1. Physical Metallurgy
Content
Tutoring of
METALLURGY
Matter states
• gaseous
• liquid
• solid
Amorphous
Atoms are placed without
a particular order.
Metals
Crystalline
Atoms
are
placed
according to a precise
geometrical order.
1
Chemical bonds:
• Van der Waals: related to the small variations of atoms
electronical charge.
• Ionic : electrostatic bond between ions
• Covalent: due to interaction of atomic orbitals
• Metallic: the atoms valence electrons create an electronic
cloud on the whole lattice.
Electronic gas
• high bond energy
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The Body Cubic Centred Lattice (BCC)
Iron α (untill 912°C); Iron δ (from 1394°C to 1538°C); Chromium; Molibdenum;
a
Number of atoms per cell = 1 + 8*1/8 = 2
Volume of a single cell= a3 = 12.32 r3
Diagonal= 3 a = 4 r
Vatomi = 2
FC =
4
π r 3 = 8.38 r 3
3
a=
4r
3
r = 0.124 nm (Iron)
Volume of atoms inside a single cell
Vatoms
= 0.68
Vcell
2
The Face Cubic Centred Lattice (FCC)
Iron γ (from 912°C to 1394°C); Alluminium; Nickel; Copper
a
Number of atoms per cell = 6*1/2 + 8*1/8 = 4
Volume of a single cell = a3 = 22.63 r3
4r
a=
Diagonal= 2 a = 4 r
2
Vat om i = 4
FC =
4
π r 3 = 16.75 r 3
3
r = 0.124 nm (Iron)
Volume of atoms inside a single cell
Vatoms
= 0.74
Vcell
BCC
FCC
Cell Volume
12.32 r3
22.63 r3
Numbers of atoms
2
4
Available Volume
per atom
6.16 r3
5.66 r3
FC
68 %
74%
3
Hexagonal Lattice
Magnesium, Zinc, Titanium α (untill about 882°C)
Number of atoms per cell = 12*1/6 + 2*1/2+3 = 6
FC =
Vatoms
= 0.74
Vcell
Crystal
4
grans
Grain boundary
Defects inside crystal lattice:
• point defects
• Vacancies: some atoms are lacking inside the ordered
lattice
• interstitial atoms: atoms, different from the lattice
ones, are placed inside void spaces inside the lattice
itself
• Substitutional atoms: some atoms, different from the
lattice ones, replaces one or more atoms inside the
lattice.
5
Defects inside crystal lattice:
• line defects
• edge dislocation
• screw dislocation
Edge Dislocation
The plastic deformation in metals is related to the dislocations
movement.
Thanks to the dislocations it’s possible to deform a material with
stresses much lower than a perfect crystal.
6
The grab
movement
The edge dislocation
moves parallel to force
direction.
•The macroscopic plastic deformation of a metal is related
to the movement of a very high number of dislocations
7
Plastic deformation of polycrystalline metals
• The shear bends, along which the dislocations movement
occurs, can be different depending on the kind of lattice.
• The deformation of a crystal depends even on the
deformability of neighbour crystals.
• The dislocation movement is obstructed by grain boundaries.
So, as the number of the grains increases, the dislocation
movement becomes harder and harder
It’s more difficult to plastically deform a fine grained material,
even if, on the other side, this results in higher mechanical
properties
8
Strengthening Mechanisms
• A metal can deform if the dislocations can move. So, in order
to make it stronger, we can do something to change its
condition.
Strengthening Mechanisms
• Make the grain finer
• Strain hardening
• Alloying
Strain Hardening
• If we deform at low temperature (for example room
temperature) soft materials, their mechanical properties
improve.
• The strain hardening is due to the increased dislocation
density during plastic deformation
The dislocations can obstruct one each other during their movement
9
Strengthening due to chemical composition (alloying)
• A metal alloy is a material with metal properties and made by at
least two chemical elements; at least one of these two element must
be a metal.
Heterogeneous
Alloy
Combination of different
solid phases (pure metals,
solid solutions, compounds)
Homogeneous
Solid solution
Substitutional
Interstitial
Compounds
Intermetallic
Interstitial
10
• Solid Solution = macroscopically homogeneous mixture created by
the addition of a solute inside a pure metal that is the solvent. The
lattice is quite the same of the solvent one.
• substitutional: the solute atoms replace solvent atoms inside the
solvent lattice
Ordered
Not ordered
• interstitial: the solute atoms (usually of small dimensions) go
inside the void places inside solvent lattice; this can create a small
deformation of the lattice itself
Compound = it’s a solid solution with a certain chemical
composition that can be expressed as AxBy
• intermetallics: they are made by different metals
linked by strong chemical bonds (ionic or covalent);
their properties are not metallic. Ex.: Mg2Pb, Mg2Sn
• interstitial: they are made by metals togheter with
small dimensions atoms placed in lattice void spaces
Ex.: TiC, TaC, Fe4N, Fe3C.
11
The strengthening by alloying is due to the lattice deformation
caused by solute atoms; this can obstruct dislocation movement
12
METALLURGY
Matter states
• gaseous
• liquid
• solid
Amorphous
Atoms are placed without
a particular order.
Metals
Crystalline
Atoms
are
placed
according to a precise
geometrical order.
1
Chemical bonds:
• Van der Waals: related to the small variations of atoms
electronical charge.
• Ionic : electrostatic bond between ions
• Covalent: due to interaction of atomic orbitals
• Metallic: the atoms valence electrons create an electronic
cloud on the whole lattice.
Electronic gas
• high bond energy
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
The Body Cubic Centred Lattice (BCC)
Iron α (untill 912°C); Iron δ (from 1394°C to 1538°C); Chromium; Molibdenum;
a
Number of atoms per cell = 1 + 8*1/8 = 2
Volume of a single cell= a3 = 12.32 r3
Diagonal= 3 a = 4 r
Vatomi = 2
FC =
4
π r 3 = 8.38 r 3
3
a=
4r
3
r = 0.124 nm (Iron)
Volume of atoms inside a single cell
Vatoms
= 0.68
Vcell
2
The Face Cubic Centred Lattice (FCC)
Iron γ (from 912°C to 1394°C); Alluminium; Nickel; Copper
a
Number of atoms per cell = 6*1/2 + 8*1/8 = 4
Volume of a single cell = a3 = 22.63 r3
4r
a=
Diagonal= 2 a = 4 r
2
Vat om i = 4
FC =
4
π r 3 = 16.75 r 3
3
r = 0.124 nm (Iron)
Volume of atoms inside a single cell
Vatoms
= 0.74
Vcell
BCC
FCC
Cell Volume
12.32 r3
22.63 r3
Numbers of atoms
2
4
Available Volume
per atom
6.16 r3
5.66 r3
FC
68 %
74%
3
Hexagonal Lattice
Magnesium, Zinc, Titanium α (untill about 882°C)
Number of atoms per cell = 12*1/6 + 2*1/2+3 = 6
FC =
Vatoms
= 0.74
Vcell
Crystal
4
grans
Grain boundary
Defects inside crystal lattice:
• point defects
• Vacancies: some atoms are lacking inside the ordered
lattice
• interstitial atoms: atoms, different from the lattice
ones, are placed inside void spaces inside the lattice
itself
• Substitutional atoms: some atoms, different from the
lattice ones, replaces one or more atoms inside the
lattice.
5
Defects inside crystal lattice:
• line defects
• edge dislocation
• screw dislocation
Edge Dislocation
The plastic deformation in metals is related to the dislocations
movement.
Thanks to the dislocations it’s possible to deform a material with
stresses much lower than a perfect crystal.
6
The grab
movement
The edge dislocation
moves parallel to force
direction.
•The macroscopic plastic deformation of a metal is related
to the movement of a very high number of dislocations
7
Plastic deformation of polycrystalline metals
• The shear bends, along which the dislocations movement
occurs, can be different depending on the kind of lattice.
• The deformation of a crystal depends even on the
deformability of neighbour crystals.
• The dislocation movement is obstructed by grain boundaries.
So, as the number of the grains increases, the dislocation
movement becomes harder and harder
It’s more difficult to plastically deform a fine grained material,
even if, on the other side, this results in higher mechanical
properties
8
Strengthening Mechanisms
• A metal can deform if the dislocations can move. So, in order
to make it stronger, we can do something to change its
condition.
Strengthening Mechanisms
• Make the grain finer
• Strain hardening
• Alloying
Strain Hardening
• If we deform at low temperature (for example room
temperature) soft materials, their mechanical properties
improve.
• The strain hardening is due to the increased dislocation
density during plastic deformation
The dislocations can obstruct one each other during their movement
9
Strengthening due to chemical composition (alloying)
• A metal alloy is a material with metal properties and made by at
least two chemical elements; at least one of these two element must
be a metal.
Heterogeneous
Alloy
Combination of different
solid phases (pure metals,
solid solutions, compounds)
Homogeneous
Solid solution
Substitutional
Interstitial
Compounds
Intermetallic
Interstitial
10
• Solid Solution = macroscopically homogeneous mixture created by
the addition of a solute inside a pure metal that is the solvent. The
lattice is quite the same of the solvent one.
• substitutional: the solute atoms replace solvent atoms inside the
solvent lattice
Ordered
Not ordered
• interstitial: the solute atoms (usually of small dimensions) go
inside the void places inside solvent lattice; this can create a small
deformation of the lattice itself
Compound = it’s a solid solution with a certain chemical
composition that can be expressed as AxBy
• intermetallics: they are made by different metals
linked by strong chemical bonds (ionic or covalent);
their properties are not metallic. Ex.: Mg2Pb, Mg2Sn
• interstitial: they are made by metals togheter with
small dimensions atoms placed in lattice void spaces
Ex.: TiC, TaC, Fe4N, Fe3C.
11
The strengthening by alloying is due to the lattice deformation
caused by solute atoms; this can obstruct dislocation movement
12
