Electronic structures of stable Cu-centered Cu-Zr icosahedral clusters studied by density functional theory

Abstract

Cu-Zr alloy system,as a representative of transition metal-transition metal (TM-TM) metallic glass (MG),has attracted considerable attention due to its high glass-forming ability in a wide range of compositions.Many researchers have realized that the GFA of Cu-Zr alloy is intimately related to Cu-centered Cu-Zr icosahedral atomic cluster in supercooled liquid and rapidly solidified into amorphous solid.And lots of molecular dynamics simulations have shown that Cu-centered Cu-Zr icosahedral clusters not only affect the thermo-dynamical properties of metal or alloy melts,but also exhibit excellent structural stability and configuration heredity ability during the rapid solidification.Hereof a model of the metallic glass structure based on like icosahedron has become widely accepted,which plays an important role in the glass transition and its strong kinetic constraint on nucleation.However,though more and more standard and distorted Cu-Zr icosahedral clusters have been found and reported in Cu-Zr metallic glass,the fundamental understanding of these Cu-Zr icosahedral clusters of MGs is still lacking.More essential properties of Cu-centered Cu-Zr icosahedral cluster, especially on the electronic structure are still unclear.Based on this,as a further step towards in depth understanding the electronic structures of those icosahedral clusters,we will investigate the electronic structures of the stable Cucentered CunZr13-n (n=6,7,8,9) icosahedral clusters in this work,and consider all the possible atomic configurations for given chemical composition in view of originate in theory And a DMol3 molecular orbital package based on density functional theory (DFT) is adopted to calculate the energetics and electronic structures of Cu-centered Cu-Zr icosahedral clusters.During optimization and total energy calculation,electronic exchange-correlation energy functions in reciprocal space with the Perdew-Burke-Emzerhof type under general gradient approximate are used.A double-numerical basis set together with d-polarization functions (DNP) is chosen to describe the electronic wave functions of Cu and Zr atoms. And only core electrons described by the DFT Semi-core Pseudopots are calculated.All atomic positions in Cu-centered CunZr13-n (n=6,7,8,9) icosahedral clusters are relaxed by geometry optimization under a root mean square (RMS) force of 0.002 Ha/ and RMS displacement of 0.005 .The calculations of total energy and electronic structure are followed by the geometry optimization with self-consistent field tolerance of 110-5 Ha.It is found that homogeneous atoms in the shell of clusters with low binding energy prefer to bond to each other.In this case,the results of electronic structures reveal this segregation at low energy and stable configurations can be attributed to their low N (EF) at EF to some extent.A further analysis of Mulliken'population shows that these 4s and 4p of shell Cu atoms are all donees in the formation of icosahedral cluster,different from the donations of 3d and 4s of core Cu atoms and 5s of shell Zr atoms, and this charge transfer tendency does not change with order parameter nor chemical composition of Cu-centered Cu-Zr icosahedral cluster.In addition,calculating the infrared vibration spectrum of Cu-Zr icosahedral cluster is a new idea for accurately characterizing the cluster structure.