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descripcion de estructuras cristalinas en Materiales
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CRISTAL STRUCTURS
MATERIAL ENGINEER
Short-Range Order versus
Long-Range Order
Short-range order - The regular and predictable arrangement of the atoms over a
short distance - usually one or two atom
spacings.
Long-range order (LRO) - A regular repetitive arrangement of atoms in a solid which extends
over a very large distance.
Levels of atomic arrangements
Levels of atomic arrangements
in materials:
(a) Inert monoatomic gases
have no regular ordering of
atoms:
(b,c) Some materials, including
water vapor, nitrogen gas,
amorphous silicon and silicate
glass have short-range order.
(d) Metals, alloys, many
ceramics and some polymers
have regular ordering of
atoms/ions that extends through
the material.
Lattice, Unit Cells, Basis, and Crystal
Structures
Lattice - A collection of points that divide space into smaller equally sized segments.
Basis - A group of atoms associated with a lattice point.
Unit cell - A subdivision of the lattice that still retains the overall characteristics of the entire lattice.
Atomic radius - The apparent radius of an atom, typically calculated from the dimensions of the unit
cell, using close-packed directions (depends upon
coordination number).
Packing factor - The fraction of space in a unit cell occupied by atoms.
Basis
NET BASE
UNIT CELD
ATOMIC
RADIOS
PACKING FACTOR
The fourteen types of
Bravais lattices
grouped in seven
crystal systems. The
actual unit cell for a
hexagonal
(c) 2003 Brooks/Cole Publishing / Thomson Learning
Characteristic of the crystal system
Definition of the
lattice
parameters and
their use in
cubic,
orthorhombic,
and hexagonal
crystal systems.
(c) 2003 Brooks/Cole Publishing / Thomson Learning
Commoun crystal systems
For the 14 crystal system,
FACE CENTERED CUBIC (FCC)
BODY CENTERED CUBIC (BCC)
HEXAGONAL CLOSE PACKED (HCP)
They are the commun system on the nature, about 98%
of the metals exibiht it
FACE CENTERED CUBIC- FCC
CC o FCC
(Face cubic center)
Aluminium
Cooper
Gold
Nickel
Iron
FACE CENTERED CUBIC- FCC
How many atoms are in the unit celd?
What is the coordination number?
What is the packing factor?
What is the ratio lattice parameter and the atomic ratio?
Un octavo de tomo por
celda unidad
Each atom is in contact with other 12
Coordination number: Atoms or ions which are in contact with each
other
FACE CENTERED CUBIC- FCC
Atoms number in FCC
atoms = (1/2)x6 + (1/8)x8 = 4 atoms per unit celd
1/8
1/2
4
240
ra
Relationship between Atomic Radius and Lattice
Parameters
By Pitagora
h2= c2 + c2
But h = 4r y c = ao
Then (4r)2 = 2ao2
ao2 = (4r)2 / 2
FACE CENTERED CUBIC- FCC
Atomic Packing factor: Is the fraction of volume in a crystal
structure that is occupied by atoms
APF = Volume of everyone atoms on the unit celd
Volum of unit celd
Atoms are supposed as rigid sphere
FACE CENTERED CUBIC- FCC
BODY CENTERED CUBIC - BCC
All atoms are the
same element and
same size
Chrom
Molibden
Tantalium
Wolframium
Iron
BODY CENTERED CUBIC - BCC
How many atoms are in the unit celd?
What is the coordination number?
What is the packing factor?
What is the ratio lattice paremeter and the atomic ratio?
BODY CENTERED CUBIC - BCC
No atomos = (1/8)x8 + 1
2 atoms in BCC
1/8
1
Coordination number = 8
by Pitgoras
h2= c12 + c22
But h = 4r c1 = ao2
c2 = ao
(4r)2 = ao 2 + (ao 2 )2
(4r)2 = 3ao 2
BODY CENTERED CUBIC - BCC
3
40
ra
Relationship between Atomic Radius and Lattice
Parameters
Atomic packing factor
BODY CENTERED CUBIC - BCC
2
Hexagonal close packedHCP (Hexagonal
close packed)
Magnesium
Berilium
Cobalt
Titanium
Cinc
The unit cell can be
a complete hexagon
or one prism for the
six
HCP (a complete hexagon)
The unit cell can be a complete hexagon or one prism for
the six
Atoms by cell
To the hexagon
2*1/2= 1 face
3 center
6*1/3*1/2*2= 2 corner
Total 6 atoms by cell
HCP (a complete Hexagon)
Packing factor = 0.74 the same value in everyone FCC
Number coordination = 12
On HCP there are four different axes, a1, a2 a3
y c and the calculus of the atomic ratio is more
complicated to calculate
a1
a2
a3
c
Change of the cristal
structure
Change of the
volume
Change of the mechanical
properties
Allotropy - The characteristic of an element being able to exist in more than one crystal structure, depending
on temperature and pressure.
Polymorphism - Compounds exhibiting more than one type of crystal structure.
Allotropic or Polymorphic
Transformations
Fusion point
Deltha iron FCC
Gamma iron BCC
Alpha iron FCC
Room temperature
Determining the Density of BCC Iron
SOLUTION
Atoms/cell = 2, a0 = 0.2866 nm = 2.866 10-8 cm
Atomic mass = 55.847 g/mol
Volume of unit cell = = (2.866 10-8 cm)3 = 23.54 10-24 cm3/cell
Avogadros number NA = 6.02 1023 atoms/mol
3
0a
3
2324/882.7
)1002.6)(1054.23(
)847.55)(2(
number) sadro'cell)(Avogunit of (volume
iron) of mass )(atomicatoms/cell of(number Density
cmg
Determine the density of BCC iron, which has a lattice
parameter of 0.2866 nm.
Determining the Density of BCC IronDetermine the density of aluminium, which has a lattice parameter of
0.2866 nm.
2