As a start I'm using 2" pink foam with aluminum tape as radiant barrier on the inside surface:
The foam is rated R-10. I'll put a liter of hot water in this and log the rate of change to get an idea of how much it reduces heat loss over open air. That should give me an idea of how much power I'll need the microcontroller temperature controller to handle.
I'd like to be able to keep it as low as 0.1degC per hour while minimizing fluctuations, but at this point I don't have any idea how challenging that will be.
As described above I put a 1 liter beaker of hot tap water into the chamber and stuck a thermometer through the top down into the water. I recorded the temperature every 10 minutes for a couple of hours, then wandered off for a while and then came back and got a final reading:
So I figure 1000L dropping 0.578C in 10 minutes is about 578 calories per 10 minutes, or 4.03 joules/second, 4 watts.
Room temp was 24C, and I was testing around 62C. The box surface is about 0.25 square meters, so that would be 4.03W/0.25sq.m, 16.1W/sq.m. R-value is ΔT/W/sq.m, so 38/16.1 = 2.36. The 2" pink foam spec is is R-10. Even with my shoddy construction I'd expect better than R-2.36.
Maybe that value is in RSI units. Wikipedia says the conversion from RSI to R-US is RSI * 5.68, so R-13.4. That sounds pretty reasonable considering the radiant barrier.
I might want to ramp the crystallization down to very cold temps, and it's a lot easier to just put the box in the freezer than it is to make a box that can cool itself, so the temp outside the box might be down at -20C. So, if I want to hold the box at 100C in a -20C environment, how much power do I need? Flipping the equation around and using the RSI value of 2.36: W/sq.m = ΔT/R, ΔT is 120C, so: 120C/2.36 = 50.9W/sq.m, or 12.7W for the 0.25 square meters of the box. Within my ability to measure that's linear scaling, which seems pretty reasonable from eye-balling the graph, which is also pretty linear over this narrow temperature range.
I'll give it some headroom and call the target 15W. On a 12V power supply I'll need to switch 1.25A. I've got a pile of IRF540N that'll be fine for that. My power supply is 12V at 3A, so my heating element needs to be between 4 and 10 ohms. Too low and I'll send the PSU into protection, too high and I can't get enough power out of it. That's probably another junk-box item.
Next up is electronics. I've got some old LM77 temp sensors laying around. They're not very accurate, but they'll be fine for a first iteration.
Started prototyping the controller:
The chip is an LM75 I had laying around. It's only 9 bit with the LSB reporting 0.5C increments. That's fairly awful, but it's good enough to get started. I can swap in a better sensor later.
I dug up an old nichrome toaster element to see if it would work as a heater:
I connected it to the desktop supply (which seems to be running 15V open-circuit, I may need to get in there and see what's going on with the regulation), and it runs at 13.7V and 2.05A, for 28.1W. That'll be perfect, I just need to put a MOSFET on to drive it and I should be able to hold the chamber at any temperature I like.
The insulated board it is wrapped around is 5 inches across which is just right to fit inside the chamber. I think that if I leave it on the board I can put it on one side of the chamber so that convection will prevent any stratification. I'll probably use one of the other toaster elements which is wrapped with all the turns on one side. I can face it toward the wall to create a chimney while avoiding radiant heating of the solution, That could definitely disturb crystal formation.