Solving The Unsolved In Multicomponent Diffusion: The Concept Of Constrained Diffusion Couple Methods

Abstract

Quantitative diffusion analysis in multicomponent metallic systems has been a formidable task historically and despite decades of research, most of the diffusivity estimations were limited to interdiffusion and some intrinsic diffusion coefficients in binary systems and interdiffusion coefficients in a few ternary systems until recently. The experimental complications associated with the need to intersect (n-1) serpentine diffusion paths in the n dimensional space for determining the 〖(n-1)〗^2 interdiffusion coefficients lead to various approaches like average diffusivity, square root diffusivity estimations that approximate a representative value of the diffusivity across a composition range from a single experiment. However, these values are not material constants and do not provide any information about the atomic interactions. This lack of diffusivity data in multicomponent systems has hampered the development of mobility databases essential for various simulations and physico-chemical studies of materials. This work resolves the issues with quantitative multicomponent diffusion analysis via several newly proposed methods that solves the issue of intersecting diffusion paths through the application of special constrained diffusion paths. The equations necessary to apply these methods are derived and their application is discussed mathematically and applied experimentally to the model alloy system, the NiCoFeCr equiatomic multiprincipal element alloy to compare with available radiotracer data measured for this system. The work first employs the pseudo-binary diffusion couple approach that develops a rectilinear diffusion path in the multicomponent space to the NiCoFeCr system to estimate the tracer coefficients from the intrinsic coefficients at the marker plane. The mathematical formulations derived for the same justify its namesake and the obtained tracer coefficients can be used to back calculate the intrinsic and interdiffusion coefficients. The pseudo-ternary method improves on the shortcomings of the pseudo-binary diffusion couple method and enables the estimation of tracer coefficients of three components by crossing two constrained diffusion paths in a 2d plane in addition to the main and cross interdiffusion coefficients. The body diagonal method originally proposed for determination of interdiffusion coefficients is modified here to determine the tracer coefficients of all components using only two diffusion profiles thus reducing the errors associated with crossing (n-1).paths per the original approach. This work then explores the possibilities of crossing dissimilar constrained diffusion paths by crossing pseudo ternaries of different types. Strategically crossing a rectilinear pseudo-binary diffusion path with a serpentine conventional (body diagonal) diffusion path overcomes all the previous drawbacks of pseudo binary, pseudo ternary and body diagonal methods to determine the full set of diffusivities at any desired composition and generalizes the constrained diffusion path approach to any order multicomponent system. The obtained tracer coefficients show a good match with the diffusivities measured in radio tracer experiments. Finally, based on the ideas from the constrained diffusion path experiments in the NiCoFeCr system, a constrained path approach is devised to measure the diffusivities in an Al based NiCoFeCr multiprincipal element alloy system which was not possible earlier due to unavailability of radio isotopes and the complexities of interdiffusion experiments in higher order systems. The obtained tracer diffusivities, show an excellent match with the trends extrapolated from lower order systems. Calculated intrinsic and interdiffusion coefficients demonstrate the importance of vacancy wind effect as well as the issues with using diffusivities having different dependent components to make predictions on diffusion trends among different elements.