structure of solid materials classification of solids solids classified as crystalline, amorphous or...
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STRUCTURE OF SOLID MATERIALSCLASSIFICATION OF SOLIDS
• SOLIDS CLASSIFIED AS CRYSTALLINE, AMORPHOUS OR A COMBINATION OF THE TWO.
• CRYSTALLINE- BUILT UP OF CRYSTALS OF SIMILAR/VARYING SIZES
• CRYSTAL AS LARGE TO FORM A COMPLETE BODY- SINGLE CRYSTAL
• AMORPHOUS- MOLECULES AS BASIC STRUCTURAL UNIT; PRINCIPAL CHARACTERISTIC MORE OR LESS DISORDERED; NO REGULARITY OF ARRANGEMENT- LOWER IN DENSITY
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CRYSTALLINE SOLIDS• During solidification, atoms arrange
themselves into ordered, repeating,
3 – dimensional pattern• Such structures called Crystals.
• Or, Crystal is said to have formed whenever atoms arrange themselves in an orderly 3- D pattern
• Rows can be identified – in various directions- along which atoms are regularly spaced.
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SCHEMATIC REPRESENTATION OF CRYSTAL LATTICE
Eg: all metals, salts, many oxides &
certain plastics
• Axes of this lattice are three lines at right angles to one another
• Lines that make up the lattice are parallel to the axes and equally spaced along them
• Atoms of a single cubic crystal occupy the lattice points- at intersections of the lines
• Atoms oscillate about fixed locations and are in dynamic equilibrium, rather than statically fixed.
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Three dimensional network of
imaginary lines connecting the
atoms called SPACE
LATTICE
Smallest unit having the full symmetry of the
crystal called- UNIT CELLLATTICE PARAMETERS- edges of unit cell and angles
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14 possible different networks of lattice points
All crystals based on these possible space lattices
BRAVAIS LATTICES
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Body Centered Cubic (BCC)
Face Centered Cubic(FCC)
Hexagonal Close Packed
(HCP/CPH)
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BODY CENTERED CUBIC• Atoms at corners,
one at geometric centre of volume, total-9 atoms
• Each corner atoms shared by 8 adjacent cubes
No. of atoms/cell= 2
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FACE CENTERED CUBIC• Atoms at corners, one
atom at centre of each face
• Each face atom shared by one adjoining cube
No. of atoms/ cell = 4
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HEXAGONAL CLOSE PACKED• Basic unit cell is
hexagonal prism• Three atoms in the form
of triangle midway between the two basal planes. When 6 equilateral triangles considered, 3 atoms on alternate triangles Total 17 atoms
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COORINATION NUMBERNo. of equally spaced nearest neighbours that each atom has in a
given crystal structure
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ATOMIC PACKING FACTORRatio of volume of atoms to volume of unit cell
no. of atoms /unit cell X volume of atom
Volume of unit cell Centre and corner atoms touch one another along cube diagonal. a and R are related through a = 4R/√3
Thus,in BCC, a = 4R/√3 and APF = 0.68
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For FCC, a = 2R√2
APF = 0.74
Similarly,
For HCP, APF = 0.74
4R a
a
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CRYSTAL STRUCTURE- EXAMPLES
STRUCTURE METALS
BCC Molybdenum, Tantalum, Tungsten, Chromium, alpha iron
FCC Copper, Aluminum, Silver, gold
HCP Cadmium, Cobalt, Titanium (α), Zinc
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HCPHCP
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Knowledge of crystal structure
For computing theoretical density ρ
AcNV
nA
Where n = number of atoms associated with each unit cellA = Atomic weightVc= volume of the unit cellNA= Avogadro’s number (6.023 X 1023 atoms/mol)
Eg: Copper- FCC - atomic radius = 0.128nm (1.28A0) Atomic weight= 63.5g/mol
Here, n = 4, A= 63.5 ; for FCC, Vc = a3 ; a = 2R √2,
ρ = 8.89 g/cm3
The value from tables is 8.94 g/cm3
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CRYSTALLOGRAPHIC DIRECTIONS A LINE BETWEEN TWO POINTS, OR A VECTOR.
STEPS IN DETERMINING THE 3 DIRECTIONAL INDICES:1. A vector of convenient length is positioned such that it passes
through the origin of the coordinate system. Any vector can be translated without alteration, if parallelism maintained.
2. The length of the vector projection – on each of 3 axes- is determined, measured in terms of unit cell dimensions
3. These 3 nos. are multiplied/divided by common factor to reduce to smallest integer values
4. 3 indices- not separated by commas, are enclosed in square brackets– each corresponds to reduced projections along x, y and z axes. Both +ve and -ve coordinates can exist. –ve represented by a bar over index
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X
Y
Z
X Y ZPROJ. a/2 b 0ca=b=c 1/2 1 0reduction 1 2 0
Crys. Direction: [1 2 0]
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• 1 [1 0 0]
• 2 [1 1 0]
• 3 [1 1 1]
3
12
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INDICES: [1 1 1]
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INDICES: [ 2 0 1 ]
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INDICES: [1 0 1]
NOT as [ 1 0 -1]
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INDICES: [1 1 1 ]NOT as [ 1 -1 1]
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INDICES: [1 0 1 ] NOT as [ 1 0 -1]
INDICES: [1 1 1 ] NOT as [ 1 -1 1]
SIMILARLY, THE CRYSTALLOGRAPHIC PLANES ARE ALSO INDICATED .
Eg: (2 0 1)