Introduction underlying principle is that, upon heating into regimes

Introduction
to segregation engineering and grain boundary segregation engineering

Segregation
engineering refers to the self-organized microstructure manipulation whereby
the solutes, under thermodynamic driving force, are segregated to specific
lattice defects and consequently trigger microstructural changes at the site of
segregation. The underlying principle is that, upon heating into regimes good
enough for diffusion, the solute atoms show strong segregation at the
attractive trap sites i.e. lattice defects such as grain boundaries and
dislocations. The resulting local strain fields and alteration in chemical
composition at the lattice defects can induce structural transitions, phase
transformations and solute ordering. In order to realize segregation
engineering, certain thermodynamic and kinetic factors have to be taken into
account 1. Rather than considering such solute segregation just as an
undesirable phenomenon, segregation engineering aims to exploit it as a tool
for site-specific manipulation of interfaces or microstructures so as to obtain
desirable macroscopic material behavior.

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Grain
boundaries are inevitable defects in polycrystalline metallic materials. They
can either strengthen or weaken a material as they influence a range of
properties such as tensile strength, fracture toughness and corrosion. A lot of
grain boundary properties such as cohesion and strength are sensitive to solute
decoration. Thus, grain boundary segregation engineering (GBSE), which is the
manipulation of grain boundaries “via solute decoration or even confined
transformation”,
is an important branch of segregation engineering 2.

Adsorption isotherm

The amount of
segregation of a solute at a specific site such as grain boundary is inversely proportional
to the solubility of that solute in the bulk phase (matrix). Moreover, the
thermodynamics of grain boundary segregation are similar to monolayer gas
adsorption and hence can be modeled using the adsorption isotherm.

?i =
– (1/RT) x (d?/dln xi)T,V

Where,

?i = excess concentration of element at
grain boundary

xi = molar concentration of
element i in bulk

d?
= change in Gibbs energy upon segregation at constant temperature and volume

The equation
above represents the Gibbs adsorption isotherm. It shows the relation between
bulk concentration and solute segregation (excess concentration). However, due
to the challenge of experimentally measuring the interfacial energy as a
function of temperature and composition in the case of Gibbs adsorption isotherm,
it is more natural to use the Langmuir-McLean isotherm, which is approximates
to (system taken as dilute case):

?i
= ?iGB / ?iB = exp (-?GiGB
/ RT)

Where,

?i = segregation coefficient or grain
boundary enrichment factor

?iGB = molar grain boundary
occupation fraction of element i

?iB = molar concentration of
element i in bulk

?GiGB
= segregation free energy

The
Langmuir-McLean isotherm states that: grain boundary segregation occurs for ?GiGB