Final Exam Summary Notes

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McMaster University
Materials Science and Engineering
Igor Zhitomirsky

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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