Solidification

Superfusion

The curve of cooling is in fact slightly different. The temperature of the liquid goes down in lower part from the melting point, then goes up abruptly to form the plate. This is called the superfusion .

Superfusion is due to the energy of solid-liquid interface (surface Tension). In a simplified way, one can consider that the small germs of solid are unstable because they are dissolved by thermal agitation, it should be waited until the liquid is “calmer” so that they can be formed. In a more rigorous way, seen under a Thermodynamic angle , the energy released by solidification (latent heat of fusion) does not compensate for energy spent to create the solid-liquid interface. The liquid thus continues to cool without solidifying.

When the profit of energy is sufficient to compensate for the creation of the interface, the germs are created very quickly, and released heat makes go up the temperature. Then, the germs grow slowly, which corresponds to the plate.

The profit of energy becomes sufficient when:

the temperature is sufficiently low, or
an impurity comes to decrease the energy of interface; it is the famous example of the horses of the lake Ladoga brought back by Malaparte (1942).

Energy assessment

Let us consider a spherical germ of ray R . It has a Volume V of 4/3·π· R ³, which corresponds to the solidification of a mass m = ρ· V if ρ is the density of the solid. Energy E_V released is thus

E_V = - L · m = - L ·ρ·4/3·π· R ³.

This germ has a surface S = 4·π· R ². To create it, it is thus necessary to spend an energy E_S which is worth σ· S , where σ is the surface tension. There is thus

E_S = σ·4·π· R ²

The creation of the germ is not possible that if the system decreases its energy, i.e. if

E_V + E_S < 0

that is to say

- L ·ρ·4/3·π· R ³ + σ·4·π· R ² < 0

and thus if

r > \ frac {3 \ sigma} {L \ rho}

As σ decreases with the temperature, the small germs will be stable at low temperature. When the system has just the melting point, the minimal ray is too large so that a germ can be formed. This critical ray can decrease only if σ decreases, therefore either by the arrival of an impurity, or by the reduction in the temperature. The impurity can also act like a pre-germ of sufficient ray.

To support solidification, one can thus introduce a flocculating agent (impurity), or create defects in the wall of the container (for example of the stripes or the asperities).

Solidification of binary

Solidification with balance

Let us consider binary, i.e. a mixture of two pure substances has and B . The binary diagram of this system makes it possible to predict the way in which solidification will occur. Let us take to simplify the case of a system with single solid solution.

Let us take a liquid made up of 100 - C ₀ % of phase has and of C ₀ % of phase B (one uses mass concentrations in general).

It is supposed here that at any moment, all the solid is with balance with the liquid, which means in particular that the solid is homogeneous. In practice, that means that solidification is slow, and that the diffusion in solid phase makes it possible to homogenize the solid (the convection makes it possible to homogenize the liquid phase).

One puts a liquid in a mould, and one lets the mixture cool. At the temperature T ₁ defined by the intersection enters the liquidus and the vertical line corresponding to C ₀, the first germ solid is formed; it is formed against the wall of the container since it is the coldest part.

This first germ is a solid with balance with liquid with T ₁; it is thus on the solidus, and has a concentration C ₁; one notices that C ₁ is worth almost 0, it is body has almost pure.

At a given temperature T ₂, the horizontal line corresponding to this temperature cuts the solidus to a concentration C _{2 S} and the liquidus to a concentration C _{2 L}. At this temperature, the solid has a concentration 100 - C _{2 S} of has ; the solid being richer in has than the initial mixture, the liquid was impoverished and nothing any more but 100 - C _{2 L} contains; % of has .

At the end of solidification, the solid has obviously a content 100 - C ₀ in has . This determines the temperature of end of fusion T ₃. The last drop of liquid to be solidified has a content 100 - C _{3 L} in has , very weak, it is almost B pure; as the solid is still slightly richer in has than the initial mixture, this drop completes “to dilute” has .

Regulate moments

When solidification is done with balance, the diagram of phase makes it possible to know which is the proportion of mixture which solidified and which proportion remains solid.

At a temperature T ₂ given, the formed crystals have a concentration C _{2 S} in has , and the liquid has a concentration C _{2 L} in has . The matter propotion in liquid and solid form is given by the rule of moments :

let us consider the segment horizontal T = T ₂ uniting the solidus and the liquidus; this segment is cut by the vertical line C = C ₀, which forms two segments length L ₁ and L ₂

the report/ratio length of the segments L ₁/ L ₂ thus defined gives the report/ratio of the proportions of solid Liquide and .

It is as if there were a balance whose pivot is not in the center of the plague, one of the plates carrying the liquid, the other the solid (from where the reference to the moment of a force).

Solidification except balance

Now, we will consider that solidification is too fast so that the diffusion allows the homogenization of the solid. Then, only the surface layer of the solid to the contact with the liquid is with balance; the part of the solid under this surface layer is isolated from the liquid and thus does not contribute to the balance of solidification. It is as if the concentration C ₀ evolved/moved during solidification; indeed, the liquid is impoverished in has and grows rich in B .

As previously, the first germ is a solid with balance with liquid with T ₁; it is thus on the solidus, and has a concentration C ₁; one notices that C ₁ is worth almost 0, it is body has almost pure. These first germs are formed on the wall of the mould (the coldest part).

The liquid is impoverished in has progressively. At a given temperature T ₂, it is not it solid in entirety which has a concentration C _{2 S}, but only the germs formed at this time there.

The liquid continues to be impoverished during solidification, and the last formed germs, which are in the center of the mould, are very rich in B pure; the temperature of end of fusion T ₃ is then lower than the temperature of solidification to balance.

It is seen that the formed part is heterogeneous; this is why the ice floes have bubbles in the medium (the pure water freezes on the sides and rejects the air dissolves towards the center, until the moment when one has fresh air).

Crystalline structure

If the formed solid is Cristallin, the structure of the ingot is in general the following one:

at the edge, one has a column-like structure: the crystals are lengthened, perpendicular to the wall, there is a preferential crystalline orientation (texture);
in the center, a structure équiaxe: the crystals are symmetrical and Isotrope S (without preferential orientation).

In certain cases, one observes Dendrite S at the edges of the ingot.

Simple: Freezing

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