Packing of more than one type of sphere
- Slides: 6
Packing of more than one type of sphere into unit cells: - Packing of ions in salts Which is usually larger, negative (anions) or positive (cations) ions? - Construct binary salts in lattice with anions usually occupying positions in unit cell and cations in holes in cell How do you describe salts with more than one atom type? By unit cells and holes Na. Cl Space fill
Types of Holes 109. 50 Ion in hole 3 atoms e clouds in plane TETRAHEDRAL Tetrahedron – 4 identical equilateral triangles • What's a tetrahedron • What's an octahedron • Holes: Chemtube 3 D • Cubic close packed / • Face-centred cubic (ccp/fcc) • CCP and holes 5 atoms/ e clouds in plane SF 6 OCT AHEDRAL CUBIC Cube – Octahedron – 8 identical triangles
SIMPLE CUBIC PACKING HOLES CUBIC C C CUBIC CLOSEST PACKING – FACE CENTERED CUBIC HOLES T T T O T O tetrahedral octahedral Unit Cell Packing Eff Coord # Holes ≈ Hole Size (r=1), Simple Cubic 0. 52 6 cubic 0. 732 -1. 00 Face centered 0. 74 12 4 Octahedral Tetrahedral 0. 414 -0. 732 0. 225 -. 0. 414 O
z Example: Na. Cl (Jmol) • What type of unit cell is defined by the Cl- ions? x y z=1 Top face z=0. 5 z=0 Bottom face Tetrahedral Holes • How many tetrahedral holes are there in the fcc unit cell? • Are there any Na+ ions occupying the holes? Octahedral Holes • How many octahedral holes are there in one fcc unit cell? • In what type of holes are Na+ ions in edges throughout the whole lattice?
Hexagonal Closest Packing A Z=1 Arsenide Nickel Z=0. 75 B Z=0. 5 Example: Nickel Arsenide (this Jmol link shows lattice based on Ni as in workbook pg 49, #4) • In what type of hole is Ni found in the structure above • How many As are in the unit cell to the right? How many Ni? • What is the formula for nickel arsenide? • Locate a tetrahedral hole? Are there any Ni ions there? Z=0. 25 Z=0 A Unit cell: hexagonal closest packing Of Arsenide with Ni in what holes?
Determining the empirical formula from unit cell data: A salt must be electrically neutral. If you know the charge on the cations and anions, you can determine Mx. Ny. Alternatively, you can use crystal data to determine the structure of the unit cell and hence the empirical formula. Determine the number of each different ion in the following unit cells. Does it correspond to the formula from charge balance? 1. Copper (I) chloride Cl Cu 2. Barium Chloride 3. Rhenium oxide Examples from Chemtube 3 D 4. Based on Clalone, what type of unit cell is this? What type of “hole” is occupied by Cu+?
