Metallurgy & Material Science

Dr.S.JoseDept of Mechanical Engg.,

TKM College of Engineering, Kollam

2

Diffusion in crystals

Theory of Alloys

Equilibrium Diagram

TTT Diagram

Heat Treatment

Recovery, Recrystallisation & Grain Growth

Module II

Diffusion

What is Diffusion

Mechanisms of diffusion

Vacancy

Interstitial

Steady-state diffusion

Non-steady-state diffusion

Fick’s laws

What is Diffusion

The phenomenon of material transport by atomic motion.

Diffusion couple Cu&Ni is heated to high temperature and cooled.

Cu atoms migrated or diffused into Ni and Ni atoms into Cu.

The process in which atoms of one metal migrate into another - Inter-diffusion or impurity diffusion

Diffusion occurring in pure metals –atoms exchanging positions- called self diffusion

Mechanisms of diffusion

Diffusion is a stepwise migration of atoms from lattice site to lattice site.

For an atom to make such a move, There must be an empty adjacent site. The atom must have sufficient energy to break

bonds with its neighboring atom.

Vacancy diffusion Interchange of an atom with an adjacent vacant

lattice site. (self- and inter-diffusion)

Interstitial diffusion Migration of atoms from an interstitial position

to a neighboring empty one.

Mechanisms of diffusion

Diffusion – time function?

Steady-state and Non-steady-state diffusion processes are distinguished by the parameter –diffusion flux, J.

Flux is defined as number of atoms crossing a unit area perpendicular to a given direction per unit time.

Flux has units of atoms/m2.sec or moles/m2.sec.

If the flux is independent of time, then the diffusion process is called steady-state diffusion.

On the other hand, for non-steady-state diffusion process, flux is dependent on time.

Fick’s first law

States that diffusion flux is proportional to concentration gradient

CJ D

xC

x is the gradient of the concentration C

The proportionality constant, D, is called diffusion coefficient or diffusivity. It has units as m2/sec.

The diffusion coefficient of a material is also referred to as 'diffusion constant’.

The negative sign of the right side of the equation indicates that the impurities are flowing in the direction of lower concentration.

Fick’s second law

Fick's First Law does not consider the fact that the gradient and local concentration of the impurities in a material decreases with an increase in time, an aspect that is important to diffusion processes.

The Second Law states that the change in impurity concentration over time is equal to the change in local diffusion flux

is the rate of change of concentration with respect to time at a particular position, x.

C J

t xC

t

Theory of alloys

What is an alloy

Types of alloys

Solid solution

Substitutional

Interstitial

Intermetallic compounds

Hume – Rothery Rules

Superalloys

Alloys

An alloy is a phase comprising of one or more components.

There are three distinguishable types: Substitutional: solute substitutes the

solvent in the crystal lattice without structural changes.

Interstitial: solute does not occupy the sites in the lattice of the solvent, but resides in crystallographic pores.

Transformational: A completely new lattice is formed. Usually occurs as a result of intermetallic compound formation.

Substitutional Solid Solution

In substitutional solid solution, the arrangement of the solute atoms may be disordered (random) or ordered.

Some alloy systems exhibit complete solid solubility (e.g. Cu-Ni, Cd-Mg), others show only limited solubility at any temperature.

Several factors determine the limits of solubility.

These are expressed as a series of rules often called Hume-Rothery Rules.

Substitutional Solid Solution

Hume-Rothery Rules

The Hume-Rothery rules are a set of basic rules describing the conditions under which an element could dissolve in a metal, forming a solid solution.

There are two sets of rules, one which refers to substitutional solid solutions, and another which refers to interstitial solid solutions.

Hume-Rothery Rules

Hume-Rothery Rule 1:Atomic Size Factor Rule. The atomic radii of the solute and solvent

atoms must differ by no more than 15%: Extensive substitutional solid solution occurs

only if the relative difference between the atomic diameters (radii) of the two species is less than 15%. If the difference >15%, the solubility is limited.

Hume-Rothery Rules

Hume-Rothery Rule 2:Crystal Structure Rule . The crystal structures of solute and solvent

must match. For appreciable solid solubility, the crystal

structures of the two elements must be identical.

Hume-Rothery Rule 3: Valency Rule . Maximum solubility occurs when the solvent

and solute have the same valency. Metals with lower valency will tend to dissolve metals with higher valency.

A metal will dissolve a metal of higher valency to a greater extent than one of lower valency.

Hume-Rothery Rules

Hume-Rothery Rule 4: The Electronegativity Rule The solute and solvent should have similar

electronegativity. If the electronegativity difference is too

great, the metals will tend to form intermetallic compounds instead of solid solutions.

Interstitial solid solution

Interstitial solid solutions are formed if a solute is smaller than the pores in the lattice

of a solvent

a solute has approximately the same electronegativity as a solvent.

There are very few elements that create ions, small enough to fit in interstitial positions, therefore, appreciable solubility is rare for interstitial solid solutions.

Ions that often may be a solute in solid solutions are: H, Li, Na, B.

Hume-Rothery Rules

For interstitial solid solutions, the Hume-Rothery rules are:

Hume-Rothery Rule 1:

Solute atoms must be smaller than the pores in the solvent lattice.

Hume-Rothery Rule 2:

The solute and solvent should have similar electronegativity.

Intermetallic compounds

Ordered intermetallic compounds are formed if the components have very different electronegativity.

Classification scheme for alloys.

Superalloys

Superalloys is a name for a group of alloys that retain high strength at elevated temperatures.

The main strengthening mechanism is preventing grain boundaries from sliding via dislocation.

Most of the superalloys are Substitutional solutions, where one of the components tends to form covalent bonds (Al in Ni3Al, W in Ta or Nb.)

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Diffusion in crystals

Theory of Alloys

Equilibrium Diagram

TTT Diagram

Heat Treatment

Recovery, Recrystallisation & Grain Growth

Module II