Solid Crystal Structures
(based on Chap. 12 Sec 11
of Jespersen 6th Ed)
Dr. C. Yau
Fall 2014
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What are Crystals?
They are solids made of
particles (atoms, ions or
molecules) that are arranged in
a rigid, orderly 3-dimensional
array often referred to as a
lattice: the crystal lattice.
Link to some neat videos of formation of crystals:
http://www.youtube.com/watch?v=uoexANHeWoU&feature=related
http://www.youtube.com/watch?v=HnSg2cl09PI&feature=related
http://www.youtube.com/watch?v=xTIzMaSDZ3k
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The unit cell is the smallest repeating unit in
the lattice.
Simple Cubic Cell:
Atoms are drawn smaller
to show 3-D layout.
Actual size is such that corner atoms touch.
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Simple Cubic Cell
Polonium (Po) has the simple cubic cell structure.
Each unit cell contains 8 corners, with one atom at
each corner.
Each atom is shared by how many cells?
Thus, only 1/8 of the atom is in a cell.
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What is the # of atom per cell?
Figure shows how an atom at the corner of a
cubic cell is shared by 8 cells.
Therefore only 1/8 of the atom belongs to a cell.
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Face-Centered Cubic Cell
Cu, Au, Ag and Al have the face-centered cubic
cell structure.
Each unit cell has an atom at each corner and
one at the center of each face.
How many cells share the atom at the center of
the face?
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What is the # of atoms per cell?
Face-Centered
Cubic Cell
The figure shows how an atom at the
center of a face is shared by 2 cells.
It therefore counts only as ½ of an atom.
Note that the corner atoms don’t
touch, but each corner atom
touches the atom at the center of
the face.
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Body-Centered Cubic Cell
Cr, Fe, Pt have the body-centered cubic cell,
with one atom at each corner plus one in
the center of the cube.
What is the # of atoms per cell?
Note that corner atoms don’t touch but each
corner touches the atom at center of the cell.
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• So far we examined only metals,
where all the lattice points are of
the same species.
• Copper has only Cu atoms.
• Silver has only Ag atoms.
• How are ionic cmpds different?
Lattice points are occupied by two
different species: the cation & the
anion.
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Rock Salt Structure
Fig.12.40: NaCl crystal. Chloride ions are in a facecentered cubic cell with sodium ions between them,
plus one in the center of the each cube.
(Center Na+ not visible here)
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What is the number of Na+ and Cl- per cell?
Unit Cell of Cesium Chloride
Fig. 12.41: The unit cell
for cesium chloride,
CsCl.
Cl- is located in the
center of the unit cell.
Cs+ are at the corners
of the unit cell.
Note: Ions are not
drawn to full size.
What is the formula based on the
crystal structure?
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Zinc Blende Structure
S2- has the face-centered cubic cell structure.
There are 4 Zn2+ inside the cell.
What is the formula based on the crystal
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structure?
Calcium Fluoride Crystal Structure
Ca2+ is in a face-centered cubic cell structure.
There are 8 F- inside the cell.
What is the ratio of Ca2+ to F- based on the
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crystal structure?
Determining Formula from Crystal Structure
A new compound, boganium sulfide, has
been discovered. X-ray crystallographic
studies reveal that it has a cubic unit cell
with a sulfide ion forming a body-centered
unit cell and a boganium ion (Bo) in the
center of each of the cube faces in the unit
cell. Based on this structure, what should
the formula for the compound be?
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Amorphous Solids
Not all solids are crystalline.
Some are “amorphous.”
Glass is noncrystalline.
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X-Ray Crystallography
Fig 12.49: X-ray diffraction: X-ray hitting a crystal is
diffracted & gives a characteristic diffraction pattern
(b). Shown is the diffraction pattern of NaCl on a
photographic film..
You do not need to know Bragg equation. Just know
that X-Ray crystallography tells us the type of crystal
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structure and the distance between the atoms.
Example 12.7 p.570
X-Ray diffraction measurements reveal that
copper crystallizes with a face-centered
cubes lattice in which the unit cell length is
3.62Ǻ. What is the radius of a Cu atom
expressed in angstroms and in picometers?
(1nm = 10 Å, 1m = 1010 Å; 1m = 1012 pm)
m _ _ mm _ _ m _ _ nm Å
_ _ pm
Remember that the
corner atoms do not
touch each other in the
face-centered cell.
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Paper HW (due date will be announced).
Barium has a body-centered cubic structure. If
the atomic radius of barium is 222 pm, what is
the density (in g/cm3) of solid barium?
Hint: D of the unit cell = D of the solid.
Remember D = M/V. Find the volume of the unit
cell. Determine # atoms per cell and calculate
the mass in g of those atoms (not moles of
atoms).
Remember to review which atoms touch which
in a body-centered cubic structure.
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Hint for Paper HW(continued)
c
a
b
a
To determine the volume
of a unit cell, you need to
know the length of the
cell (a).
a
First calculate c from the atomic radius.
Write a Pythagorean theorem equation for the triangle
with c as the hypotenuse in terms of a and b.
Next, write the Pythagorean eqn for the triangle with b
as the hypotenuse in terms of a. Finally, solve for a. 19
Physical Properties of Solids
• Ionic crystals have cations and anions at the
lattice points.
• Molecular crystals have neutral molecules at
the lattice points.
• Covalent crystals have atoms at the lattice
points, covalently bonded to neighboring
lattice points. These are often called
“network solids.”
• Metallic crystals have cations at the lattice
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points.
Network Solids
quartz
diamond
= oxygen
= silicon
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Electron Sea Model of Metal
This model describes
the metal as cations
surrounded by a sea
of valence electrons.
The sea of electrons
acts as a buffer
between the positive
ions, thus allowing it
to be malleable,
ductile and able to
conduct electricity. 22
Table 12.7: Types of Crystals
Study the table on p.573.
It compares the type of attractive forces and
typical properties of various types of
crystals:
• ionic
• molecular
• covalent (network)
• metallic
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Example 12.8 p.574
The metal osmium, Os, forms an oxide with
the formula OsO4. The soft crystals of
OsO4 melt at 40 C, and the resulting
liquid does not conduct electricity. To
which crystal type does solid OsO4
probably belong?
Do Practice Exercise 19, 20, & 21 p.574
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