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Knowing the volume fraction of a minor phase in a composite material is important for characterizing its mechanical properties. Assuming that a rod-like phase with a constant diameter is aligned but dispersed randomly in a matrix, a mathematical model for estimating the volume fraction of a rod-like phase has been developed. This model predicts how many rods are required for an accurate estimation of volume fraction. One of the effective features of this model is that the real dimensions do not need to be considered due to the similarity of their shape. According to this model, it is sufficient to measure the area that includes at least 20 rods to estimate an accurate value for volume fraction. This prediction was confirmed by measuring a unidirectionally solidified Sn-Cu eutectic alloy system. [doi:10.2320/matertrans.M2014424]

An unusual microstructure consisting of both Sn-Ag3Sn and Sn-Cu6Sn5 binary eutectic structures is observed in actual solder balls. In this study, the solidification process of the Sn-Ag3Sn binary eutectic structure after the growth of primary b-Sn in an undercooled Sn-2.8Ag-0.3Cu alloy was investigated by using thermal analysis and interruption tests to understand the formation of the unusual microstructure. First, fine Ag-enriched liquid zones formed around b-Sn after the growth of primary b-Sn. The Ag-enriched zones then gradually enlarged with the accumulation of Ag from the remnant liquid with a decrease in temperature. This indicated that the liquid-phase separation occurred in the remnant liquid after the nucleation of b-Sn. Eventually, when the temperature of the specimen decreased to approximately the binary eutectic temperature, eutectic Ag3Sn nucleated in the Ag-enriched zones. From interruption tests, we determined the precursor of the Sn-Ag3Sn binary eutectic structure before the beginning of Sn-Ag3Sn binary eutectic solidification. This finding corresponds to the precursor of the Sn-Cu6Sn5 binary eutectic structure observed in the Sn-1.0Ag-0.5Cu alloy.

In this study, the mechanism of equalization for λ1 has been investigated using succinonitrile-1.0 mass% water alloy. Approximately 15 columnar dendrites have been observed and the maximum and the minimum value of λ1 (λ1Max and λ1Min, respectively) have been characterized. It is found that λ1Max decreased and λ1Min increased with time, i.e., the tip of primary arm grow to the region of wide from region of narrow of dendrite arm spacing. And also, Local primary arm spacings are gradually equalized due to propagation of position of primary trunk. The time necessary for the equalization for λ1 is found to be longer than that of the process for adjusting dendrite tip radius and the change in λ1 due to branching or over growth. This may suggest that solutal filed in the interdendritic region plays and important role for equalization for λ1.

In order to investigate the mechanism for equalization of primary dendrite arm spacing, in-situ observation of solutal field using succinonitrile-H2O-dye system has been carried out. The brightness, which corresponds to the concentration of dye, has been characterized by an image analyzer along the centerline of interdendritic region. When the local primary dendrite spacings were uneven, the brightness along the centerline of interdendritic region was low in case of local primary dendrite arm spacing was large. After growth with rather long distance, the local primary dendrite arm spacings became even and the brightness along the centerline of interdendritic region became uniform. The solutal profile along the interdendritic region qualitatively agreed with the calculation results of newly developed model. A dendrite trunk is prone to grow toward the wide-spacing-region because the solute concentration of this side is lower than that of the other side. This leads to equal primary spacing.

In Sn-Ag-Cu solder balls, unusual microstructures consisting of both Sn-Ag3Sn and Sn-Cu6Sn5 binary eutectic stratures are sometimes observed. However, the formation mechanism of these unusual microstructures is still unclear. Therefore, in this study, the solidification process has been investigated to clarify the nucleation and growth of binary and ternary eutectic structures in Sn-1.0Ag-0.5Cu alloy by using thermal analysis and interruption tests.Cu-enriched zone was observed around β-Sn in the liquid before the nucleation of Sn-Cu6Sn5 binary eutectic structure. Sn-Cu6Sn5 binary eutectic structure formed in these regions. Moreover, some Ag-enriched zones were observed around the Sn-Cu6Sn5 binary eutectic structure in the liquid before the initiation of the ternary eutectic solidification. The unusual Sn-Ag3Sn binary eutectic structure formed in these regions just after the temperature reached the ternary eutectic point. The ternary eutectic structures were classified into three types depending upon the fluctuation of the remaining liquid composition at the ternary eutectic temperature.

A modified 9Cr-1Mo steel was cooled to a temperature between the Ms point and room temperature from the normalizing temperature and then directly heated to the tempering temperature. It was found that the time to rupture at 650 and 700°C of the steel heat-treated by the new heat treatment increased 2–3 times longer than that of the steel conventionally normalized and tempered. The microstructure of the improved steel was tempered martensite and the size of martensite blocks was larger than for the conventional heat treatment. The hardness of the improved steel was fully recovered after tempering. This strengthening is not caused by fresh martensite, but caused by the refining of M23C6 and V(C,N) particles in addition to the increase in the martesite block size, where M denotes metallic elements.

The tin-zinc binary alloy is one of the candidates for lead-free solder and plating. In order to investigate the evolution of solidified structure of the tin-zinc binary eutectic alloy, the unidirectional solidification technique has been applied using a Bridgman type furnace. The primary β-tin is obtained as dendritic structure. On the other hand, the primary zinc is obtained as plate crystal because of high anisotropy in surface tension. Coupled-zone is found to be extended to tin-rich side and to be rather symmetric. The lamella spacing in coupled zone agrees with Jackson-Hunt model. Furthermore, the broken-lamellar to fibrous transition has been observed at high growth velocity.

Solidified structure near the chill zone is complex, since the growth directions of dendrites are not in accordance with the observed plane. Many lines, which are called ghost lines, can be observed in the solidified structure. The ghost lines have been analyzed applying the solid analytical geometry. Dendrite of cubic metals has been simplified with rod as a dendrite trunk and four plates with the same thickness. In order to characterize the solidified pattern, angles of ghost lines (η and ξ) are chosen and calculated using θ, φ and β, which are the important parameters to indicate the dendrite orientation in the space. The calculated results have been confirmed by the experimental results solidified unidirectionally of Al–20mass%Cu alloy. It has been found that the spacing or thickness of ghost lines may be the useful parameters to characterize the spatial array of dendrites with respect to the plane for observation.

It has been found that 3D-CAD is a powerful tool for analyzing the apparent pattern of solidification structure. Using 3D-CAD, the apparent patterns of model dendrites have been analyzed in this study. The effect of distribution of dendrites and the morphology of secondary dendrite arms on the apparent pattern have been investigated. As far as secondary dendrite arms form, it has been found that it can be recognized the ghost lines and it is possible to measure the characteristic parameters of ghost lines, η, ξ and γ, which are defined previously. Therefore, we can analyze the spatial relation of dendrite using these characteristic parameters of ghost lines. On the other hand, when the solidified structures are constituted by cells, which have no secondary arms, ellipses stand in a row on the cross section. Therefore, one could recognize the apparent pattern. However, it is not possible to analyze the spatial relation of the cell, since the ghost lines cannot be specified because of the distribution of cells.

Solidified structure near the ingot surface is complex and it is difficult to analyze the crystallographic orientation by the solidified structure. The reason of complexity is that the growth direction of dendrite does not agree with the plane for observation. Thus thick lines called ghost lines are often observed. The ghost lines have been characterized in this study.Simplifying the shape of dendrite, the ratio of widths of ghost lines (=γ) has been formulated and the change of γ in orientation of dendrite have been analyzed. It has been found that the angles of ghost lines (η and ξ) as well as γ are the important factors to characterize the solidified structure. In order to determine the spatial orientation of dendrite (θ, φ and β) from η, ξ and γ, the computer program had been developed. Applying this computation method, the solidified structure has been compared with the cross sections of dendrite model. The cross sections obtained by 3D-CAD agreed quite well to the real solidified pattern.

In the chill zone of the alloy casting, many fine grains nucleate on the surface and many dendrites grow their preferred growth direction. Therefore, it is rare that a “typical” dendritic structure can be observed near the chill zone. Usually, the solidified structure exhibits a quite complex pattern. In this study, the observed shape of dendrite will be investigated. Using Al–20mass%Cu alloy, unidirectional solidification with constant temperature gradient and growth velocity was performed. Then the solidified structure was observed on a cross section, which was intentionally inclined from the heat flow direction. The spatial relationship between dendrite and plane for observation has been defined using three angles, θ, φ and β. The solidified patterns were analyzed as a function of these angles. 3D-CAD model for solidified pattern has been developed assuming that secondary dendrite arms form plates. Solidified patterns agree quite well with 3D-CAD model.

Mold flux is widely used in continuous casting of steel. The heat transfer control in the mold is one of the important roles of mold flux. The mild cooling due to crystallization of mold flux is established for middle carbon steel, which has a high tendency for longitudinal cracking. However, the mechanism of crystallization has not well understood. Therefore, the kinetics of crystallization via glassy state has been analyzed in this study, using a commercial mold flux, which easily crystallizes.Quenched mold flux was prepared and heat treated at some temperatures for various periods. After heat-treatment, the mold flux was analyzed by XRD to confirm the phase, glass or crystalline. The time for crystallization as a function of heat-treatment temperature was experimentally determined. Then the apparent activation energy for crystallization was estimated using Arrhenius plot. The calculated value is 193 kJ/mol and this may correspond to the activation energy for diffusion of some molecules or ions in a glassy state of mold flux.

The Sn-Cu Alloy is one of the candidate alloys for lead-free solder. It is important to understand the solidified structure of this alloy, but such reports are few. In order to make in-situ observation during solidification of this alloy, a laser confocal microscope has been used. Three alloys, hypo-eutectic, eutectic and hyper-eutectic alloys have been prepared. In the case of hypo-eutectic alloy, primary β-Sn dendrite and interdendritic eutectic were observed. A large recalescence was observed when the primary β-Sn nucleated in thermal histories. In the case of eutectic alloy, only eutectic structure was observed by the laser microscope. However, primary β-Sn dendrites were observed on the cross section. There was a large recalescence during solidification. This corresponded to the nucleation of β-Sn. In the case of hyper-eutectic alloy, fibrous primary Cu6Sn5 grew and then β-Sn dendrite grew as halo. This followed by the formation of eutectic. It was observed that a large recalescence after growth of primary Cu6Sn5 precedes the nucleation of β-Sn as halo.

Control of nucleation on the surface of solidified shell is of importance to establish the whole structure of continuously-cast products. In the conventional continuous casting of steel, the nucleation of steel takes place on the molten state of mold flux. Lab-scale dipping tests have been carried out, where the solidification satisfied the above-mentioned condition. Changing the material of chill block and mold flux, the cooling rates of initial solidification have been varied systematically. The detailed observations of the surfaces and cross section of solidified shells have been made.The grain size was affected by cooling rate and decreased monotonously with increasing cooling rate. Many small protrusions have been found on the surface of the solidified shell. They resembled discs as Biloni et al. named. The density of discs was affected by cooling rate and increased with increasing cooling rate. The effective nucleation ratio was defined as the ratio between the number of grains and that of discs. The effective nucleation ratio obtained was a few percent and indicated small dependence on cooling rate in the range of this study.

In continuous casting of steel, mold fluxes are used to prevent surface defects, such as longitudinal cracks. The crystallization of mold flux promotes mild cooling of the steel shell, but crystallization behavior has been still uncertain. Therefore, this study has been carried out to analyze the crystallization processes of mold flux. Mold flux used in this study has high tendency for crystallization. Quenched specimens were heat-treated in various conditions and characterized. Glassy specimen heat-treated in the electric furnace over 550°C for 180 min crystallized. These crystalline were confirmed to be cuspidine by XRD analysis. The number of grains decreased and the average grain size increased with rise of temperature of heat treatment. The growth velocity also increased with rise of temperature.In-situ observation by the laser microscope revealed that the glassy specimen crystallized in a moment over 600°C and the surface of the specimen turned to be rough. This may lead to mild cooling in the mold.

In order to clarify the stability of precipitates in 8%Cr-2%W-0.09%Ta steel at high temperatures, tempering and precipitation behavior of the steel has been examined precisely. Tempering was performed mainly at 740°C for 0.5-1 000 h. Hardness peak was found in a tempering curve at 650-740°C for 3.75-8 h. Discontinuous changes in X-ray diffraction intensity of the matrix, apparent lattice strain and apparent crystalline particle size, which were estimated from integral breadth, the amount of extracted residue, and the Cr and Ta content in the residue were observed at 740°C for 2-12 h tempering. These discontinuous changes correspond to the rotation of preferred orientation or the generation of subgrains accompanying the dissolution and the subsequent re-precipitation of M 23 C 6 and TaC. The re-precipitation of fine M 23 C 6 particles is responsible for the hardness peak. Three kinds of TaC with different chemical composition and different size are found. The amount and the size of the coarse and medium TaC particles are affected by the discontinuous changes in microstructure. Fine particles of TaC grow very slowly, which is caused by the continuous dissolution of TaC due to the annihilation of precipitation site, dislocations, and re-precipitation on dislocations. Particle sizes of TaC and M 23 C 6 estimated using X-ray diffraction peak coincide with those observed in transmission electron microscopy.

Creep testing was carried out at around 650°C for a martensitic 8Cr-2WVTa steel (F82H), which is a candidate alloy for the first wall of the fusion reactors of the Tokamak type. Rupture strength of the double tempered steel (F82HD) is lightly higher than that of simply tempered steel (F82HS). On the other hand, creep rate of F82HD is obviously smaller than that of F82HS in acceleration creep, though creep strain of F82HD in transition creep, where creep rate decreases with increasing strain, is larger than that of F82HS. Hardness of the crept F82HD decreases with increasing creep strain, which corresponded with the transmission electron microscopy (TEM) observation. On the contrary, X-ray diffraction and electron back-scattered diffraction pattern measurements show that fine sub-grains are created during transition creep. The creep curves were analyzed using an exponential type creep equation and the apparent activation energy, the activation volume and the pre-exponential factor were calculated as a function of creep strain. Then, these parameters were converted into two parameters, i.e. equivalent obstacle spacing (EOS) and mobile dislocation density parameter (MDDP). While EOS decreases with increasing creep strain, MDDP increases with increasing strain during transition creep. The decrease in EOS and the increase in either EOS or MDDP are rate-controlling factors in transition and acceleration creep, respectively. On the other hand, in case of F82HS, EOS increases and MDDP decreases during transition creep. In this case, the decrease in MDDP controls the creep rate during transition creep of F82HS. It is concluded that both EOS and MDDP are representative parameters of the change in substructure during creep.

Seed crystal for equiaxed grain may be suffered from the temperature change in the liquid phase. Seed crystal may grow and/or melt depending on the thermal field. In order to analyze the growth and melting of a solid particle, in-situ observation using succinonitrile-water alloys with the newly constructed experimental equipment have been performed. In the central region of the ring heater, a small spherical solid particle is held for a while. When the voltage for the ring heater was abruptly changed, the solid particle grew or melted. The morphological change was recorded and analyzed.In case of growth, it indicated that the solid/liquid interface is dendritic. After stopping growth, the solid phase became round if the solute content is low. On the other hand, if the solute content is high, solid/liquid interface remained dendritic.In case of melting, the solid/liquid interface is complex. If the solid phase is round after growth, it melted remaining round. If the solid/liquid interface was dendritic after growth, dendrite arms became slender and the tip of dendrite became pointed. Some secondary dendrite arms may have been detached.It has been found that the melting velocity is lower than the growth velocity. Because of the difference in solid/liquid interfacial morphology and because of the difference in the traveling velocity of solid/liquid interface, the kinetics of growth and melting are different. One of the important reasons is the difference in operating point for growth and melting. In case of growth, the operating point is dendrite tip. On the other hand, in case of melting, it is rather wide area, which is inside of the envelope of the tips of the solid phase.

Metallurgical observation of 9%Cr–1%Mo–0.2%V steel tempered at 750°C for a maximum of 100 h has been made. Accompanying the recovery of martensitic structure, discontinuous changes in hardness, intensity of an X-ray diffraction peak of the matrix, the lattice strain calculated from the integral width of an X-ray peak, the amount of extracted residue and the size of M23C6 were observed when tempering time is around 10 h. These changes are caused by the annihilation of dislocations and the coalescence of martensite lath followed by the formation of subgrains in the later stage of tempering, which is supported by electron back scattered pattern (EBSP) measurements. The ultra fine grains of the order of 0.1 μm were confirmed around martensite lath and block by EBSP, which is obviously correlated with the discontinuous changes in the hardness and the lattice strain. Precipitation of M23C6 on excess dislocations of martensite induces a larger amount of precipitates as compared with the thermal equilibrium, which causes the dissolution of M23C6 during consequent tempering. The dissolution of M23C6 results in slower growth rate as compared with the Ostwald ripening. The observed over-all time exponent is 1/16.

The growth direction of solid phase, which has a great influence on the grain selection, has been investigated. Transparent organic systems, succinonitrile-H 2 O alloy and pivalic acid-H 2 O alloy have been used for unidirectional solidification. Essential parameters of phase diagrams, distribution coefficient of H 2 O (k) and liquidus slope (m) have been determined experimentally. The relationship is analyzed between dimensionless growth velocity (V/V c , where V c is the critical growth velocity for constitutional supercooling) and dimensionless growth direction (π'). The change in π' with V/V c is common and similar for both alloy systems. π' increases rapidly at low growth velocity region. Then, π' increases slowly and approaches unity with increasing V/V c . When the anisotropy of surface energy increases, the growth direction of solid phase becomes close to the preferred growth direction even at low growth velocity region, where cellular interface is observed.

Sn-Ag 3 Sn eutectic alloy is known as an attractive candidate to replace Sn-Pb soldering alloy. Since the solidified structure directly relates to the mechanical properties of joints, understanding of solidified structure of this alloy system is very important. Therefore, in order to understand the revolution of solidified structure, unidirectional solidification experiments have been carried out using eutectic Sn-Ag 3 Sn alloy. When the growth velocity is larger than the critical value, Sn-dendrites solidifies as a primary phase. This is attributed to the skewed coupled zone in this alloy system. In this case. the volume fraction of the primary Sn increases with increasing growth velocity and approaches a constant value. Interdendritic eutectic is composed with fibrous Ag 3 Sn and Sn matrix. On the other hand, when the growth velocity becomes lower, a eutectic structure appears without any primary phase. In this case, a piece of eutectic Ag 3 Sn becomes large and changes from fibrous to plate-like with decreasing growth velocity. This morphological change may be due to the anisotropy of surface tension of eutectic Ag 3 Sn.

In order to investigate the interaction between gas bubbles and solidified shell, in-situ observations using transparent substance have been made. The movement of argon gas bubbles has been observed and recorded by a VTR. The effect of diameter of gas bubbles, the angle of a copper plate and solid/liquid interfacial morphology on the entrapment of gas bubbles have been characterized. The entrapment of bubbles increases with decreasing the diameter of gas bubbles and with increasing the angle of the copper plate. Furthermore, it is found that the entrapment of gas bubbles increases with increasing the roughness of the solid/liquid interface. A physical model has been developed taking the force balance affecting a bubble into account. Using this model, the results of the present experiment have been consistently interpreted.

Precipitation behavior of VN during isothermal tempering at 740-800°C of 7%Cr-0.4%V-0.09%N steel (% denotes mass%, hereinafter) has been studied. Initially, rapid softening takes place accompanied by the precipitation of VN and, after that, the quasi-steady state in a hardness vs. tempering time diagram is continuing for a while. After the quasi-steady state, re-dissolution of VN particles rapidly occurs followed by final precipitation of VN. Just before the peak time of the re-dissolution of VN particles, both the temporal decrease in hardness and the temporal increase in the integral breadth of an X-ray diffraction peak take place. The similar precipitation phenomenon is confirmed in 0.14%C-9%Cr-1%Mo-0.2%V-0.09%Nb steel. In both steels the re-dissolution of VN or NbC (hereinafter MX) accompanies the decomposition of martensite. The following reactions are suggested as a mechanism for the re-dissolution of MX type particles: local stresses induced by the recovery of martensite unlock the pinning of dislocations by the MX type particles and the consequent isolated particles, which become energetically unstable, are re-dissolving into the matrix.

In order to investigate the multiplication of equiaxed grains by the forced convection, in-situ observation using a transparent organic substance have been made. The emission of some spherical particles from the columnar zone was observed by a fiber scope installed in an ingot case. These particles are originally the secondary dendrite arms and are detached by the fluctuations of thermal and/or solutal fields and/or mechanical breaking. Then the particles fell down in the liquid along with the natural convection. This event has taken place approximately 30 s before the well- developed equiaxed grains started to form. Therefore, these particles developed to equiaxed dendrites floating around in the liquid.A physical model for formation of equiaxed grains based on the observation has been proposed. The experimental results on the change in multiplication rate with time could be reasonably explained by this physical model.

A 2-D engineering model for grain selection has been developed taking the columnar dendrite growth theory into consideration. After evaluating this model via a unidirectional solidification experiment, the single-crystal casting process was simulated. Since the time required for calculation is rather short, a statistical analysis has been performed for the first time. The yield rate of well-oriented single crystal is increased by increasing the initial number of grains on the chill plate. However, the yield rate does not exceed approximately 90%. A detailed investigation of the formation mechanism of misorientation has revealed two possible processes (Type A and Type B) that may occur during single crystal casting process.

A phase-field simulation was carried out to investigate the growth behavior of a cellular and dendritic interface of an Fe–C binary alloy in a constrained growth condition. The simulated results were in good agreement with the experimental results. The effect of the magnitude of anisotropy at solid/liquid interface energy was examined, and it was found that the magnitude of anisotropy affected the growth direction when the growth rate was low. Dimensionless growth direction, � 0 , was used to examine the obtained results, and it was found that � 0 increases from zero and approaches unity with increase in growth velocity. A good correlation was obtained between calculated growth velocity and growth direction by using dimensionless growth velocity (V=Vc), and this correlation was in agreement with the experimental results.

An exponential type creep equation has been developed for heat resistant steels by the authors. This equation was induced assuming both a thermally activated process for a mobile dislocation and rather high applied stress. The applicability of the new creep equation was examined for a pure iron, two kinds of Ni-base super alloys and an eutectic solder alloy in a Pb-Sn system which were tested at relatively high temperatures and under very low stresses. All of the data obtained were completely explained by the new creep equation. The data for each alloy were classified into a few groups, where a deformation mechanism may be different with each other. The new creep equation is valid for stresses higher than the half value of the slope in a logarithm of time to rupture vs. linear stress diagram.

Dissolved V in austenite of 7%Cr-0.4%V-0.09%N steel (hereinafter, % means mass%) was measured and the solubility product of VN was determined as follows:log([%V][%N]) = 4.38−(8436/T)where T is the absolute temperature in K. The solubility product obtained is 3 to 5 times larger than those in the literature and about one order larger than that for iron. The decrease in the activity coefficient of nitrogen due to the presence of Cr and V in the experimental steel is responsible for the increase in the solubility product of VN.

Refinement of the solidified structure is of importance for soundness of cast products. Formation of the grains on the surface is very important for the understanding of evolution of solidified structure. The evaluation method for grain density on the chill plate is proposed in this study. Using an engineering model for grain selection, which has been separately developed, the number of grain decreases linearly in a first stage of solidification. Therefore, the solidified structure should be observed at least two cross sections. Extrapolating the data to the chill surface, the grain density on the surface can be evaluated. Validity of the proposed method has been checked using Al-10mass%Cu alloy. A solidified shell, which was produced by dipping a chill plate in a molten alloy, has been closely observed. A grain is defined as a group of the dendrites that have the same orientation. Densities of grains were measured at two cross sections. Extrapolating these data to the surface, the grain density on the surface has been estimated. This estimated value agrees well with the density of grains, which was directly measured on the surface of the solidified shell.

In-situ observation of unidirectional solidification using transparent substance has been performed to investigate the growth direction of solid phase. Cell and/or dendrite, the preferred growth directions of which are not parallel to the heat flow direction, were observed with various solidification conditions. Dimensionless growth direction (π' = (angle between heat flow direction and growth direction)/(angle between heat flow direction and preferred growth direction)) changes from zero to unity with increasing growth velocity at a constant temperature gradient. Introducing the normalized growth velocity (V/ V c , where V c is the critical growth velocity for breaking down a planar interface), the relation between π' and growth condition could be correlated and π' could be expressed by a unique line with respect to the normalized growth velocity. Furthermore, the growth directions of cells or dendrites under the condition of unidirectional solidification have been analyzed by the phase-field model. The calculated results agree with the experimental results and the functional relationship between growth velocity and growth direction is qualitatively explained.