# PhD Thesis Defence: Mr. Anuj Dash (01/09/23)

### Thesis title:

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

### Faculty advisor(s):

Prof. Aloke Paul

### When?

1^{st} September, 2023 (Friday), 11:00 AM (India Standard Time)

### Where

KPA Auditorium, Dept of Materials Engineering

### Abstract

Diffusion studies in multicomponent systems present formidable challenges even after half a century of work in the field since the s= ystematization of the phenomenological formalism of diffusion. The chemical interdiffusion method is the most popular approach for experimental studies in diffusion. However, the requirement to fulfil the stringent mathematical conditions of Onsager’s formalism in experimental studies of multicomponent systems has historically limited most studies to binary and ternary systems. Historically, all types of diffusion coefficients could be estimated in binary systems, while only interdiffusion coefficients were estimated in ternary systems. The experimental complications associated with the need to intersect (n-1) serpentine diffusion paths in the n dimensional space led to unsolved problems and estimation of composition dependent diffusion coefficients were considered impossible for higher order systems until recently. The lack of diffusivity data in multicomponent systems has hampered the generating mobility databases essential for microstructural simulation and correlation with various physical and mechanical properties of materials highlighting the performance and durability of the product.

Recently, a number of new methods that elegantly overcome the experimental difficulties in fulfilling the mathematical preconditions in multicomponent systems have come to fore, thus enabling the estimation of the diffusivities. NiCoFeCr Multi Principal Element (MPE) system is considered as a model system for these analyses to compare the data estimated by the new methods proposed in this thesis with the available radiotracer data for the equiatomic alloy.

This work first explores the intricacies of the pseudo-binary (PB) diffusion couple approach in the NiCoCr system and later extends it to the NiCoFeCr system. The evolution of the mathematical formalism for pseudo-binary diffusion couples from conventional multicomponent systems, and its extension to estimate the interdiffusion coefficients and then the modifications to Darken-Manning relations necessary for the determination of the intrinsic and tracer coefficients from PB couples for the equiatomic NiCoFeCr alloy is explored in this section.

This work then extends the recently proposed pseudo-ternary (PT) method by modifying the Darken-Manning formalism for the case of three components developing a diffusion profile, keeping rest of the components constant, to enable the calculation of tracer coefficients and the intrinsic coefficients at the intersection of two PT diffusion paths. Application of the PT approach to the NiCoFeCr system via two different sets of PT diffusion couples (Cr constant and Fe constant) enables the estimation of the tracer coefficients of all four components which can be subsequently used to estimate the intrinsic and interdiffusion coefficients as well.

The body diagonal method originally proposed for determination of interdiffusion coefficients only is extended in this thesis for benefits of determination of the tracer coefficients of all elements from only two diffusion profiles. This reduces the laborious task of producing (n-1) diffusion paths that need to pass within negligible but equal distances to each other to reduce the complex unknown errors that arise due to the lack of direct intersection between the diffusion paths. Using the modified body diagonal approach proposed in this work, the tracer coefficients of all components can be estimated from the intersection of just two diffusion paths, which can be used to estimate the conventional intrinsic and interdiffusion coefficients by the application of Darken-Manning (with vacancy wind effect) or Kirklady-Lane relations (without vacancy wind effect). The obtained tracer diffusion coefficients show a good match with the data estimated from radio tracer methods extended to the temperature of interest.

This work then explores the possibilities of intersecting diffusion paths of a dissimilar nature to take advantage of the constrained nature of the PB and PT diffusion paths to target intersection at a specific composition and also determine diffusivities of all components from a single set of experiments only. First, we demonstrated that intersecting a PT diffusion path with a PB diffusion path is easier compared to intersecting two similar PT diffusion paths. Further, we have demonstrated that intersecting two, but dissimilar PT diffusion paths brings the advantage of estimation of diffusion coefficients of four elements. Following, we demonstrated that intersecting a conventional diffusion path in which all the elements produce the diffusion profiles by a rectilinear diffusion path of a PB couple is far easier for estimation of diffusion coefficient of all the elements in multicomponent systems with any number of elements (n≥3). This overcomes the limitations of all the methods demonstrated until now for estimation of diffusion coefficients of all the elements by intersecting only two diffusion paths at a desired composition. The equation scheme required for such analysis is established and described in detail. The influence of vacancy wind effect on the intrinsic coefficients and the interdiffus= ion coefficients is studied in detail to demonstrate the importance of estimating the diffusivities considering the vacancy wind effect. Vacancy wind factor strongly influences certain cross coefficients, to the extent that it may even change the sign of certain cross coefficients as well. Compared to the intrinsic coefficients, however interdiffusion coefficients are relatively less affected by the vacancy wind factor but it is still crucial to consider the vacancy wind factor in the calculations.

Having established the efficacy of these approaches in the NiCoFeCr system, the ideas are extended to the five component NiCoFeCrAl to estimate the diffusivities of all the components. Following, a design strategy for intersecting the diffusion paths in Ni-Co-Fe-Cr-Al multi-principal element alloy is demonstrated. This is guided by the possibilities of producing PB diffusion profiles in the NiCoFeCr system, This, for the first time, facilitates the estimation of the tracer, intrinsic, and interdiffusion coefficients of all the elements purely experimentally in this quinary system. The tracer diffusion coefficients estimated in this quinary system are compared with the impurity and tracer diffusion coefficients in pure Ni (taken from literature), and at (or near) equiatomic compositions of binary Ni-Co, ternary Ni-Co-Cr, and quaternary Ni-Co-Fe-Cr systems estimated in this study. The relative mobilities of the elements are found to follow the trend D_Ni^

<(>= «)>D_Co^

<(>«)>D_Fe^

<(>«)>D_Cr^

<(>«)>D_Al^

in all the systems. However, the tracer diffusion coefficients of the elements first decrease and then increase with the increasing order of the systems. The contribution of the vacancy wind effect on certain cross-intrinsic diffusion coefficients is found to be very significant and cannot be ignored. The influence of the vacancy wind effect on interdiffusion coefficients is found to be less significant compared to the intrinsic diffusion coefficients since interdiffusion coefficients are kind of average of multiple intrinsic diffusion coefficients. We h= ave further shown that describing the relative mobilities of the elements with main interdiffusion coefficients instead of the tracer diffusion coefficients can be misleading or confusing. Consideration of different elements as the dependent component of interdiffusion coefficients may indicate a very different or even a completely opposite trend for the diffusivities.

The methods described in this work are simple and enable the estimation of tracer diffusion coefficients as well as intrinsic diffusion and interdiffusion coefficients from interdiffusion based experiments. The advantage of the need for only two diffusion paths for the estimation of all types of diffusion coefficients is demonstrated, which are needed for understanding the nature of diffusion paths (from the interdiffusion coefficients) or the data (tracer and intrinsic diffusion coefficients) needed for microstructural simulation and correlation with the high-temperature mechanical properties. This can now be extended to other systems, for example, Ni, Co, and Fe-rich multicomponent materials used extensively in various applications or the Al, Si, Pt, etc. containing materials in which the radiotracer method cannot be utilized.