Aerospace Materials II: Solidification of Metals

Solidification of Metals

1. Solidification

Transformation from liquid (melt) to solid state.
During solidification:
- Liquid ↔ Solid + Heat (latent heat of fusion)
Solid forms from liquid at an interface.
Necessary conditions:
- Negative free energy change (\Delta G < 0).
- Heat extraction → Undercooling, $\Delta T$ ( $\Delta T = T_m - T$ ), where:
 - $T_m$ : Melting temperature
 - $T$ : Real temperature
Solidification occurs in two stages:
- Nucleation
- Growth

Variation of Free Energy with Temperature

Above $Tm$ , free energy of liquid ( $Gl$ ) < free energy of solid ( $G_s$ ), so liquid is in equilibrium.
Below $Tm$ , solid is stable ( Gs < G_l).
Driving force ( $\Delta G$ ) is the difference between the two curves.

1. Solidification. Nucleation

Nucleation

Formation of stable groups of atoms (nuclei).
Homogeneous Nucleation: Formation of a small cluster (nucleus) surrounded by liquid.
- Thermodynamic considerations: $\Delta G$ must be < 0 for transformation.
- Critical Radius, $r_c$ : Size of stable nuclei.
- Undercooling: $\Delta T = T_m - T$
Transformation from Liquid to Solid involves:
- Creation of interface.
- Nucleation with no preferential sites.
- Isotropic solid → sphere.
Total free energy change ( $\Delta G$ ) for homogeneous nucleation:
- $\Delta G = - \frac{4}{3} \pi r^3 Gv + 4 \pi r^2 \gamma{LS}$
 - Where:
 - $\Delta G_v$ : Volume free energy change
 - $\gamma_{LS}$ : Liquid-solid interfacial energy

Interface term

$\Delta G{interface} = 4 \pi r^2 \gamma{LS}$

Volume term

$\Delta G{volume} = \frac{4}{3} \pi r^3 \Delta Gv$

1. Solidification. Nucleation

Clusters are stable only if $r \geq r{critical}$ , i.e., if $\Delta G{total}$ decreases.
$r{critical}$ is defined as the radius at which $\Delta G{total}$ is maximum: $\frac{d(\Delta G_{total})}{dr} = 0$
At higher undercooling, lower critical radius, and higher nuclei number.
For pure metals and homogeneous nucleation: $\Delta T{under} = 0.2 Tm$ (very large).
The number of nuclei determines the grain size of the solid metal, and therefore its properties.
Critical radius formula:
- $rc = \frac{2 \cdot \gamma{LS}}{\Delta Gv} = \frac{2 \cdot \gamma{LS} \cdot T_m}{\Delta H \cdot \Delta T}$
 - $\Delta H$ : Latent heat of fusion
 - $\Delta T$ : Undercooling
 - $\gamma_{LS}$ : Liquid-solid interfacial energy

1. Solidification. Nucleation

Lower undercooling is necessary for heterogeneous nucleation.
Heterogeneous Nucleation:
- Existing surfaces provide low energy nucleating sites.
- The initial interface is provided by a foreign particle (impurity, inclusion) and existing surface (i.e., mold wall).
- A greater radius is achieved with very little total surface between the solid and liquid and lower nuclei volume.
- Most common nucleation process.

2. Solidification. Growth

Structure in Detail:
- Fine structure (Chill zone)
- Coarser structure (Columnar zone)
- Equiaxed grains
Growth:
- Parallel
- Opposite to the direction of heat flow.

2. Solidification. Growth

Growth: Incorporation of atoms from the liquid to the solid.
A nucleus can only grow if $r \geq r_{critical}$ (since this will cause a decrease in G).
Latent heat of fusion must be removed → undercooling.
Heat extraction way and rate determine the growth mechanism and structure of the solidification front (planar, cellular, dendritic, equiaxed).
Growth occurs opposite to the heat flux direction and in preferred orientations depending on the material:
- Cubic <100>
- HC <0001>
Development of a preferred texture at a cool mold wall. Only favorably oriented grains grow away from the surface of the mold.

2. Solidification. Growth in pure systems

High number of grains nucleate at the mold walls because the undercooling is highest.
Heterogeneous nucleation typically initiates at the mold walls
Positive thermal gradient.
Negative thermal gradient.
Any protuberance is surrounded by liquid at T > T_m d it will not grow (dissolves) → Planar solidification front (Latent heat is removed through the solid).
If the liquid ahead of the interphase is undercooled, a protuberance will grow as a Dendrite → Dendritic solidification front (Latent heat is removed by raising the temperature of the liquid to $T_m$ . Secondary and tertiary dendrite arms develop).
For a pure metal, solidification takes place at a constant temperature $T_m$ .

2. Solidification. Growth in pure metals

Temp. gradient → dendritic solidification front
planar
cellular
dendritic

2. Solidification. Growth - Binary alloys

Solute distribution coefficient, $k$ .
- $k = \frac{CS}{CL}$
Alloys solidify in a range of temperatures:
- Freezing range = $TL - TS \neq 0$
Constitutional Supercooling:
- Solute is partitioned into the liquid ahead of the solidification front → corresponding variation in the liquidus temperature.
- There is, however, a positive temperature gradient in the liquid, giving rise to a supercooled zone of liquid ahead of the interface.

2. Solidification. Growth Binary alloys

Transition of growth morphology from planar to cellular to dendritic, for alloys as constitutional undercooling increases → equivalent to G/v↓).
- planar
- cellular
- dendritic
G: thermal gradient ( $10^2 - 10^3$ K/m)
v: velocity (rate) at which the liquid/solid interface moves ( $\sim 10^{-3} - 10^{-4}$ m/sec)
$G = \frac{v \Delta T}{D}$
- D : diffusion coefficient of solute in the liquid. (For most metallic systems, $D \approx 10^{-9}$ m²/s)
- $\Delta T$ : freezing range ( $TL - TS$ )
- V: Interface velocity
Constitutional Supercooling Criterion:
- $G/v \sim 10^{10} - 10^{12}$ : planar solidification front
- $G/v \sim 10^5 - 10^7$ : dendrite solidification front

2. Solidification. Growth Binary alloys

Interface got to move with:
- Transfer of atoms across the boundary
- Solute diffusion: The composition of the solid is not the same as the composition of the liquid
G: thermal gradient ( $10^2 - 10^3$ K/m) ACTUAL TEMPERATURE GRADIENT IN THE LIQUID G= $10^4$ K/m
v: velocity (rate) at which the liquid/solid interface moves (~ $10^{-3} - 10^{-4}$ m/sec)
$V_{cr} = ?$
$\Delta T$ : freezing range ( $TL - TS$ ) → GRADIENT OF THE LIQUIDUS PROFILE AT THE INTERFACE. $\Delta T \approx 5K$
2x $10^{-6}$ m/sec

2. Solidification. Growth Binary alloys

planar
cellular
dendritic
How must be the velocity of the interface with respect to the critical velocity to avoid constitutional supercooling?
- $\frac{Gv \Delta T}{D}$
- If v < v_{cr}, then constitutional supercooling is avoided

2. Solidification. Growth

Secondary Dendrite Arm Spacing (SDAS) depends on solidification time and defines the strength of alloy.
Rapid solidification procedures fine dendritic structure: higher strength
$SDAS = k (t_s)^m$
- k, m → constants
- $t_s$ → solidification time
Effect of solidification time on secondary dendrite spacing and on mechanical properties of a cast aluminum alloy.

2. Solidification. Growth

The effect of solidification time on the microstructure of an Al7.4Si3.3Cu alloy:
- Average solidification time 0.7 min (average SDAS 23 μm).
- Average solidification time 16 min (average SDAS 70 μm).
- Average solidification time 43 min (average SDAS 100 μm)

2. Solidification. Growth in alloys

Most common form of growth in engineering alloys is in the form of dendrites: tree-like form structures (from the Greek word δεντρο which means tree).
Examples:
- cobalt-samarium-copper alloy showing primary cobalt dendrites when the Co17Sm2 matrix is etched away
- Dendrites in Al alloy
- Ice dendrite formation on a snowflake
- Al-Si alloy (A356)

3. Cast structures

Structures of castings are controlled by:
- Composition: solidification of pure metals or alloys. Cooling curve
- Heat flow conditions: Solidification regarding the heat flow of the mold
In general, as-cast metal exhibits three distinct zones of grain structures:
- A chill zone of very small crystals produced by rapid cooling at mold walls
- A zone of long, thin columnar crystals lying along the direction of heat flow
- A region of roughly spherical equiaxed crystals at the center of the casting
All three zones may not be present in a particular case.
Relative sizes of zones depend on many factors, among them temperature of the melt, cooling rate, thickness of casting

3. Cast structures: pure metals

Columnar zone
Chill zone (equiaxed)
Cooling curve for solidification of pure metals:
- Solidification takes place at constant temperature $Ts$ ( $TL = 0$ )
- $T_s$ : Solidification temperature
- $T_L$ : Liquidus temperature
- $t_t$ : total solidification time
- $t_r$ : real(local) solidification time
- ∆T: Superheat
- ∆t: cooling rate

3. Cast structures: cooling curves

Alloys solidify in a range of temperatures: freezing range = $TL - TS \neq 0$
Columnar zone
Chill zone (equiaxed)
Equiaxed zone
Cooling Curve for Solidification of Alloys:
- $t_r$ = real (local) solidification time
- $t_t$ = total solidification time
- Solidification range (approx.):
  - Iron alloys: 50°C
  - Mg Al alloys: 110°C

3. Cast structures

Theories on origin of central equiaxed nuclei:
- Dendrite detachment: Nuclei for the equiaxed zone come from the detached dendrite arms that are carried to the centre of the mold by convection currents.
- Big Bang: Equiaxed grains result from the pre-dendritic nuclei formed during metal pouring due to the initial chilling action of the mold. The grains are then carried into the bulk by fluid flow and survive (for low superheats)
- Constitutional supercooling: As liquid solidifies, remaining liquid has a higher solute concentration and hence lower liquidus temperature. Therefore, liquid at the center of the cast is undercooled and heterogeneous nucleation can occur.

3. Cast structures

Eutectic alloys:
- For eutectic compositions: solidification takes place at constant temperature $T_{eutectic}$ ( $L → \alpha + \beta$ ).
- For hypo-eutectic or hyper eutectic: a final amount of liquid solidifies at the eutectic temperature (and has the eutectic composition and structure).
Formation of cells with intercellular eutectic in the directionally solidified Sn-20Pb alloy.
- G = 31 K/mm and v = 1.2 μm/s (The nearly flat eutectic interface is at the eutectic temperature.

3. Cast structures

Alloys can be classified into three types based on their freezing ranges:
- Short: liquidus-to-solidus interval < 50 °C (skin forming alloys)
- Intermediate: interval of 50 to 110 °C
- Long: interval > 110 °C (mushy forming alloys)
Examples:
- Skin forming alloys: low carbon steels, low alloys steels, aluminum bronze, manganese bronze
- Mushy forming alloys: aluminum alloys, magnesium alloys, some brasses

3. Cast structures

Effect of casting parameters on microstructure:
- Superheat: ↑ superheating (pouring temperature) increases the extent of columnar growth
- Composition: ↑ alloying content tends to decrease the extent of columnar region
- Fluid flow (natural or forced): ↑ fluid flow decreases the extent of the columnar region
- Mechanical vibration: ↑ mechanical vibration promotes grain refinement and can extend the equiaxed zone

3. Cast structures

Effect of casting parameters on microstructure:

Inoculation and grain refining: Grain-refining additions can reduce the extent of columnar growth (grain size depends on cooling rate)
Size: ↑ cross section yields higher proportion of equiaxed grains
Freezing range: short freezing range promotes more progressive solidification front which tends to increase the size of the columnar zone
Melting point: High melting point promotes high thermal gradients which tends to increase the size of the columnar zone
High thermal gradients: promote progressive solidification front that promotes columnar growth
- Al–5 wt-%Cu alloy solidified with a chill plate at its base (solidification is left to right). Decreasing temperature gradient in the range of 113-234 K/m → increase of equiaxed zone

3. Cast structures

Contours of equal grain size shown on plot of solidification velocity versus thermal gradient together with locus for CET (Columnar to Equiaxed Transition)

4. Defects in Casting

Defects in Castings are due to:
- Segregation: microsegregation or macrosegregation
- Surface tension
- Volume shrinkage during solidification
- Viscosity (fluidity)
- Inclusions (oxides, nitrides)
- Wide solidification temperature range
- Convection
- Incorrect mold selection and design

4. Defects in Casting

Physical Defects:
- Trapped gases
- Shrinkage and Pipes
- Incorrect shape
Chemical Defects:
- Microsegregation
- Macrosegregation (normal, inverse, by gravity)

4. Defects in Casting: Segregation

Microsegregation: microscopic scale
- There is a concentration gradient in the grains due to solute rejection during solidification.
Macrosegregation: Macroscopic differences in composition throughout the cast

4. Defects in Casting: Segregation

Normal segregation:
- In planar growth solidification front: The centre of the casting (last metal to solidify) has a high concentration of alloying elements with lower melting point.
Inverse segregation:
- In dendrite structures: liquid metal (with a higher concentration of alloying elements of low melting point) enters cavities in-between dendrite arms. The center of the casting has a lower concentration of alloying elements with a low melting point.
Gravity segregation:
- Higher density inclusions or compounds sink and lighter elements float.

4. Defects in Casting: Trapped Gasses

Liquid metals have > solubility for gases than solids. When metal cools and solidifies gases are expelled.
Gases can result from reaction of molten metal with mold (example: H2O in sand with Fe C Al Si)
Problems:
- Cavities: blowholes, pinholes
- Formation of solids and oxides ⇒ embrittlement
- Microporosity (interdendritic)
  - i.e. 3H2O+2Al = Al2O3+3H2 ⇒ Thermodynamically favourable
  - Pitting (due to water vapor)

4. Defects in Casting: Trapped Gasses

Solutions:
1. Reduce amount of gases OR/AND
2. Facilitate gas evacuation
Methods:
- Lower pouring temperature
- Keep melt in ladle as long as possible
- Inert gas flushing
- Vacuum melting and pouring
- Reduce humidity
- Increase permeability of mold and cores
- Make adequate provision for evacuation of air and gas from the mold cavity
- Reduce pouring height
- Proper mold design (gating, runner height)

4. Defects in Casting: Shrinkage

Contraction occurs in three stages:
1. Liquid contraction: Shrinkage of the liquid from $T{pouring}$ to $T{melting}$
2. Solidification contraction: Solidification shrinkage as liquid turns to solid
3. Solid contraction during cooling to RT
In general, for metals: \rho{liq} < \rho{sol}
- (e.g.) Cobalt ( $Tm$ =1495ºC) : $\rho{liq} = 7.19$ , $\rho_{sol} = 7.66$
 - Volumetric contraction: -16.55%
- Total contraction: liquid contraction + solidification contraction + solid contraction
- Solidification shrinkage ranges from 3 to 8% for pure metals
Shrinkage: Can cause defects at a macroscopic and/or microscopic level
- Macro-shrinkage: macroscopic level contraction
- Micro-shrinkage: microscopic level contraction (it appears in interdendritic spaces when liquid filling them solidifies)

4. Defects in Casting: Shrinkage

Shrinkage defects:
- Pipes (shrinkage cavities, macroscopic):
  - As the surface of the cast begins to solidify, funnel-like cavities develop at the center of the cast
- Caved surface:
  - Shallow cavities that form across the surface of the casting
- Macroporosity (macroscopic):
  - Large shrinkage cavities formed within the casting
- Microporosity (or microshrinkage):
  - Liquid metal solidifies and shrinks between dendrites

4. Defects in Casting: Shrinkage

Shrinkage porosity in the sand castings of alloys that freeze in a mushy/pasty manner
Pipe in pure metal or casting in metallic mold (strong cooling)
Pipe in metal with a wide solidification range or casting in sand mold

4. Defects in Casting: Shrinkage

Solutions:
- High thermal conductivity molds
- Use chills (internal or external)
- Adequate metal feeding (risers)
- Hot isostatic pressing (expensive)

4. Defects in Casting: Shrinkage

Sprue/Riser: Liquid metal reservoir in the mould, designed to provide liquid metal to the casting and compensate for solidification shrinkage.
They must be hot during all casting processes.
If they are open, the atmospheric pressure effect can help to avoid the formation of micro-shrinkage.
Refractory material.

4. Defects in Casting: Shrinkage

Chills:
- External chills: Pieces of a high-thermal conductivity material that are placed into the mold and increase solidification rate in critical regions.
- Internal chills: Pieces of a metal that are placed within the mold cavity to absorb heat and increase solidification rate. Must be from the same material as cast to get faster cooling. Small metal pieces, in a cavity or outside.

4. Defects in Casting

Other defects:
- Metallic projections (fins, flash, swells)
- Cavities (gases, shrinkage)
- Discontinuities (cracks, lack of filling)
- Defective surfaces (folds, scars, sand, oxides)
- Incomplete casting (lack of material)
- Incorrect dimensions or shape
- Inclusions