Chapter 2 - Crystal Structure Flashcards
What does manufacturability depend on?
Crystal structure
Why do we use Zircaloy as fuel cladding?
Because of limited swelling due to underlying crystal lattice structure
What are metallic glasses?
metals without a crystal structure
What is the unit cell?
The smalles unit translation of space lattice that reproduces a macroscopic crystal
What are cubic crystals characterized by?
The number of lattice sites per unit cell
What are close packed planes?
The planes containing the highest atom density
What are close packed directions?
direction of smalles atomic separation
How do we determine the crystal strucutre?
X-ray spectroscopy
How do we specify planes and indices?
With millers notations
What crystalline structure is circonium?
HPC
What are ionic solids?
solids formed from electro-negative and -positive elements (cations and anions).
Name some examples of ionic solids in nuclear?
UO2 B4C
How are ionic solids sub-lattices represented?
mixture of simple lattices formed by the elements
What is the usual structure for MX solids?
The NaCl and the CsCl structure
What is the usual structure for MX2 solids?
box withing box
What are point deffects?
- Vacancy
- SIA
- Interstitial Solute
- Subtitutional Solute
Name the three type of mixed crystals?
substitutional random
substitutional ordered
interstitial
What determines solid solution or precipitation?
The hume rothery rules
What are the hume rothery rules?
Atom radius not more than 15%
Similar crystal structure
Small electro negativity difference
Number of valence electrons should be similar
What is the electronegativity?
Chemical potential of an element. It describes the tendency of a material to attract electrons.
What is the principal product of neutron irradiation of the structural metals in LWR?
highly non-equilibrium concentrations of vacancies and self-interstitials in equal numbers
What is the effect of a vacancy in the nearby atoms?
Attractive force of neighboring atoms into vacancy creates a tensile stress (strain) field which is elastic isotropic.
What is the equilibrium vacancy fraction a function of (#/atom sites)?
The gibs free energy of vacancies and the temperature. X = exp(-G/RT)
What does the gibs free energy of vacancies depends on?
Entropy, temperature and enthalpy. G=H-TS=E+pV-TS
What does the enthalpy depend on?
H depends on the energy of the vacancy, the pressure and the volume of the vacancy, H=E+pV
What is the energy of the vacancy?
E=Ne where N is the number of vacancies and e is the formation energy of single vacancy (1.5 +- 0.5eV)
What is the entropy dependant on?
The entropy is dependent on the number of vacancies and the vibrational entropy (0.5-3k)
Is there an alternate way of determining the equilibrium point defect concentrations?
Yes, by calculating the equilibrium constant Kv
What is the equilibrium constant for vacancies?
K = conc. of vacancies/conc. of sites
What are the three main mechanisms by which vacancies increase?
- Quenching
- Deformation
- Irradiation
- Temperature Increase
What test other than mechanical property tests exists to verify the increase in vacancy concentration?
Electrical resistivity which increases due to increased vacancy concentration
What are frenkel pairs?
a vacancy and a interstitial atom/ion
What are the recovery stages for irradiated metals with high vacancy concentration as the temperature is increased?
- Frenkel pairs collapse (recombination of vacancy and SIA)
- Interstitial clusters grow leading to small interstitial loops
- Vacancie migration and adualte at interstitial clusters
- the vacancy cluster surviving stage 3 grow in size and dissociate thermally.
How can you measure vacancies using positrons?
Since vacancies have lower electrond ensity positrons are traped for longer times and are therefore a mesure of vacancy density. In other sites vacancy and electron annihilate and gammas are emitted. No gammas are observed in high vacancy regions.
What should point defects in ionic crystals mantain?
local electrical neutrality
What is Schottky Defect
missing anion and cation
What is cation frenkel pair?
a cation site vacancy and a cation interstitial
What is anion frenkel pair?
a anion site vacancy and an anion interstitial
What are the 0 dimension al defects?
point defects (vacancies, interstitials, frankel pairs, shottkey defect, etc.)
What are 1 dimensional defects?
dislocations
What are 2 dimensional defects?
grain boundaries, interfaces, etc
What are 3d defects?
precipitates, pores, particles, inclusions, etc
Why do materials deform before theoretical stress is reached?
Because theory assumes all atomic bounds are moved at the same time which is not true.
How can you visualize dislocations?
With TEM since the crystal around a dislocation etches quicker than bulk
What does dislocations cause or lead to?
Introducing dislocaitons lead to a shape change of the crystal leading to elastic stress in the lattice
What is the poisson ratio?
the ratio of the fraction (or percent) of expansion divided by the fraction (or percent) of compression, for small values of these changes. Or describes the phenomena that a compressed material in one direction elongates in the other direction
What two phenomena do dislocations host and where?
Compression in the dislocations ide and tension in the normal part.
Can dislocations interact with dislocations? if so how?
Yes, dislocation annihilation is possible. The compression side attracs tension sides and can merge to “fix” dislocation.
How does the number of grains vary with respect to the crystal seeds?
few seed crystals lead to bigger and fewer grains and viceversa
What is the close packed plane?
Plane containing the highest atom density
What is the close packed directions?
the direction of smallest atomic serapation
What notation is it used to specify crystallographic planes and indices
miller notation
How are ionic sub-lattices usually represented?
a mixture of simple lattices formed by the elements.
What is the difference between a LWR and FR?
The energy spectrum of the neutron flux.
Why do we care about the energy spectrum of the reactor?
More energy means more radiation damage therefore it can cause reduced lifetime in traditional materials
What is the average neutron energy of a fast neutron?
0.5 MeV
What crystal structure does UO2 have?
cubic (fluorite)
What determines if an element stays in solid solutions?
The hume rothery rules
What is the energy per atom of a dislocation
7 eV
What is a schottky defect?
when a cation and anion leave the lattice site and create pair of vacancy defects.
What are the effects of schottky defect on electrical neutrality and density?
Electrical neutralitiy is still mantained but density reduces because of the vacancies
What is a frenkel defect?
when an ion leaves original lattice site and occupies an interstitial position on the same crystal
In a frenkel defect what ion is usually displaced?
the cation
What is the difference between a schottkey defect and a frenkel defect?
- Shottky occurs in ionic cyrstals where difference ins ize between cation and anion is small while in frenkely the difference is large.
- In shottky, both the cation and anion leave while in frenkely only the smaller ion leaves.
- In the shottky the pair leave the cyrstal completeley while in frenkely the ions stay
What happen to the point defects in the shotkey and frenkel defect?
In shottkey, both the anion and cation leave the crystal while in frenkel the cation creates a vacancy and gos to an insterstitial place
What are the two types of dislocations?
edge and screw dislocations
What do dislocations mean for the crystal?
Being a defect in the crystal lattice leads to shape change of the crystal leading to elastic stress in the lattice.
How are grain boundaries visualized and stacking faults visualized?
optical microscopy.
Why are dislocations important?
It introduces malleability and ductility to metals which cannot be explained using the simple model of layers slipping past one another. When a force is applied the dislocations move through the lattices sturcture (less force than that needed to produce a splip) because very few bonds are bing broken at any one time.
What are dislocations?
defect in the lattice structure in which a few ions in a layer are missing causing neighbouring layers to be displaced slightly to minimise the strain from the defect.
How do grain boundaries affect dislocations?
Dislocation movment is hindered by grain boundaries therefore making the metal stiffer and harder but also stronger.
How is the grain size correlated to strenght?
Fine grained stronger due to dislocation stops
How are dislocations created?
When stress is appleid to a material.
Where do dislocations end?
at a free edge or form a loop withing a cristal
What is a slip system?
set of symmetrically identical slip planes and associated family of slip directions for which dislocation motion can easily occur and lead to plastic deformation. The magnitude and direction of slip are represented by the Burgers vector.
How do dislocations move?
They move along the densest planes because the stress needed to move the dislocations increases with the spacing between the planes. FCC and BCC metals have many dense planes, so dislocations move relatively easy therefore being more ductile.
How are materials strengthened?
By making it more difficult for dislocations to move by introducing instertiail atoms or grain boundaries.
Can dislocations impede dislocation movement?
as a material plastically deforms, more dislocations are produced and they will get into each others way and impede movement. This is why strain or work hardening occurs.
What is strain
Strain is the response of a system to an applied stress. When a material is loaded with a force, it produces a stress, which then causes a material to deform. Engineering strain is defined as the amount of deformation in the direction of the applied force divided by the initial length of the material.
How do dislocations interact with each other?
Two dislocations of the same sign moving on the same slip plane exert a repulsive force on each other, which causes them to repel each other. while opposing sing causes anhiliation.
What are stacking faults?
stacking fault is a type of defect which characterizes the disordering of crystallographic planes. It is thus considered a planar defect
What do stakcing faults have to do with dislocations
As the partial dislocations repel, stacking fault is created in between. By nature of stacking fault being a defect, it has higher energy than that of a perfect crystal, so acts to attract the partial dislocations together again. When this attractive force balance the repulsive force described above, the defects are in equilibrium state
Where do precipitates accumulate on the material?
precipitates on dislocations and grain boundaries.
What is a darken gurry map
it is a graph of electronegativity vs ionic radii where the inner circle represents complete solubility and the outer circle partial solubility. It is graph for each element.
Why do materials deform before the theoretical stress is reached?
dislocation movement.
What is the average dislocation density in an annealed metal?
10^10 to 10^12 /m2
What is the average dislocation density in a deformed metal?
10^14 to 10^16 /m2
What is the density change in a deformed metal relative to that of the annealed metal?
10^2 to 10^6 /m2 more
What is the energy per atom of a dislocation?
7 eV
Can a dislocation end in the middle of the crystal?
No, it only ends on interfaces or form loops.
What is the frank read source?
is a mechanism explaining the generation of multiple dislocations in specific well-spaced slip planes in crystals when they are deformed. When a crystal is deformed, in order for slip to occur, dislocations must be generated in the material. This implies that, during deformation, dislocations must be primarily generated in these planes. Cold working of metal increases the number of dislocations by the Frank–Read mechanism. Higher dislocation density increases yield strength and causes work hardening of metals.
Does the dislocation reduce or increase the stress require to plastically deform materials?
It reduces the stress needed.
What is orowan looping?
Precipitates act as pinning points for dislocations and bowing leads to unpinning leaving behind dislocation loops around the precipitate particles
What is the coordination number?
how many equidistant neighbors a given atom is surrounded by
What is the coordination number for BCC?
8
What is the atomic packing factor
the volume of space occupied by atoms in a unit cell
What is the APF for BCC?
0.68
Why are close packed planes important?
Because the discance between close packed planes are the larges in the crystal resulting in weaker bonds which makes them likely sites for split to ocurr.
What is the coordinat number of FCC?
12
What is the atomic packing factor of FCC?
0.74
Which is the densest cubic system posible?
FCC
Which material is more densely packed? Fcc or bcc?
FCC
Name three common m aterials that adopt FCC?
gamma-Fe, Ni, Al
Name three common m aterials that adopt BCC?
alpha-fe, beta-zr, cr, Mo
What is the coordinat number of HPC?
12
What is the atomic packing factor of FCC?
0.74
What is the difference between the FCC and HPC?T
The stacking sequence
Is HPC isotropic or anisotropic?
Anisotropic
What does being anisotropic mean?
Mechanical properties vary with direction they are measured in
What is the most famous HPC element in nuclear systems?
Zr
wHAT IS THE ENERGY ASSOCIATED with creating a vacancy?
1 eV
What is a SIA?
a lattice atom occupies an interstitial site instead of a regular position since the interstitial site is smaller than the atom size, this puts strain on the surrounding lattice
What is the energy associated with the formation of SIA? What does this mean in terms of vacancy and SIA concentration?
4 eV, since the energy is higher the eq. concentration is much smaller.
Are vacancies created just by thermal energy? How about SIAs
Yes but not sufficient to create SIA so these are only generated under radiation or stress.
What are interstitial solutes?
solute atoms with sizes much smaller than the parent atom size – can occupy interstitial spaces easily. These can be on purpose or impurity
What are the benefits of on purpose interstitial solutes?
solute atoms in the alloy that increase strength and can reduce unwanted impurity atoms
What is an interstitial solid solution?
homogeneous mixture of two or more kinds of atoms, at least one of which is dissolved in the hose lattice by occupying the interstitial sites
- most common interstitials = elements with relatively small atomic radii
What are common interstitial solutes?
H, O, N, B, C
What are the two rules that must be met for interstitial solid solutions?
1) Solute atoms must be smaller than the interstitial sites in the solvent lattice (Note: in practice, extensive interstitial solubility results only if the apparent solute atom diameter is 0.59 smaller than that of the solvent)
2) The solute and solvent should have similar electronegativity
What are substitutional solid solutions?
solute atoms substitute the parent lattice atoms in their original sites
What is the name of the rules for substitutional solid solutions
hume rothery rules
What is a frenkel defect?
an ion leaves its original lattice site creating a vacancy, and becomes an interstitial by moving into a nearby interstitial space (it is a pair of vacancy and interstitial)
What is the schottkey defect?
composed of differently charged pairs of vacancies – unique to ionic compounds only
Why are dislocations important
they accommodate plastic deformation via slip. If there are too many dislocations around or there are too many obstacles to their motion, the material’s ability to deform at a given stress level is inhibited.
Are dislocations equilibrium defects? Why?
No, Because the energy associated with dislocations is higher than the resulting increase in enthalpy
How are dislocations created?
they are created during solidification, cooling, and mechanical working
How are dislocations introduced?
introduced into the crystal in a nonequilibrium fashion due to mechanical stresses, thermal stresses, collapse of vacancies, precipitation growth, or exposure to high-energy radiation
How does plastic deformation beging?
occurs via planes of atoms slipping against each other, along certain crystallographic directions
how to observe dislocations?
x-ray topography and tem
What is an edge dislocation different than a screw dislocation?
the edge dislocaiton si complete while the screw is incomplete
How can edge dilsocation smove?
glide and climb
how can screw dislocations move?
glide and cross slip
How can materials plastically deform?
- by dislocation slipping
2. and by twinning
How are stacking fault tetrahedra created?
quenching and radiation damage
What is the effect of stacking fault tetrahedra?
These are also obstacles for dislocation motion therefore introducing hardening and embrittlement.
What is slip?
movement of one crystal part over another causing plastic deformation
What is the critical resolved shear stress
the critical value of shear stress required to initiate slip on the slip plane in the slip direction
What is the peierls nabarro stress?
The stress needed to move a dislocation in a particular direction of the crystal
Why are dislocations in freshly grown crystals formed?
- Preexisting dislocations in the freshly grown crystals
- accidental nucleation
- heterogeneous nucleation of dislocations
What is the packing fraction of BCC?
0.68
What is the packing fraction of FCC?
0.74
Is the separation of close packed planes higher or lower for BCC and FCC?
FCC has closer packed planes and therefore closer nearest neighbor distance
What is the formula relating the wavelength of the xrd and the spacing between planes?
nlambda = 2dsin(theta)
What atomic radius difference is optimal for complete solubility?
8%
What is the formula for atomic radius difference?
ra - rb / ra
How does solubility behave with increasing valence electrons?
As valence electrons is increasing the solubility reduces
What values should the electronegativity difference have to be intermetallic compound or substitutional solid solution?
electronegativity difference close to 0 gives max. solubility meaning probable formation of intermetallic compound. As this difference increases a substitutional solid solution is formed.
What is bigger, the octahedron site on the bcc or fcc structure?
the octahedron site in the fcc and therefore the solubility is higher.
What is the slip plane in BCC?
110
What is the slip plane in FCC?
111
hOW DO WE MANTAIN the large number of vacancies at high temperatures?
by quenching which ensures these are retained at room temperature
What is the orowan equation?
it realtes macroscopic strain rate to the microscopic parameters such as dislocation density, velocity and burgers vector
Which structure is more relaxed? Bcc? or FCC?
BCC making it more swelling resistant.
What is the swelling percent per dpa of FCC Fe-35Ni-Cr alloys?
1%/dpa
How is martensite formed?
- Ferrite steel heated to an austenite solution
- transformed into bct martensite air cooled
- further cooling creates bcc ferrite matrix with accompanying precipitates
What two types of precipitates can be found in martensite?
M-Carbon and M-Nitrogen
What metals form precipitates in martensite?
Cr, Fe, Mn, Mo, W, Nb, V
Where are the carbide precipitates located in the martensitic microstructure?
- subgrain boundaries,
- martensite lath
- packet boundaries
- prior austenite grain boundaries
Is chromium a ferrite or austenite stabilizer?
ferrite
Where do precipitates concentrate mainly in austenite?
grain boundaries
What is the swelling rate for BCC martensite % /dpa
0.2%/dpa
superior swelling behaviour of ferritic/martensitic steels was attributed to ?
the high number density of precipitates in the tempered martensite microstructure
Swelling requires void formation. What needs to happen to stabilize these?
Under irradiation these are stabilized by gaseous atoms like Helium
Where does void formation occur? Precipitate deficient or rich regions? What does this mean in terms of swelling in austenitic or martensitic steels?
precipitate defficient. Since austenitic is precipitae defficient it allows for high rates of swelling while martensitic has a lot of natural preipitates therefore being highly swelling resistant
even though a high precipitate density is avaliable in martensite do bubbles still appear?
Yes, even though ther eis a limited amount of irradiation-induced helium in steels irradiated in fast reactors. Nano-size bubbles form on precipitates
and boundaries but never reach critical size for void growth
Why is less helium in fast reactor steels?
Because of the lower nickel content.
Do we need to minimise martensite lath size or maximize to avoid swelling? Why?
Minimize to eliminate delta ferrite and precipitate deficient volume where swelling predominately occurs
