Dear waqasmalik,

I know of something called 'Constitutional Supercooling'.

Phase diagrams are drawn based on equilibrium conditions. But this is rarely the case. During solidification (be it welding or casting), the liquid adjacent to the solid has a higher percentage of solute. So, it is at a different (lower) temperature than prescribed by the liquidus of the equilibrium phase diagram. This difference is known as Constitutional Supercooling as it is due to composition of the liquid.

Regards.

DHURJATI SEN
Kolkata, India

Solidification in a complex multi-component/multi-phase system is not a smooth uniform process.
You have temperature gradients, composition variation, and then you have the thermodynamic effects of solidification (latent heat).
In the process of solidification (of most real alloys) you get things solidifying, and then at least partially re-melting in the process.
A lot of work have been done trying to get single crystal parts cast, they have tackled this from both the alloy design side and the physical design of both the part and the casting process. That is a place to find a lot of this research.

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P.E. Metallurgy

Thanx for responses. Please find attached the mathematical relationship for the temperature gradient which establishes the criteria for the stabillity of planar growth.

• https://files.engineering.com/getfile.aspx?folder=445a3a34-9670-453c-93b0-7

Here is the formula. The text in above and in this image is from Welding metallurgy by Sindo kou.

The confusion is that if we look at G/R criteria individualy then Ofcourse, for stable planar growth, G should be high and R should be low which leads to higher value of G/R.

Confusion is when we look at G/R in terms of Delta T/ Diffusion coefficient. Author says that "higher freezing range delta T and lower diffusion coefficient will make it difficult for planar interface to grow". Although this will lead to higher G/R which the author previously stated that higher G/R is required for stability of planar growth.

Why this different position of author? Or am i missing something?

• https://files.engineering.com/getfile.aspx?folder=857f2f56-f40a-487f-9a06-c

link in case anyone wants context

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Rightly posted.

Solidification is a fundamental for being a good metallurgist (my hypothesis). There are so many theories, math models over there, some of which are trying to confuse people. If one does not scratch the basic, you will lose.

Constitutional Supercooling is nothing more than that, the composition change in liquid (compositions varies with decrease of temp) will change the solidification temperature. For stable planar growth, you must have a position temperature gradient to compensate the so-called Constitutional Supercooling. G/R >= Delta T/D_L, is an extremely simplified formula. It applies only two component system, and with only diffusion in liquid being taken into consideration. It ignores latent heat, heat conductivity difference solid and liquid phases, and interface disturbs etc. You can imagine latent heat will change the temperature profile at L/S interface.

Solidification is a very complicated process. However people can still use G/R>= ΔT/G_L as a general criteria for "Constitutional Supercooling". @OP, i do not see the contradiction from what the author says. he just tried to say the same thing from two perspectives: high temp gradient (somewhat high cooling rate which could also lead to high growth rate) is beneficial for a stable planar growth, while wide solidification range (large ΔT) leads to deep Constitutional Supercooling, and so damages planar growth, leading to cellular and columnar/equiaxed dendritic growth.

Thanx for your response Magben.

Agreed that higher value of G/R is required for stable planar growth. Higher value of G and lower value of R will give us higher value of G/R. This is true if we do not consider the other side of equation as given below.

G/R= ΔT/D.

About this formula author says that higher value of ΔT and lower value of D will make it difficult for planar growth to be stable. You see higher value of ΔT and lower value of D will be give us higher value of G/R mathematically. We have already established that higher value of G/R gives stability to planar growth. So why having higher value of freezing range and lower value of D (which is giving me higher G/R) makes it difficukt for planar growth to be unstable. This thing should be more conducive for continuation of planar growth.

@OP, no, this is not a formula, but rather a criteria. It tells you to judge/make efforts from two perspectives to obtain a stable planar growth: One is to increase G and/or decrease R, so high G/R, that is something you can do to control. The other is to decrease ΔT and/or increase D, so lower ΔT/D , that is determined by the alloy system, not something you can do unless you can change the composition of your alloy.
Increasing G/R and/or decreasing ΔT/D will make your easer to meet the criteria: G/R>=ΔT/D, for a stable planar growth.

Great. Thankyou Magben. I understand now.

Hello Magben. I f you dont mind i have another question regarding this topic.

The figure in the same book quotes that

"if the actual temperature gradient in the liquid is greater than liqiudus temperature then planar growth is stable"

Why the word growth is there, if the actual temperature of the liquid is greater tha melting temperature then the Gibbs energy change is positive, liquid is a stable phase there. Solid will not form as it is thermodynamically unfavorable. Then why growth will take place? I admit that solid liquid interface will be stable, it will remain planar but will it grow? How?

I am having hard time understanding this.

Best Regards

I do not read the book but I bet the author meant the temperature gradient, not the temperature. When dT_actual/dx > dT_L/dx, there is no constitutional supercooling, the growth is planar model.
A side note, for a pure metal, there is NO constitutional supercooling, only the temperature profile affect growth model. But it can still go with a columnar/dendritic growth when latent heat creates a negative temperature gradient in liquid.