Crystal Packing (12.3.5) Flashcards
• The seven primitive unit cells can be arranged as simple cubic, body-centered cubic, and face-centered cubic.
• The seven primitive unit cells can be arranged as simple cubic, body-centered cubic, and face-centered cubic.
• The most efficient packing of atoms occurs with hexagonal close-packing and face-centered cubic (also called cubic close-packed).
• The most efficient packing of atoms occurs with hexagonal close-packing and face-centered cubic (also called cubic close-packed).
X-ray diffraction is used to determine the position
of atoms in a crystal lattice. The seven primitive
unit cells are: cubic, tetragonal, orthorhombic,
monoclinic, hexagonal, trigonal (also known as
rhombohedral), and triclinic.
Simple cubic unit cells only have atoms in their
corner regions.
Not all crystals only contain atoms in their corner
regions. Many crystal systems have atoms packed
between the atoms of the primitive structures.
Placing an atom inside a cubic cell creates a bodycentered
cubic unit cell (bcc).
Adding an atom to each of the faces of a cubic cell
creates a face-centered cubic unit cell (fcc).
Hexagonal close-packed structures are composed
of layers of hexagonally arranged atoms, each layer
being slightly shifted from the one below it in such
as way that the atoms from one layer fit into the
crevices of the other. This formation aligns the third
layer with the first layer.
The cubic close-packed arrangement is a densely
packed arrangement in a crystalline structure in
which the fourth hexagonal layer is aligned with the
first layer. It is the same as the face-centered cubic
structure. This looks like a hexagon from the top.
The same hexagonal base is used to create a facecentered
cubic lattice (cubic close-packed) but the
stacks above it are arranged to align every fourth
level.
The chloride ions in sodium chloride are structured
in a face-centered cubic, close-packed arrangement
with sodium ions in between. The spaces between
the atoms of a face-centered cubic lattice are called
octahedral holes (surrounded by ions in the shape
of an octahedron).
Zinc sulfide (ZnS) contained two crystal structures:
a face-centered cubic lattice with tetrahedral holes
in addition to the octahedral holes. The zinc ions
shown are in the tetrahedral holes; they are
surrounded by ions in the shape of a tetrahedron.
There are two tetrahedral holes in the face-centered
unit cell.
X-ray diffraction is used to determine the position
of atoms in a crystal lattice. The seven primitive
unit cells are: cubic, tetragonal, orthorhombic,
monoclinic, hexagonal, trigonal (also known as
rhombohedral), and triclinic.
Simple cubic unit cells only have atoms in their
corner regions.
Not all crystals only contain atoms in their corner
regions. Many crystal systems have atoms packed
between the atoms of the primitive structures.
Placing an atom inside a cubic cell creates a bodycentered
cubic unit cell (bcc).
Adding an atom to each of the faces of a cubic cell
creates a face-centered cubic unit cell (fcc).
Hexagonal close-packed structures are composed
of layers of hexagonally arranged atoms, each layer
being slightly shifted from the one below it in such
as way that the atoms from one layer fit into the
crevices of the other. This formation aligns the third
layer with the first layer.
The cubic close-packed arrangement is a densely
packed arrangement in a crystalline structure in
which the fourth hexagonal layer is aligned with the
first layer. It is the same as the face-centered cubic
structure. This looks like a hexagon from the top.
The same hexagonal base is used to create a facecentered
cubic lattice (cubic close-packed) but the
stacks above it are arranged to align every fourth
level.
The chloride ions in sodium chloride are structured
in a face-centered cubic, close-packed arrangement
with sodium ions in between. The spaces between
the atoms of a face-centered cubic lattice are called
octahedral holes (surrounded by ions in the shape
of an octahedron).
Zinc sulfide (ZnS) contained two crystal structures:
a face-centered cubic lattice with tetrahedral holes
in addition to the octahedral holes. The zinc ions
shown are in the tetrahedral holes; they are
surrounded by ions in the shape of a tetrahedron.
There are two tetrahedral holes in the face-centered
unit cell.
There are how many different types of cubic unit cells?
three (C)
The three cubic unit cells are simple, body-centered, and face-centered.
X-ray diffraction tells us what about a crystalline lattice?
Where the atoms are (D)
In principle, X-ray diffraction can tells us where the atoms are in a crystal lattice.
In a body-centered cubic lattice, each atom has 8 nearest neighbors. How many nearest neighbors does an atom in a face-centered cubic lattice have?
12 (C)
Because of the hexagonal arrangement, each atom in the lattice is touching the six around it, three above, and three below, for a total of 12 neighbors.
The seven types of unit cell discussed are known as what?
Primitive unit cells (B)
The term primitive refers to the cells use as a repeating unit and building block, not to its lack of sophistication or uncivilized ways.
In a sodium chloride crystal, the chlorine ions form all of the following types of crystal lattice except
simple cubic (D)
A sodium chloride crystal is closely packed. Simple cubic does not represent close packing.
What are the two different cells that can be produced by hexagonal close packing?
hexagonal and face-centered cubic (B)
It may seem counterintuitive that close packing can produce both a cubic unit cell and a hexagonal unit cell, but it does.
How many octahedral holes are contained in a face-centered cubic crystal?
the same as the number of atoms or large ions (D)
There is a complete octahedral hole in the center and one along each edge. the edge holes are shared with three other cells, but there are 12 edges. So that adds up to 1/4 times 12, plus one, which is the same as the number of atoms
In a sodium chloride crystal, the sodium ions occupy ____
octahedral holes between chlorine atoms in the unit cell. (D)
Each of the cubic unit cells contains a certain number of atoms that is characteristic of that type of cell. Which arrangement of cell names are ordered from least to greatest number of atoms they contain?
simple, body-centered, face-centered (D)
A simple cubic unit cell, with an atom at each corner, contains one atom. A body-centered cubic cell contains two atoms, and a face-centered cubic cell contains four.
In one type of hexagonal close packing, the layers are designated as aba. Using the same notation, the next layer for this type of packing would be designated as
b (B)
The next layer would be a b layer. In this particular hexagonal close packing, the layers alternate, ababab…
