Titles from last week

• A: Separation and Spectroscopic Characterization of the Four Common Oxidation States of Vanadium

• B: Contributions to the visible spectrum as a result vanadiums various oxidation states

• C: Reduction of Vanadium and the separation of its oxidation states through ion exchange chromatography

• D: Using Column Chromatography and UV-vis to separate and analyze oxidation states of Vanadium

• E: Separation of the multicolored oxidation states of Vanadium using a resin packed chromatographic column

• F: separation of vandium’s oxidation states through ion exchange chromatography

• G: Generation and separation of four oxidation states of Vanadium via ion exchange chromatography

Today’s goals

• Writing exercise

• What is a crystal?• Assigning unit cells• Fractional coordinates

– Alternative method of counting atoms in a cell

• Crystal systems• Bond valence sums

– Periodic table atomic radii exercise

What makes a crystal a crystal?

• Periodic lattice(translational symmetry)

• Specify lattice vectors

http://escher.epfl.ch/escher/

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

Always find same contents at +na and +mb

n,m integers

a,b lattice vects

b

a

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

How do we choose a lattice?

(1) Fill space (2) Minimize volume (3) Preserve symmetry (T&R)

Arrangement of unit cells give crystals facets

The seven crystal systemsCrystal system Essential point symmetry Axis restrictions

• Cubic 4 triad axis along <111> (cube long diagonals) a = b = c

• Hexagonal hexad or inverse hexad (6 or -6) a = b

• Trigonal triad axis (3) a = b

• Tetragonal tetrad axis or inverse tetrad (4 or -4) a = b

• Orthorhombic three orthogonal diad/mirrors

• Monoclinic diad or mirror (2 or -2) = = 90

• Triclinic none none

= angle between b and c; = angle between a and c; = angle between b and c

Simple description for complex crystals

Atomic coordinates

Atom Ox. Wyck. x y z

Mg1 +2 8a 0 0 0

Al1 +3 16d 5/8 5/8 5/8

O1 -2 32e 0.38672(20) 0.38672(20) 0.38672(20)

Typical data sheet from ICSD

Journal of Physics and Chemistry of Solids (1957) 2, 100-106 XRef

La Fe O3 - Lanthanum iron(III) oxide [cP5]

3.926, 3.926, 3.926, 90., 90., 90.PM3-M (V=60.51)

Demo ICSD database copyright 2003-2005 Fachinformationszentrum (FIZ) Karlsruhe PHP/MySQL Interface V05-02-04 copyright 2003-2005 by Peter Hewat email: Peter.Hewat@gmail.com

Atom (site) Oxid. x y z Occupancy

La1 (1a) 3

Fe1 (1b) 2

Fe2 (1b) 3

Fe3 (1b) 4

O1 (3c) -2

0 0 0 1

0.5 0.5 0.5 0.05

0.5 0.5 0.5 0.9

0.5 0.5 0.5 0.05

0.5 0.5 0 1

Atomic radii• From crystal structures, it is possible (but not trivial) to deduce

atomic radii. Fortunately, tables of radii have been produced by Shannon (Acta Cryst., A32, 751, 1976). They were calculated assuming that the radius of oxygen in 1.40Å.

d = 2*r1 d = r1 + r2

Metallic (covalent) radii Ionic radii

Atomic radius varies ~linearly with CN

(This is in addition to the variation with valence)

http://navrotsky.engr.ucdavis.edu/pages/classes/2006ClassArchive/EMS289C/class_docs/materials_chemsitry_class_notes-8.pdf

Chemistry influences radii trends

http://navrotsky.engr.ucdavis.edu/pages/classes/2006ClassArchive/EMS289C/class_docs/materials_chemsitry_class_notes-8.pdf

Atomic radius changes with valence

http://navrotsky.engr.ucdavis.edu/pages/classes/2006ClassArchive/EMS289C/class_docs/materials_chemsitry_class_notes-8.pdf

Should be possible to use the size of an atom to deduce its valence

Bond valence sum analysis

• The valence of an atom can be deduced by examining its bond lengths.

• Each bond contributes to the total valence of the atom of interest in a manner dependent on its length

See: http://orlov.ch/bondval/

Bond valence sum analysis

V = total valence of metal

vi = contribution from ith bond

R0 = coefficient specific for bond

b = 0.37

For iron:

R0 ~ 1.747

BVS sum indicates Fe+2.17

V = 2.17

(.23 + .37 + .55 +.39 +.25 +.38)

bRRi

ii

iev

vV

/)( 0

0.55

0.370.23

0.38

0.25 0.39

Charge order

• Average: Fe2.5+

• Locally: Fe2+ or Fe3+