Study of Electronic and Magnetic Properties of CuPd , CuPt , Cu 3 Pd and Cu 3 Pt : Tight Binding Linear Muffin-Tin Orbitals Approach

Electronic structure of ordered alloys CuPd, CuPt, Cu 3 Pd and Cu 3 Pt have been studied using Tight Binding Linear Muffin-Tin Orbitals Atomic Sphere Approximation (TB-LMTO-ASA). For the electronic properties, we have performed band structure calculations. Our findings show that all the systems considered are metallic in nature. To know the contribution of the orbitals in the bands, the system is analyzed via fat bands which reveal most of the contributions on valence band for CuPd, CuPt, Cu 3 Pd and Cu 3 Pt is from d-orbital and on conduction band is from s and p-orbitals. We have also checked the magnetic properties of the alloys. The density of states for spin up and spin down electrons have found to be same in each and every steps, showing non-magnetic nature of CuPd, CuPt, Cu 3 Pd and Cu 3 Pt. Journal of Institute of Science and Technology, 2014, 19(1): 137-144


INTRODUCTION
The main basis for understanding materials ultimately rests upon understanding their electronic structure (Martin, 2004).The cohesive, electronic, optical, magnetic and super-conducting properties of solids are dominated by the behavior of valence electrons moving in the field of the ion-core of constituent atoms.The development of electronic structure calculations has taken place in several steps.The Tight-Binding Linear Muffin-Tin Orbital method with Atomic Sphere Approximation (TB-LMTO-ASA) (Skriver, 1984;Andersen, 1975;Andersen et al., 1984) is one of the frequently used technique to deal with the electronic properties; especially band structure and density of states of the solids (Kaphle et al. 2012, Andersen, 1984;Ganguly et al. 2011 ).In the present work we have used TB-LMTO-ASA method to study the electronic and magnetic properties of different alloys of Copper (Cu), Palladium (Pd) and Platinum (Pt) i.e., CuPd, CuPt, Cu 3 Pd & Cu 3 Pt.The homogeneous mixture of two or more metals or of metallic elements with non metallic elements is called alloy.
If there is a mixture of only two types of atoms, it is called binary alloy.Binary alloys may be ordered or disordered depending upon atomic positions (Ashcroft & Mermin, 1976;Kittel, 1966).If the atoms are situated by making symmetry in the crystals then they are called ordered alloys and if the atoms are situated randomly in the crystals so that they fail to have crystal symmetry then they are called disordered alloys.Metals and alloys are materials of great scientific as well as practical importance.

RESULTS AND DISCUSSION
This section includes the results and discussion of the calculations carried out to obtain the band structure and density of states of CuPd, CuPt, Cu 3 Pd and Cu 3 Pt.

Band Structure of CuPd and CuPt
The energy minimization curve for CuPd is shown in Fig. 1.To deal with CuPd, we used space group Pm-3m (space group No. 221) (Mighell et al. 1977).The lattice parameter for the ground state (GS) geometry of CuPd is found to be equal to 2.94 A (5.56 a.u.) which is around 1% less than the experimental result (2.99 Å (5.65 a.u.)).In case of CuPt we have used rhombohedral crystal structure with hexagonal axes (Bornstein, 2009) having space group R-3m (space group No. 166).The c/a ratio for the CuPt alloy is 4.90 (Bornstein, 2009).The lattice parameter is taken to be 3.79 Å (Mohl et al. 2011).Further calculations are performed using these optimized parameters.

Fig. 1. Plot of Energy vs lattice constant for CuPd.
The band structure of CuPd is shown in Fig. 2. We found eighteen bands with valence band and conduction bands overlapping with each other showing CuPd has a metallic nature.The minimum energy value for the valence band is labeled as 'a', which is found to be -0 .6238Ry and the maximum value of energy for conduction band, labeled as 'b', is found to be 2.4014 Ry.These are located below and above the Fermi level at Gamma point respectively.energy is obtained as 3.63 Å (6.86 a.u.) which is about 1.5% less than experimental observed value i.e. 3.69 Å (6.98 a.u.) (Kart 2008;Pearson, 1967).Similarly the lattice parameter for the lowest energy value of Cu 3 Pt is found to be 3.65 Å (6.91 a.u.) which agrees with experimental 3.69 Å (Schneider & Esch, 1944)

Density of States for CuPd and CuPt
The plots of TDOS (total density of states) and PDOS (projected density of states) calculated using optimized parameters and experimentally given structures for Cu 3 Pd and Cu 3 Pt are shown in Figs. 13 to 17. Fig. 13 represents the TDOS plot of CuPd , showing major contributions on up and down states comes from those d-orbitals of copper and palladium.The total DOS is simply the sum of DOS of all the orbitals of copper and palladium.This plot is due to the results of the charge distribution for s, p and f orbitals which are very less compared to charge on d-orbitals.The total up and down DOS is shown in Fig. 13 showing nonmagnetic in nature.This behavior is due to strong competition between up spin and down spin components so that effective magnetization is zero.16, we found that large numbers of peaks lie below Fermi energy and few peaks are observed above Fermi energy.The highest peak of up spin as well as down spin both lie below the Fermi energy.This shows that most of the orbitals below Fermi level are occupied.The peaks in the DOS signify the large number of states at the corresponding energy.This can be illustrated from the band structure of CuPt (Fig. 7).The contribution of individual atoms (Cu and Pt) in the DOS of CuPt is shown in Fig. 17.The main contribution d-orbitals are found to be dominated to s and p -orbital electrons for both Cu and Pt.From the DOS plot we simply find the magnetic moment.Basically, the magnetic moment is the integration of the difference of the density of states between up and down spin states up to the Fermi level.The magnetic moment of CuPt is found be zero.This is mainly due to cancellation of up and down spins in every steps and points.

CONCLUSIONS
In the present work, we have studied the band structure and density of states of ordered binary alloys CuPd, CuPt, Cu 3 Pd and Cu 3 Pt by using TB-LMTO-ASA.We calculated the electronic and magnetic properties of CuPd, CuPt, Cu 3 Pd and Cu 3 Pt.In ordered binary alloys CuPd & CuPt, we have found 18 bands and in Cu 3 Pd & Cu 3 Pt, we found 36 & 37 bands respectively with valence and conduction bands overlapping with each other.The band structures show the metallic nature of the systems under study.Furthermore, we have calculated the fat band structure of CuPd and CuPt.We observed that below Fermi level, most of the bands were occupied with d-orbitals as expected.Above Fermi level, we see that the bands were occupied mostly with s and p orbitals.We also studied the density of states of all the systems.The up and down DOS is found to be nearly same, thus giving the total magnetic moment nearly equal to zero which shows our systems are non-magnetic in nature.Finally, We are planning to use augmented space recursion (ASR) method (Mookerjee, 1973;Saha et al. 1996;Chakraborty et al. 2001 ;Mookerjee, 1973) to deal with disordered calculations of these systems, which are left for the further communication in future.

Fig. 6 .
Fig. 6.Fat band structure of t 2g (left) and e g orbitals (right) of Pd in CuPd.The band structure of CuPt is shown in Fig. 7 which also contains 18 bands including s, p and d orbitals.The minimum energy level in valence band and maximum energy level in conduction band both are observed at -point.We found that the lowermost occupied valence band represented by 'l' with energy -0.2531Ry and the topmost unoccupied conduction band represented by `i' with energy 0.9576 Ry.From the band structure of the ordered alloy CuPt, we see that the conduction bands and valence bands are overlapping in their energies near Fermi level.This reveals that CuPt forms an ordered state which is metallic in nature.
Fig. 10.Plot of Energy vs lattice constant for Cu 3 Pd and Cu 3 Pt.

Fig. 13 .Fig. 16 .
Fig. 13.TDOS of CuPd, vertical dotted line represents the Fermi level.The low magnetic moment of CuPd can also be explained from the Figs. 13 & 15 where the curve for up and down DOS is almost the same.The calculated DOS from the present calculation is comparable to the DOS calculated by S. Takizawa et al. (Takizawa et al., 1991), which is shown in Fig. 14.The contribution of individual DOS of Cu and Pd is shown in Fig. 15.The peaks in the DOS signify the large number of states at the corresponding energy.This can be illustrated from the band structure of CuPd, Fig. 2 and the fat band structure of different orbitals of CuPd Figs. 3 to 6. Relating the figures of fat band structure, band structure and DOS, we see peaks in DOS at certain energies.The energies are the ones where majority of the bands are found in the band structure diagrams and so the large number of electrons can be filled.
Density of States for Cu 3 Pd and Cu 3 Pt The plots of DOS calculated using optimized parameter and experimentally given structures for Cu 3 Pd and Cu 3 Pt are shown in Figs.18 & 20 respectively.From these Figs., it can be said that the density of electron is more in the d-orbital, showing major contributions on the observed density of states of up and down state comes from those d-orbitals of copper and palladium.This also indicates that the density of charge distribution for s, p and f orbitals is very less compared to d-orbital.The total up and down DOS is shown in Fig. 18.

Fig. 18 .
Fig. 18.Density of states of Cu 3 Pd, vertical dotted line represents the Fermi level.

Fig. 19 .
Fig. 19.Density of states of Cu and Pd in Cu 3 Pd, vertical dotted line represents the Fermi level.It is simply the sum of DOS of all the orbitals of copper and palladium.The contribution of individual DOS of Cu and Pd is shown in Fig. 19.The peaks in the DOS signify the large number of states at the corresponding energy.This can be illustrated from the band structure of Cu 3 Pd, Fig 11.Relating the figures of band structure and DOS, we found peaks in DOS at certain energies.The energies are the ones where majority parts of the bands are found in band structure diagrams and so the large number of electrons can be filled.Further, the magnetic moment of the Cu 3 Pd is also calculated.The magnetic moment is the integration of the difference between up and down spin states up to the Fermi level.The magnetic moment of Cu 3 Pd is found to be zero which reflects equal contributions of up and down spins in all the steps by cu and Pd respectively.The TDOS of Cu 3 Pt is shown in Fig. 20.The densities of states are plotted taking reference as Fermi energy.From Fig. 20, we observed that the large number of peaks lie below Fermi energy and few peaks are observed.

Fig. 20 .
Fig. 20.Plot of density of states for Cu 3 Pt.Stripped shade represents the DOS of up spin and checked