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Crystallography World of Wonders (CWOW)

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Claudia J. Rawncrawn@utk.edu

University of Tennessee

New Mexico Museum of Natural History and Science May 24, 2014

Crystallography World of Wonders

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2014 is the International Year of Crystallography

IYCr2014Some of the major objectives of the IYCr2014 are:•to increase public awareness of the science of crystallography and how it underpins most technological developments in our modern society•to inspire young people through public exhibitions, conferences and hands-on demonstrations in schools•to illustrate the universality of science•to promote education and research in crystallography and its links to other sciences

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Acknowledgments

Thanks to United States National Committee for Crystallography (USNCCr)American Crystallographic AssociationCenter for Materials Processing, University of Tennessee, Knoxville

For providing the funds for travel and CWOW kits and labor

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Crystallography World of Wonders (CWOW)

Previous CWOW workshops presented in conjunction with American Crystallographic Association Annual meetings in•Chicago, IL (2010)•Boston, MA (2012)

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Al vs Al2O3

AlMelts at 660 oCFCC a = 4.0495 ÅDensity = 2.71 gm/cm3

Al2O3

Melts at 2000 oCBased on HCP a = 4.7589 and c = 12.991 ÅDensity = 3.98 gm/cm3

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• Non dense, random packing

• Dense, regular packing

Dense, regular-packed structures tend to have lower energy

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Face Centered Cubic - FCC

• Coordination # = 12

• Atomic Packing Factor = 0.74

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• Coordination # = 12

• APF = 0.74

Adapted from Fig. 3.3, Callister 6e.

HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)

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FCC and HCP close-packed lattices

• Both lattices are formed by a sequential stacking of planar layers of close packed atoms.

• Within each layer each atom has six nearest neighbors.

A layer

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FCC and HCP close-packed lattices

The “A” layer all positions that are directly above the centers of the A atoms are referred to as “A” positions, whether they are occupied or not

• Both FCC and HCP lattices are formed by stacking like layers on top of this first layer in a specific order to make a three dimensional lattice.

• These become close-packed in three dimensions as well as within each planar hexagonal layer.

• Close packing is achieved by positioning the atoms of the next layer in the troughs between the atoms in the “A” layer

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FCC and HCP close-packed lattices

• Each one of these low positions occurs between a triangle of atoms. Some point towards the top of the page and some point towards the bottom of the page.

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FCC and HCP close-packed lattices

• Any two of these immediately adjacent triangles are too close to be both occupied by the next layer of atoms.

• Instead the next close-packed “B” layer will fill every other triangle, which will all point in the same direction.

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FCC and HCP close-packed lattices

• The “B” layer is identical to the A-layer except for its slight off translation.

• Continued stacking of close-packed layers on top of the B-layers generates both the FCC and HCP lattices.

“A” layer

“B” layer

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The FCC close-packed lattice

• The FCC lattice is formed when the third layer is stacked so that its atoms are positioned in downward-pointing triangles of oxygen atoms in the “B” layer.

• These positions do not lie directly over the atoms in either the A or B layers, so it is denoted as the “C” layer

“A” layer

“B” layer

“C” layer

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The FCC close-packed lattice

• The stacking sequence finally repeats itself when a fourth layer is added over the C atoms with its atoms directly over the A layer (the occupied triangles in the C layer again point downward) so it is another A layer.

• The FCC stacking sequence (ABCA) is repeated indefinitely to form the lattice:

• …ABCABCABCABC...

“A” layer

“B” layer

“C” layer

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The FCC close-packed lattice

Even though this lattice is made by stacking hexagonal planar layers, in three dimensions its unit cell is cubic. A perspective showing the cubic FCC unit cell is shown below, where the body-diagonal planes of the atoms are the original A, B, C, and layers of oxygen atoms

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The HCP close-packed lattice

• The HCP lattice is formed when the third layer is stacked so that its atoms are positioned directly above the “A” layer (in the upward facing triangles of the “B” layer).

• The HCP stacking sequence (ABAB) is repeated indefinitely to form the lattice:

• …ABABABAB...

“A” layer

“B” layer

Repeat “A” layer

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Ceramics

• Characteristics– Hard– Brittle– Heat- and corrosion-resistant

• Made by firing clay or other minerals together and consisting of one of more metals in combination with one or more nonmetals (usually oxygen)

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Nomenclature

• The letter a is added to the end of an element name implies that the oxide of that element is being referred to:

• SiO2 - silica Si4+ + 2(O2-)

• Al2O3 - alumina 2(Al3+) + 3(O2-)

• MgO - magnesia Mg2+ + O2-

Positively charged ions cations example: Si4+, Al3+, Mg2+

Negatively charged ions - anions example: O2-

Charge balanced

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Closed Packed LatticesThe Basis for Many Ceramic Crystal Structures

• Ionic crystal structures are primarily formed as derivatives of the two simple close packed lattices: face center cubic (FCC) and hexagonal close packed (HCP).

• Most ionic crystals are easily derived from these by substituting atoms into the interstitial sites in these structures.

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Closed Packed Lattices

• The larger of the ions, generally the anion, forms the closed-packed structure, and the cations occupy the interstices.– We will often consider the anion to be oxygen (O2-) for

convenience since so many important ceramics are oxides. However, the anion could be a halogen or sulfur.

– In the case of particularly heavy cations, such as zirconium and uranium, the cations are larger than the oxygen and the structure can be more easily represented as a closed packed arrangement of cations with oxygen inserted in the interstices.

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Location and Density of Interstitial Sites

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• The interstitial sites exist between the layers in the close-packed structures

• There are two types of interstitial sites– tetrahedral – octahedral

• These are the common locations for cations in ceramic structures

Interstitial Sites

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• Each site is defined by the local coordination shell formed between any two adjoining close-packed layers– the configuration of the third layer does not matter– the nearest neighbor configuration of oxygen atoms

around the octahedral and tetrahedral cations is independent of whether the basic structure is derived from FCC or HCP• FCC and HCP have the same density of these

sites

Interstitial Sites

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Interstitial sites

• Octahedral: 3-6-7-b-c-f– 3 from the A layer and 3 from the B layer– an octahedron has eight sides and six vertices– the octahedron centered between these six

atoms, equidistant from each - exactly half way between the two layers

31 2 4

5 6 78 9 10

a b c

d e f g

h i j

Numbers = A siteslower case letters = B sites

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Interstitial sites

The octahedral site neither directly above nor directly below any of the atoms of the A and B layers that surround the site

– The octahedral site will be directly above or below a C-layered atom (if it is FCC)

– These octahedral sites form a hexagonal array, centered exactly half-way between the close-packed layers

31 2 4

5 6 78 9 10

a b c

d e f g

h i j

Numbers = A siteslower case letters = B sites

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Interstitial sites

• Tetrahedral: 1-2-5-a and e-h-i-9– 1 negative tetrahedron

– 1 positive tetrahedron

– three of one layer and one of the second layer

– 3A and 1B – one apex pointing out of the plane of the board

– 3B and 1 A – one apex pointing into the plane of the board

31 2 4

5 6 78 9 10

a b c

d e f g

h i j

Numbers = A siteslower case letters = B sites

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Interstitial sites

• Tetrahedral: 1-2-5-a and e-h-i-9– For both tetrahedral sites the center of the

tetrahedron is either directly above or below an atom in either the A or B layers

– The geometric centers are not halfway between the adjacent oxygen planes but slightly closer to the plane that forms the base of the tetrahedron

31 2 4

5 6 78 9 10

a b c

d e f g

h i j

Numbers = A siteslower case letters = B sites

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Octahedral sites in the FCC Unit Cell

oo

oo

oo

o

o

o

o

oo

The FCC cell contains four atoms

six faces that each contribute one half and atom

eight corners that each contribute one-eighth an atomFCC cell contains four octahedral sites

12 edges each with one quarter of a site

one site in the center

o

One octahedral site halfway along each edge and one at the cube center

The ratio of octahedral sites to atomsIs 1:1

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Tetrahedral sites in the FCC Unit Cell

One tetrahedral site inside each corner

Eight tetrahedral sites

The ratio of tetrahedral sites to atoms is 2:1

t

t

ttt

ttt

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• T2nOnXn

T – Tetrahedral sites

O – Octahedral sites

X – Anions

General Structural formula for close-packed structures

An Example Applying the Formula

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A2nBnXn

A = tetrahedral sitesB = octahedral sitesX = anions

MgAl2O4

If fully occupied A8B4X4

Mg in tetrahedral sites - 1/8 of the sites occupiedAl in octahedral sites - 1/2 of the sites occupied

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• Nobel Prize in Chemistry 1954– “for his research into the nature of the chemical bond

and its application to the elucidation of the structure of complex substances”

• Nobel Peace Prize 1962• Born in 1901 and died in 1994• We may use Pauling’s rules to predict the

tendency for a specific compound to form a specific crystal structure

Linus Pauling

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• Pauling’s rules are based on the geometric stability of packing for ions of different sizes and simple electrostatic stability arguments.– These geometric arguments treat the ions as

hard spheres which is an over implication

Pauling’s Rules

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• Ionic radii (as defined by interatomic spacings) do vary from compound to compound– they tend to vary most strongly with the

valance state of the ion and the number of nearest neighbor ions of the opposite charge

• We may consider an ionic radius to be constant for a given valance state and nearest-neighbor coordination number

Ionic crystal radii

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stable stable unstable

Pauling’s Rule 1

The radius ratio rule: rc/ra

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CN Disposition of ions rc/ra

about central atom

8 corners of 0.732 a cube

6 corners of 0.414 an octahedron

4 corners of 0.225 a tetrahedron

2 corners of 0.155 a triangle

1 linear 0

When the radius ratio is less than this geometrically determined critical value the next lower coordination is preferred

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• NaCl, KCl, LiF, MgO, CaO, SrO, NiO, CoO, MnO, PbO– for all of these the anion is larger than cation

and forms the basic FCC lattice

The lattice parameter of the cubic unit cell is “ao” and each unit contains 4 formula units

ao

Rocksalt

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• NiO -rocksalt structure

a = 4.1771 Å space group Fm3m

Atom Ox Wy x y z

Ni +2 4a 0 0 0

O -2 4b 0.5 0.5 0.5

n’(∑MNi +∑MO)

Vunit cellNAV

4(58.69 + 15.999) g/mol

((4.1771 x 10-8 cm)3)(6.022 X 1023 atom/mol) =

g/molcm3 x molecules/mol

= 6.81 g/cm3

Calculating density

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Corundum Structure

x

x - empty site

x

x xO

Al

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Corundum Structure

A

A

A

A

B

B

B

x

x

x

x

x - empty site

O

Al

[0001]Columns of face-sharing octahedra

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Cubic a = b = c = =

Hexagonal a = b c = =

Tetragonal a = b c = =

Rhombohedral a = b = c = =

Orthorhombic a b c = =

Monoclinic a b c = =

Triclinic a b c

Seven Crystal Systems

VESTA and the American Mineralogist Crystal Structure Database

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http://jp-minerals.org/vesta/en/download.html

http://rruff.geo.arizona.edu/AMS/amcsd.php

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• http://education.mrsec.wisc.edu/LEGO/crystal.html

FCC – Fractional atomsRocksalt – Fractional atoms

Building Crystal Structures from Legos

Let’s build!

Crystal Jars – Prototype 1

Contents: Mason jar, ½ cup Borax, two pipe cleaners, popsicle stick, 18 inches of dental floss

Costs

60 Crystal Jars for approximately $70All supplies purchased at the grocery store

Trial Run 1

• Pre-prototype 1• Materials Processing

students were given a ½ cup of Borax and a pipe cleaner and asked to grow crystals

• Several students experimented with cooling rates (green tetrahedron placed in freezer) and stirring (purple blob used stirring rod)

Trial Run 2 – Gadget Girls Adventures in STEM

A collaborative effort between the Girl Scout Council of the Southern Appalachians and the University of Tennessee, Knoxville

Attracted more that 150 middle school girls from southwest Virginia, eastern Tennessee, and northern Georgia – each girl that attended our session received a crystal jar to take home

14 STEM activities and growing crystals using Borax was among the activities they enjoyed the most

The ResultsHi Claudia,

Please find attached 2 pics of Natasha's borax crystals that she grew.  Rather than boil water on the stove in a kettle, she decided to use our electric teapot.  She placed the borax in the canning jar, brought the water to boil in the teapot, then poured boiling water into the jar and stirred it with a chopstick until the liquid was clear.  As you can see by the picture, she decided to use the wonderful shape of a circle again.  We were surprised and delighted to see one small crystal form on the end of the floss.  I suggested that this was probably due to the fact that there wasn't much wax on the cut end.  Natasha really enjoyed your presentation and thought it was great fun to bring a "science kit" home to be able to do it on her own.

Thank you and your staff for taking time to spend the day opening the doors of science a little wider for girl scouts.

Sincerely,Paige L. Long