4.5 Solids

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4.5.1 Introduction

I The nature of the solid depends on the type of forces that hold its components together

1. amorphous solid: atoms, ions, or molecules that lie in a disorderly array

   1. amorphous solids are short-range order like liquids; they are “frozen liquids”

      1. butter, rubber, and glass are typical examples of amorphous solids

2. crystalline solid: atoms, ions, or molecules that lie in an orderly array

   1. crystalline solids are long-range order

   2. they are typically flat and have well-defined planar surfaces known as crystal faces

II crystalline solids can be further categorized by the types of bonds that hold them together:

1. molecular solids: discrete molecules that are held together by intermolecular forces

2. network solids: atoms extensively covalently bonded to their neighbors

3. metallic solids: metal cations with a sea of electrons

4. ionic solids: ions held together through mutual attraction

4.5.2 Molecular Solids

III physical properties of molecular solids are based on strength of their intermolecular forces

1. amorphous molecular solids are soft

   1. its weak intermolecular forces and disorder makes it easy to push past one another (like wax, spreads easily)

2. crystalline molecular solids are hard and brittle

   1. its strong intermolecular forces and order makes it very hard to push past one another (like sugar, doesn’t spread at all)

3. molecular solids can also be tough

   1. ultrahigh-density polyethylene used in bulletproof vests

4.5.3 Network Solids

IV network solids have atoms held together by strong covalent bonds throughout the solid, like a network

1. network solids are often very hard, rigid materials with high melting and boiling points

V the two allotropes of carbon, graphite and diamond, are both network solids. The two allotropes have strikingly different properties:

1. diamond has each carbon atom in a tetrahedral arrangement with sp3 hybridization

   1. the strong $\sigma$ bonds of carbon atoms explain its hardness

   2. diamonds are formed under extreme pressures

2. graphite consists of flat sheets of sp2 hybridized carbon atoms in a hexagonal arrangement

   1. it possesses a delocalized π network; its π electrons are delocalized throughout the entire molecule

   2. graphite is anisotropic; its electrical conductivity is much better in the parallel direction than perpendicular

   3. if impurities exist within the graphite layers, they can be used as a lubricant as the layers slide very easily

VI ceramic materials are non-crystalline inorganic oxides with a network structure

1. its bonds have strikingly significant covalent character

4.5.4 Metallic Solids

VII an array of metal cations that are bounded together by a sea of electrons

1. metallic solids are lustrous, malleable, and ductile

2. its luster occurs due to mobilized electrons

   1. an incident light strikes the surface of the metal

   2. an electron absorbs this and oscillates in step with the incident light

   3. the electron then emits light in the same frequency

3. its malleability and ductility can also be explained by mobilized electrons

   1. even if its cations move drastically, the sea of electrons can adjust easily

VII many metallic solids have different types of structures; in these structures, atoms are illustrated as hard spheres for convenience.

1. close-packed structure: atoms stacked together with maximum efficiency

   1. close-packed structures have the least amount of empty space; the atoms occupy 74% of space

2. there are two close-packed structures you need to know:

   1. hexagonal close-packed structure (hcp): ABAB configuration

   2. cubic close-packed structure (ccp): ABC configuration

3. coordination number (CN): the number of nearest neighboring atoms of each atom

   1. all close-packed structures have a coordination number of 12

IX tetrahedral holes: a dip between three atoms

1. the size of tetrahedral holes allows atoms with 0.225 times the radius of the atoms that form the hole to fit it.

X octahedral holes: a hole which a dip in one layer coincides with a dip in another layer

1. the size of octahedral holes are around double the size of tetrahedral holes.

4.5.5 Unit Cells

XI unit cell: the smallest unit that can reproduce the entire crystal

XII some common unit cells are:

1. face-centered cubic (fcc) structure: one atom at each corner, one atom at the center of each face

   1. this is equivalent to the cubic close-packed structure, has coordination number of 12 and occupies 74% of the space

   2. there are four atoms in total that contribute to one fcc unit cell.



2. body-centered cubic (bcc) structure: one atom at each corner, and a single atom at the center

   1. has a coordination number of 8 (not a close-packed structure) and occupies 68% of the space

   2. there are two atoms that contribute to one bcc unit cell.



3. primitive cubic structure: one atom at each corner

   1. has a coordination number of 6, and occupies 52.3% of the space

   2. there is only one atom in total that contributes to this unit cell.

XIII Bravais lattices: 14 basic patterns of unit cells that can express any crystal structure

XIV the density of these solids (through the unit cell) can be calculated by the equation below:

$d = \frac{m}{V} = \frac{n \times m_{atom}}{V} = \frac{n \times m_{r}}{N_{atom} \times a^{3}}$ (Eq.53)

1. $a$ is the side length of a unit cell.

   1. for FCC structures, $a = 2 \sqrt{2r}$

   2. for BCC structures, $a = \frac{4}{\sqrt{3}} r$

   3. for primitive cubic structures, a = 2r

4.5.6 Ionic Solids

XV ionic solids have structures that are similar to metallic solids, but have much more variables

1. some of these variables are that ion sizes are different, and charges of ions are opposite

2. ionic solids are not an electron sea model; in fact, it is the exact opposite

3. the ions (represented as hard spheres) stack together in the arrangement that has the lowest total energy

XVI radius ratio (ρ): the ratio between the cation radii and the anion radii

$\rho = \frac{r_{smaller}}{r_{larger}}$ (Eq.54)

XVII some of the ionic solid structures are (when anions are larger than cations):

1. rock-salt structure (0.4 < $\rho$ < 0.7): anions in fcc configuration, cations in octahedral holes

   1. sodium chloride (NaCl), magnesium oxide (MgO)

2. cesium-chloride structure ($\rho$ > 0.7): anions in expanded cubic array, cations in cubic holes

   1. cesium chloride (CsCl), thallium chloride (TlCl)

3. zinc-blende structure ($\rho$ < 0.4): anions in expanded ccp, cations occupying half the tetrahedral holes

   1. one type of zinc sulfide (ZnS)

XVIII The sphere packing model may break down if the bonds are not entirely ionic.