[susdujcrd]

I have three elements, Ba, Pb, Sn, that when undergo combustion and then rapid condensation from gas phase (about 3000K/1ms)
form one ABC phase solid (BaPbSn). When I add a fourth element, Al, I get primarily two phase (BaAl, PbSn) solid.
Obviously this phenomena is thermodynamically favourable. My guess (still undergraduate)
is that there is a solubility limit in the solid phase of these elements in a way that beyond a
certain amount of Al, the chemical potential of the single phase solid is higher than that of two-phase
solid.

I want to offer a theoretical/computational model that will explain this phenomena. Problems are:
1. This is a proccess that occurs in high temperatures and pressure (4000K and 40,000psi in 1 millisecond) so it can't be reproduced in the lab.
2. This is obviously in the field of non-equilibrium therodynamics, seems way over my league (I recently finished an introductory course on thermodynamics).
2. Prior research on the subject is almost non existent.


I really don't know where to start. This is not homework, it's a research project I'm interested in.
I'll appreciate any help/direction.

[Enthalpy]

By spraying the hot metal on a cold rotating drum, you can achieve this kind of cooling speed. Google:
"rapid solidification technique" "K/s"
figures like 10⁶ and 10⁷ K/s appear.

[Corribus]

Obviously this phenomena is thermodynamically favourable.

Not necessarily. It could be a kinetically favorable product that is only quasi-stable. Not saying it is, but I certainly wouldn't just assume it to be otherwise.

[curiouscat]

1. This is a proccess that occurs in high temperatures and pressure (4000K and 40,000psi in 1 millisecond) so it can't be reproduced in the lab.

So what is the basis for all the assertions you've made so far?

[susdujcrd]

Barium nitrate, lead styphnate and antimony sulfide form a gun bullet primer mix. These compounds undergo combustion during gunfire and then form particles which are analyzed by forensic means, usually SEM/EDX. Some bullet manufacturers add aluminum to the mix in order to increase the temperature during the combustion. While analyzing gunfire samples I noticed that in primer mixes that contain aluminum, there is a separation of phases in the resulting gunfire particles, from one PbBaSn phase to particles that contain two primary phases, AlBa and PbSn. This is the phenomena I'm trying to explain.  Maybe it's just a matter of differences of solidification temperature of the new phases. I didn't find any information on these newly formed compounds.

[Enthalpy]

Could it be that aluminium reacts with the nitrate, and the resulting heat lets remaining aluminium alloy with barium? That would result from the limited mixing of powders, something not predicted from a homogenous flame.

[curiouscat]

While analyzing gunfire samples I noticed that in primer mixes that contain aluminum, there is a separation of phases in the resulting gunfire particles, from one PbBaSn phase to particles that contain two primary phases, AlBa and PbSn.

I'm not very familiar with these techniques: How do you know there is phase separation? You mean you find no sample that registers all 3 metals?

Also, Sn or Sb?

[curiouscat]

Have you checked out the trimetallic phase diagram in a handbook?

[curiouscat]

My guess (still undergraduate)
is that there is a solubility limit in the solid phase of these elements in a way that beyond a
certain amount of Al, the chemical potential of the single phase solid is higher than that of two-phase
solid.

Sounds like a reasonable guess to me.

I want to offer a theoretical/computational model that will explain this phenomena. Problems are:
1. This is a proccess that occurs in high temperatures and pressure (4000K and 40,000psi in 1 millisecond) so it can't be reproduced in the lab.

Well if you are conjecturing it is a thermodynamic ally stable phase separation these points may not matter.

2. This is obviously in the field of non-equilibrium therodynamics,

Not necessarily. How do you know that the equilibrium does not favor phase separation as well?

I really don't know where to start.

Start with a metallurgy / material sci. textbook. Alloying & phase separation of intermetallic alloys has been studied to death. You may or may not find this particular system but the general approach to model these systems is well known.

[susdujcrd]

Hey all,
I'm resurrecting this thread. Did not have the dedication needed for the past couple of months due to personal reasons. But now I'm back in business and determined to reveal this mystery

Could it be that aluminium reacts with the nitrate, and the resulting heat lets remaining aluminium alloy with barium? That would result from the limited mixing of powders, something not predicted from a homogenous flame.

Could be. However, I have a strong intuition that this could be explained thermodynamically, so this is the lead I'm following at the moment.

I'm not very familiar with these techniques: How do you know there is phase separation? You mean you find no sample that registers all 3 metals?

Also, Sn or Sb?

When performing composition analysis with EDX (x rays dispersing from the sample) you can see particles that are mainly made of Al and Ba, and others that are mainly Sb and Pb, but not alot of ones with BaSbPb phase like in normal Al-free conditions.

You may or may not find this particular system but the general approach to model these systems is well known.

After an extensive search I didn't find this particular system. Books don't go further than trimetallic. My next best option would be to compute a theoretical 4 component phase diagram
(Barium nitrate, lead styphnate, antimony sulfide and some aluminum oxide). Where can I find the guidelines on how to model such a system?