The Crystalline Solid State, Study notes of Chemistry

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The Crystalline Solid State

Chapter 7

Monday, October 19, 2015

Midterm Exam I

Review Sessions:

Weds, Oct 21 @ 4-6 pm, SSL 270 (Juliet)Thurs, Oct 22 @ 5-7 pm in SSL 228 (Kyle)

this Friday, Oct 23, 9-9:50a

Chapters 4, 5, and today’s part of 7 (no chapter 6)

multiple short answer problems testing basic concepts

closed book, closed notes

bring pen, pencil, calculator, ID

study lectures, book, suggested and online problems

look for seating chart on lecture room door

don‘t cram!

Types of Solids

Amorphous Solids are solids that lack a regular three-dimensionalarrangement of atoms. They lack long-range structural order.Crystalline solids have atoms/ions/molecules arranged in regular,repeating patterns. They possess long-range periodicity.

minimizes free energy of the atoms/ions/molecules

the

unit cell

is the smallest repeating structural unit that has the full crystal

symmetry

SiO

2

glass

SiO

2

crystal (α-quartz)

Types of Solids

Amorphous Solids are solids that lack a regular three-dimensionalarrangement of atoms. They lack long-range structural order.Crystalline solids have atoms/ions/molecules arranged in regular,repeating patterns. They possess long-range periodicity.

minimizes free energy of the atoms/ions/molecules

the

unit cell

is the smallest repeating structural unit that has the full crystal

symmetry

Types of crystalline solids:

-^

Ionic Crystals

-^

Covalent or Network Crystals

-^

Molecular Crystals

-^

Metallic Crystals

-^

Group VIII Crystals (frozen Noble Gases)

The 14 Bravais Lattices

All 3D crystals belong to one of 14 Bravais lattices.^ Bravais lattice

: An infinite array of points with an arrangement and

orientation that looks exactly the same from any lattice point.

Types of Cubic Lattices

There are three cubic Bravais lattices:

Simple Cubic

Body-Centered Cubic

Face-Centered Cubic

The lengths of the unit cell edges (

a

,

b

,

c

) are called

lattice constants

.

For cubic crystals,

a

=

b

=

c

, so there is only one lattice constant (

a

).

a

b

c

Contents of a Unit Cell

An important feature of the unit cell is the number of lattice points itcontains. Atoms/ions/molecules are often located at lattice points.

Atoms

Shared Between:

Each atom counts:

corner

8 cells

face center

2 cells

body center

1 cell

edge center

4 cells

8 × 1/8 =

1

8 × 1/

• 1 × 1 =

2

8 × 1/

• 2 × 1/2 =

2

8 × 1/

• 4 × 1/2 =

4

Contents of a Unit Cell

Cl at corners: (



1/8) = 1

Cl at face centres (



1/2) = 3

Na at edge centers (



1/4) = 3

Na at body centre = 1

Unit cell contents: 4(Na

Cl

)

Consider

sodium chloride:

rock salt

(not Bravais)

Close-Packed Structures

The Hexagonal Close-Packed Structure

A

B

To construct: 1

st

layer: 2D HCP array (layer A)

nd

layer: HCP layer with each sphere placed in alternate interstices in 1

st

layer (B)

rd

layer: HCP layer positioned directly above 1

st

layer (repeat of layer A)

A

…ABAB…

A B A

HCP is two interpenetrating simple hexagonal

lattices displaced by

a

1

a

2

a

3

An HCP crystal is a close-packed structure with the stackingsequence …ABABAB…

The Hexagonal Close-Packed Structure

The Cubic Close-Packed Structure

To construct: 1

st

layer: 2D HCP array (layer A)

nd

layer: HCP layer with each sphere placed in alternate interstices in 1

st

layer (B)

rd

layer: HCP layer placed in the

other

set of interstitial depressions (squares, C)

A

B

C

th

layer: repeats the 1

st

layer (A)

…ABCABC…

It turns out that the CCP structure is

just the FCC Bravais lattice!

stacking

of HCP layers

along

body diagonal

A CCP crystal is a close-packed structure with the stackingsequence …ABCABC…

Metallic Solids

Most metals crystallize in ccp, hcp, or bcc structures

Metallic bonding is stronger than London dispersion forces, butweaker than covalent bonding

Solid

M

/ g mol

-

Melting Point / °C

Kr

Cu

C (diamond)