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The modulated structure characterized by periodic concentration fluctuations is caused by the up-hill diffusion of solute atoms due to the spinodal decomposition, when the Gibbs free energy surface of the solid solution has a convex curve. This convex shape in the free energy surface will appear in multi-component systems, even though the energy in each binary system does not show the convex curve, when a binary system exhibits a strong attractive interaction, i.e., the Gibbs free energy shows a deep concave curve. This may be the case that steel containing an element having a strong tendency of carbide forming. The Fe-Ni-V-C system was selected in this study. V is a strong carbide forming element and forms VC carbide based on f.c.c. lattice. A series of experiments was carried out using Fe-25Ni-3V-3C (mol%) alloy after aging at elevated temperatures. A modulated structure was observed in specimens aged at temperature range of 550 °C to 650 °C, and the maximum temperature occurring the spinodal decomposition was estimated to be 715 °C in Fe-25Ni-3V-3C alloy. Furthermore, the coefficient of the gradient energy caused by composition fluctuations was estimated to be 2.8 x 10-15 J.m2/mol.

A phase-field simulation is performed to examine the effect of elastic inhomogeneity between the  and ’ phases on coarsening of the ’ phase in Ni-based superalloys. In the calculation of elastic strain energy, the mechanical equilibrium equation in elastically inhomogeneous system is solved by an iterative-perturbation scheme. On the basis of the elastic constants of a practical Ni-based superalloy, a series of simulations is performed in which both elastic anisotropy and shear modulus are varied independently. The variation of elastic anisotropy gives significant effect on both morphology and size distribution function of the ’ particles, whereas the variation of shear modulus gives little effect on them. Furthermore, it is found that the coarsening rate constant of the cubic growth raw changes and increases with increasing the standard deviation of the ’ size distribution.

Interdiffusion coefficients of Al replacing elements in Ni-Al-X (X=Ti, V and Nb) were estimated by a series of experiments using diffusion couples of Al rich pseudo-binary systems at three different temperatures of 1423, 1473 and 1523K. In order to obtain interdiffusion coefficients of the pseudo-binary systems, the experimental data was analyzed by the Sauer and Freise method, and also impurity diffusion coefficients of Ti, V and Nb in Ni3Al were estimated by applying the Darken-Manning equation. The magnitude of interdiffusion coefficient decreased in order of V, Ti and Nb at all three temperatures. Impurity diffusion coefficients were described by the expressions: , , . The activation enthalpies obtained from the experimental data confirmed the retardation of Ti, V and Nb diffusion in Ni3Al by the anti-site diffusion mechanism. These results are consistent with our previous work on diffusion of Re and Ru in Ni3Al .

The hydrogen solubility and the hydrogen permeability have been measured for Nb-based alloys in order to investigate the alloying effects on the hydrogen diffusivity during hydrogen permeation. The hydrogen diffusion coefficient during hydrogen permeation is estimated from a linear relationship between the normalized hydrogen flux, , and the difference of hydrogen concentration, C, between the inlet and the outlet sides of the membrane. It is found that the hydrogen diffusion coefficient during the hydrogen permeation is increased by alloying ruthenium or tungsten into niobium. On the other hand, the activation energy for hydrogen diffusion in pure niobium under the practical permeation condition is much higher than the reported values measured for dilute hydrogen solid solutions. It is interesting that the activation energy for hydrogen diffusion decreases by the addition of ruthenium or tungsten into niobium.

The hydrogen diffusion coefficients are investigated during the hydrogen permeation through Nb-based hydrogen permeable membranes at high temperature. It is found that the hydrogen diffusion coefficient for pure niobium under practical conditions is much lower than the reported values measured for dilute hydrogen solid solutions. Surprisingly, the hydrogen diffusion is found to be faster in Pd-Ag alloy with fcc crystal structure than in pure niobium with bcc crystal structure at 773K during the hydrogen permeation. It is also found that the addition of Ru or W into niobium increases the hydrogen diffusion coefficient under the practical conditions.

Interdiffusion coefficients of the refractory elements in Fe-W-Re and Fe-Cr-X (X=Mo, W) ternary alloys have been measured on the basis of the modified Boltzmann-Matano method for ternary system. Both the cross interdiffusion coefficients, Fe ReW ~D and Fe WRe ~D were negative in Fe-W-Re ternary alloys. This result indicates that attractive interaction exists between W and Re atoms in iron alloys [1]. This is consistent with our previous experimental results that Re suppresses W diffusion in Fe-15Cr alloy [1]. In addition, the value of cross interdiffusion coefficient Fe CrW ~D was positive in Fe-Cr-W diffusion system, whereas Fe MoCr ~D was negative in Fe-Cr-Mo diffusion system.

Ni-based superalloys are strengthed by refractory elements such as Re, Ru and W [1]. Thus, the information on the interdiffusion coefficient as well as the thermodynamic interaction between the refractory elements is important for the future alloy design. In this study, interdiffusion coefficients of the refractory elements in Ni-X-Y (X, Y=Co, Re, Ru, W) ternary systems were estimated by a series of experiments. In the all systems studied in the present works, the main interdiffusion coefficients were much larger than the cross interdiffusion coefficients. In some systems, two cross interdiffuion coefficients had opposite signs each other. For example, in Ni-Co-Ru system, the main interdiffusion coefficients are 2.7 10 14 ~ Ru = × − CoCo D and 15 6.8 10 ~ Ru = × − RuRu D , while the cross interdiffusion coefficients are 16 6.6 10 ~ Ru = − × − CoRu D and 16 8.9 10 ~ Ru = × − RuCo D at 1523K. In Ni-Co-Ru and Ni-Re-Co systems, the activation energies and frequency factors for two main interdiffusion coefficients. For example, Q (kJ ) Co = 268 , 5 ( 2 1 ) 0( ) 4.4 10 D = × − m s − Co , 3 ( 2 1 ) 0( ) 2.9 10 D = × − m s − Ru in Ni-Co-Ru system.

It is known that two main interdiffusion coefficients, ık Dii and ık Djj , as well as two cross interdiffusion coefficients, ık Dij and ık Dji , are necessary for understanding the atomic diffusion for ternary system. Here, k is the host element of ternary system, and i and j are solute elements. These four interdiffusion coefficients are obtained from a series of experiments using two kinds of ternary diffusion couples. In general, it is believed that ık Dij and ık Dji indicate the same sign to each other, but there are a lot of experimental data showing that ık Dij and ık Dji indicate opposite sign [1]. In such a case, the physical meaning of the cross interdiffusion coefficient has not always been understood thoroughly. The purposes of this study are to measure the interdiffusion coefficients by a series of experiments and to elucidate the physical meaning of the two cross interdiffusion coefficients on the basis of the consideration about the relationship between the thermodynamic functions and the cross interdiffusion coefficients. It is concluded that ık Dij exhibits the opposite sign to ık Dji without contradicting the Onsarger’s reciprocity theorem when the ( 2 2 ) c j ∂ G ∂c shows the opposite sign to ( 2 2 ) c i ∂ G ∂c . Here, c G is Gibbs free energy of the ternary system.

The diffusivity of refractory elements in heat resistant steels is crucial for the basic understanding of the microstructural stability during creep. The purposes of this study are to estimate the diffusivity in Fe-Cr alloys as a base alloy for the bcc matrix phase in high Cr ferritic steels and also to investigate the alloying effect of Re on the W diffusivity in them. Fe-15Cr and Fe-20Cr binary alloys, Fe-15Cr-5Re, Fe-15Cr-5W, Fe-20Cr-5Re ternary alloys [mol%] were used in this study. On the basis of the modified ternary Boltzmann-Matano method, the interdiffusion coefficients were obtained in Fe-Cr-Re ternary system. The apparent interdiffusion coefficient for the Re-doped Fe-Cr-W alloy was about one fifth of that for the Re-free alloy. It is concluded that the existence of Re retarded significantly the W diffusion in Fe-15mol%Cr based alloy. This is probably the main reason why a small amount of Re addition suppress the microstructural evolution of W containing high Cr ferritic steels.