nuclear materials midterm

1, 2, 3

Materials

metals

ceramics

polymers /plastics

composites

nuclear materials

metals

strong & ductile

high thermal and electrical conductivity

opaque & reflective

ductile meaning

-material can be stretched/deformed without breaking

-ability to undergo plastic deformation (permanent) without breaking

opaque meaning

light does not pass through the material (not see-through)

ceramics

ionic bonding (refactory)

oxides, carbides, nitrides, silfides

brittle, glassy, elastic

non-conducting (insulators)

examples: building brick, glass vase, a teacup

ionic bonding

bonding of oppositely charged ions

refactory meaning

refactory = heat resistant

material is able to withstand very high temps without melting or breaking down

brittle meaning

material breaks with little deformation

elastic

returns to its original shape after deformation

polymers / plastics

covalent bonding

soft, ductile, low strength, low density

thermal & electrical insulators

translucent or transparent (see-through)

covalent bonding

sharing of electrons between atoms

insulators

does not conduct heat or electricity very easily

composite materials

materials composed of two or more individual materials (metals + polymers + ceramics)

composite purpose

to achieve a combination of properties that a single material cannot provide and combine the best characteristics of its components

naturally occurring composites

wood and bone

composite materials Examples

fiberglass & CFRP (carbon fiber-reinforced polymer)

fiberglass: glass fiber + polymer (epoxy) = strong, stiff, and flexible

CFRP: carbon fiber + polymer (epoxy) = Stronger and stiffer but expensive

stiff meaning

resists deformation

what does the nuclear reactor do?

nuclear reactions produce a large amount of thermal energy through fission CHAIN REACTIONS

nuclear reactors are simply heat-generating units

nuclear reactor process

reactor —> heat —>(produces steam)—> turbine rotates —> generator rotates —> electricity

what is the purpose of steam

steam is needed to rotate the turbines

what is the purpose of turbines

to rotate electrical generators which produces electricity

nuclear reactor primary loop

reactor side

contains components responsible for generating and managing heat

components:

-fuel: material where nuclear fission occurs

-neutron source

-moderator: slows down neutrons

-reflector: redirects escaping neutrons towards reactor

-control rods: controls the chain reaction

-coolant: removes heat

-shield: protection from radiation

-supporting structure

nuclear reactor secondary loop

power generation side

contains components responsible for converting heat into electrical power

components:

-heat exchanger: transfers heat between fluids

-turbines

-electrical generators

-condenser: converts steam back into liquid water

-cooling tower

material selection

general consideration

-Fabricability

-dimensional stability

-corrosion resistance

-design

-heat transfer

-availability and cost

fabricability

a) definition

b) why is it important?

a) how easily the material can be made into the required shape/component (forming, welding, machining)

b) if fabricability issues are not dealt with during the first stage, it may cause problems at later stages.

dimensional stability definition

the material should keep its shape and properties over time, especially at high temperatures

corrosion resistance definition

corrosion: electrochemical process that causes metals/alloys to degrade in a chemical environment

corrosion resistance: the ability to resist corrosion degradation

design definition

components designs’ should avoid stress concentration shapes such as sharp corners or holes.

heat transfer definition

in a reactor, heat must move safely from the fuel through the cladding

high thermal conductivity is important

material selection

special consideration

-neutronic properties

-susceptibility to induced radioactivity

-radiation stability

neutronic properties

how the material interacts with neutrons

fuel cladding materials should have low neutron absorption cross section - so that is why zirconium alloys are used in LWR (light water reactor)

control materials need high neutron absorption to control the chain reaction

susceptibility to induced radioactivity

when some materials absorb neutrons, they become radioactive themselves. which produces radioactive isotopes that can emit alpha, beta, or gamma radiation.

radiation stability

how well a material withstands radiation damage

fast neutrons can displace atoms from their positions, creating defects inside the material.

fuel cladding

material that surrounds and contains the nuclear fuel

zirconium-based materials are suitable for fuel cladding in LWR

advantages of zirconium-based materials for fuel cladding

low neutron absorption cross section

corrosion resistance

thermal conductivity

high melting point

high-temp strength

ductility

fuel compatibility

fabricability

abundance

cost

semiconductors

material whose electrical properties are intermediate between conductors and insulators

doping

adding impure atoms to a semiconductor

adding even a tiny amount of another element to a semiconductor can greatly change how well it conducts electricity

types of doped semiconductors

-N-type (extra electrons)

example: Si doped with phosphorus (P) leaves one extra electron which conducts more electricity

-P-type (missing electrons=creates holes)

example: Si doped with boron (B) leaves us with one electron missing which creates a hole.

semiconductors advantages

reliability

compactness

low cost

controlled electrical conduction

applications of semiconductors

transistors

diodes

photosensors

superconductors

allows current to flow unimpeded (without being opposed/obstructed)

has zero electrical resistance

biomaterials

materials used in components which are implanted into the human body to replace diseased/damaged body parts

must be non-toxic and biocompatible (compatible with body tissues and doesn’t cause opposing biological reactions)

biomaterials materials

metals

ceramics

polymers

composites

semiconductors

crystalline materials

materials whose atoms are arranged in a regular, repeating three-dimensional pattern over large atomic distances.

this is called long-range order

examples: metals, many ceramics, some polymers

noncrystalline materials

also called amorphus

materials whose atoms dont have a periodic arrangement over large distances

noncrystalline arrangements can occur in complex structures or with rapid cooling

unit cell

the basic repeating block of a a crystal structure

lattice

a periodic arrangement of points in 3D space

basis

atom or group of atoms associated with each lattice point

crystal structure

the way atoms are arranged in a space

lattice + basis = crystal structure

crystal system

crystal system classifies lattice geometry (edge lengths: a,b,c) and symmetry (angles: alpha, beta, gamma)

primative unit cell

contains one lattice point

non-primative unit cell

contains more than one lattice point

SC

simple cubic

-atoms at the 8 corners

-1 atom per unit cell (N=1)

-coordination number = 6

-a = 2R

-APF=0.52

SC

simple cubic

-atoms at the 8 corners

-1 atom per unit cell (N=1)

-coordination number = 6

-a = 2R

-APF=0.52

BCC

body-centered cubic

-atoms at the 8 corners + 1 body center

-2 atom per unit cell (N=2)

-coordination number = 8

-a = 4R/root(3)

-APF=0.68

FCC

Face-centered cubic

-atoms at the 8 corners + 6 face centers

-4 atom per unit cell (N=4)

-coordination number = 12

-a = 2root(2)R

-APF=0.74

how to count atoms (N)

corner atomic position —> 1/8

face center —> ½
body center —> 1

coordination number

number of nearest-neighbor atoms surrounding a given atom

drawing FCC

1- draw a cube

2- put one atom at each of the eight corners

3- put one atom at the center of each of the six faces, including the hidden faces

which of the three structures (SC, FCC, BCC) is the most efficient

FCC has the highest atomic packing factor of the three structures

so its atoms are packed most efficiently

HCP

hexagonal close-packed structure

-atoms at the 12 corners + 2 face centers + 3 body centers

(N = 12×1/6 + 2×1/2 + 3) = 6

-6 atoms per unit cell (N=6)

-coordination number = 12

-APF=0.74

Diamond

N=8

coordination number = 4

HCP stacking sequence

ABABAB…

miller indices

miller indices are used to identify crystallographic directions and planes in a crystal

miller indices notations

(x, y , z) — coordinates of a point

[uvw] — one crystal direction

〈uvw〉 — family of equivalent directions

(hkl) — one crystal plane

{hkl} — family of equivalent planes

family of directions

directions that are equivalent due to crystal symmetry

example:

in a cubic crystal: [100], [010], and [001] belong to the same family — 〈100〉

how to calculate miller indices for directions

1. identify the starting point (tail) and the ending point (head)

2. subtract head by tail (head-tail)

3. if necessary, convert coordinates to unit-cell length by dividing x by a, y by b, and z by c.

4. if we have a fraction, divide all components by the same number to get the smallest whole number.

5. if we have a negative number, replace the negative symbol with a bar (line) above it in the final answer

6. write the results in square brackets [uvw]

what if direction doesnt pass through the origin (0, 0, 0)

draw a straight line through the origin

two parallel arrows pointing the same way have the same direction indices. meaning translating an arrow without rotating, doesnt change its direction.

Bragg’s law

n: order of reflection

Lamda: x-ray wavelength

d: distance between parallel crystal planes

Theta: angle between x-ray beam and crystal plane

What causes constructive interference

Path difference equals an integer number of wavelengths

BBC reflection rule

h+k+l must be even

FFC reflection rule

h, k, l must all be odd or all even

Crystal defects

An irregularity or imperfections in the normal crystal lattice

Some defects help improve material properties

Defect types

Point defects

Line defects

Interfacial defects

Volume (bulk) defects

Line defects

1D

Examples:

Dislocations (edge, screw, mixed)

Line defects

1D

Examples:

Dislocations (edge, screw, mixed)

Interfacial defects

2D

Examples:

Grain boundaries, phase boundaries

Volume defects

3D

Examples:

Cavities, voids, precipitates

Vacancy

An unoccupied lattice site where an atom should normally exist

Vacancies increase entropy which can lower free energy of the crystal

Self insistial

A host atom occupies an interstitial space instead of a normal lattice site

Self interstitials produce large lattice distortions because the atom is crowded into a small space

Divacancy and binding energy

A pair if neighboring vacancies

BE: the energy required to separate a divacancy into two isolated vacancies

Frenkel defects

An ion moves from its normal position into an interstitial site, creating a vacancy-interstitial pair

-vacancy + interstitial

Volume, mass, density = unchanged

Important for ionic crystals and nuclear materials exposed to radiation damage

Schottky defect

A positive ion (cation) and a negative (anion) leave their lattice sites, creating paired vacancies

-two vacancies = mass+volume increase = density decreases

Frenkel and schottky defect

Both defects preserve electrical neutrality

Temperature effect on vacancy

As temp increases, vacancy concentration increases

Vacancy concentration formula

N(v): number of vacancies

N: number of atomic sites (per m³)

Q(v): vacancy formation energy (J/mol or eV/atom)

K: boltzmann constat

T: temp in kelvin

Vacancy fraction

The ratio of vacancies to total atomic sites

Number of atomic sites (or number of atoms)

p: density

N(A): avogadro’s number (6.022E23)

A: atomic weight

Celsius to kelvin

T(k)=T(C)+273

Scattering

The change in direction of a wave when it interacts with an obstacle such as atoms in a crystal

Diffraction

Waves scatter by regularly spaced obstacles interfere with one another, producing reinforcement under suitable conditions

Edge-dislocation Burgers-vector relationship

The burger vector is perpendicular to the dislocation line

Screw-dislocation

Burger-vector

Relationship

The vector is parallel to the dislocation line

mixed dislocation

Burgers-vector

Relationship

The burger vector is at an oblique angle to the dislocation line

Grain boundary

A boundary separating two neighboring crystals with different orientations

Low angle grain boundary

Boundary with small misorientation angle

Modeled as an array of dislocations

High angle grain boundary

A boundary with large misorientation angle and greater atomic mismatch

Grain size effects

Smaller grains provide more grain-boundary area and generally increases yield strength

Hall-patch Strengthening

The strengthing effect cause by grain boundaries

Cause of screw dislocation

A shear stress that displaced one part of the crystal relative to another