[Paper Review] An integral method for the calculation of the reduction in interfacial free energy due to interfacial segregation

Ivan Blum, Sung‐Il Baik+2 more|arXiv (Cornell University)|Mar 2, 2020

Advanced Materials Characterization Techniques50 references9 citations

TL;DR

This paper presents an integral method based on Gibbs' adsorption isotherm to calculate the reduction in interfacial free energy due to solute segregation at internal interfaces, using atom-probe tomography (APT)-measured concentration profiles. The method enables discrete, quantitative assessment of interfacial energy reduction for both homo- and hetero-phase interfaces, demonstrated in PbTe-PbS:Na and Ni-based Alloy 600 systems with B/Si segregation.

ABSTRACT

A method based on the Gibbs' adsorption isotherm is developed to calculate the decrease in interfacial free energy resulting from solute segregation at an internal interface, built on measured concentration profiles. Utilizing atom-probe tomography (APT), we first measure a concentration profile of the relative interfacial excess of solute atoms across an interface. To accomplish this we utilize a new method based on J. W. Cahn's formalism for the calculation of the Gibbs interfacial excess. We also introduce a method to calculate the decrease in interfacial free energy that is caused by the segregating solute atoms. This method yields a discrete profile of the decrease in interfacial free energies, which takes into account the measured concentration profile and calculated Gibbsian excess profile. We demonstrate that this method can be used for both homo- and hetero-phase interfaces and takes into account the actual distribution of solute atoms across an interface as determined by APT. It is applied to the case of the semiconducting system PbTe-PbS 12 mol.%-Na 1 mol.%, where Na segregation at the PbS/PbTe interface is anticipated to reduce the interfacial free energy of the {100} facets. We also consider the case of the nickel-based Alloy 600, where B and Si segregation are suspected to impede inter-granular stress corrosion cracking (IGSCC) at homo- (GB) and hetero-phase metal carbide (M7C3) interfaces. The concentration profiles associated with internal interfaces are measured by APT using an ultraviolet (wavelength = 355 nm) laser to dissect nanotips on an atom-by-atom and atomic plane-by-plane basis.

Motivation & Objective

• To develop a quantitative method for calculating the reduction in interfacial free energy due to interfacial segregation.
• To enable accurate assessment of interfacial energy changes using experimentally measured solute concentration profiles from atom-probe tomography (APT).
• To extend the Gibbsian formalism to internal interfaces in both homo- and hetero-phase systems.
• To provide a discrete, profile-based calculation of interfacial energy reduction that accounts for actual atomic-scale segregation distributions.
• To apply the method to real materials systems where segregation is suspected to influence interfacial stability, such as PbTe-PbS:Na and Ni-based Alloy 600.

Proposed method

• Utilizes J. W. Cahn's formalism to calculate the Gibbs interfacial excess from APT concentration profiles.
• Applies the Gibbs adsorption isotherm in an integral form to compute the reduction in interfacial free energy due to solute segregation.
• Processes APT data collected via ultraviolet (355 nm) laser ablation to obtain atomic-scale, plane-by-plane concentration profiles across interfaces.
• Constructs a discrete profile of interfacial energy reduction by integrating the measured solute excess and concentration distribution across the interface.
• Validates the method on both heterophase (PbS/PbTe) and homophase (Ni-based alloy GBs and M7C3 carbides) interfaces.
• Employs a numerical integration approach to compute energy changes based on the actual spatial distribution of segregating solutes.

Experimental results

Research questions

• RQ1 How can the reduction in interfacial free energy due to solute segregation be quantitatively calculated from measured concentration profiles?
• RQ2 To what extent does Na segregation at PbS/PbTe interfaces reduce interfacial energy, and how does this affect interfacial stability?
• RQ3 How do B and Si segregation at grain boundaries and M7C3 carbide interfaces in Alloy 600 influence interfacial energy and resistance to intergranular stress corrosion cracking?
• RQ4 Can the Gibbsian formalism be adapted for internal interfaces with non-uniform solute distributions as measured by APT?
• RQ5 What is the spatially resolved contribution of solute segregation to interfacial energy reduction across atomic planes?

Key findings

• The method successfully computes a discrete, spatially resolved profile of interfacial free energy reduction based on APT-measured concentration and Gibbs excess profiles.
• Na segregation at {100} facets of PbTe-PbS 12 mol.%-Na 1 mol.% is predicted to significantly reduce interfacial free energy, stabilizing the interface.
• B and Si segregation at grain boundaries and M7C3 carbide interfaces in Ni-based Alloy 600 are shown to reduce interfacial energy, potentially inhibiting intergranular stress corrosion cracking.
• The approach is applicable to both homo- and hetero-phase interfaces, demonstrating broad material system compatibility.
• The use of UV laser APT enables high-resolution, atomic-plane-by-plane measurement of solute distribution critical for accurate energy calculations.
• The integral method provides a direct, experimentally grounded pathway to link atomic-scale segregation to macroscopic interfacial energy changes.