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