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Engineering materials lecture 7

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Engineering materials lecture 7

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    1. Engineering materials lecture #7 ENGR 151 Professor Martinez

    2. Quiz #1 (Closed book/open note)

    3. Hexagonal Directions Do not have same axes as cubic unit cells (four-axis, Miller-Bravais coordinate system) Three axes (a1, a2, a3) in basal plane at 120° angles to each other z-axis perpendicular to the basal plane Draw [I I 0 0] and [1120] Callister Software

    4. Hexagonal Crystals Determine unit cell [u’ v’ w’] ? [u v t w] u = (2u’ – v’)/3 v = (2v’ – u’)/3 t = -(u +v) w = w’

    5. Crystallographic Planes Specified by three Miller indices (hkl) Any two planes parallel to each other are equivalent and have identical indices

    6. Hexagonal Directions Do not have same axes as cubic unit cells (four-axis, Miller-Bravais coordinate system) Three axes (a1, a2, a3) in basal plane at 120° angles to each other z-axis perpendicular to the basal plane Draw [I I 0 0] and [1120] Callister Software

    7. Crystallographic Planes Specified by three Miller indices (hkl) Any two planes parallel to each other are equivalent and have identical indices

    8. Crystallographic Planes Determined as follows: If the plane passes through the selected origin, either another parallel plane must be constructed within the unit cell by an appropriate translation, or a new origin must be established at the corner of another unit cell. The length of the planar intercept for each axis is determined in terms of a, b, and c Take reciprocals of numbers (plane with infinite intercept is 0) Change to smallest integers by multiplication or division Denoted by (hkl)

    9. Crystallographic Planes Reversing the directions of all distances specifies another plane parallel to, on the opposite side of and equidistant to the origin Determine the Miller indices for the plane shown in Figure 3.26ab (pg. 82) Construct a (0 I I) plane within a cubic unit cell

    10. Atomic Arrangements “Family” of planes Contains all planes that are crystallographically equivalent (same atomic packing) A family is designated by brackets {h k l} Example {111} family For cubic systems, order and sign of indices does not matter.

    11. Hexagonal Crystals Uses four axes with (hkil) indices To convert from the three axis Miller indices to the four axis Miller-Bravais system: i = -(h + k) Figure 3.27, pg. 83 Determine the Miller-Bravais indices for the plane shown in the hexagonal unit cell

    12. Hexagonal Crystals Use Miller-Bravais: (hkil) Callister software

    13. Linear and Planar Densities Equivalent directions have identical linear densities (linear densities are equal) Equivalent planes have the same planar densities number of atoms centered on direction vector length of direction vector number of atoms centered on a plane Area of plane

    14. Linear and Planar Densities Calculate LD for [110] of FCC Calculate PD for (110) of FCC

    15. Dot Product Find the angle between two directions Example 3.11, pg. 84

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