estructuras cristalina eng
DESCRIPTION
descripcion de estructuras cristalinas en MaterialesTRANSCRIPT
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CRISTAL STRUCTURS
MATERIAL ENGINEER
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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.
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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.
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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.
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Basis
NET BASE
UNIT CELD
ATOMIC
RADIOS
PACKING FACTOR
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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
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Characteristic of the crystal system
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Definition of the
lattice
parameters and
their use in
cubic,
orthorhombic,
and hexagonal
crystal systems.
(c) 2003 Brooks/Cole Publishing / Thomson Learning
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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
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FACE CENTERED CUBIC- FCC
CC o FCC
(Face cubic center)
Aluminium
Cooper
Gold
Nickel
Iron
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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?
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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
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Atoms number in FCC
atoms = (1/2)x6 + (1/8)x8 = 4 atoms per unit celd
1/8
1/2
4
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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
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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
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BODY CENTERED CUBIC - BCC
All atoms are the
same element and
same size
Chrom
Molibden
Tantalium
Wolframium
Iron
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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?
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BODY CENTERED CUBIC - BCC
No atomos = (1/8)x8 + 1
2 atoms in BCC
1/8
1
Coordination number = 8
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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
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Relationship between Atomic Radius and Lattice
Parameters
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Atomic packing factor
BODY CENTERED CUBIC - BCC
2
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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
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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
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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
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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
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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.
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Determining the Density of BCC IronDetermine the density of aluminium, which has a lattice parameter of
0.2866 nm.
2