Metals and Alloys: Diffusion

Topic 4 – Metals and Alloys

Topic 4.1 Diffusion

• Diffusion involves mass transport through atomic motion
• Gases and liquids diffuse randomly(Brownian motion)
• Solids diffuse via vacancies or interstitials movements

Driving Force of Diffusion

• Diffusion occurs from areas of high concentration to low concentration attempting to equalize concentration gradients

Substitutional Diffusion

• Atoms move via vacancy jumping
• Vacancy diffusion requires a vacancy for the atom to move into
• The rate of substitutional diffusion depends on vacancy concentration and frequency of jumping
• Both vacancy concentration and frequency increase with temperature
• Inter-diffusion involves different elements, while self-diffusion involves the same element

Interstitial Diffusion

• Interstitial atoms diffuse between matrix atoms
• Faster than vacancy diffusion
• Increases with temperature

Diffusion at Grain Boundaries

• Diffusion is faster at grain boundaries and surfaces
• Dislocations also increase the rate of diffusion

Fick's First Law

• Fick's first law: 𝐽 = −𝐷(𝑑𝐶/𝑑𝑥)
• J represents flux in (kg m⁻² s⁻¹)
• D is the diffusion coefficient (m²/s)
• C is concentration (kg/m³ or mol/m³)
• dC is the change in concentration across distance dx
• x is the distance, typically in meters

Temperature Dependence of Diffusion Coefficient

• The diffusion coefficient (D) is temperature-dependent, following the equation: 𝐷 = 𝐷ₒ 𝑒(⁻^Qa/RT)
• D₀ represents the diffusion pre-exponent(constant) in m²/s
• Qd is the activation energy of diffusion in J/mol
• R represents the universal gas constant
• T represents the temperature measured in Kelvin

Fick's Second Law

• Describes non-steady-state diffusion

Topic 4.2 – Phase Diagrams

• Phase diagrams determine how composition and temperature affect microstructure and mechanical properties
• Phases are physically and chemically distinct material regions
• Solutions can be solid, liquid, or gas and are single-phase
• Mixtures contain more than one phase
• Phase equilibrium occurs when phases reach their lowest energy state which doesn't change over time

Phase Equilibria

• Phase diagrams map regions where a substance dissolves or remains undissolved with temperature and composition of variables
• Solubility limit indicates the maximum concentration for a single-phase solution
• Phase diagrams for alloys determine phases present, composition, and relative amounts at specific temperatures and compositions
• Alloys consist of liquid and solid solutions where solids can be stoichiometric compositions

Solid solutions

• Describes a material where one or more elements are dissolved in a solid

Phase Diagram Analysis:

• Rule 1: Knowing temperature (T) and composition (Co) determines the phases present
• Rule 2: Determine the composition of each phase at a given T and Co
• The process involves drawing a tie line across the phase field
• Rule 3: Phase fraction or % of each phase at a given T and Co
• The Lever rule is used

Microstructure Prediction

• Microstructural changes during cooling can be predicted using phase diagrams

Eutectic Reaction

• Describes when a liquid cools into two solid phases without a solid/liquid transition

Eutectic Microstructural Developments

• Room temperature depends on alloy composition relative to the eutectic point, resulting in varying micro structures

Topic 4.3 – Dislocations and Strength in Metals

Dislocations

• Dislocations are line defects responsible for plasticity in metals, decreasing alloy strength
• Plasticity and strength in metals depend on dislocations and the force needed for movement

Dislocation Motion

• Dislocation motion is called slip, involving the movement of an edge dislocation over adjacent atomic planes
• If dislocations cannot move, plastic deformation is impossible
• Dislocations move along a slip plane in a slip direction

Slip Systems

• Slip is easiest on close-packed planes (slip plane) and in close-packed directions (slip directions)
• Structures can have slip on multiple planes and directions

Slip in Single Crystals

• Results in a step-like deformation along the slip plane

Slip in Polycrystals

• Stronger than single crystals due to grain boundaries which are barriers to dislocation motion
• Grains have different orientations, that is why it slips on different planes

Strengthening Alloys:

• There are four main strategies to improve the strength in alloys
• Reduce grain size
• Solid solution strengthening
• Precipitation strengthening
• Dislocation strengthening
• Inhibiting dislocation motion increases the applied force needed to move them

Reduce Grain Size

• Grain boundaries act as barriers to dislocation slip
• Smaller grain size means more barriers
• Hall-Petch Equation helps with this: σyield = σo + kyd-1/2
• The aim of many industrial processes is to reduce grain size

Solid Solution Strengthening

• Both interstitial and substitutional elements causes solute strengthening
• Location in the lattice causes and forms and this inhibits the motion of dislocations
• The bigger the difference in size between the solute and solvent which causes a larger strengthening effect
• Alloying elements are able to concentrate around dislocations, forming a "dislocation atmosphere," which decreases the mobility of dislocations and increases strength

Precipitation Strengthening

• Dislocation motion is inhibited by precipitates in the lattice.
• Small precipitates can be sheared
• Larger precipitates need to be bypassed which requires an extra applied force.

Dislocation Density (Work Hardening)

• Dislocation density increases by increasing force strain and create dislocations within the microstructure
• Plastic deformation increases density by 10,000 times
• Dislocations entangle with one another during force work
• This makes dislocation motion more difficult, which in turn increases alloy strength