journal article·2026-01

Extracting composition-dependent diffusion coefficients over a very large composition range in NiCoFeCrMn high entropy alloy following strategic design of diffusion couples and physics informed neural network numerical method

Suman Sadhu, Saswata Bhattacharyya, Aloke Paul

Acta Materialia· Volume 302
Publisher page

Abstract

Estimating composition dependent diffusion coefficients in multicomponent alloys was a longstanding challenge due to limitations in experimental methods. In this study, we have first demonstrated a strategic design of producing only three diffusion couples to estimate all types, that is tracer, intrinsic, and interdiffusion coefficients at the Kirkendall marker planes. This establishes a systematic variation of diffusion coefficients with composition in a very wide composition range of the NiCoFeCrMn system in comparison to the data available on impurity diffusion coefficients in pure elements and tracer diffusion coefficients at the equiatomic composition estimated by the radiotracer method. Following, a physics-informed Neural Network based numerical inverse method is developed to extract composition-dependent diffusivities over the whole composition range of the diffusion couples.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: High Entropy Alloys Studies · High-Temperature Coating Behaviors · Additive Manufacturing Materials and Processes

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (63)

Show source-provided references
1. Recent advances in understanding diffusion in multiprincipal element systems10.1146/annurev-matsci-081720-092213 ↗
2. Thermodynamics
3. The trouble with diffusion10.1590/S1516-14392002000300002 ↗
4. Body-diagonal diffusion couples for high entropy alloys10.1007/s11669-017-0606-z ↗
5. First report on entire sets of experimentally determined interdiffusion coefficients in quaternary and quinary high-entropy alloys10.1557/jmr.2019.378 ↗
6. Estimation of tracer and intrinsic diffusion coefficients from body diagonal diffusion couples in a multi-principal element alloy10.1007/s11669-022-00990-5 ↗
7. Diffusion in multicomponent metallic systems: intrinsic diffusion behaviour and the Kirkendall effect in ternary solid solutions10.1139/p66-169 ↗
8. A physics-informed neural network-based numerical inverse method for optimization of diffusion coefficients in NiCoFeCr multi principal element alloy10.1016/j.scriptamat.2022.114639 ↗
9. Utilising physics-informed neural networks for optimisation of diffusion coefficients in pseudo-binary diffusion couples10.1080/14786435.2023.2237900 ↗
10. A. Dash, A. Paul, S.V. Divinski, S. Bhattacharyya, Estimation of reliable diffusion coefficients following the diffusion couple method and developing a constraint-enhanced multi-objective optimization framework for mobility data generation: Ni-Co-Cr System as a case study, unpublished research, under review (2025).
11. An experimental estimation method of diffusion coefficients in ternary and multicomponent systems from a single diffusion profile10.1016/j.actamat.2024.120000 ↗
12. Estimation of diffusion coefficients in NiCoFeCrAl multi-principal element alloy following an inventive design strategy of diffusion couples10.1016/j.actamat.2023.119296 ↗
13. Estimation of diffusion coefficients by intersecting different types of diffusion paths in a multi-principal element alloy10.1016/j.actamat.2022.118547 ↗
14. Concepts for estimating all types of diffusion coefficients of NiCoFeCr multi-principal element alloys using two dissimilar or a combination of ideal and non-ideal pseudo-ternary diffusion couples10.1016/j.scriptamat.2023.115719 ↗
15. A numerical inverse method for calculating the interdiffusion coefficients along a diffusion path in ternary systems10.1016/S1359-6454(02)00358-0 ↗
16. Investigations on diffusion behaviors in Ti-rich Ti–Nb–Zr–Cr system: experimental measurement and CALPHAD modelling10.1016/j.calphad.2018.07.005 ↗
17. Diffusivity and atomic mobility in fcc Cu–Mn–Si alloys: measurements and modeling by CALTPP program10.1007/s10853-022-06948-9 ↗
18. An efficient method of calculating composition-dependent inter-diffusion coefficients based on compressed sensing method
19. A pragmatic method to determine the composition-dependent interdiffusivities in ternary systems by using a single diffusion couple10.1016/j.scriptamat.2014.07.016 ↗
20. Determination of accurate interdiffusion coefficients in fcc Ag-In and Ag-Cu-In alloys: a comparative study on the Matano method with distribution function and the numerical inverse method with HitDIC10.1016/j.jallcom.2019.05.224 ↗
21. High-throughput determination of high-quality interdiffusion coefficients in metallic solids: a review10.1007/s10853-020-04805-1 ↗
22. Automation of diffusion database development in multicomponent alloys from large number of experimental composition profiles10.1038/s41524-021-00500-0 ↗
23. A pseudo-binary approach to study interdiffusion and the Kirkendall effect in multicomponent systems10.1080/14786435.2013.769692 ↗
24. Pseudo-binary and pseudo-ternary diffusion couple methods for estimation of the diffusion coefficients in multicomponent systems and high entropy alloys10.1080/14786435.2019.1619027 ↗
25. Solving the issues of multicomponent diffusion in an equiatomic NiCoFeCr medium entropy alloy10.1016/j.actamat.2020.03.041 ↗
26. Correlation between estimated diffusion coefficients from different types of diffusion couples in multicomponent system
27. Practicing pseudo-binary diffusion couple method in ternary and multicomponent systems10.1016/j.actamat.2025.121127 ↗
28. A novel concept of pseudo ternary diffusion couple for the estimation of diffusion coefficients in multicomponent systems10.1016/j.scriptamat.2018.01.002 ↗
29. Diffusion simulation based on atomistic model and mobility determination via Kirkendall experiment for multicomponent systems10.1016/j.scriptamat.2023.115884 ↗
30. Introducing concepts of estimating tracer and intrinsic diffusion coefficients in a ternary system: a case study in the FCC Fe-Mn-Cr solid solution
31. Sluggish diffusion in Co-Cr-Fe-Mn-Ni high-entropy alloys10.1016/j.actamat.2013.04.058 ↗
32. A mystery of ’sluggish diffusion’ in high-entropy alloys: the truth or a myth10.4028/www.scientific.net/DF.17.69 ↗
33. Bulk tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys10.1016/j.actamat.2017.12.052 ↗
34. Ni tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys10.1016/j.jallcom.2016.07.239 ↗
35. Tracer diffusion in single crystalline CoCrFeNi and CoCrFeMnNi high-entropy alloys: kinetic hints towards a low-temperature phase instability of the solid-solution?10.1016/j.scriptamat.2020.05.060 ↗
36. Tracer diffusion in single crystalline CoCrFeNi and CoCrFeMnNi high entropy alloys10.1557/jmr.2018.162 ↗
37. Concentration-dependent atomic mobilities in FCC CoCrFeMnNi high-entropy alloys10.1016/j.actamat.2018.12.033 ↗
38. Zr diffusion in BCC refractory high entropy alloys: a case of ‘non-sluggish’ diffusion behavior10.1016/j.actamat.2022.117970 ↗
39. Tracer diffusion under a concentration gradient: a pathway for consistent development of mobility databases in multicomponent alloys10.1016/j.jallcom.2022.167301 ↗
40. The impact of non-equilibrium vacancies on mobilities and Kirkendall porosity formation in diffusion couples: experiments and theory for the Cu–Fe–Ni system as a case study10.1016/j.actamat.2025.121035 ↗
41. Multiphase diffusion in binary and ternary solid state systems10.1016/0079-6786(90)90007-3 ↗
42. On the determination of diffusion coefficients in a binary metal system10.1016/0001-6160(70)90009-X ↗
43. Development of different methods and their efficiencies for the estimation of diffusion coefficients following the diffusion couple technique10.1016/j.actamat.2018.04.051 ↗
44. Diffusion in bin¨ aren gemischen mit volumen¨anderung, Zeitschrift Für Elektrochemie, Berich
45. Reciprocal relations in irreversible processes I10.1103/PhysRev.37.405 ↗
46. Theories and problems of liquid diffusion10.1111/j.1749-6632.1945.tb36170.x ↗
47. Cross terms in the thermodynamic diffusion equations for multicomponent alloys10.1007/BF02811561 ↗
48. Diffusion and the Kirkendall shift in binary alloys10.1016/0001-6160(67)90363-X ↗
49. Kirkaldy · 1987
50. DeepXDE: a deep learning library for solving differential equations10.1137/19M1274067 ↗
51. Self-diffusion and isotope effect in γ-iron10.1016/0022-3697(68)90103-0 ↗
52. Diffusion of manganese in cobalt and cobalt-manganese alloys10.1080/14786437708235985 ↗
53. High-temperature creep of nickel-tungsten alloys (on the relation between high-temperature creep and diffusion in nickel-base solid solutions. part VI)10.2320/jinstmet1952.28.5_253 ↗
54. Solute diffusion in nickel-base substitutional solid solutions
55. Interdiffusion and its size effect in nickel solid solutions of Ni-Co, Ni-Cr and Ni-Ti systems10.1007/BF00729354 ↗
56. Diffusion of Ni63 in iron, cobalt, nickel, and two iron–nickel alloys10.1139/v59-237 ↗
57. Lattice diffusion and grain boundary diffusion of cobalt in γ-iron10.2320/matertrans1960.2.176 ↗
58. Diffusion of nickel into iron10.1016/0001-6160(61)90138-9 ↗
59. Iron nickel and cobalt diffusion in transition metals of iron group10.1016/0001-6160(69)90138-2 ↗
60. High throughput determination of diffusion coefficients and hardness using diffusion couple technique of γ-phase Fe-Ni-Cu alloys at 1000 °C10.1016/j.calphad.2025.102809 ↗
61. Square root diffusivity analysis of body-diagonal diffusion couples in FeNiCoCr quaternary and FeNiCoCrMn quinary systems10.1007/s11669-022-01007-x ↗
62. Thermodynamic and kinetic study of diffusion paths in the system Cu-Fe-Ni10.1007/BF02651877 ↗
63. On the relation between interdiffusion and tracer diffusion coefficients in ternary solid solution10.4028/www.scientific.net/DDF.194-199.189 ↗