Materials Midterm 2

diffusion, diffusion and ion conductors, phase diagrams I II, nano materials, ceramics, composites, electrical properties

diffusion net motion direction and speed

from high to low concentration, happens quickly in liquids and gases

interdiffusion

in an alloy, atoms tend to migrate from regions of high concentration to regions of low concentration

diffusion is driven by ____ but atoms must move via _____.

concentration gradients, specific mechanisms

two types of diffusion mechanisms in solids

vacancy diffusion and interstitial diffusion

vacancy diffusion rate depends on

number of vacancies, activation energy to exchange

interstitial diffusion

smaller atoms can diffuse between atoms

vacancy and interstitial diffusion comparison chart

case hardening

diffuse carbon atoms into host iron at the surface, iron (steel) becomes harder

semiconductor processing

deposit phosphorous on silicon surface, heat it, doped semiconductor regions

rate of diffusion: diffusion coefficient ____ with increasing T

increases

diffusion coefficient equation

D = Do exp ( -Qd / R*T )

activation energy

___ (Q) is required to squeeze atoms past one another during diffusion. generally, more energy is required for a substitutional atom than for an interstitial atoms.

example of different diffusion coefficients in silicon chart

same material, different atoms, orders of magnitude difference

diffusion coeffcient: example

@ 300 deg C the diffusion coefficient and activiation energy for Cu in Si are:
D(300 deg C) = 7.8E-11 m²/s
Qd = 41.5 kJ/mol
What is D @ 250 deg C?

D = 15.7E-11 m²/2

rate of diffusion (fick’s first law)

J = -D (dc/dx)

J is flux, D is diffusion coefficient, dc/dx is concentration gradient

flux during diffusion

the number of atoms passing through a plane of unit area per unit time

fick’s second law

dC/dt = D * d²C/dx² (partials not normal d)

diffusion factors chart (rate)

____ controls materials processing and performance

diffusion (heat treatment, doping, batteries, alloys)

ion conductor

material that allows ions (charged atoms or molecules) to move through it, enabling the transport of electrical charge without the flow of electrons

how does ion conduction work?

ions move through medium, move occurs due to electric fields, concentration gradients or temperature, charge is carried by ions not free electrons

ion conduction is driven by ___ , produces ____

concentration gradient and electric field, electrical current

ionic versus electronic conductivity comparison

__ crystals do not conduct ions

perfect, defects are essential (schottky defects (paired vacancies, frenkel defects (vacancy + interstitial))

vacancy migraton

ion hopes into neighboring vacancy (requires lattice distortion, energy barrier determines mobility)

interstitial mechanims

direct interstitial hopping (often faster for small ions)

ionic conductivity equation

sigma = n x mu x q

structural features of good conductors

open frameworks, connected pathways, low activation barriers

types of ion conductors

liquid electrolytes, polymer electrolytes, solid-state eelctrolytes

ion conductors in batteries

phase

homogeneous in chemical composition, physics properties, uniform crystal structure, separated by boundaries

phase diagram

plots the equilibrium phase as a function of composition, temperature and pressure

equilibrium phase depends on:

temperature pressure and composition

gibbs free energy

the stable phase is the one with the lowest gibbs free energy

equilibrium and free energy graphically

equilibrium (stable) state exists at the lowest point on free energy diagram, unstable state is on a slope and transforms rapidly into metastable/stable phases, metastable state is local minimum and transforms slowly

phase boundary

set of conditions where two phases have equal free energy

unary phase diagrams axes

typically temperature and pressure

triple point

three phases, equal G

critical point

disappearance of liquid gas phase distinction

solubility limit

maximum amount of solute that can added before forming a new phase

binary isomorphous phase diagram

exhibit complete liquid and solid solubility, contain two single-phase regions

binary eutectic phase diagrams

eutectic: a system in which a single composition melts and solidifies at a lower temperature than the individual components of any other mixture

why is salt more effective than sugar for keeping streets from icing over?

the minimum freezing temperature for sugar and ice is around 7 degrees C warmer than ice and salt. you need a large % of sugar before there is a noticeable decrease in freezing temperature, salt begins decreasing the freezing temperature linearly.

determine phase composition and fraction table

why do phase transformations matter?

properties depend on microstructure, microstructure depends on how phases form, phase diagrams only tell eq phases

__ predict eq phases

phase diagrams

steel phase diagram

TTT diagram

time temperature transformation digram, describes how fast a phase transformation occurs at a constant temerpature

TTT diagrams predict and help:

predict when transformations start and finish, help determine resulting microstructures

austenite transformation in steel summary

high T yields pearlite, intermediate T yields bainite, rapid quenching yields martensite

microstructure control properties: pearlite, bainite, martensite

p: moderate strength, good ductility

b: strong and tough

m: very hard but brittle

nanomaterials and light

strong and unusual interactions with light

what happens when materials are smaller than light?

optical properties are determined by the band structure of the material, in nano materials shape size determine optical properties

why nanomaterials are special?

large surface to volume ratio, many surface atoms, quantum confinement of electrons, interacts with light

nano and light

quantum dots: color depends on particle size, photonic crystals: nanostructure controls light

ceramics can be () or (); atomic structure contians strong covalent or ionic bonds

amorphous, crystalline

key ceramic properties

brittle, strong at high T, insulators

why are ceramics brittle?

atoms cannot slide easily, charges repel, bonds are directional

the more electronegativity difference the more ionic the bond, this produces what property of ceramics

strength

ceramic ocide crystal structure

oxygen anions much larger than metal cations, close packed oxygen in lattic (FCC) cations in the holes of oxygen lattice

visualizing coordination

coordination number (CN)

the number of nearest enighbor ions surrounding a central ion

radius ratio formula

radius of cation/ radius of anion

radius ratio predicts

the crystal structure based on the size of the hole the cation can stably occupy (ion size determines structure)

crystalline versus amorphous properties

amorphous tend to be transparent and let light pass though, crystalline show greater strength, stability at high T, and are opaque from scattering light

polymers (many repeating units)

type of macromolecule, have large molecular weights

a long chain made of repeating small units

polymer (monomer)

the __ of polymer chains determines mechanical behavior

structure

chain flexibility in polymers

polymers chains are not straight, can bend twist and rotate

copolymer shapes

two or more monomers polymerized together

molecular weight

mass of a mole of chains (longer chain has higher M)

polymers have chains of different length so use:

average molecular weight

resistance (R) of a wire depends on:

resistivity of the material and geometry of the wire

resistivity (rho)

property of the material itself rho = R * A/L

electrical conductivity is the inverse of

resistivity (sigma = 1/ rho)

band gaps graphic