Magnetic,structural and electrical properties of ordered and disordered Co50Fe50 films

Co₅₀Fe₅₀ films with thickness varying from 100 to 500 Å were deposited on a glass substrate by sputtering process, respectively. Two kinds of CoFe films were studied: one was the as-deposited film, and the other the annealed film. The annealing procedure was to keep the films at 400 °C for 5 h in a vacuum of 5×10⁻⁶ mbar. From the X-ray study, we find that the as-deposited film prefers the CoFe(1 1 0) orientation. Moreover, the body-centered cubic (bcc) CoFe(1 1 0) line is split into two peaks: one corresponding to the ordered body-centered tetragonal (bct) phase, and the other, the disordered bcc phase. After annealing, the peak intensity of the ordered bct phase becomes much stronger, while that of the disordered bcc phase disappears. The annealing has also caused the ordered CoFe(2 0 0) line to appear. When the amount of the ordered bct phase in Co₅₀Fe₅₀ is increased, the saturation magnetization (M_s) and coercivity (H_c) become larger, but the electrical resistivity (ρ) decreases. From the temperature coefficient of resistance (TCR) measurement, we learn that the bct grains in the CoFe film start to grow at temperature 82 °C.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Analysis of atomic arrangement in magnetic Fe–Pt nanoparticles

The order parameter S of Fe–Pt nanoparticles is estimated from X-ray diffraction (XRD) patterns. The total intensity of a diffraction peak is obtained by Rietveld analysis as well as simply integrating the intensity. The Rietveld analysis is found to provide a plausible value of S even for a sample showing an XRD pattern with broad and overlapped peaks. Another order parameter Q, which is obtained from Mössbauer spectra, is introduced, and it is confirmed that Q is equivalent to the probability of Fe atoms being in the L1₀-type atomic arrangement. The coercivity of Fe–Pt nanoparticles is directly proportional to Q, while it vanishes at S=0.4, indicating that the magnetic property of Fe–Pt nanoparticles has a closer relationship to Q than S.     

Effect of crack tip sharpness on the strength of vulcanized rubbers

The effect of crack tip sharpness on crack propagation in vulcanized rubbers has been studied. For very sharp cracks, tearing is found to occur on a small scale at very low energies not far above the threshold required for the onset of mechanical crack growth. The “small-scale” tearing energies show relatively little variation for rubbers that differ widely in tear strength as normally measured. Thus the latter property appears to be strongly influenced by variations in the ability of rubbers to promote tip blunting. The small-scale tear behavior is of relevance to other fracture phenomena, including cutting by sharp objects and tensile failure. Natural variations in tip sharpness occur during cyclic or time-dependent mechanical crack growth and influence the form of the crack growth characteristics.     

The way of Diophantus: Some clarifications on Diophantus' method of solution

In the introduction of the Arithmetica Diophantus says that in order to solve arithmetical problems one has to “follow the way he (Diophantus) will show.” The present paper has a threefold objective. Firstly, the meaning of this sentence is discussed, the conclusion being that Diophantus had elaborated a program for handling various arithmetical problems. Secondly, it is claimed that what is analyzed in the introduction is definitions of several terms, the exhibition of their symbolism, the way one may operate with them, but, most significantly, the main stages of the program itself. And thirdly, it is argued that Diophantus' intention in the Arithmetica is to show the way the stages of his program should be practically applied in various arithmetical problems.     

An algebraic index theorem for orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem.