Spherical-Periodic Resonance Structures In Crystalline Phases

There exists short-range ordered behavior in disordered states,such as liquid states,metallic glasses,and solid solutions;and the root cause of the short-range order is Friedel oscillations;when the Friedel oscillation wave of electrons and the radial distribution wave of atoms reach the resonance state,the structures will exhibit the spherical-periodic order.Based on the above resonance theory,this thesis will study the spherical-periodic features of three simple crystals(including the face-centered cubic,hexagonal close-packed,and body-centered cubic structures),and the complex crystals related to metallic glasses.Then the spherical-periodic resonance structures in crystalline phases will be applied to the composition analyses and design of the short-range ordered metallic glasses and solid solutions,trying to reveal the structural homology of these completely ordered crystalline phases and the disordered states showing short-range order.In combination with the cluster-plus-glue-atom model proposed by our research group earlier,according to the structural homology of metallic glasses and devitrification phases,and that of simple crystals and solid solution alloys,we further develop the short-range ordered structural models and the related composition design methods for metallic glasses,eutectic alloys,and solid solutions.After a comprehensive summary of the short-range ordered behavior in liquid states,metallic glasses,and solid solutions,and the basic Friedel oscillations,this thesis gives the following four academic contributions:(1)Firstly,based on the resonance theory,the structural origin of face-centered cubic,hexagonal close-packed,and body-centered cubic structures is explained,that is,they are all generated from the resonances between the periodic and dense-packed atomic planes and the electron scattering waves on the Fermi surface.Specifically,the resonance-related planes are{111} and {200} in face-centered cubic structure;{100},{002},and {101} in hexagonal close-packed structure;and single {110} in body-centered cubic structure.The resonance-related lattice planes enclose the nearest-neighbor coordination polyhedral cluster configurations in simple crystals.Furthermore,it is pointed out that the spherical-periodic and atomic dense-packing features of body-centered cubic structure are the closest to those of liquid states.According to the atomic radial distributions in face-centered cubic,hexagonal close-packed,and body-centered cubic structures,the spherical-periodic features are revealed,verifying the structural origin of simple crystals based on the spherical-periodic resonance,and also verifying the structural homology of simple crystals and liquid states.(2)Then,extending the resonance theory into the binary complex crystalline phases,the spherical-periodic features similar to those in simple crystals are also revealed.Taking the Cu-(Zr,Ti)binary systems as examples,for the crystalline phases,by estimating the Fermi vector lengths kF and the diameters of the Brillouin-or Jones-zones Kpe,the resonance condition of Kpe = 2kF is proved.According to the atomic radial distributions in the crystalline phases in Cu-(Zr,Ti)binary systems,remarkable spherical-periodic features are also observed,which verify the structural homology of crystalline phases and the related liquid states and metallic glasses.On this basis,the atomic radial distributions in all the binary bulk-glass-relevant phases in Cu-(Zr,Hf),Ni-(Nb,Ta),Al-Ca,and Pd-Si systems are analyzed in detail.The results exhibit the spherical-periodic features so long as centered by the principal clusters,which reveal the structural homology of metallic glasses and the corresponding devitrification phases,and indicate that the structural units are constructed by the principal clusters plus a few glue atoms.(3)Based on the structural homology of metallic glasses and the corresponding devitrification phases,the detailed composition interpretation procedures of metallic glasses based on the cluster-plus-glue-atom model are given,among which the key step is to determine the principal clusters via the criteria such as spherical-periodic feature and cluster isolation degree.This thesis mainly solves the composition interpretation problems of metallic glasses in Ni-(Nb,Ta)systems,and gives appropriate cluster formulas of the bulk metallic glasses Ni62Nb3 and Ni59-62Ta38-41.According to the 24-electron rule and the cluster-resonance condition,the corresponding cluster formulas are verified.(4)Combining the cluster-plus-glue-atom model,using the resonance theory,the detailed procedures of constructing the composition formulas of the solid solution alloys are given for the hexagonal close-packed solid solution alloys and the related eutectic alloys.According to the atomic radial distribution in the hexagonal close-packed crystal and introducing the Friedel oscillation theory,the cluster configuration in the hexagonal close-packed solid solution alloys is determined to be the twinned octahedron.Then,stacking the clusters according to the spherical-periodic order,for the hexagonal close-packed solid solution alloys with approximately equal atomic radii,the number of glue atoms in the cluster formula is determined to be 3 from the physical nature of structural stability,resulting in a universal cluster formula:[cluster](glue atom)3.This cluster formula is successfully applied to the interpretations of the eutectic compositions related to hexagonal close-packed solid solution structures in Al-Co,Co-Cr,Mg-Hg,and Mg-Sb systems.Particularly,for the eutectic point Co56Cr44 in the Co-Cr system,when the solid solubility of these two elements is large,the clusters selected to construct the dual-cluster formula should be from the Co3Cr high-temperature phase and CoCr a phase.Four clusters in the Co3Cr phase are given:[Co-Co8Cr4]Co3,[Co-CO8Cr4]Co2Cr,[Co-Co8Cr4]CoCr2,and[Co-CO8Cr4]Cr3.The composition interpretations of Co-Cr-based industrial alloys are carried out using these four cluster formulas.The composition interpretation procedures of solid solution alloys based on cluster-plus-glue-atom model are summarized,which are used as the general composition design procedures of solid solution alloys,and can provide theoretical guidance for the development of new alloys and the optimization of original alloy properties.