04 Imperfections in Solids Flashcards
- Describe both vacancy and self-interstitial crystalline defects.
Point defects are those associated with one or two atomic positions; these include vacancies (or vacant lattice sites) and self-interstitials (host atoms that occupy intersitial sites).
- Given the density and atomic weight for some material, as well as Avogardo’s number, compute the number of atomic sites per cubic meter.
of atomic sites = # of atoms (per cubic meter) =: N
N = NA*density/molar mass
[atoms/m3] = [atoms/mol] * [g/m3] / [g/mol]
molar mass = atomic mass = atomic weight
NA…Avogadros number = 6.022E23 atoms/mol
see Exercise 3 - Problem 1
- For some material, given the number of atomic sites per cubic meter, the energy required for vacancy formation, and, in addition, the value for the gas constant, compute the equilibrium number of vacancies at some specified temperature.
? How should this work without knowing the temperature or at least the pressure ?
pV = kNT = nRT
R = k*NA
pressure p [Pa] and Volume V [m3]
k…Boltzmann constant
NA = Avogadros number [atoms/mol]
N…number of atoms/molecules [atoms]
n…amount of gas [mol]
R…gas constant [J/molK]
T…temperature [K]
- Define what is meant by the term alloy.
An alloy is a metallic substance that is composed of two or more elements.
- Name the two types of solid solutions, and provide a brief written definition and/or schematic diagram of each.
soltution := a homogeneous mixture composed of two or more substances
a solid solution (ss) may form when impurity atoms are added to a solid, in which the original crystal structure is retained (“bewahrt”) and no new phases are formed. The new substances only occur as impurities in the solid. However, even a new second phase can be formed depending on the kinds of impurity, their concentrations and the temp. of the alloy.
- type: substitional ss - impurity atoms substitute for host atoms
- type: interstitial ss - form for relatively small impurity atoms that occupy interstitial sites among the host atoms
- State the criteria for the formation of each of substitutional and interstitial solid solutions.
criteria for the formation of substitutional ss and appreciable solubility of the solute in the solvent (Hume-Rothery rules):
- atomic diameters and e-negativities for both atom types are similar
- both elements have the same crystal structure
- impurity atoms have a valence that is same or less than the host material
example for the octahedral (coordination number = 6) and tetrahedral (c.n. = 4) interstitial sites in a FCC crystal structure is Na+ in Cl-
- Given the atomic radii of host and impurity atoms, as well as their crystal structures, electronegativities, and valences, determine if solid solutions that form are
(a) substitutional with appreciable solubility,
(b) substitutional with limited solubility, or
(c) interstitial.
?
- Given the masses and atomic weights of two or more elements in a metal alloy, compute the weight percent and atomic percent of each element.
it is often necessary to express the composition (= concentration) of an alloy in terms of its constituent elements:
- weight percent C1
- atomic percent C1’
(b) Make a composition conversion from atom percent to weight percent.
formula 6.9 a,b and 6.10 a,b
Note that:
C1+C2 = C1’+C2’ = 100
if we assume that there are only 2 elements in the solution
- For each of edge, screw, and mixed dislocations:
(a) describe and make a drawing of the dislocation;
(b) note the location of the dislocation line; and
(c) indicate the direction along which the dislocation line extends.
dislocations are 1D crystalline defects of which there are two pure types:
a)
- edge - may be thought of in terms of the lattice distortion along the end of an extra half-plane of atoms
the Burger’s vector b is perpendicular to the dislocation line - screw - the upper front region of the crystal is shifted one atomic distance to the right relative to the bottom portion - a helical planar path/ramp is formed whereby the “symmetry line” is associated with the dislocation line
b is parallel (II) to the dislocation line - mixed - components of both 1. and 2.
b is neither perpendicular nor parallel
b) edge: the end of the extra half-plane of atoms is termed dislocation line
screw: see a) 2.
c) The magnitude and direction of lattice distortion associated with a dislocation are specified by its Burgers vector. Even though a dislocation changes direction and nature within a crystal, the Burger´s vector is the same for all points.
- (a) Describe the atomic structure within the vicinity of a grain boundary.
Interfacial (Planar) Defects: e.g. external surfaces, grain boundaries, phase boundaries, twin boundaries, stacking faults etc.
In the vicinity of a grain boundary (which is several atomic distances wide), there is some atomic mismatch between two adjacent grains that have different crystallographic orientations
(b) Make a distinction between high- and small-angle grain boundaries.
high-angle: angle of misalignment between grains is relatively large
small-angle: this angle is relatively small
(c) Explain how a small-angle tilt boundary is formed by an array of edge dislocations.
- Describe the arrangement of atoms in the vicinity of a twin boundary.
twin boundary: a grain boundary across which there is a specific mirror lattice symmetry; that is, atoms on one side of the boundary are located in mirror image positions to those of the atoms on the other side (see Fig 6.15)
- Note the role of surface defects in the operation of automobile catalytic converters, which reduce polluting exhaust emissions.
A catalyst is a substance which increases the rate of chemical reaction without being consumed
catalytic reactions normally occur at surface defect sites
a mixture of exhaust gases and introduced air passes over the catalyst, which on its surface adsorbs (=adhesion of atoms/ions/molecules to a surface) molecules of CO, NOx, and O2. The NOx dissociates into N and O. CO is oxidized to form CO2.
