Pauling's Rules for Ionic Compounds: Coordination, Valence, Sharing, and Parsimony, Lecture notes of Mineralogy and Mineral Processing

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LECTURE 4 (PART II):

Chemistry and Structure of Minerals

• Packing of Ions – Pauling Rules.

CHEMISTRY AND STRUCTURE OF MINERALS

PACKING OF IONS

coordination polyhedron --- central coordinating ion

coordinated ions clustering in such a way that their centers lying at the apices of a polyhedron coordination number (C.N.) --- # of coordinated ions Packing of Ions

CHEMISTRY AND STRUCTURE OF MINERALS

PACKING OF IONS

coordination polyhedron --- central coordinating ion

coordinated ions clustering in such a way that their centers lying at the apices of a polyhedron coordination number (C.N.) --- # of coordinated ions Packing of Ions

Packing of Ions Ionic Compound Formation

• Anions – negatively charged
  • Larger than the un-ionized atom
• Cations – positively charged
  • Smaller than the un-ionized atom
  • Attraction » Anion – Cation
  • Repulsion » Anion – Anion » Cation – Cation

PACKING OF IONS

e.g. halite (NaCI) --- each Na+^ --- 6 closest Cl-^ neighbours – octahedral --- each Cl-^ --- 6 closest Na+^ neighbours – octahedral --- both Na

and Cl

• --- C.N. 6

PACKING OF IONS

Packing of Ions

PAULING’S RULES

Pauling’s Rules

Linus Carl Pauling

He was an American chemist,

biochemist, chemical engineer,

peace activist, author, and

educator. He published more

than 1,200 papers and books,

of which about 850 dealt with

scientific topics.

PAULING’S RULES Pauling’s Rules

4 rules

➢ to determine with broad generalizations structure of solid

matter (Pauling, 1929 )

➢ deal with the energy state of the crystal structure

Rule 1. The Coordination Number Principle

Rule 2. Electrostatic Valence Principle

Rule 3. Polyhedral Sharing Principle

Rule 4. The Principle of Parsimony

https://www.youtube.com/watch?v=Z-CWav2gq

Pauling’s Rules

the cation-anion distance =  radii

C.N. of a cation --- determined by

radius ratio of cation (A) and anion (X)

R

A

/R

X

PAULING’S RULES

Rule 1. The Coordination Number Principle:

Pauling’s Rules

PAULING’S RULES

Rule 1. The Coordination Number Principle:

1 mm = 10 million angstrom

Pauling’s Rules

Linear or 2 - coordination

Triangular or 3 - coordination

Tetrahedral or 4 - coordination

Octahedral or 6 - coordination

Cubic or 8 - coordination

Cuboctahedral or 12 - coordination

PAULING’S RULES

Rule 1. The Coordination Number Principle:

Pauling’s Rules Linear or 2 - coordination RA/RX < 0. 155 ; very rare e.g., uranyl group (UO 2 )^2 - , nitrite group (NO 2 )^2 - and Cu 2 O Cup.

PAULING’S RULES

Rule 1. The Coordination Number Principle:

Pauling’s Rules Tetrahedral or 4 - coordination RA/RX= 0. 255 - 0. 414 --- typified by (SiO 4 )^4 -^ silicates e.g. Spi, Sph and Dia structures = 1 = 2

PAULING’S RULES

Rule 1. The Coordination Number Principle:

Pauling’s Rules Octahedral or 6 - coordination R A

/R

X

e.g. halite, and many cations in silicates.

PAULING’S RULES

Rule 1. The Coordination Number Principle: