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The geometries, stabilities and electronic structures of AlnCum (n = 5–9, m = 1–3) clusters were explored by using the genetic algorithm combined with ab initio methods. The geometric structures are almost spherical when the valence electrons are around the magic number 20, otherwise the structures are oblate or prolate. The stabilities of the clusters are related to both the Cu/Al ratios and the electronic configurations. The clusters with lower Cu/Al ratios have high stabilities. The molecular orbitals are in accord with the shell structures predicted by the jellium model. The 3d orbitals of the Cu atoms are localised, although their orbital energies are between the 1P and 1D jellium orbitals. The Al6Cu2 with 20 valence electrons forms closed 1S21P61D102S2 shells, and shows large binding energy and removal energy, large ionisation potential and small electron affinity. For the no-magic clusters, the structure deformation leads to crystal-field-like splitting of the degenerate shells and stabilises the clusters. [ABSTRACT FROM AUTHOR]

The low-energy structures of Al n Mg m (n = 4–8, m = 1–3) are determined by using the genetic algorithm coupled with a modified embedded-atom interatomic potential. The close-packed structures are preferable in energy for Al-Mg clusters and in most cases there exist a few isomers with close energies. The stabilities of the Al-Mg clusters are governed by Mg/Al ratios and the electronic configurations. The clusters with lower Mg/Al ratios are more stable. The valence molecular orbitals and the density of states consistently demonstrate that the electronic structures of Al-Mg clusters can be described by the jellium model but the 2S level interweaves with the 1D levels. Al 6 Mg corresponds to a magic number structure with pronounced stability and large energy gap; the 20 valence electrons form closed 1S 2 1P 6 1D 10 2S 2 shells. Natural bond orbital analysis indicates that magnesium transfer electrons to aluminum; the average charge on Mg atoms is 0.61, but the charge on Al atoms depends strongly on the number of the connected Mg atoms. [ABSTRACT FROM AUTHOR]

The low-energy structures of Al8Sim(m= 1–6) have been determined by using the genetic algorithm combined with density functional theory and the Second-order Moller-Plesset perturbation theory (MP2) models. The results show that the close-packed structures are preferable in energy for Al–Si clusters and in most cases there exist a few isomers with close energies. The valence molecular orbitals, the orbital level structures and the electron localisation function (ELF) consistently demonstrate that the electronic structures of Al–Si clusters can be described by the jellium model. Al8Si4corresponds to a magic number structure with pronounced stability and large energy gap; the 40 valence electrons form closed 1S21P61D102S21F142P6shells. The ELF attractors also suggest weak covalent Si–Si, Si–Al and Al–Al bonding, and doping Si in aluminium clusters promotes the covalent interaction between Al atoms. [ABSTRACT FROM AUTHOR]

Genetic algorithm combined with the semi-empirical Hamitonian AM1/PM3 is used to search the low energy isomers of AlSi (n = 3, 5, m ≤ 3 and n = 4, m ≤ 4) and the charged clusters with 20 and 28 valence electrons. The candidate structures were optimized by the density functional theory PBE0 and B3LYP models with the triply split basis sets including polarization functions. The electronic structures show that Al-Si binary clusters behave like metal clusters. The molecular orbitals accord with that predicted by the jellium model, and the electron localization function shows the valence electrons are delocalized over the entire clusters. The clusters having 20 and 28 valence electrons exhibit pronounced stabilities and large energy gaps. The 20 valence electrons of AlSi and AlSi , AlSi form closed shells 1 S 1 P 2 S 1 D . AlSi and AlSi have oblate structures and the P, D, F levels spilt considerably in these clusters. The electron density distributions suggest that doping silicon in the aluminum clusters enhances the stability considerably. [ABSTRACT FROM AUTHOR]

The low-energy structures of Al 5 Na m (m = 1–5) and Al 6 Na m (m = 0–4) are searched by using the genetic algorithm combined with MOPAC package. The stabilities and the electronic structures are studied by density functional theory models and by first principle perturbation theory at MP4 level. The results show that the Na atoms are located at the outside of the clusters. Analysis on the density of states and the charge distribution indicate the sodium atoms transfer their 3s electrons to aluminum and exist as +1 cations. The molecular orbitals agree with the types predicted by the jellium model, and Al 5 Na 5 and Al 6 Na 2 show enhanced stabilities as the 20 valence electrons form closed electronic shells. However, the valence orbitals don’t encompass the Na + cores. The electron localization function clearly demonstrates that the valence electrons reside at the outside of the Al 3+ cores, and the Na + cores are exposed at the outside of the valence electrons. All the results confirm that Al n moieties in the Al Na binary clusters form Zintl anions and the Na + cations are ionically bonded to them. It suggests Al Na clusters can be used as building blocks to form cluster-assembled Zintl-phase materials. [ABSTRACT FROM AUTHOR]

The spherical jellium model predicts that metal clusters having 18 and 20 valence electrons correspond to the magic numbers and will show specific stabilities. We explore in detail the geometric structures, stabilities and electronic structures of Al-Mg clusters containing 18 and 20 valence electrons by using genetic algorithm combined with density functional theories. The stabilities of the clusters are governed by the electronic configurations and Mg/Al ratios. The clusters with lower Mg/Al ratios are more stable. The molecular orbitals accord with the shell structures predicted by the jellium model but the 2S level interweaves with the 1D levels and the 2S and 1D orbitals form a subgroup. The clusters having 20 valence electrons form closed 1S1P1D2S shells and show enhanced stability. The Al-Mg clusters with a valence electron count of 18 do not form closed shells because one 1D orbital is unoccupied. The ionization potential and electron affinity are closely related to the electronic configurations; their values are determined by the subgroups the HOMO or LUMO belong to. Graphical abstract: [ABSTRACT FROM AUTHOR]

Abstract: Generalized fractional Maxwell model is applied to simulate the creep and the relaxation behavior of PEEK and PPS measured at different aging stages and different temperatures. Genetic algorithm and the conjugated gradient method are combined to optimize the model parameters. The results show that the fractional Maxwell model can describe both the creep and relaxation data very well when the model parameters are fitted properly. The momentary creep compliance and the relaxation modulus change with the time at an increasing rate; the fractional orders of the two fractional elements building up the model correspond to the creep or relaxation exponents at the initial glassy stage and the terminal fluid state. The relaxation time τ of the model, which corresponds to the characteristic time of α transition of the sample, shifts towards longer time with increasing the aging time and lowering the aging temperature. In the time domain scaled by the relaxation time τ, all the creep or relaxation curves measured at different aging times and temperatures superpose automatically, which means the time–aging time superposition and the time–temperature superposition present themselves. The shift rates and the temperature shift factors can be then obtained from the model parameters. Good simulation for the creep and relaxation behavior and optimum superposition of the experimental data achieved by the fractional model may offer reliable predictions for the long-term stress-strain response. [Copyright &y& Elsevier]