Structure of materials: Crystalline Structure

qa

lattice position referenced to the x axis

rb

lattice position referenced to the y axis

sc

lattice position referenced to the z axis

directional equivalency is related to

linear density for a particular material, equivalent directions have identical linear densities.

Polycrystalline

made up of many small crystals

slip

mechanism by which metals plastically deform occurs on the most densely packed crystallographic planes, in those planes, along directions having the greatest atomic bonding

u,v,w indices

normalized representation of point coordinate indices

planes and directions having the same indices are ______ to one another (only for cubic crystals)

perpendicular

cubic crystals, all the directions represented by the follow- ing indices are equivalent: [100], [1'00], [010], [01'0], [001], and [001']. (2) also, directions in cubic crystals having the same indices without regard to order or sign—for example, [123] and [2'13']—are equivalent.

point (2) not true for crystals of tetragonal symmetry, the [100] and [010] directions are equivalent, whereas the [100] and [001] are not.

point coordinate indices

q r s fractional multiples of a, b and c unit cell edge

grains

small crystals that compose crystalline solids

grain boundary

some atomic mismatch within the region where two grains meet

(T/F) Isotropic behavior is present in crystal structures that has grains in anisotropic orientations

true

directional indices of Miller-Bravis

u v t w where u v t relate to vector coordinate differences referenced to the respective a1, a2, and a3 axes in the basal plane; fourth index is for z plane

degree of anisotropy increases

with decreasing structural symmetry

A plane that parallels an axis is considered to have an infinite intercept and therefore a ____ index.

zero

single crystals

For a crystalline solid, when the periodic and repeated arrangement of atoms is perfect or extends throughout the entirety of the specimen without interruption,

crystallographic planes are represented by..... in all but the _______ crystal system

Miller indices h k l hexagonal

Miller-Bravis

a1, a2, and a3 axes are all contained within a single plane (called the basal plane) and are at 120 degree angles to one another. z axis is perpendicular to basal plane

anisotropy

directionality of properties, meaning physical properties within a crystal vary depending on what direction you take associated with the variance of atomic or ionic spacing with crystallographic direction

A problem arises for crystals having hexagonal symmetry in that some

equivalent crystallographic directions do not have the same set of indices ex: [111] direction is equivalent to [101] rather than to a direction with indices that are combinations of 1s and 1s.

ruled net coordinate system

grid has been constructed on the basal plane that consists of sets of lines parallel to each of the a1, a2, and a3 axes. two sets of parallel lines (a2, a3) lie on and trisect the other axis (i.e., divide a1 into thirds) within the hexagonal unit cell z axis is also apportioned into three equal lengths (at trisection points m and n)

calculating i for hexagonal crystalls

i = -(h + k)

isotropic

independent of direction physical properties same everythwere

planes for hexagonal crystals

(hkil)

HCC APF

0.74

HCC coordination number

12

HCC a =

2R

HCC atom number per unit cell

6