crystalline structures edward a. mottel department of chemistry rose-hulman institute of technology

Crystalline StructuresEdward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

04/18/23

Crystalline Solid State

Study of the arrangement of atoms/ions in metallic and ionic crystals.

Enables the calculation of the size of atoms/ions.

Allows the "environment" (the number of atoms/ions and the types of atoms/ions) surrounding each atom/ion to be studied.

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Physical PropertiesRelated to Solid Structure

Density Luster Hardness Electrical Properties Melting Point Magnetic Properties

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Distinctions Between Solid Structures

Crystalline versus Amorphous Solids Crystal Structure versus Crystal Morphology Equivalent Sphere versus Ionic Structures

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Unit Cells

Simple Cubica = b = c

= 90°

ab

c

Triclinica b c

90°

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Crystal Structure Definitions

Unit cell• cell dimensions• unit cell length (a, b, c)• cell angles ()

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Cell relationships• edge• face-diagonal• body-diagonal• cell volume

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If the cell edge is a, how long is the face diagonal?

If the cell edge is a, how long is the body diagonal?

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The Unit CellCrystal Structure Definitions

Begin working on page J-4 of laboratory manual

Refer to page J-1 for definitions• Unit Cell

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Solid State Model Kit

Obtain one kit for every 3-4 people. Sit in a circle so that everyone can see the models

as they are being built. Refer to pg. 5 of the Model Kit Manual (in the box)

for instructions• how to select the plastic base to use.• which holes of the base to use.• how to build the models.• how to take them apart.

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Equivalent Sphere StructuresCrystal Structure Definitions

Start at page J-5 of laboratory manual; work through page J-10

Refer to page J-1 for definitions• Net atoms per unit cell• Percentage void space (packing efficiency)• Coordination Number (CN)

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Questions to ConsiderWhen Studying Solid State Structures

How do the atoms touch? What is the length of the edge of the unit cell in

terms of the atomic radii? How many net atoms are there per unit cell? What is the percentage void space in the structure? Build the primitive (simple) unit cell (pg. 9, 102)

• Build the small cube, then the large cube• Answer questions on page J-5 of lab manual

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Solid State Model KitModels to Build

Primitive (simple) unit cell (pg. 9, 102)• Build the small cube, then the large cube• Page J-5 of lab manual

Body-Centered Cubic (bcc) pg 18, J-6 Face-Centered Cubic (fcc) pg 27, J-7 Cubic Closest Pack (ccp) pg 26, J-8

• Shaded area and hollow numbers Hexagonal Closest Pack (hcp) pg 24, 99, J-8

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Simple (Primitive) Cubic

1) 6 2) 2r 3) 22 r 4) 23 r 5) 1 net atom per unit cell 6) 47.6%

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Body-Centered Cubic

1) 8 2) 8 3) 4r 4) 4r/3 5) 2 net atoms per unit cell 6) 31.9%

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Face-Centered Cubic

1) 12 2) 4r 3) 22 r 4) 4 net atoms per unit cell 5) 25.9%

Equivalent Sphere Summary

Structure

Along which dimensionsof a cube do the atoms

touch Length

simple (primitive)cubic

body-centeredcubic

face-centeredcubic

edge 2 r

body-diagonal

face-diagonal

4 r

4 r

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Diamond Hardest naturally occurring material Strong because

• strong covalent bonds• 3-dimensional strength

Same structure is formed by• silicon and germanium

Similar structure formed by several semiconducting materials• GaAs, GaP

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Diamond StructureAtoms occur at

the corners of theunit cell

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Diamond Structure

Atoms occur atthe face centersof the unit cell

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Diamond StructureAtoms occur atfour positions

withinthe unit cell

The four positionsare at the centers

of alternatesmaller cubes

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Diamond StructureAtoms occur atfour positions

withinthe unit cell

The four positionsare at the centers

of alternatesmaller cubes

Atoms occur atthe corners of the

unit cell

Atoms occur atthe face centersof the unit cell

How many net carbon atoms are there per unit cell?

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Diamond Structure

Some atomstouch along

thebody-diagonal

How long is thebody-diagonalin terms of r?

The density of diamond is 3.51 g·cm3.What is the radius of a carbon atom?

Graphite Structure

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How many spheres can fit into the following square (2-D)

17

7

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49

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52 + 8/2

Hexagonal packing is efficient.

Experiment JJ: Solid State IIElectrical Resistance

Ele

ctr

ical

re

sis

tan

ce

Temperature

A

B

C

Based on your observations, which type of material corresponds to which line?

metal

semiconductor

superconductor

metal

semiconductor

superconductor

Sodium nitrate crystal formation Bobby Pin heat treatment Copper wire work hardening

Experiment JJ: Solid State IIStructure

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Solid State Model KitModels to Build

Cubic Closest Pack (ccp) pg 26, J-8• Shaded area and hollow numbers

Hexagonal Closest Pack (hcp) pg 24, 99, J-8 Hole Calculation, Radius Ratio and

Coordination Number pg 93, J-11• How is r/R calculated?

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Cesium ChlorideTwo Different Kinds of Ions

One type of ionoccurs at thecorners ofa cube The other ion

occurs at thecenter ofthe cell

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One type of ionoccurs at

the cornersof a cube

Sodium ChlorideA Different Structure with Two Kinds of Ions

the centersof a each face

The other ionoccurs at

the center ofthe each edge

the center ofthe cell

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Questions to ConsiderWhen Studying Solid State Structures

How do the ions touch? What is the length of the edge of the unit cell

in terms of the ionic radii? How many net ions are there per unit cell? What is the percentage void space in the

structure?

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Ionic Structures

Cesium Chloride (CsCl) pg 96• Answer questions on page J-12 of lab

manual Rock Salt (NaCl) pg 33, 31

• Answer questions on page J-13 of lab manual

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Cesium Chloride Structure

i) 8, 8, 0 ii) 8, 8, 0 iii) cubic hole iv) 2r+ + 2r-

v) 1 cation vi) 1 anion

vii) 5.50/3 = 3.18 Å viii) 32.0 Å3

ix) 30.3%

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Rock Salt Structure

i) 6, 6, 0 ii) 6, 6, 0 iii) octahedral hole iv) 2r+ + 2r-

v) 4 cations vi) 4 anions

vii) 125 Å3

viii) 38.0%

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crystalline structures edward a. mottel department of chemistry rose-hulman institute of technology

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