Metallic & Ionic Bonding: In-depth Study of Lattices, Unit Cells, & Bonding in Solids - Pr, Study notes of Inorganic Chemistry

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Metallic and Ionic

Bonding

Chapter 3

Metallic Bonding

Ch 3 — Part I

Lattice & Unit Cell

Lattice

 (^) 3D array of atoms or molecules each surrounded by in an identical way by neighboring atoms or molecules

Unit Cell

 (^) Imaginary parallel-sided region from which entire crystal can be built up by purely translational displacements.  (^) Cells fit perfectly together with no space excluded

7 Crystal Systems

Basic Lattices Primitive lattice (P)  (^) 1 lattice point in unit cell  (^) Translation symmetry is just that on unit cell Body centered cubic (bcc)  (^) 2 lattice points in unit cell  (^) Translational symmetry  (^) On unit cell  (^) (½, ½, ½) body of cell Face centered cubic (fcc)  (^) 4 lattice points per unitl cell  (^) Translational symmetry  (^) On unit cell

Counting Atoms per Unit Cell

 4 types of site in unit cell

 (^) Central or body position – atom is completely contained in 1 unit cell  (^) Face site –face atom shared by 2 unit cells  (^) Edge site –edge atom shared by 4unit cells  (^) Corner site –corner atom shared by 8 unit cells Site Counts as Shared with X other unit cells Body 1 1 Face 1/2 2 Edge 1/4 4 Corner 1/8 8

Packing of Simple Spheres

3 common arrangements based on close

packing of spheres

1. Cubic Close Packed ( ccp ) also called face centered cubic ( fcc ) 2. Hexagonal Close Packed ( hcp ) 3. Body Centered Cubic ( bcc )

Assumption: atoms (ions, or molecules)

are spheres

Solid = close packed array of spheres

(atoms ions, or molecules).

Close Packing in 2 Dimensions

 Most efficient arrangement of spheres in

2-D

 Each sphere has 6 nearest neighbors

ABA

Above Atoms

ABC

Above Holes

Two Ways to Put on 3 rd Layer

Close Packing

Cubic Close-Packed

Face Centered Cubic

Hexagonal

Close-Packed

Molecules Can Also Sit on Lattice Points

 C

60

molecules

crystalize into fcc

lattice with a C

60

on

each lattice site

 Bigger than when

single metal atom

sits on each site.

Non Close-Packed Lattices

Simple Cubic

Body Centered

Cubic

CCP(FCC) & HCP

In each of these 2 close packed geometries,

 12 nearest neighbor atoms = coordination

number is 12

 (^6) in plane of atom  (^3) above plane of atom  (^3) below plane of atom

 Fraction of total space occupied by spheres in

0.7405 for hcp or ccp (fcc)

 These are NOT ONLY close packed structures,

just most common!!!

 (^) Array of complex stacking arrangements  (^) ABACBABABC … etc

Two Types of Holes in Lattice

1. Tetrahedral ( T

d

 (^) Cleft between 4 spheres  (^) Hole left by triangular plane + 1 atom over cleft  (^) Can fit atoms up to 0.225 r (where r = radius of spheres)

2. Octahedral ( O

h

 (^) Cleft between 6 spheres  (^) Hole left by 2 oppositely overlapping triangular planes  (^) Can fit atoms up to 0.414 r