Hardness of covalent crystals

Based on the idea that the hardness of covalent crystal is intrinsic and equivalent to the sum of the resistance to the indenter of each bond per unit area, a semiempirical method for the evaluation of hardness of multicomponent crystals is presented. Applied to beta-BC2N crystal, the predicted value of hardness is in good agreement with the experimental value. It is found that bond density or electronic density, bond length, and degree of covalent bonding are three determinative factors for the hardness of a polar covalent crystal. Our method offers the advantage of applicability to a broad class of materials and initializes a link between macroscopic property and electronic structure from first principles calculation.

Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness.

It is known that the exact density functional must give ground-state energies that are piecewise linear as a function of electron number. In this work we prove that this is also true for the lowest-energy excited states of different spin or spatial symmetry. This has three important consequences for chemical applications: the ground state of a molecule must correspond to the state with the maximum highest-occupied-molecular-orbital energy, minimum lowest-unoccupied-molecular-orbital energy, and maximum chemical hardness. The beryllium, carbon, and vanadium atoms, as well as the CH(2) and C(3)H(3) molecules are considered as illustrative examples. Our result also directly and rigorously connects the ionization potential and electron affinity to the stability of spin states.

Fracture surface, impact energy and hardness of Ni-free high-Mn steels

Two manganese steels were investigated: Fe-19.7%Mn (VM339A) and Fe-19.7%Mn stabilized with 0.056%C, 0.19%Ti and 0.083%Al (VM339B). The toughness of VM339A was higher than VM339B, but VM339B had higher hardness. Tempering does not affect the toughness of the alloys. SEM images of the fracture surface for both the alloys revealed ductile fractures. A further alloy with a lower manganese content, Fe-8.46%Mn-0.24%Nb-0.038%C, and thus even lower cost than the conventional 3.5Ni cryogenic steel, was tested for its impact toughness after heat treatment at 600°C, giving promising results.

NP-hardness of MAP in Ternary Tree Bayesian Networks

This paper strengthens the NP-hardness result for the (partial) maximum a posteriori (MAP) problem in Bayesian networks with topology of trees (every variable has at most one parent) and variable cardinality at most three. MAP is the problem of querying the most probable state configuration of some (not necessarily all) of the network variables given evidence. It is demonstrated that the problem remains hard even in such simplistic networks.

Processability, hardness, andmagnetic properties of rubber ferrite composites containingmanganese zinc ferrites

Rubber ferrite composites have the unique advantage of mouldability, which is not easily obtainable using ceramic magnetic materials. The incorporation of mixed ferrites in appropriate weight ratios into the rubber matrix not only modi es the dielectric properties of the composite but also imparts magnetic properties to it. Mixed ferrites belonging to the series of Mn(1 – x )Znx Fe2O4 have been synthesised with diVerent values of x in steps of 0·2, using conventional ceramic processing techniques. Rubber ferrite composites were prepared by the incorporation of these pre-characterised polycrystallineMn(1 – x )Znx Fe2O4 ceramics into a natural rubber matrix at diVerent loadings according to a speci c recipe. The processability of these elastomers was determined by investigating their cure characteristics. The magnetic properties of the ceramic llers as well as of the rubber ferrite composites were evaluated and the results were correlated. Studies of the magnetic properties of these rubber ferrite composites indicate that the magnetisation increases with loading of the ller without changing the coercive eld. The hardness of these composites shows a steady increase with the loading of the magnetic llers. The evaluation of hardness andmagnetic characteristics indicates that composites with optimummagnetisation and almost minimum stiVness can be achieved with a maximum loading of 120 phr of the ller at x=0·4. From the data on the magnetisation of the composites, a simple relationship connecting the magnetisation of the rubber ferrite composite and the ller was formulated. This can be used to synthesise rubber ferrite composites with predetermined magnetic properties