We present a rapidly converging, real-space expansion to compute the electrostatic energy of point-charge configurations on a fixed lattice. The rapid convergence is obtained by requiring that the expansion only reproduce well the configurations with energies below some cutoff energy. The convergence rate can be systematically varied by changing this cutoff. This expansion should prove useful for computations in which only low-energy states are required, such as free-energy and phase-diagram computations.
Mo-Si-B silicides consisting of the phases {alpha}-Mo (Mo solid solution), Mo{sub 3}Si, and Mo{sub 5}SiB{sub 2} have melting points on the order of 2000 C and have potential as ultra-high temperature structural materials. Mo-Si-B alloys can be processed such that the {alpha}-Mo is present in the form of isolated particles in a silicide matrix, or as a continuous matrix ''cementing'' individual silicide particles together. The latter microstructure is similar to that of WC-Co hard metals. This paper focuses on the relationship between the topology as well as scale of the microstructure of Mo-Mo{sub 3}Si-Mo{sub 5}SiB{sub 2} alloys, and their creep strength and fracture toughness. For example, the creep strength of Mo-Si-B alloys is improved by reducing the {alpha}-Mo volume fraction and by making the {alpha}-Mo phase discontinuous. The fracture toughness is improved by increasing the {alpha}-Mo volume fraction and by making the {alpha}-Mo phase continuous. Room temperature stress intensity factors as high as 21 MPa m{sup 1/2} were obtained. The room temperature fracture toughness of Mo-Si-B alloys can also be improved by microalloying with Zr. The room temperature ductility of Mo itself can be improved by adding MgAl{sub 2}O{sub 4} spinel particles suggesting yet another way to improve the ductile phase toughening of Mo-Si-B alloys.
In a recent experiment on CoNb_2O_6, Coldea et al. [Science 327, 177 (2010)] found for the first time experimental evidence of the exceptional Lie algebra E_8. The emergence of this symmetry was theoretically predicted long ago for the transverse quantum Ising chain in the presence of a weak longitudinal field. We consider an accurate microscopic model of CoNb_2O_6 incorporating additional couplings and calculate numerically the dynamical structure function using a recently developed matrix-product-state method. The excitation spectra show bound states characteristic of the weakly broken E_8 symmetry. We compare the observed bound state signatures in this model to those found in the transverse Ising chain in a longitudinal field and to experimental data.
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