Transcript Eqilibrum phase diagram

Materials science I - Metallic materials
Metallic materials
Solid state
Pure materials
Alloys
atomic structure
atomic arrangement
microstructure
macrostructure
- components
- phases
- systems - homogeneous
- heterogeneous
Materials science I - Metallic materials
Solid state
Atomic structure – forces between atoms are strong, changes of
volume and shape needed high energy.
Bonding of atoms in metallic materials is „METALLIC“
electrons on last orbital of atoms are released, atoms becomes
positive ions. Free electrons are sheared as the „cloud“ or
„sea“ with other ions.
•
Metallic bond is equally strong in all directions
•
Compounds with metallic bonds form a regular lattice
structures.
•
The free electrons can move – materials with metallic
bonds are electrical conductive
Materials science I - Metallic materials
Atomic structures:
Crystalline - regular atom distribution form the lattice
(long distance regularity)
Amorphous - irregular atom distribution
(short distance regularity)
Metallic metals are mostly formed in 3 lattices:
FCC
BCC
HCP
- face centred cubic
K8
- body centred cubic
K12
- hexagonal close - packed H12
Materials science I - Metallic materials
Microstructure:
Monocrystalline: whole bulk has the same orientation of lattice
Ideal monocrystalline is free of the lattice imperfections
Point faults
(vacancies, interstitial atoms, substitution atoms)
Line faults
(dislocations – edge, screw and general)
Areic faults
(stacking faults, free surfaces, grain boundaries)
Volume faults
(coherent particles)
Polycrystalline:
in bulk of material exists areas or volumes with different lattice
orientation called grains.
Places, where grains are connected are grain boundaries
- narrow areas (about 5 atoms) where the mismatch of connecting
lattices are compensed by suitable distributed imperfections - atoms,
vacancies and dislocations.
Materials science I - Metallic materials
Microstructure:
Small structure components visible only using the suitable type
of microscope:
atoms, dislocations, grains, grain boundaries, secondary phase
particles (precipitate), impurities, number of presented phases,
their distribution, portion …
In dimensions about nm and bigger
Macrostructure:
Visible by eye or with help of magnifying glass.
Large structure components as big or dendritic grains
(after casting, or some heat treatment), impurities, …
In dimensions about tens of mm and bigger.
Materials science I - Metallic materials
Pure metals:
Ideal pure metals are composed only with the same atoms.
Real material content impurities becoming from their
manufacturing.
Pure metals are marked as 99,9 %. Very pure materials content
99,999 % of matrix atoms
Alloys:
Are solid state multicomponent systems containing except
atoms of fundamental metal the added alloying elements and
elements of impurities more.
Materials science I - Metallic materials
Alloys:
Terms:
Components: alloying elements
Phase :
homogeneous portion of a system that has
uniform physical and chemical characteristics
e.g. polymorphic forms in solid state
Single phase systems are termed homogeneous
e.g. melts, pure metals
Multiphase (two or more phases) are heterogeneous.
Most of the metallic alloys are heterogeneous systems.
Materials science I - Metallic materials
Solubility
Solubility is a maximum concentration of solute atoms in solid
solution.
Solid solution
Solid solution is formed in host material latice, where the atoms
of impurities are solved.
Atoms, which are smaller than atoms of the host material forms
interstitial solid solution. Atoms fill the volumes between atoms
of the host material lattice (carbon in iron).
Atoms with close diameter (difference les 15 %) replaces some
atoms in host materials. This type of solid solution is
substitutional (cooper and nickel).
Materials science I - Metallic materials
Solid solutions
Solubility
unlimited
the atoms are mixed in whole range
of concentrations (from 0 to 100 %)
limited
exist some maximum concentration of atoms
which can be solved in host material. Generally it
is connected with temperature.
Interstitial solid solutions have in every cases limited solubility
(max 10 %) due to limited free interstitial volume in lattice, where
the solute atoms can be placed.
Materials science I - Metallic materials
Equilibrium
Equilibrium between phases in the system is described with the
Gibbs free energy G = H – TS.
The temperature and pressure play role.
Every change in system is described by change of free energy ΔG
The system is in equilibrium state, when the free energy reaches
minimum value. This state is termed stable. Each change in
system may lead to changes in equilibrium.
In real alloys, in solid state, if the changes needs more time, the
equilibrium state is not reached. System will decrease free energy
during the time. The equilibrium is termed metastable.
Materials science I - Metallic materials
Gibbs phase rule
Is the criterion of number of phases, which will coexist in
equilibrium conditions in the system
P+F=C+N
P
- number of present phases
F
- number of degrees of freedom
(temperature, pressure, composition etc.)
C
- number of components (elements or stable
compound of phase diagrams)
N
- number of noncompositional variables
(temperature, pressure)
Materials science I - Metallic materials
Gibbs phase rule
We search possible number of freedom
F=C+N-P
Generally N = 2 (if the temperature and pressure play role)
(equilibrium in system with gaseous, liquid and solid state)
When we consider no pressure influence, the N = 1
(equilibrium phase diagrams of alloys)
For pure metal is C = 1  exist only one temperature, when
coexist melt and solid state – solidification (crystallization)
proceed at constant temperature
Materials science I - Metallic materials
temperature
temperature
Cooling curves
time
pure metal
time
alloy
Materials science I - Metallic materials
Diffusion
Phenomenon of material transport by atomic motion – in solid
state only one possible. Phase changes in the solid state systems
are mostly possible due to diffusion.
In pure materials the atoms changes their positions, there are no
changes in chemical composition - self diffusion.
In real alloy, the moving of atoms lead to chemical content
changes. This phenomenon is termed as interdiffusion or impurity
diffusion.
Materials science I - Metallic materials
Diffusion
Difusion couple Cu - Ni
Materials science I - Metallic materials
Mechanisms of diffusion
For atom moving into the lattice, there must be an empty place,
and the atom must break the attraction forces their neighbours.
Vacancy mechanism – moving own or substitutional atoms to position of
existing vacancies.
Interstitial diffusion – moving interstitial atoms into neighbour
interstitionals positions in lattice.
The possible but low frequented are exchange and ring mechanisms.
Materials science I - Metallic materials
Diffusion
The moving atoms from their positions is influenced by vibration in
lattice. If the amplitude of vibrations reach the value when the barrier
of atomic attraction forces is exceeded, the atom can change your
position. The energy needed for amplitude increasing is called
activation energy Qd.
Diffusion rate of steady state diffusion is described by 1st Fick’s law:
dC
J  D
dx
J
D
C
x
D0
- diffusion flux
 Q 
- diffusion coefficient
D  D0 exp  d 
 RT 
- concentration
- position
- temperature independent diffusion constant
Materials science I - Metallic materials
Diffusion
The term
dC
dx
is concentration gradient of concentration profile
ΔC C A  C B

Δx
x A  xB
Driving force of the steady state diffusion is concentration gradient
Nonsteady state diffusion
The time t of the process is considered – 2nd Fick’s law
C
 2C
D 2
t
 x
Solution is
C x  C0
 x 
 1  erf 

C s  C0
2
Dt


erf is the Gausian error function
Materials science I - Metallic materials
Diffusion
The depth of diffusion can be expressed as h ≈ (Dt)1/2
or from equation for middle quadratic distance of moving atoms
x 2  2Dt
Volume or bulk diffusions is relative slow process
The diffusion is accelerated by lattice imperfections.
The other diffusion paths are along dislocation, through the grain
boundaries or along free external surfaces.
Temperature accelerates diffusion but is not the driving force!
increases diffusion coefficient, increase the atom vibration amplitude,
increase the number of vacancies.
Materials science I - Metallic materials
Solidification
Solidification is process of changing atomic coupling. The liquid state
of metal – melt transforms to a solid state. The system is driven to
minimize the free energy.
ΔG 
ΔT
ΔH
Tm
ΔG = GL - GS
If the temperature decreases, the equilibrium between liquid and solid
state is violate, and nuclei of solid state (phase) can rise.
Materials science I - Metallic materials
Solidification
Nucleation
Consider formation of small spherical nucleus with radius r,  is the
surface energy of nucleus interface
Surface free energy
Critical nucleus size r* is the
minimum size of nucleus,
which is able further growth.
ΔG* is the nucleation barier
Volume free enrgy
Materials science I - Metallic materials
Solidification
Nucleation
homogeneous – fluctuation of energy, spontaneously
heterogeneous on existing surfaces
Number of nuclei
s is the number of available
nucleation sites
Rate of nucleation
q is activation energy for
diffusion
Materials science I - Metallic materials
Solidification
Nucleation
homogeneous – fluctuation of energy, spontaneously
heterogeneous on existing surfaces
Materials science I - Metallic materials
Growth of new phase
Planar – the growth is controlled by heat removing through the
solid phase
Dendritic – heat removing is possible through the solid phase
and through the melt.
Materials science I - Metallic materials
Casting structure
Chill zone
- first and fast cooled part
of ingot - near to surface
Columnar zone - area of long crystals
Eqiuaxed zone – in the middle of the ingot
Materials science I - Metallic materials
Eqilibrum phase diagram
Materials science I - Metallic materials
Eqilibrum phase diagram
Lever rule
Weight of solid solution of composition m = bm
Weight of liquid of composition q
qb
Ratio = bm/pb
Materials science I - Metallic materials
Eqilibrum phase diagram
Structure development
Materials science I - Metallic materials
Eqilibrum phase diagram
With eutectic reaction
Materials science I - Metallic materials
Eqilibrum phase diagram
Hypoeutectic alloy
Materials science I - Metallic materials
Eqilibrum phase diagram
Hypoeutectic alloy
Materials science I - Metallic materials
Eqilibrum phase diagram
Hypoeutectic alloy
Materials science I - Metallic materials
Eqilibrum phase diagram
eutectic alloy