Study of Electronic Structure of Clusters and Disordered Solids

Abstract

We have carried out the first-principles calculation of Pd (n = 2-19) clusters with plane augmented wave (PAW) based Density Functional Theory (DFT) using the Perdew, Burke, Ernzerh of (PBE) exchange correlation functional implemented in Vienna abinitio Simulation Package (VASP) to understand the structural evolution, electronic and magnetic properties of the clusters. Our findings show that the highly symmetric structures like Icosahedral, Buckle Bi-planner, Cube-Octahedral and Hexagonal closed pack do not represent the minimum energy configurations for all the clusters. Present calculations show that the enhanced stabilities for clusters size (n) = 2, 8, 13 and 18 indicating that pristine Pd n n clusters follow the magic number effect. The highest occupied molecular orbital (HOMO)-Lowest unoccupied molecular orbital (LUMO) gap is higher for these highly stable clusters in comparison to their neighbors. Interestingly, even though bulk structure of Palladium is nonmagnetic, some of the finite size clusters possess significant magnetic moment. The highest value of magnetic moment is found to be 6.57µ for n = 13 in Icosahedral structure. To get further insight into the effect of Mn and Mn B 2 doping on magnetic properties of Pd clusters, calculations have been carried out to study the magnetic properties of Pd n (n−1) Mn and Pd for n = 2-13. For Pd (n−1) (n−2) Mn, the cluster of size (n) = 4, 7, 10 and 12 are more stable than their neighbors and magnetic moments for all the clusters increase due to Mn doping. The highest magnetic moments 9.64µ B is for Pd 12 Mn clusters. In case of Pd , the clusters of sizes n= 3, 7, 9 are more stable than their neighbors. The magnetic moments enhance due to Mn 2 doping on Pd (n−2) Mn 2 except for Pd clusters. It may be due to the fact that in Pd 11 Mn 2 11 cluster the spin of two Mn atoms align antiparallel. To perform adsorption and dissociation properties of hydrogen and nitrogen molecules on Ta n and Nb (n = 2-7) clusters, we have carried out structural stability, charge transfer, chemisorption energy as well as HOMO-LUMO gap. Our findings show that Ta n and Nb n n clusters favor the dissociation of both hydrogen and nitrogen except TaH 2 and NbH 2 . This indicates that Ta n and Nb clusters can be used as catalyst for the dissociation of hydrogen and nitrogen molecules which is necessary for the synthesis of ammonia. Present result agrees well with results of Yadav and Mookerjee for the case of Ta n H 2 for n ≥ 4. It is also found that Ta n n and Nb clusters bind nitrogen more strongly than hydrogen. It it mainly due to the fact that binding of nitrogen with triple bond which requires large amount of force to break the bond than single bonded hydrogen atom. It is also concluded that Ta n and Nb n n nano-structures may be used for the hydrogen storage materials. This will be the important task for future generation. We have performed density functional based ab-initio calculations through VASP to carry out the stability and magnetic properties of ZnO nanosystems with different morphologies like nanosheet, nanotube and fullerene type structures in pristine form. Our findings show that nanosheet favors most energetic than nanotube and fullerene like structures. All the morphologies in elemental(ZnO) form do not bear any magnetic properties. Further to get insight into the magnetic properties after doping of TM elements (Mn, Fe, Co, Ni, Cu) in pristine system, we perform near and far dop case in all the systems. Present study showed that ZnO:Mn always favors the near dop AFM alignment in all three morphologies. In case of ZnO:X (X=Fe, Co, Ni), the AFM alignment favors for sheet and this alignment changes while moving sheet to fullerene like vii Mn Mn 2 2 (n−2) Mn 2 structure. Our findings also show that there is lack FM alignment in ZnO:X (X = Mn, Co) indicating that these are not suitable candidate for spintronics applications at low temperature. Such properties agrees well with the previously reported data for bulk. This trends found to be changed while we are moving from tube to fullerene-like structures. To analyze the band gap properties, we used both PBE (GGA) and HSE06 version of hybrid functionals through VASP. We found there is no change in magnetic moments after the inclusion of Heyd-Scuseria- Ernzerhof (HSE). After the inclusion of HSE we found that Ni and Cu doped ZnO sheet show blue shift where as Mn, Fe and Co dope ZnO sheet show blue shift. Further ZnO:Ni tube shows blue shift with band gap 3.98 eV. We found red shift for all cases in ZnO doped TM fullerene like structures. We have discussed electronic and magnetic properties of disordered NiMn experimentally as well as theoretically. For the theoretical work, we used self consistent ASR code and performed calculation on different concentrations of Ni 1−x Mn with 15%, 20%, 25%. 30%, 35% and 30% of Mn by atom. For that we used lattice parameters 3.572 A x , 3.583A 0 , 3.595A 0 , 3.615A 0 , 3.654A 0 and 3.670A 0 coming through XRD analysis for increasing concentrations. It is observed that our theoretical and experimental phase diagram exactly matched with phase diagram of Montecarlo calculations. Further we used spin dynamics code to get more insight in to the spin glass behavior. From the present study we found that Ni 75 Mn shows anomalously slow relaxations which is one of the signature of spin glass phase. Further we studied the electronic and magnetic behavior of disordered Pt-Mn, Pd-Mn and Ni-Mn alloys. For this we used non-collinear version of TB-LMTO-ASR for the electronic and magnetic properties as well as linear muffin-tin orbital green function (LMTOGF) based on CPA code for the exchange pair energy interactions. We found SG behaviors in all the three systems. The magnetic phase diagrams of Pd-Mn and Pt-Mn are found to be more or less same kinds. In case of Pd-Mn SG phase stretches from 0.0 to 0.17 atomic concentration of Mn with tri-critical point around 200K and around 7% atomic concentration of Mn. Similarly, in Pt-Mn SG phase stretches from 0 to 0.2 atomic concentration of Mn with tri-critical points around 150K and 10% of Mn concentration. For Ni-Mn, the phase diagram is different from Pd-Mn and Pt-Mn on which random ferromagnet and anti-ferromagnet flanking either side (both Mn as impurity or Ni). The spin-glass phase stretches from 0.1 to 0.3 atomic concentration of Mn. The Ni-Mn phase diagram qualitatively agrees with experiment. 25 Keywords: Transition metal clusters, Nanosystems, Magnetic phase diagram, Augmented space recursion technique, Disordered alloys.