Formation of nanocrystalline Fe73.5Cu1Nb3Si13.5B9 alloy under high pressure

The formation of nanocrystalline Fe_73.5 Cu₁Nb₃Si_13.5 B₉ alloy by annealing an amorphous Fe_73.5Cu₁Nb₃Si_13.5B₉ alloy at a temperature of 823 K under pressures in the range of 1–5 GPa is investigated by using X-ray diffraction, electron diffraction, and transmission electron microscopy. The high pressure experiments are carried out in belt-type pressure apparatus. Experimental results show that the initial crystalline phase in these annealed alloys is a-Fe solid solution (named a-Fe phase below), and high pressure has a great influence on the crystallization process of the a-Fe phase. The grain size of the a-Fe phase decreases with the increase of pressure (P). The volume fraction of the a-Fe phase increases with increasing the pressure as the pressure is below 2 GPa, and then decreases (Pδ2 GPa). The mechanism for the effects of the high pressure on the crystallization process of amorphous Fe_73.5Cu₁Nb₃Si_13.5B₉ alloy is discussed Project supported by the National Natural Science Foundation of China (Grant No. 19674070) and the Natural Science Foundation of Hebei Province.     

Heating effect of BaTiO3 in microwave field and microstructure of BaTiO3

Microwave equipment at 2 450 MHz was employed to prepare BaTiO₃. The heating effect of the system in the microwave field, which was influenced by several factors including dielectric properties of synthesis system and thermal insulate structures, was discussed in detail. The heating rates of the synthesis system were mainly determined by BaCO₃ and TiO₂ at low temperature and by TiO₂ and BaTiO₃ at high temperature. The results show that the heating effects in microwave field are greatly different from those in conventional furnace. The reaction of BaCO₃ and TiO₂ only lasts for 3 min at 1 100°C, and the fine, narrow-distributed and well-crystallized powders were prepared. Project supported by the National Natural Science Foundation of China.     

Effects of Nb and Si on densities of valence electrons in bulk and defects of Fe3Al alloys

Positron lifetime measurements have been performed in binary Fe₃Al and Fe₃Al doping with Nb or Si alloys. The densities of valence electrons of the bulk and microdefects in all tested samples have been calculated by using the positron lifetime parameters. Density of valence electron is low in the bulk of Fe₃Al alloy. It indicates that, the 3d electrons in a Fe atom have strong-localized properties and tend to form covalent bonds with Al atoms, and the bonding nature in Fe₃Al is a mixture of metallic and covalent bonds. The density of valence electron is very low in the defects of Fe₃Al grain boundary, which makes the bonding cohesion in grain boundary quite weak. The addition of Si to Fe₃Al gives rise to the decrease of the densities of valence electrons in the bulk and the grain boundary thus the metallic bonding cohesion. This makes the alloy more brittle. The addition of Nb to Fe₃Al results in the decrease of the ordering energy of the alloy and increases the density of valence electron and the bonding cohesion of the grain boundary. However, since the radius of Nb atom is larger than that of Fe atom, when Nb atoms substitute for Fe atoms, they will distort the lattice and enlarge the volume of the lattice, which decreases the density of valence electron and the cohesion of metallic bond in the bulk of the alloy. Project supported by the National Natural Science Foundation of China (Grant No. 59561001) and the Foundation of Guangxi Education Committee.     

Solutions for an operator equation under the conditions of pairs of paralleled lower and upper solutions

In this paper, under the condition of two pairs of strict lower and upper solutions and using the concept of (e₁,B)-limit increasing operator, some multiplicity results for an operator equation are obtained by the method of the fixed point index.