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MATLS 2X03
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Igor Zhitomirsky
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Final

# Final Exam Summary Notes

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McMaster University

Materials Science and Engineering

MATLS 2X03

Igor Zhitomirsky

Fall

Description

2X03 – Crystallography
Note: bar-1 = ̅
Definitions
Term Definition
Amorphous Have no well-defined shape. Break to give curved/irregular
faces. Soften and melt over range of temperatures.
Crystal A solid material that has discrete diffraction patterns
Ferroelectric Has 2 orientation states in the absence of an electric field.
Can be shifted from 1 to another of these states by an electric
field.
Frenkel Defect A type of point defect where an atom/ion is displaced from
regular position to an interstitial one
Glide Plane Plane at which the crystal is reflected and then translated.
Heteropitaxy Has different substrate and film materials
Homoepitaxy Has the same substrate and film material
Inorganic Periodic All are in order and are in a solid state. Every cell is the same
Crystals as before.
Inversion Corresponding points are located equidistance from the
centre on a line drawn through the centre
Neutron Diffraction Highly penetrating. Lighter materials can be seen. Small
magnetic moment.
Pauling’s Rules – 1 of 3 A coordinated polyhedral of anions A formed around cation X
has
X-A distance calculated by r xrAand coordination number r /rx A
Pauling’s Rules – 2 of 3 -ΣpI(i=1,m) of the m Pauling’s bond strengths p cilculated for
each (X-A) iond formed by an anion is equal to the charge
on the anion
Pauling’s Rules – 3 of 3 Sharing the faces (and edges) between coordination
polyhedral decreases the stability of the structures.
Particularly in the case of cations with large charge and low
coordination number.
Piezoelectric Effect – Production of strain in crystals by the application of an electric
Converse field
Piezoelectric Effect – Crystals exhibit electrical polarity when subject to stress
Direct
Polar Axis Direction which is not symmetry equivalent to its opposite
direction
Polar Rotation Axis Directions parallel and antiparallel to a polar axis have distinct
physical properties
Preferred Orientation Polycrystalline samples of the crystal grains causes radical disagreement between calculated and observed intensities.
Protein Crystals Not very ordered, are in liquid state.
Pyroelectric Possesses so-called polar axis (admits no inversion)
Pyroelectric Effect Change in electrical polarity due to a change in temperature
Reflection Plane Body is symmetrical with respect to plane passing through it if
reflection of half of the body in the plane as in a mirror will
produce the other half.
Rotation Axis The axis where the body is rotated around to bring it in
coincidence with itself
Rotation-Inversion n-fold if it can be brought into coincidence by a rotation of
360/n about the axis followed by inversion
Rotoinversion Axis The axis where the body is rotated around and inverted to
bring it in coincidence with itself
Schottky Defect Defect in ionic crystal where single atom/ion is moved from
interior site to surface of lattice
Zone Faces whose lines of intersection are parallel to one another.
Sample Questions
Why are JCPDS files important for X-ray Contain information about the actual
analysis of crystals? analysis (i.e. intensities at different d
lengths, etc.)
What are the 7 crystal systems? Cubic, trigonal (rhombohedral),
monoclinic, triclinic, tetragonal,
orthorhombic, hexagonal
Intensities of diffracted beams depend on Lorentz-polarization, absorption,
which 5 factors? multiplicity, temperature, structure
If 5-fold symmetry possible? Only in quasi (non-periodic) crystals. Not
possible in periodic crystals.
Do either [010] or [432] lie parallel to Apply dot product.
(002)? (010) ◦ (002) = (0*0+1*0+0*2) = 0
(432) ◦ (002) = (4*0+3*0+2*2) = 4
Therefore [010] is parallel and [432] is not.
What is the zone axis for (200) and (030)? Apply cross product twice.
[(0*0-3*0),(0*0-2*0),(2*3-0*0)] = [006]
[(3*0-0*0),(2*0-0*0),(0*0-2*3)] = [00bar-6]
What is the difference in XRD peaks of Nanocrystals have broad peaks in XRD
polycrystalline samples containing and macrocrystals have sharp peaks in
nanocrystals (5-50nm) and larger XRD.
(size>100nm) crystals?
What is the influence of uniform strain on Results in a graph shifted left or right
XRD patterns? dependent on tension or compression
What is the influence of non-uniform strain Reduce XRD intensity. Results in broad
on XRD patterns? peaks and high error in calculation
What is the highest packing density in the 74%. This makes them both very stable. HCP and FCC structures?
What is the stacking sequence in FCC? ABCABC
What is the stacking sequence in HCP? ABABAB
Describe relationships between A vector drawn from the origin to a point
parameters of direct and reciprocal [hkl] in the reciprocal lattice is
lattices. perpendicular to a plane in the direct
lattice with parameters (hkl). The length of
the direction vector in the reciprocal lattice
is equal to the reciprocal of the spacing
between planes in the direct lattice.

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