ELASTIC AND MECHANICAL PROPERTIES OF Zr2TiAl FROM FIRST PRINCIPLE CALCULATION D. Sornadurai, G. Jaiganesh, S. Mathi Jaya and N. Subramanian Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam – 603102, India Pressurized heavy water reactors work with around 30% efficiency; this is due to the difference in the circulation water temperature through the pressure tubes and the heat exchanger. A slight increase in the temperature and with a maximum temperature of exiting water temperature around 300 oC disastrously deteriorate the pressure tube properties made up of Zircalloy (Zr - 2.5 % Nb). Hence instead of Zircalloy, Zr3Al based materials are being considered as an alternative due to positive properties like high strength, thermal stability, poor thermal absorption etc. However Zr3Al based materials have poor mechanical properties. Hence efforts are going on to improve its mechanical properties by adding different elements in place of Zr in Zr3Al. Titanium - aluminum based materials are in usage as structural materials in high temperature applications - for example Ti3Al based materials are used as aerospace engine material on account of their good strength and light weight. Titanium belongs to the same group of Zr with lower density than Zr. Zr3Al and Ti3Al are iso-electronic in nature, hence this study is of interest from research as well as application point of view. There are many experimental and computational reports on higher amount of Ti substituted phase viz. Ti2ZrAl which form as a single phase material. But this materials severely undergoes hydrogen induced amorphization. Out recent efforts to make single phase Zr2TiAl yielded a multi–phase alloy along with Zr2TiAl as a major phase and its structure determined using micro-XRD technique [Ref. 1]. Because of multiphase nature the elastic and mechanical properties of the alloy could be approximately determined but not to good accuracy. In the present work elastic and mechanical properties of Zr2TiAl alloy have been investigated using ab-initio techniques based on the density functional theory (DFT). The calculations were performed using the VASP package and the results are discussed. INTRODUCTION CALCULATION OF ELASTIC AND MECHANICAL PROPERTIES The elastic constants have been calculated from the total change in energy of the system by applying small strain () and can be written in the form of Taylor expansion as: where V0 and P(V0) are the volume and pressure of the undistorted lattice at volume, Cij are the elastic constants which are playing the major role in determining elastic and mechanical properties of the materials. For cubic structural materials C11, C12 and C44 are sufficient for calculating the elastic and mechanical properties. The calculated elastic constants and other mechanical properties Elastic constants in GPa C11 112.723 Shear constant in GPa C΄ 5.904 C12 100.914 Cauchy pressure in GPa C΄΄ 61.730 C44 39.184 Poisson’s ratio ν 0.386 Kleinman parameter ζ 1.566 Bulk modulus in GPa B0 104.850 Young’s modulus in GPa Y 71.717 Anisotropy constant A 6.636 Shear modulus in GPa Voigt’s Gv 25.872 Transverse sound velocity in m/s νs 2201.135 Reuss’ GR 12.040 Longitudinal sound velocity in m/s νl 6246.192 Hills’s, GH 18.956 Average sound velocity in m/s νm 2501.557 Pugh ratio B0/GH 5.531 Density in g/cm3 ρ 5.340 Lame’s coefficients in GPa λ 87.602 Molecular weight in g/mol M 257.30 µ Debye temperature in K θD 274.407 The main mechanical parameters, i.e. bulk modulus B0, shear modulus G, Young’s modulus Y, Poisson’s ratio ν and anisotropic ratio A, which are important for industrial applications are calculated and shown in the table above. The positive values of C11 C12, C11 + 2C12 and C44 demonstrate that this compound is stable against pressure which is also satisfying Born stability criteria viz. C11 - C12 > 0; C44 > 0; C11 + 2C12 > 0. The ductile and brittle nature of this compound are also investigated using the Cauchy pressure and Bo/GH ratio which showed that Zr2TiAl is ductile in nature , i.e. when the B0/G ratio is greater than 1.75 the material is ductile and in the case of Zr3Al, this ratio is nearly 1.75 (1.7649). However, substitution of one Ti in Zr site improves the ductile nature significantly as the B0/G becomes 5.531 which indicates that Zr2TiAl more ductile compare to Zr3Al. The density of states plot (Figure 3) showed that the alloy exhibits metallic character without any band gap. The states, which are approximately located between −4.5 and −1.0 eV below the Fermi level in Zr2TiAl, originate from the hybridization of Zr and Ti d-like states and Al p-like states. At low energy between -7 eV and -5 eV the DOS is mainly due to Zr-s and Al-s orbital. The charge density distribution is an important property of solid materials and provides good information about the chemical bonding. Figure 4, shows the contour plots of the distribution of the electron charge densities of Zr2TiAl along the (1 1 0) plane. Charge density of Ti atom is highly localized compare to Zr and Al charge density contours as observed in DOS. RESULTS AND DISCUSSIONS Zr2Ti Al has L21 type FCC structure (space group Fm-3m) with 16 atoms per unit cell and the Pearson symbol is cF16. (Figure 1). Calculations in this study were performed using the Vienna ab-initio simulation package (VASP) based on the projector-augmented wave (PAW) method of the density functional theory (DFT). The local density approximation (LDA) and generalized gradient approximation (GGA) were used to describe the exchange correlation function. The 4d, 5s (3d, 4s) orbitals of Zr (Ti) atom and 3s, 3p orbitals of Al atoms were considered as valence states. The plane wave cutoff energy of the basis functions fixed at 500 eV; arrived after performing the convergence tests. The Monk horst-Pack scheme with 15×15×15 k-point mesh is used for the Brillouin zone integration and the tetrahedron scheme is used for obtaining the density of states. A tolerance of 10-6 eV in the total energy was used for the self-consistency criteria. A full structural optimization of Zr2TiAl was carried out and the optimization of the structure done using the conjugate gradient scheme. The convergence of forces on atom was taken less than 10 meV/Å. The optimized lattice parameter used for the calculation is 6.8047 Å (Figure 2). COMPUTATIONAL DETAILS Figure 1. Unit cell structure of Zr2TiAl Figure 2. Total energy as a function of volume Figure 3. Total DOS and atomic decomposed DOS Figure 4. Charge Density contour along (1 1 0) plane CONCLUSION The elastic and mechanical properties of Zr2TiAl calculated using ab-initio methods based density functional theory (VASP). The results show that Zr2TiAl is mechanically stable and highly anisotropic. The Pugh’s index of ductility (Bo/G) showed that the alloy is highly ductile in nature. These mechanical and elastic properties of Zr2TiAl confirms its potential application in nuclear industry. The DOS shows the metallic nature of the alloy and the charge density contour in the (1 1 0) plane showing the covalent bonding nature between Zr and Al . Ref 1. D. Sornadurai, V.S. Sastry, V. Thomas Paul, Roberta Flemming, Feby Jose, R. Ramaseshan, S. Dash, Intermetallics 24 (2012) 89-94.