Reviewed in this paper are mathematical analyses for prediction of segregations and chemical compositions change of nonmetallic inclusions during solidification of steels. The studies conducted by the present author are used to construct the main stream of this article, and the author’s view is delivered by introducing the related studies by other researchers and in comparisons among them.
In order to predict segregations of solutes during solidification of steels with more precision than previous microsegregation models such as Flemings-Brody equation and Clyne-Kurz equation, finite difference method was utilized to solve the Fick’s law of solute diffusion in combination of thermodynamic equilibrium calculation at the solid/liquid interface. Stemming from the work, various attempts were conducted for its modifications, improvements and extensions of applicability. In order to control the chemical compositions of nonmetallic inclusions preferable to properties of steel products, mathematical analyses were done for the prediction of their chemical compositions change during solidification of steels. It utilized a microsegregation model by Clyne and Kurz and the assumption of equilibrium throughout the residual liquid including nonmetallic inclusions. In the most universal calculation method developed by the present author et al. simulation softwares developed in the field of calculation of phase diagram were fully utilized. An improved simulation method for solidification path analysis was introduced, which utilized a finite difference method to solve the solute diffusion between adjacent finite segments and equilibrium calculation in each finite segment to solve transformation.
The author’s view for the future task in these field is summarized at the end. Development of mathematical models are highly promising, which consider macroscopic transport of solute and nonmetallic inclusions if necessary among the segments consisting the system interested and appropriate reaction models in each segment.

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The effects of displacement damage rate, helium generation rate and other irradiation conditions on irradiation-induced microstructural changes and swelling in an austenitic stainless steel were investigated by numerical calculations. The computer model developed in this study dynamically integrates rate equations which describe the evolution of point defects, small point defect clusters including cascade vacancy clusters, cavity nucleation and the evolution of the cavity size distribution.
The model was calibrated using data obtained from a dual-beam ion irradiation experiment. In this experiment, solution annealed Type 316 stainless steel was irradiated by 4 MeV nickel ions with simultaneous implantation of helium ions up to 25 dpa at 873 K. The He/dpa ratios and the displacement damage rates were in the range of 1 to 50 appm He/dpa and 2×10⁻³ to 1×10⁻² dpa/s, respectively. These experiments showed that helium effects on dislocation evolution significantly influence the nucleation and growth of cavities. The predicted effects of helium over a broad range of damage rates were calculated using the calibrated model.

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In order to investigate the deformation and fracture behavior of a Ti-50 mol%Al alloy, discontinuous compression tests have been performed at room temperature. Surfaces of specimens were observed by optical microscopy and scanning electron microscopy (SEM) to reveal the formation of deformation bands, initiation sites and propagating routes of cracks, and fracturing process at every a few per cent of plastic stain by interrupting the tests.
The compressive plastic strain at crack initiation is 2–3% which is nearly twice as large as the tensile fracture strain reported in the other studies. From the observation of structural changes with cumulative strain the modes of initiation and propagation of cracks are classified. The interfaces of the α₂ phase which is present in equiaxed γ phase grains, in grains with a lamellar structure and on grain boundaries, give an initiation site for cracking at the early stage of deformation while the α₂ phase itself acts as an obstruction against crack propagation by necking and kinking on crack propagation routes.

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Aluminium–Silicon alloys have high wear resistance and are being used for bearings and pistons. Lead and graphite have been introduced into these alloys in the present work through the rheocasting technique and thermal properties of these alloys have been measured. Microstructural details of the rheocast alloys have also been incorporated. It has been demonstrated that the thermal conductivity and specific heat of rheocast Al–Si alloys increase with temperature unlike the other metallic alloy systems which show decreasing conductivity.

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The effects of in situ 20 MeV proton pulse-irradiation and thermal-pulse on the high-cycle fatigue properties of low carbon 316 stainless steels were investigated at 333–573 K with variations of carbon content, 0.001, 0.002 and 0.005 mass%C, and were compared with those reported for 316 stainless steels with 0.038 mass%C and 316(ST-1) with 0.077 mass%C. The fatigue hardening associated with the fatigue induced precipitation decreased with decreasing carbon content. For the case of high C content, the fatigue induced precipitation played the major role in the whole fatigue process, where the fatigue life N_f could considerably be modified by in situ thermal-pulse and radiation damage through their effects on the fatigue induced precipitation. In contrast, for the case of low C content, the fatigue hardening was associated with both the fatigue induced precipitation and the usual work hardening, where the different effects of radiation damage and thermal-pulse were found on the fatigue hardening and the fatigue life N_f: At 333 K, radiation damage caused enhancement of the fatigue hardening and a decrease in N_f, and thermal-pulse caused suppression of the fatigue hardening and an increase in N_f. We surmised that under radiation damage as well as thermal-pulse, N_f was modified mainly through some changes in the usual work hardening process and on the other hand, the fatigue hardening preferentially reflected the changes in the fatigue induced precipitation. For both 316PSI and 316P, suppression of the fatigue hardening due to radiation damage was observed, suggesting that even in 316PSI and 316P the fatigue induced precipitation occurred but the precipitates (or carbon-solute complexes) were too fine to stand against irradiation dispersion.

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The dynamical response of a linear viscoelastic solid, when a distribution of relaxation or retardation times is present, is studied in detail. It is shown how the internal friction or loss tangent can be expressed in terms of the expression for a standard anelastic solid, using a distribution which is related to the original distribution of relaxation or retardation times, introduced into the dynamical moduli or compliances, respectively. The internal friction is analyzed both as a function of temperature or the frequency and the concepts developed in the paper are applied to actual experimental data for the Snoek relaxation in Nb–O alloys.

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This paper deals with the effect of N₂ gas flow rate on the rate of Se and Te transfer from molten copper to sodium-borate slag (37.1 mass% Borax, 18.5 mass% Na₂CO₃, 27.8 mass% CaO, 16.6 mass% CaF₂) at 1473 K. It has been found that the overall mass transfer coefficient of Se for Cu–0.228 mass% Se alloy increases from 2.04×10⁻⁵ m/s to 3.06×10⁻⁵ m/s and the overall mass transfer coefficient of Te for Cu–0.143 mass% Te increases from 3.41×10⁻⁵ m/s to 5.02×10⁻⁵ m/s with increases in gas flow rate from 5×10⁻⁶ m³/s to 17×10⁻⁶ m³/s. The overall mass transfer coefficients for Se and Te can be represented quantitatively as
k_{ov, Se}=2.346×10⁻⁴G^0.20 and k_{ov, Te}=5.649×10⁻⁴G^0.23
where G represents the gas flow rate (m³/s) at normal temperature (≈300 K).

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Elemental niobium powder and Nb₅₀Al₅₀ elemental powder mixture were milled in a vibrational ball mill, Spex 8000, under nitrogen atmosphere, and the structures of milled powders and their sintered materials were examined by means of X-ray analysis, SEM and HRTEM observations.
The niobium powder absorbed 50 at% of nitrogen during milling. Several types of nitrides were formed during milling, i.e., γ-Nb₄N₃ (FCT), δ-NbN (FCC) and δ′-NbN (hexagonal) with increasing nitrogen content. The mean grain size of these nitrides were about 5 nm. After sintering the milled powder at 1573 K and above, the structure consisted of δ′-NbN and ε-NbN (hexagonal) phases, which were assumed to be formed during cooling from δ-NbN stable at the sintering temperature.
The Nb₅₀Al₅₀ powder mixture absorbed also about 50 at% of nitrogen during milling and formed a solid solution nitride (Nb_0.5Al_0.5)N with NaCl type structure. By sintering the (Nb_0.5Al_0.5)N powder at 1573 K and above, the structure decomposed to stable phases of δ-NbN and AlN (hexagonal). In contrast to the case of the Nb-N system, the δ-NbN remained stable after furnace-cooling from sintering temperatures.

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Mg₂Si_1−xGe_x Solid Solution Semiconductors were prepared in the composition range 0.0≤x≤0.4. At a composition x=0.4, effects of impurities were investigated for dopants of Sb and Ag. Carrier concentrations were controlled up to 1.5×10²⁶ electrons/m³ and 5.5×10²⁵ holes/m³ by doping Sb and Ag, respectively. The thermal conductivity κ was measured at 300 K. By calculating the electronic thermal conductivity κ_el based on the Fermi integration, the lattice thermal conductivity κ_ph was estimated to be 2.10 Wm⁻¹ K⁻¹. Figure-of-merits Z’s of Mg₂Si_0.6Ge_0.4 at 300 K were 0.69×10⁻³ K⁻¹ for the n-type sample with an electron concentration of 5.4×10²⁵ m⁻³ (3000 ppmSb) and 0.47×10⁻³ K⁻¹ for the p-type one with a hole concentration of 5.2×10²⁵ m⁻³ (16000 ppmAg).

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The thermoelectric properties of Sb-doped n-type and Ag-doped p-type Mg₂Si_0.6Ge_0.4 samples were investigated in the temperature range 300 to 900 K. The scattering factor r was determined to be 0.0 by measuring the temperature dependence of the Hall mobility. Thermoelectric power and electrical conductivity were measured and discussed on the basis of the degenerated carriers. The thermal conductivity was evaluated from the values measured at 300 K. The maximum figure-of-merits Z’s were estimated to be 1.61×10⁻³ K⁻¹ at 663 K for the n-type and 2.67×10⁻³ K⁻¹ at 629 K for the p-type, respectively. From the fact that the dimensionless figure-of-merits ZT’s exceeded unity, the Mg₂Si_1−xGe_x solid solution semiconductors can be expected as a new promising material for high-efficiency thermoelectric energy conversion in the middle-temperature range of 500 to 800 K.

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Aging at room-temperature in the logarithmic decrement δ and crystal structure were investigated for heat-treated and cold-drawn Al–Zn alloys. The value of δ was measured by an inverted pendulum method and the crystal structure was confirmed by using an X-ray diffractometer method.
The value δ of the Al–Zn alloys containing Zn less than 70 mass% is very low just after water quenching from a temperature of 673 K in the region of the α phase, but becomes higher over time, decreasing gradually after reaching a maximum. The nearer the eutectoid composition, the shorter the decomposition time at which the maximum of δ appears. On the other hand, in the alloys which were water-quenched from 573 K in the region of the (α+β) phase, δ shows a maximum in a short time than that from the α phase. Which the alloys contained 80 and 90 mass% Zn and were water quenched from the region of the (γ+β) phase, δ from 623 K is higher than from 573 K, and both values reach maxima just after quenching, and then decrease gradually. The variation in δ may be explained as follows. In the alloys with the α phase, δ is very low but becomes gradually higher with the increase in precipitation of the β phase due to the eutectoid decomposition reaction, it then decreases gradually with the slow growth of the grains after reaching a maximum.
The value δ upon furnace cooling is very low, whereas upon cold drawing it becomes higher because of the refinement of grains and the increasing dislocations caused by working. Further, by cold drawing after water quenching, δ is increased considerably. However, in the cold states, δ becomes lower gradually with time.

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A rheocasting unit in which solidifying alloy agitated at a high speed of 53 s⁻¹ was applied to produce aluminium-lead bearing alloys containing up to 20 mass%Pb. It was found by morphological observation of Al–Pb alloys that a continuous lead-rich phase existed between aluminium-rich phases, the thickness and the length of the lead-rich phase increased with increase in lead content, and the aluminium-rich phase was refined with increased lead content. A drastic decrease in bulk wear was observed in Al–Pb alloys even with a small amount of lead. The bulk wear continuously increased with load as a result of propogation of cracks with increasing load. With increase in lead content in these alloys, a minimum in bulk wear with sliding velocity has been observed, but with increase in lead content for a particular sliding velocity, the bulk wear been observed to decrease continuously till about 20 mass% lead, the maximum lead content in Al–Pb alloys in the present investigation.

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