable, respectively, amongst all the investigated CsCl compounds formed between Ti and group VIII transition metals. Although in the case of the VASP code the close stability competition between Ti50Ir50 and Ti50Pt50 is noted that calculated heats of formation for Ti50Pt50 and Ti50Au50 are the most (-0.754 eV/atom) and least (-0.295 eV/atom) stable, respectively, signalling a slight discrepancy from the trend obtained in CASTEP.
It is further noted from Fig. 2 that heats of formation for some of the B2 compounds as predicted by both CASTEP and VASP codes were found to be very close, i.e. Ti50Ni50, Ti50Ru50, Ti50Os50 and perhaps Ti50Au50. However, some level of discrepancy was found between the two codes on other compounds such as Ti50Fe50, Ti50Rh50, Ti50Pd50, Ti50Ir50 and Ti50Pt50, with Ti50Fe50 being the worst. The results from the current work were also plotted against some theoretical values reported in the literature [26,32,36,37,38,39], and a good match is found in most binary compounds, indicating the level of accuracy.  Figure 3 (a) and (b) graphically represent the total density of states (TDOS) of all the investigated B2 compounds using both CASTEP and VASP codes, respectively. The TDOS are used to predict the electronic stability by observing the behaviour of states near the Fermi level (E-EF=0) with respect to the pseudogap. It also provides insights into phase stability [40].

Electronic properties
Furthermore, if an ordered intermetallic phase is stable at low temperature, EF cuts the pseudogap at the centre whereas if the ordered phase forms but is only stable at high temperature then the EF shift and cuts on the shoulder of either of the DOS peaks, indicating instability of the phase at 0 K. Thus, low and high DOS at EF is considered to be related to the structural stability and instability, respectively [41].
Moreover, taking into account that the DOS values in the anti-bonding region are higher, the phase having a high transition temperature will undergo structural reconfiguration in an attempt to minimize the higher energy indicated by N (EF). Consequently, those systems with higher energy at the anti-bonding region (above EF) will undergo the martensitic transformation and hence often exhibit the shape memory effect [8,40].
From both codes, one can note that DOS curves for all the B2 compounds were found to be non-zero at the Fermi level indicating they all consist of metallic bonds. Similar behaviour was previously by Zhang and Guo [42]. Their DOS resembles that of BCC metal that consists of two sets of peaks, with peak A (the lower energy -also known as the anti-bonding region that emanates from the d-states of the TM elements) and peak B (the higher energy -also known as bonding region that emanates from the d-states of Ti metal) that are separated by a dip valley [43]. Furthermore, it is observed the EF cuts TDOS of Ti50Fe50, Ti50Ru50 and Ti50Os50 near the centre of the pseudogap, indicating that B2 remain stable with no prospect of phase transition, from both codes. This observation is in good agreement with other work reported in the literature [32]. It is revealed that the VASP code finds Ti50Ru50 and Ti50Ni50 while CASTEP finds Ti50Fe50 and Ti50Ir50 to be the most stable and unstable B2 compounds at 0 K, respectively.

Vibrational properties
To further study the structural stability of the investigated CsCl compounds in this work, we calculated the phonon dispersion curves as well as their corresponding phonon density of states (PHDOS) using both codes. The information of phonons is very useful for accounting variety of properties and behaviour of crystalline materials, such as thermal properties, mechanical properties, phase transition, and superconductivity [44].
A compound is considered stable at 0 K if there are no soft modes along high symmetry directions in the Brillouin zone (BZ). In addition, the presence of soft modes or negative frequencies indicates the instability of the crystal, an indication of the likelihood to undergo a phase transition, accompanied by lattice deformation [27,44]. Figure 4 and 5 graphically show the set of phonon dispersion relations and density of states that were computed at 0 K for the investigated CsCl compounds using CASTEP and VASP codes, denoted by (a) and (b), respectively. The obtained results show that phonon spectra for Ti50Fe50, Ti50Os50 and Ti50Ru50 were found to consist of only the positive frequencies, as expected [10,27]. This is an indication that the B2 compounds do not undergo any phase transition to lower temperature phases. Therefore, they cannot be categorised as alloys that display shape memory effect, as their high symmetry B2 phase remains stable down to lower temperature with no phase transition. On the other hand, it is observed that Ti50Ni50, Ti50Pt50, Ti50Pd50, Ti50Au50 and Ti50Ir50 consist of both positive and negative frequencies indicating that the B2 phase undergoes a phase transition to lower temperature phases, resulting in shape memory effect owed to underlying martensitic transformation. This is in accordance with the work reported by other researchers [45,46,47].
In comparison, this work also noted a slight discrepancy in the predicted phonon curves of Ti50Rh50 obtained from both codes. Using VASP, B2 compound shows no negative frequencies while CASTEP clearly shows that B2 phase has a slight chance of undergoing phase transition due to the presence of small negative frequencies, see Figure 5. The abovementioned discrepancy in the VASP code seems to be in contrast to the electronic structure stability (DOS) discussed earlier, where VASP also predicted that the Fermi level of Ti50Rh50 does not fall within the pseudogap, signifying it as a less stable phase with possible phase transition. The work carried out by Si et al. on the MT phase transformation of Ti50Rh50 has found that B2 does indeed undergo a phase transition to L10, and this was also shown by the soft modes obtained on the vibrational frequency of this compound [27]. Figure 4 -5 also show the total phonons density of states (PHDOS) of the investigated compounds. The valence state of Ti50Fe50 and Ti50Ni50 compounds is comprised of the 3d orbitals, while Ti50Ru50, Ti50Rh50 and Ti50Pd50 consist of 4d and Ti50Os50, Ti50Ir50, Ti50Pt50 and Ti50Au50 belong to 5d transition metals of the periodic table. Their d-orbital electron filling increases from left to right, and from top to bottom. As a result, it is noted that for Ti50Ni50, Ti50Ir50, Ti50Pd50, Ti50Pt50 and Ti50Rh50 there exists no frequency gap between the positive and the negative vibrational modes across the Fermi level. This behaviour is attributed to more populated d-orbitals of the noble transition metals towards the right of the periodic table, which is an indication of ductile metallic nature. However, for Ti50Fe50, Ti50Ru50 and Ti50Os50 there is a gap between the conduction and valence band as there exist only the positive vibrational frequencies which is a possible indication of lower ductility (high rigidity) of these B2 compounds as a result lower number of electrons in the d-band.

Conclusions
Ab initio DFT approach was used to study the equilibrium lattice parameters, heats of formation, electronic density of states and phonon dispersion curves of Ti50TM50 systems. Our results of lattice parameters and heats of formation from DFT using both CASTEP and VASP were found to be in good agreement with the available theoretical and experimental data to within 3 %. From calculated heats of formation, we found that the Ti50Au50 is the least stable structure from both codes, while Ti50Ir50 and Ti50Pt50 were the most stable structures (lowest ΔHF) for CASTEP and VASP codes, respectively. The total density of states of the refractory intermetallics (Ti50Ru50, Ti50Os50 and Ti50Fe50) were found to be stable amongst the investigated B2 compounds, whereas EF for other compounds was found to have shifted towards the bonding state signifying instability of the B2 phases at 0 K. Furthermore, the phonons spectra of the same refractory intermetallics were found to have only the positive frequencies, indicating dynamic stability, while the rest of the investigated B2 compounds have shown the presence of negative frequencies, an indication of instability of this phase at low temperatures, thus signalling strong phase transition possibility. The absence of the frequency gap in the phonons density of states (PHDOS) spectra for compounds containing most noble transition metals is an indication of ductile metallic nature as a result of higher dorbital electron filling.