Any two planes parallel to each other are equivalent and have identical indicesProcedure is:

• If the plane passes through the selected origin, construct another parallel plane within the unit cell/ establish a new origin at the corner of another unit cell

• The plane intersects/ parallels each of the 3 axes; determine the length of planar intercept for each axis in terms of a, b, &c.

• Take reciprocals of these numbers. (if a plane parallels an axis, intercept is infinity & thus a zero index )

• Change to a set of smallest integers• Enclose within parentheses as (h k l)

CRYSTALLOGRAPHIC PLANESCRYSTALLOGRAPHIC PLANES

Crystallographic Planes

specified by MILLER INDICESSTEPS:

• One corner of Unit cell is Origin

• The plane cuts X axis at a, Y axis at b, Z axis at c

XX YY ZZPROJ.PROJ. a b ca=b=ca=b=c 1 1 1reciprocalreciprocal 1 1 1

Crys. PLANECrys. PLANE: : (1 1 1)

Direction [1 1 1]& Plane (1 1 1)

FOR CUBIC CRYSTALS ONLYPlanes and Directions having same indices are perpendicular to one another

[1 2 3][1 2 3]

XX YY ZZPROJ.PROJ. a/2 ∞ ca=b=ca=b=c 1/2 ∞ 1reciprocalreciprocal 2 0 1

Crys. PLANECrys. PLANE: : (2 0 1)

(0 1 1)(0 1 1)

XX YY ZZ

PROJ.PROJ. ∞ b c

a=b=ca=b=c ∞ 1 1

reciprocalreciprocal 0 1 1

Crys. PLANECrys. PLANE: : (0 1 1)

(1 1 1)(1 1 1)

XX YY ZZ

PROJ.PROJ. a b -c

a=b=ca=b=c 1 1 1

reciprocalreciprocal 1 1 1

Crys. PLANECrys. PLANE: : (1 1 1)

(1 3 0)(1 3 0)

XX YY ZZ

PROJ.PROJ. -a b/3 ∞

a=b=ca=b=c -1 1/3 ∞

reciprocalreciprocal 1 3 0

Crys. PLANECrys. PLANE: : (1 3 0)

[1 1 0] [2 1 [1 1 0] [2 1 1]1]

Problem Problem 11

Problem 2Problem 2

Problem Problem 33

Problem 4Problem 4

Problem Problem 55

Problem 6Problem 6

Problem Problem 77

Problem 8 a & bProblem 8 a & b

Sketch [0 0 0 1] and (0 0 0 1)

ProbleProblem 9m 9

Problem Problem 1010

Problem Problem 1111

Problem Problem 1212

Problem Problem 1313

Problem Problem 1414

Problem 15Problem 15