THE STRUCTURE OF SOLIDS
Solids can be either crystalline (having specific shapes), or non crystalline (amorphous).
A crystalline solid is made of atoms, molecules or ions that are ordered in well-defined, repeating
patterns. These solids usually have flat surfaces or faces that join at definite angles with each
other. The orderly stacks of particles that produce these faces also cause the solids to have
regular shapes. For example, NaCl salt crystals are cube shaped.
An amorphous solid (Greek ‘amorphous’ = without form) is a solid whose particles have no orderly
structure. These solids lack well-defined faces and shapes. Many amorphous solids are mixtures of
molecules that do not stack together well. Familiar examples include glass and many organic
polymers such as low density polyethylene, which has tangled, spaghetti-like molecular chains.
Quartz (SiO2) is a crystalline solid with a 3-dimensional structure. When quartz melts at about
1600 C, it becomes a viscous, tacky liquid. Although the silica-oxygen network remains largely
intact, many Si-O bonds are broken and the rigid crystalline order of the quartz is lost. If the melt
is cooled rapidly, the atoms are unable to return to an orderly arrangement during solidification.
An amorphous solid known as ‘quartz glass’ or ‘silica glass’ results. If the melt were cooled
slowly, crystalline quartz would be formed.
(b) amorphous SiO2
(a) crystalline SiO2 (quartz)
O
UNIT CELL
Two-dimensional
unit
Si
O
O
Actual three-dimensional
unit
O
Dark circles represent doubly bonded oxygen atoms. White circles represent tetravalent silicon atoms. The structure is
actually three-dimensional and not planar as drawn. The units shown as the basic building block (Si and three O atoms)
actually has four O atoms, the fourth coming out of the plane of the page and capable of bonding to other Si atoms.
Because the particles of an amorphous solid lack any long-range order, intermolecular forces
vary in strength throughout the sample. Thus amorphous solids do not melt at specific
temperatures. Instead, they soften over a temperature range as intermolecular forces of various
strength are overcome.
A crystalline solid, on the other hand, melts at a specific temperature.
SOLIDS
1
TYPES OF CRYSTALLINE SOLIDS
BASIC
UNITS
FORCES BETWEEN
UNITS
PROPERTIES
EXAMPLES
ATOMIC
non metal
atoms
London dispersion
soft, low mp, poor thermal
& electrical conductors
Noble gases
(frozen Ar)
MOLECULAR
molecules
London,
dipole-induced dipole,
dipole-dipole,
H-bonding
soft, low to medium mp,
poor thermal & electrical
conductors
CH4, I2, CO2,
sucrose (C12H22O11)
IONIC
+ & - ions
ion-ion electrostatic
attraction
hard, brittle, high mp,
poor thermal & electrical
conductors
NaCl, CaCO3
COVALENT
NETWORK
covalently
bonded
atoms
covalent bonds
v. hard, v. high mp, poor
thermal & electrical
conductors
diamond (C),
quartz (SiO2),
silica (SiO2),
SiC, BN
METALLIC
metal atoms
metallic bonds
soft to hard, low to v. high
mp, excellent thermal &
electrical conductors,
malleable & ductile
Cu, Fe, Al, alloys
(brass, bronze)
Atomic Crystals: Individual atoms held together by weak interatomic dispersion forces form an
atomic solid. The noble gases (Group 8A) are the only examples of atomic solids. Their melting
and boiling points and heats of evaporation and fusion are all very low, rising smoothly with
increasing atomic mass.
He
Ne
Ar
Kr
Xe
bp (C)
-269
-246
-186
-152
-62
mp (C)
-272
-249
-189
-157
-71
Molecular Crystals: In molecular crystals, the units are molecules. For example, in a crystal of
iodine, the units are I2 molecules, held together by weak London forces. As a result, molecular
solids are usually low melting (below 300C). In a crystal of ice, the units are H2O molecules held
together by the strongest kind of van der Waals forces (Hydrogen bonding). Molecular solids
have a wide range of physical properties.
F2
Cl2
Br2
I2
bp (C)
-188
-35
59
184
mp (C)
-220
-101
-7
114
In the elemental molecules, EN between atoms is 0.0, so only London forces are present,
however in non elemental molecules molecular dipoles create additional intermolecular forces
and mp’s and bp’s rise accordingly.
SOLIDS
2
Name
Formula
mp (C)
intermolecular force
oxygen
O2
-219
London
sulfur
S8
119
London
n-butane
C4H10
-138
London
sulfur dioxide
SO2
-73
dipole-dipole
water
H2O
0
H-bonding
phenol
C6H5OH
43
H-bonding
Ionic Crystals: In crystalline ionic solids, the unit cells contain two kinds of ions; cations (+) and
anions (-). Electrostatic attraction between oppositely charged particles is strong. As a result,
ionic crystals are hard and have unusually high mp’s (usually greater than 300C).
mp (C)
NaF
NaCl
KI
CaO
992
801
677
2590
Ionic crystals are brittle (shattered by strong impact) because when one layer of an ionic crystal is
pushed past another, like charges are forced together. The strong electrostatic repulsions cause
the crystal to fly apart.
IONIC SOLIDS
+
+
+
+
+
+
+
-
+
+
+
+
+
+
+
-
+
+
+
+
+
+
+
+
+
+
+
-
+
+
+
+
+
+
+
-
+
+
+
+
+
+
+
+
+
+
+
-
+
+
+
+
+
+
+
-
+
+
+
+
electrostatic
repulsion causes cleavage
Force
Electrostatic attraction between alternating rows of anions & cations hold the ions
in fixed positions. Ionic solids are hard but brittle. When struck with sufficient force,
layers of ions are forced past each other so that like charges are immediately adjacent.
Electrostatic repulsion of like charges causes the ionic solid to cleave (split).
Because the ions are fixed in position in the crystal and can only vibrate, ionic solids do not
usually conduct heat or electricity. However, when melted or dissolved, their ions become mobile
and conduct heat and electricity well. Liquids near their freezing points are called melts.
SOLIDS
3
Covalent Network Solids: In covalent network solids, few separate particles are present. The
units are atoms linked together by strong covalent bonds. Because covalent bonds are strong,
these solids are hard, high melting solids. Diamond and graphite are examples of covalent
network solids. They are allotropes of carbon, that is, they are different forms of the same
element under the same conditions of temperature and pressure.
In graphite, sp2 hybridized carbon atoms form a planar (2-dimensional) network of six membered
rings. So many resonance structures can be drawn for the network solid that the  electrons of
each ring are effectively delocalized and spread out over the entire sheet. This is why graphite is
black. A graphite  electron can absorb the energy of almost any photon of light. This also
explains why graphite conducts electricity along the direction of the sheet. An important use of
graphite is as electrical contacts (‘brushes’) in motors.
The covalent bonds within each sheet are strong but the sheets are held together only by weak
dispersion forces. As a result, the sheets readily slide past each other and allow graphite to act
as a dry lubricant and the agent in ‘lead pencils’.
Diamonds are also built of six membered rings but here each tetrahedral C atom is sp3 hybridized
and bonded to 4 other C atoms by  bonds giving a non planar 3-dimensional network. C to C 
bonds are replaced by C to C  bonds between C atoms of adjacent sheets. This cross linking of
sheets has several important effects. Diamonds are hard – sheets do not slide past each other.
Diamonds are the hardest solids known and are used industrially as abrasives. Diamonds are
denser than graphite (3.5 vs. 2.2 g/cm3). Diamonds are higher melting, colorless when pure and
non conductors of electricity.
C to C covalent bond
Length = 1.42Å
C to C covalent bond
Length = 1.54Å
Distance between
planes = 3.40Å
Dispersion forces
between hexagonal
sheets
DIAMOND: a 3-D Covalent Network Solid
(all C's have four sp 3  bonds)
GRAPHITE:
2-D sheets
(all C's have three sp 2  bonds and one  bond)
( bonds are not shown)
SOLIDS
4
A third allotrope of carbon discovered in 1985 (yellow spherical carbon) has a molecular
arrangement shaped like a geodesic dome (soccer ball), called ‘buckminister fullerene’ –
‘buckyballs’ for short.
In 1991, a 4th allotrope of carbon was discovered-concentric hollow tubes formed from graphitelike sheets capped with fullerene-like hemispheres of carbon. These tubes (called ‘c-nanotubes’)
are only nanometers in diameter but are up to microns in length.
In 1995, a 5th allotrope was reported consisting of chains of sp hybridized carbon atoms.
Silicates such as quartz (SiO2) exist in a variety of extended covalent networks. Ceramics and
many igneous rocks are composed of silicates.
Crosslinked polymers such as Bakelite (phenolic) and epoxy adhesives are covalently bonded
networks.
THE MOHS HARDNESS SCALE
German minerolagist Fredrick Mohs (1773-1839) developed a numerical ‘hardness scale’ for
identifying minerals with 1 as softest and 10 as hardest. The scale is shown below.
1. talc [Mg3Si4O10(OH)2]
6. orthoclase feldspar (KAlSi3O8)
2. gypsum (CaSO42H2O)
7. quartz (SiO2)
3. calcite (CaCO3)
8. topaz [Al2SiO4(F,OH)2]
4. fluorite (CaF2)
9. corundum (Al2O3)
5. apatite [Ca5(PO4)3(F,Cl,OH)]
10. diamond (C)
These minerals were chosen because they are readily available (with the exception of diamond).
Each mineral in the Mohs scale can scratch any mineral with the same or a lower number, and
can itself be scratched by any mineral with the same or higher number. For example, if an
unidentified specimen is scratched by all the hardest minerals down to and including apatite
(hardness 5) but not by fluorite (hardness 4), it may be assigned a hardness value of 4½. Often
crude equipment is used to perform the hardness (scratch) testing, e.g., a fingernail (hardness
2½), a penny (3), a knife blade or fragment of window glass (5½ - 6), a hardened steel file (7+) or
emery cloth (between 8 & 9).
The numbers are somewhat arbitrary. Diamond, the hardest known substance, is about four
times as hard as corundum (hardness 9). Most valuable gems are at least as hard as quartz (7);
anything softer is liable to be damaged quickly if worn as jewelry. Sapphire and ruby (varieties of
corundum) have a Mohs hardness of 9. Graphite has a Mohs hardness of 1-2.
DIAMOND FILMS:
In the 1950’s, synthetic diamonds were made slowly and expensively by exposing graphite to
extreme temperatures (ca. 1400 ºC) and pressures (50,000 atm). In the 1960’s the process of
‘Chemical Vapor Deposition’ (CVD) was developed. A stream of methane (CH4) breaks down at
moderate temperatures (ca. 600 ºC) and low pressure (0.001 atm) and the carbon atoms deposit
on the surface at rates to 100 m per hour. Because of diamond’s incredible hardness and high
thermal conductivity, this process is currently being applied to manufacture scratch proof
cookware, watch crystals, hard discs, eyeglasses, lifetime drill bits, ball bearings, razor blades
and semiconductors.
SOLIDS
5
THE STRUCTURE OF CRYSTALS
All crystals contain regularly repeating arrays of atoms, molecules, or ions (analogous to the
repeating patterns in wallpapers, but in 3-D rather than 2-D). The smallest unit of volume of a
crystal that shows all characteristics of a crystal’s growth is a ‘unit cell’. The unit cell is described
by the length of its edges – a, b, c (the spacing between layers) and the angles between the
edges - , , .
Unit cells are stacked in 3-dimensions to build a ‘crystallatice’. All unit cells fit into one of seven
crystal systems. Primitive (simple) unit cells of the seven crystal systems are shown below.
THE PRIMITIVE (SIMPLE) UNIT CELLS OF THE SEVEN CRYSTAL SYSTEMS

c

Generic Unit Cell

b
Monoclinic (1 tilt)
lengths: a <> b <> c
angles:  =  = 90º,  <> 90º
e.g.,
CaSO4.2H2O (gypsum)
Cu2CO3(OH)2 (malachite)
a
Cubic (Isometric)
lengths: a = b = c
angles:  =  =  = 90º
e.g., NaCl (rock salt)
CaF2 (fluorite)
FeS2 (pyrite)
Tetragonal (shoe box)
lengths: a = b <> c
angles:  =  =  = 90º
e.g.,
MnO 2 (pyrolusite)
TiO2 (rutile)
Orthorhombic (match box)
lengths: a <> b <> c
angles:  =  =  = 90º
e.g.,
MgSO 4.7H2O (epsomite)
BaSO4 (barite)
Triclinic (3 tilts)
lengths: a <> b <> c
angles:  <>  <>  <> 90º
e.g.,
K2Cr 2O7 (potassium dichromate)
Rhombohedral
lengths: a = b = c
angles:  =  =  <> 90º
e.g.,
CaCO3 (calcite)
Hexagonal
lengths: a = b <> c
angles:  =  = 90º,  = 120º
e.g.,
SiO2 (silica, i.e., quartz)
Fe2O3 (hematite)
SOLIDS
6
Each unit cell has variations. For example, cubic, octahedral, and dodecahedral crystals are all
variations of an isometric unit cell (a = b = c,  =  =  = 90º) obtained by cutting sections of faces
off the unit cell.
Different substances that crystallize in the same crystallatice type are said to be ‘isomorphic’.
For example, fluorite and pyrite are isomorphic (both are cubic). A single substance that can
crystallize in more than one arrangement is said to be ‘polymorphic’. For example, CaCO3 is
polymorphic. It is commonly found in two crystalline forms: calcite (rhombohedral) and aragonite
(orthorhombic).
In solid rock, grains interfere with one another’s growth so that they cannot take the macroscopic
shape they would like to take. Instead, they fill in whatever hole is available. So grains of rock
have only internal (microscopic) crystal structure, which is identified by X-ray diffraction. Minerals
that grow slowly in open cavities or water-filled pockets are free to form large perfect crystals
identical to the shape of each of the tiny unit cells.
Metallic Crystals: Metallic crystals (metals and alloys) and The Electron Sea Model
The bonding in metals is neither covalent nor ionic. The electron sea model proposes that all
metal atoms in the sample contribute their valence electrons to form a ‘sea of electrons’, which is
delocalized throughout the solid. The metal ions (nuclei with their core of inner electrons) are
submerged in and held together in an orderly array in this sea of electrons.
Electron Sea Model of Metals
+
+ + + +
+
+
+
+ + +
+ +
+
+ +
+
+
+ + +
piece of metal
sea of valence
electrons
metal atom nucleus
with inner electrons
In contrast to ionic bonding, the
metal ions are not held in fixed
positions. In contrast to covalent
bonding, no particular pair of metal
atoms is bonded through any
delocalized pair of electrons.
Rather the valence electrons are
shared among all the atoms in the
substance.
Valence electrons are free to
move explaining the thermal and
electrical conductivity of metals in
both the liquid and solid states.
If you place your hand on a piece of metal and a piece of wood (both at room temperature), the
metal feels colder because it conducts heat away from your body much faster than wood.
The electrical conductivity of metals is inversely related to temperature. With increasing
temperature, metal ions vibrate more and disrupt the electron flow through the substance.
SOLIDS
7
Melting and boiling points of metals: Electrostatic attractions between metal cations and valence
electrons are not broken when metals melt so the mp of metals are only moderately high. Boiling
a metal does require breaking these attractions so boiling points are quite high (as seen in the
following table).
mp (C)
bp (C)
Li
180
1347
Sn
232
2632
Al
660
2467
Ga
30
2403
Ag
961
2155
Alkaline Earth metals (Group 2A) have significantly higher mp’s than the Alkali metals. This can
be explained by the fact that Group 2A metals have twice as many valence electrons for metallic
bonding.
All metals, with the exception of Cu and Au, are silver colored when polished or cut smoothly.
Absorption of photons of all kinds of electromagnetic radiation by the mobile valence electrons
and reemission of the energy as light is said to cause this.
Metals are malleable and ductile. For example, 1 gram of Au (the size of a small ball bearing)
can be drawn into a wire 20m thick  165 m long (ductile) and hammered into a 1.0 m2 sheet
only 230 atoms (70 m) thick (malleable). The electron sea model explains this behavior as
metal ions sliding through a paste of electrons.
Alloys Irregularities (impurities) often make metals tougher and less workable. For example:
 Brass (a 60:40 alloy of Cu and Zn) is harder and higher melting than Cu or Zn.
 Bronze (a 90:10 alloy of Cu and Sn) is harder than Cu and Sn and was originally used to
make weapons and tools (‘Bronze Age’).
 Carbon steel (an alloy of Fe, C, Mn, Cr, and Ni) is much stronger and stiffer than Fe alone.
 Pure Au (24-carat) is soft and easily dented, however, when alloyed with 42% Ag (14-carat) it
is harder, cheaper, and more durable in jewelry without a noticeable difference in color
compared to pure Au.
Doping: The electrical conductivity of semiconductors such as Si and Ge is greatly enhanced by
doping – adding trace amounts of Group 3A (Ga) or 5A (P) elements.
 The addition of P creates n-type semiconductors – so called because of the extra non bonded
electron in Group 5A elements.
 The addition of Ga creates a p-type semiconductor – so called because of the empty p
orbitals in Group 3A elements.
By joining n and p-type semiconductors, diodes (AC to DC rectifiers) and triode (transistors) are
produced for many kinds of electronic equipment (computers, TV, radios, telephones, etc.).
SOLIDS
8
SELF-STUDY QUESTIONS FOR UNIT ON SOLIDS:
1. A crystalline solid is made of …………………… , ……………………., or ……………………..
arranged in …………………………………….. . These solids usually have …………………
surfaces that join at …………………………….. .
2. Write chemical formulas of 5 different crystalline solids (you may need to read all 8 pages
before you can complete this question).
a) …………………………..
d) …………………………..
b) ………………………….
e) …………………………..
c) …………………………..
3. An amorphous solid has no ……………………………….. .
4. Give 3 specific examples of amorphous solids
a) ………………………….
c) …………………………..
b) …………………………..
5. The repeating unit of quartz has a …..-dimensional structure. The chemical formula of its
simplest repeating unit is …………………. . When cooled quickly from the melt, silica forms a
substance commonly called …………….. …………………… .
6. State the relative difference in the melting points of crystalline versus amorphous solids ….
…………………………………………………………………………………………………………. .
7. Complete the following table
Type of
Crystalline
Solid
Basic Unit
Forces
Between Units
(List all types)
Example
(Chemical
Formula)
Relative
Hardness
(low, medium,
high)
Relative mp
(low, medium,
high)
8. Noble gases are the only examples of solids called …………………… crystals. The type of
force between Noble gases is called …………………………. . Describe the relationship
between mp and MW of the Noble gases. …………………………………………………………
…………………………………………………………………………………………………………. .
9. Water and carbon dioxide are examples of compounds that form crystalline solids called
…………………….. ……………………………….. . Such compounds typically exhibit mp’s
below ……………… °C.
SOLIDS
9
10. List 3 types of forces that can exist between molecules in molecular solids and list the
chemical formula of an example of each.
a)
………………………………………
………………………………..
c) ……………………………………….
………………………………..
b) ………………………………………..
…………………………………
11. Ionic crystals typically exhibit mp’s above …………..°C.
12. Explain why ionic crystals are hard but brittle (2 aspects/reasons) …………………………….
……………………………………………………………………………………………………………
………………………………………………………………………………………………………….. .
13. Define a ‘melt’ and give an example ……………………………………………………………….
…………………………………………………………………………………………………………. .
14. With respect to covalent network solids:
a) describe their mp’s. relative to other types of solids …………….…………………
b) describe their hardness relative to other types of solids ……………………….…………..
15. List the chemical formulas of the repeating unit of 4 different covalent network solids
a)
…………………………………….
c)
……………………………………..
b)
……………………………………..
d) ………………………………………..
16. Define allotrope ……………………………………………………………………………………….
17. List 3 allotropes of carbon ……………………… ,………………………., ……………………….
18. Name the hybridization state of Carbon in:
a) graphite ……………………….
b) diamond ………………………
19. Explain how graphite can act as:
a) an electrical conductor ………………………………………………………………………..
b) a dry lubricant …………………………………………………………………………………
20. State which is greater (diamond or graphite) with respect to:
a) density ………………..
c) mp ……………………….
b) hardness ………………
d) electrical conductivity …………….
21. List 2 industrial applications of diamond (other than in jewelry).
a) …………………………………………… b) ………………………………………………
22. State the Mohs hardness number corresponding to the following:
a) diamond
e) Cu penny
b) talc
f)
c) quartz
g) emery paper
glass/knife blade
d) fingernail
SOLIDS
10
23. The smallest repeating unit of a crystalline solid is called a …………….
These are stacked together in a ……………………………………… ..
………………… .
24. Name the 3 primitive unit cells whose angles between edges are all 90°C.
a)
……………………………………………………
b) …………………………………………………..
c) ……………………………………………………
25. Explain the meaning of the word
a) monoclinic ……………………………………….
b) triclinic ……………………………………………
26. The unit cell with all sides equal length but not all angles equal is called …………………….. .
27. Draw the hexagonal unit cell.
28. Explain what is meant when 2 substances are said to be ‘isomorphic’. ………………………..
…………………………………………………………………………………………………………. .
29. List 2 substances that are isomorphic. ……………………………………………………………..
30. Explain what is meant when 1 substance is ‘polymorphic’…………………………………………
…………………………………………………………………………………………………………. .
31. List 2 substances that are polymorphic. ………………………………………………………….
32. Describe the conditions under which minerals naturally grow near perfect crystals.
…………………………………………………………………………………………………………
………………………………………………………………………………………………………….
33. Name the model describing bonding in metals …………………………………………….. .
34. Explain why metals have high electrical and thermal conductivity ………………………….
…………………………………………………………………………………………………………. .
35. Heating a metal causes its electrical conductivity to increase or decrease (circle one).
36. The electrical resistance of metal increases or decreases as it cools (circle one).
37. Give the chemical symbols of the two elements in a bronze alloy.
a) …………………………………………
b) …………………………………………..
38. Give the chemical symbols of the two elements in a brass alloy.
a) …………………………………………
b) …………………………………………..
39. List 3 elements alloyed with Fe and C in carbon steel …………………………………….
40. Give the name and symbol of the element commonly alloyed with gold in jewelry.
41. Semiconductors such as …………….. and ………………….. are doped with trace quantities of
elements from Group ……………A such as ……………… or from Group ……..A such as
…………..
42. How is the electrical conductivity of a semiconductor affected by doping?
…………………………………………………………………………………………………………….
SOLIDS
11