A Physico-Chemical Approach in Binary Solid-State Interdiffusion

Abstract

A physico-chemical approach (theory of dissociation and reaction) is developed, which can be used in binary diffusion couple to determine diffusion parameters of the product phases with wide homogeneity range, as well as phases with narrow homogeneity range. It is demonstrated that this approach is basically equivalent to the diffusion based treatment. However, physico-chemical approach pedagogically sheds light on the chemical reactions occurring during interdiffusion at the interphase interfaces and morphology develops in the interdiffusion zone. This theory can be used in any binary systems for any end-member condition to explain single phase or multiphase diffusion controlled growth. Ni-Al and Ag-Zn systems are considered here to calculate diffusion parameters following physico-chemical approach. It is evident from our theoretical analysis and experimental evidence that in the presence of a stable Kirkendall marker plane one should expect duplex grain morphology in a particular phase layer. On the other hand, there is another model which is used rather frequently, is the theory of partitioning of flux. Although, the theory of partitioning of flux is used several times, we found that this theory does not count the mobility of both the species and therefore is not suitable to use in most of the interdiffusion systems. We have first modified this theory to take into account the mobility of both the species and then further extended to develop the relations for the integrated diffusion coefficient and the ratio of diffusivities of the species. The versatility of these two different models (that is the theory dissociation and reaction and the partitioning of flux) is examined in the Co-Si system with respect to different end-member compositions. From our analysis, we found that the applicability of the theory of partitioning of flux is rather limited but the theory of dissociation and reaction can be used in any binary systems. The theory of dissociation and reaction is then used to elucidate this behaviour in a single phase of β-NiAl and to calculate the diffusion parameter at the Kirkendall marker planes in the interdiffusion zone. To apply the physico-chemical approach, Ni-and Al-rich part of the phase is treated as two different phases and the plane corresponding to eqiatomic composition is considered as virtual interface between them. Possible dissociation and reaction equations are considered to combine with the flux equations to derive the relation for diffusion coefficient. Further experiments are conducted in the Cu-Sn, Au-Sn and Ni-Sn systems, which are important for flip chip bonding related to micro electronics industry. Different diffusion parameters, such as integrated diffusion coefficient, tracer diffusion coefficient of elements and the ratio of diffusivities are determined, which shed lights on the atomic mechanism of diffusion. Subsequently, the theory of dissociation and reaction is used when possible to explain the growth of the phases in the interdiffusion zone.