Determining the Contents of a Unit Cell

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Determining the Contents of a Unit Cell. An Example. Determine The net number of Na + and Cl - in the NaCl unit cell. Use the shown Figure and the Table. Na + : (1/4 for each edge)(12 edges) = 3 Na + (1 for each center)(1 center) = 1 Na +.

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Determining the Contents of a Unit Cell

An Example

Determine The net number of Na+ and Cl- in the NaCl unit cell

Use the shown Figure and the Table

Na+: (1/4 for each edge)(12 edges) = 3 Na+

(1 for each center)(1 center) = 1 Na+

Cl-: (1/2 for each face)(6 faces) = 3 Cl-

(1/8 for each corner)(8 corners) = 1 Cl-

4 Na+ and 4 Cl-, i.e. one Cl- for each Na+

Empirical Formula is one Cl- for each Na+

Practice Exercise

The element iron crystallizes in a form called a-iron, which has a body-centered cubic unit cell (bcc). How many iron atoms are in the unit cell?

What is the empirical formula of the compound?
• Green: chlorine; Gray: cesium

CsCl

Mass of a unit cell = 4(6.94 amu) + 4(19.0 amu) = 103.8 amu

Good agreement

Macroscopic density of LiF = 2.640 g/cm3

Using the contents and Dimensions of a Unit Cell to Calculate Density

An Example: calculate the density of LiF, where the geometric arrangement of ions in crystals of LiF is the same as that in NaCl. The unit cell of LIF is 4.02 angstroms on an edge

In an NaCl unit cell: 4 Na+ and 4 Cl-

A body-cenered cubic unit cell (bcc) of a particular

crystalline form of iron is on each side. Calculate the density of this form of iron.

Practice Exercise

Close Packing of Spheres

Hexagonal closed-packing; coordination number = 12

Cubic closed-packing; coordination number = 12

closed-packing of a single layer;

Coordination number =6

Close packing of equal-sized spheres

Coordination number: is the number of particles immediately surrounding a particle in the crystal structure

In a body-centered cube (bcc), the coordination number is 8

Give it some thoughts: what is the relation between the coordination number the packing efficiencies?

Covalent-Network Solids

Diamond

Graphite

Each carbon is bonded to other four carbon atoms

• In diamond the interconnected three-dimensional array of strong C-C single bonds contribute to diamond’s unusual hardness and high melting point
Covalent-Network Solids

Each carbon is bonded to other four carbon atoms

Each carbon is bonded to other three carbon atoms

• In graphite, C-C bonds are similar to those in benzene, with delocalized pi bonds expanding over the layers. This makes graphite a good conductor of electricity along the layers. The layers are held by weak dispersion forces, which makes graphite soft and have a low melting point

Nanoparticles

C60: The Buckyball (Fullerenes)

K3C60: is a super conductor at 18 K

Carbon Allotropes

Diamond, graphite, and the bucky ball

Recall that “allotropes” are different forms of the same element in the same state, e.g. oxygen and ozone are allotropes of oxygen

Metallic Solids
• Metals are not covalently bonded, but the attractions between atoms are too strong to be van der Waals forces.
• In metals, valence electrons are delocalized throughout the solid. This makes metals strong conductors of electricity

A cross section of a metal

Each sphere represents the nucleus and inner core electrons of a metal atom. The surrounding blue shadows represent the mobile valence electrons that bind the atoms together

Determining the Contents of a Unit Cell

An Example

Determine The net number of Na+ and Cl- in the NaCl unit cell

Use the shown Figure and the Table

Na+: (1/4 for each edge)(12 edges) = 3 Na+

(1 for each center)(1 center) = 1 Na+

Cl-: (1/2 for each face)(6 faces) = 3 Cl-

(1/8 for each corner)(8 corners) = 1 Cl-

4 Na+ and 4 Cl-, i.e. one Cl- for each Na+

Empirical Formula is one Cl- for each Na+

Practice Exercise

The element iron crystallizes in a form called a-iron, which has a body-centered cubic unit cell (bcc). How many iron atoms are in the unit cell?

What is the empirical formula of the compound?
• Green: chlorine; Gray: cesium

CsCl

Mass of a unit cell = 4(6.94 amu) + 4(19.0 amu) = 103.8 amu

Good agreement

Macroscopic density of LiF = 2.640 g/cm3

Using the contents and Dimensions of a Unit Cell to Calculate Density

An Example: calculate the density of LiF, where the geometric arrangement of ions in crystals of LiF is the same as that in NaCl. The unit cell of LIF is 4.02 angstroms on an edge

In an NaCl unit cell: 4 Na+ and 4 Cl-

A body-cenered cubic unit cell (bcc) of a particular

crystalline form of iron is on each side. Calculate the density of this form of iron.

Practice Exercise

Close Packing of Spheres

Hexagonal closed-packing; coordination number = 12

Cubic closed-packing; coordination number = 12

closed-packing of a single layer;

Coordination number =6

Close packing of equal-sized spheres

Coordination number: is the number of particles immediately surrounding a particle in the crystal structure

In a body-centered cube (bcc), the coordination number is 8

Give it some thoughts: what is the relation between the coordination number the packing efficiencies?

Covalent-Network Solids

Diamond

Graphite

Each carbon is bonded to other four carbon atoms

• In diamond the interconnected three-dimensional array of strong C-C single bonds contribute to diamond’s unusual hardness and high melting point
Covalent-Network Solids

Each carbon is bonded to other four carbon atoms

Each carbon is bonded to other three carbon atoms

• In graphite, C-C bonds are similar to those in benzene, with delocalized pi bonds expanding over the layers. This makes graphite a good conductor of electricity along the layers. The layers are held by weak dispersion forces, which makes graphite soft and have a low melting point

Nanoparticles

C60: The Buckyball (Fullerenes)

K3C60: is a super conductor at 18 K

Carbon Allotropes

Diamond, graphite, and the bucky ball

Recall that “allotropes” are different forms of the same element in the same state, e.g. oxygen and ozone are allotropes of oxygen

Metallic Solids
• Metals are not covalently bonded, but the attractions between atoms are too strong to be van der Waals forces.
• In metals, valence electrons are delocalized throughout the solid. This makes metals strong conductors of electricity

A cross section of a metal

Each sphere represents the nucleus and inner core electrons of a metal atom. The surrounding blue shadows represent the mobile valence electrons that bind the atoms together