Crystalline Structures Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

7/13/2015 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.

7/13/2015 Physical Properties Related to Solid Structure  Density  Luster  Hardness  Electrical Properties  Melting Point  Magnetic Properties

7/13/2015 Distinctions Between Solid Structures  Crystalline versus Amorphous Solids  Crystal Structure versus Crystal Morphology  Equivalent Sphere versus Ionic Structures

7/13/2015 Unit Cells Simple Cubic a = b = c  = 90° a b c    Triclinic a  b  c   90°

7/13/2015 Crystal Structure Definitions  Unit cell cell dimensions unit cell length (a, b, c) cell angles (  )

7/13/2015 Crystal Structure Definitions  Cell relationships edge face-diagonal body-diagonal cell volume

7/13/2015 Crystal Structure Definitions  Cell relationships edge face-diagonal body-diagonal cell volume

7/13/2015 Crystal Structure Definitions  Cell relationships edge face-diagonal body-diagonal cell volume If the cell edge is a, how long is the face diagonal? If the cell edge is a, how long is the body diagonal?

7/13/2015 Crystal Structure Definitions  Cell relationships edge face-diagonal body-diagonal cell volume

Crystal Lattice The repeating pattern of the unit cell creates a lattice. Find the repeating pattern What is the unit cell composition?

7/13/2015 The Unit Cell Crystal Structure Definitions  Begin working on page J-4 of laboratory manual  Refer to page J-1 for definitions Unit Cell

7/13/2015 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.

7/13/2015 Equivalent Sphere Structures Crystal 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)

7/13/2015 Questions to Consider When 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

7/13/2015 Solid State Model Kit Models 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

7/13/2015 Simple (Primitive) Cubic  1) 6  2) 2r  3) 2  2 r  4) 2  3 r  5) 1 net atom per unit cell  6) 47.6%

7/13/2015 Body-Centered Cubic  1) 8  2) 8  3) 4r  4) 4r/  3  5) 2 net atoms per unit cell  6) 31.9%

7/13/2015 Face-Centered Cubic  1) 12  2) 4r  3) 2  2 r  4) 4 net atoms per unit cell  5) 25.9%

Equivalent Sphere Summary Structure Along which dimensions of a cube do the atoms touch Length simple (primitive) cubic body-centered cubic face-centered cubic edge2 r body-diagonal face-diagonal 4 r

7/13/2015 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

7/13/2015 Diamond Structure Atoms occur at the corners of the unit cell

7/13/2015 Diamond Structure Atoms occur at the face centers of the unit cell

7/13/2015 Diamond Structure Atoms occur at four positions within the unit cell The four positions are at the centers of alternate smaller cubes

7/13/2015 Diamond Structure Atoms occur at four positions within the unit cell The four positions are at the centers of alternate smaller cubes

7/13/2015 Diamond Structure Atoms occur at four positions within the unit cell The four positions are at the centers of alternate smaller cubes Atoms occur at the corners of the unit cell Atoms occur at the face centers of the unit cell How many net carbon atoms are there per unit cell?

7/13/2015 Diamond Structure Some atoms touch along the body-diagonal How long is the body-diagonal in terms of r? The density of diamond is 3.51 g·cm -3. What is the radius of a carbon atom?

Graphite Structure

7/13/2015 How many spheres can fit into the following square (2-D) 1 7 7

7/13/2015 How many spheres can fit into the following square (2-D) 49

7/13/2015 How many spheres can fit into the following square (2-D) /2 Hexagonal packing is efficient.

7/13/2015 Solid State Model Kit Models 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?

7/13/2015 Cesium Chloride Two Different Kinds of Ions One type of ion occurs at the corners of a cube The other ion occurs at the center of the cell

7/13/2015 One type of ion occurs at the corners of a cube Sodium Chloride A Different Structure with Two Kinds of Ions the centers of a each face The other ion occurs at the center of the each edge the center of the cell

7/13/2015 Questions to Consider When 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?

7/13/2015 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

7/13/2015 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 Å 3  ix) 30.3%

7/13/2015 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 Å 3  viii) 38.0%

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