structure of crystals and diffraction exam 1

the hallmark of crystalline state is ______ symmetry, ____ range order

translational, long

crystal structure = ____ + ____

lattice, motif

what is the defining characteristic of a primitive unit cell?

only one lattice point

identify a. b. and c.

a=structure, b=lattice, c=motif

What are the symbols for a primitive, base-centered, body-centered, and face-centered unit cell?

P, C, I, F

How many lattice points does a primitive unit cell have and where?

one at 0,0,0

How many lattice points does a base-centered cell have and where?

2 at 0,0,0 and 1/2,1/2,0

How many lattice points does a body-centered cell have and where?

2 and 0,0,0 and 1/2,1/2,1/2

How many lattice points does a face-centered cell have and where?

4 at 0,0,0, 1/2,1/2,0, 1/2,0,1/2, and 0,1/2,1/2

Name the defining symmetry for a triclinic (a) crystal system.

monad (360 degree symmetry)

Name the defining symmetry for a monoclinic (m) crystal system.

1 diad parallel to [010] (180 degree symmetry)

Name the defining symmetry for a orthorhombic (o) crystal system.

3 diads parallel to each axis (180 degree symmetry)

Name the defining symmetry for a tetragonal (t) crystal system.

1 tetrad parallel to [001] (90 degree symmetry)

Name the defining symmetry for a rhombohedral (R) crystal system.

1 triad parallel to [001] (120 degree symmetry)

Name the defining symmetry for a hexagonal (h) crystal system.

1 hexad parallel to [001] (60 degree symmetry)

Name the defining symmetry for a cubic (c) crystal system.

4 triads all parallel to <111> directions (120 degree symmetry)

a monad has a ___ fold rotation axis, thus is perfectly asymmetrical

one

a diad has a ___ fold rotational axis, thus looks the same after a ____ degree turn

2, 180

a triad has a ____ fold rotational axis, thus looks the same at ___ degree intervals

3, 120

a tetrad has a ___ fold rotational axis, thus looks looks the same at ___ degree intervals

4, 90

a hexad has a ___ fold rotational axis, thus looks the same at ___ degree intervals

6, 60

fractional coordinates are only used when defining the position of atoms constituting the _____

motif

<> are used for a family of crystallographically equivalent ______ and {} are used for a family of crystallographically equivalent ____

directions, planes

for a cubic system, {100} = what planes?

±(100), ±(010), ±(001)

for an orthorhombic system, {100} = what planes?

±(100)

ZONE LAW: if the dot product of [uvw] and (hkl) = 0 then what

[uvw] vector lies in the plane

how do you represent a negative number in a direction or plane

line above number

what is this equation used to find? D²=(q-p)_ig_ij(q-p)_j

distance between two points

in an fcc unit cell, a point at 1/2, 0, 0 has how many nearest neighbors? what is its shape?

6, octahedral

in an fcc unit cell, a point at 1/4, 1/4, ¾ has how many nearest neighbors? what is its shape?

4, tetrahedral

what is the volume of a sphere?

4/3 pi r³