Correcting chemical formulae for FLiNaK and FLiNaBe

[tokasamwin]

FLiNaK and FLiNaBe are currently treated as chemical formulae, rather than material names for classes of materials.

This commit replaces these with formulae of LiF(46.5%)-NaF(11.5%)-KF(42%) for FLiNaK and LiF(31%)-NaF(31%)-BeF2(38%) for FLiNaBe, with references to where these have been taken from.

Previous atomic fractions:

Material	Li	F	Na	Be	K
FLiNaBe	25%	25%	25%	25%	0%
FLiNaK	25%	25%	25%	0%	25%

Current atomic fractions

Material	Li	F	Na	Be	K
FLiNaBe	15.5%	56.33%	15.5%	12.67%	0%
FLiNaK	23.25%	50%	5.75%	0%	21%

#Edit: @shimwell is right, FLiNaK is 50% F and this was in the .json file - I wrote the wrong value to the PR table. Corrected now.

[shimwell]

Thanks for this fix.

FLiNaK changes look great

Perhaps the table in the PR description should have 50% instead for F
Current atomic fractions

Material	Li	F	Na	Be	K
FLiNaK	23.25%	50%	5.75%	0%	21%

[shimwell]

I think there are a few FLiNaBe in this paper, could we mention which one perhaps by having mol definition

[shimwell]

Can we just double check the FLiNaBe

"chemical_equation": "Li465Na465Be380F1690"

Has the 46.5 been carried over from FLiNaK's LiF fraction?

Many thanks for the PR, really appreciate the corrections provided

[tokasamwin]

Can we just double check the FLiNaBe

"chemical_equation": "Li465Na465Be380F1690"

Has the 46.5 been carried over from FLiNaK's LiF fraction?

Many thanks for the PR, really appreciate the corrections provided

So the simple fractions are Li 15.5%, Na 15.5%, Be 12.666666%, F 56.333333%. I multiplied these by 3 so that I can put values in without rounding errors. So 46.%, 46.5%, 38%, and 169%, totalling 300% which will get renormalised to the right fractions

[shimwell]

Thanks for explaining, and sorry to keep pushing on this one.

I agree the scaling is harmless. OpenMC normalises the multipliers in add_elements_from_formula (it divides each by their sum) and it rejects non-integer multipliers outright, so multiplying up to get integers is exactly the right thing to do. My concern isn't the x3, it's the ratio of Li/Na to Be.

Working your atom fractions back to salt mole fractions:

Li 15.5, Na 15.5, Be 12.6667  ->  LiF 35.5% - NaF 35.5% - BeF2 29.0%

That isn't the LiF(31%)-NaF(31%)-BeF2(38%) quoted in the PR description. One quick way to see it: in a LiF-NaF-BeF2 mixture the fluorine atom fraction depends only on the BeF2 content, F = (1+z)/(2+z) where z is the BeF2 mole fraction. So F = 56.33 at.% implies z = 29 mol% BeF2, whereas 31-31-38 gives F = 57.98 at.%.

For 31-31-38 the fluorine count is 31 + 31 + 2*38 = 138, giving:

"chemical_equation": "Li310Na310Be380F1380"

	Li	Na	Be	F
current PR	15.5%	15.5%	12.67%	56.33%
LiF(31)-NaF(31)-BeF2(38)	13.03%	13.03%	15.97%	57.98%

Incidentally no scaling is needed at all here, since the salt mole fractions are already integers: Li31Na31Be38F138 gives the same result and is perhaps easier to check by eye against the reference. My guess is that 46.5 is FLiNaK's LiF fraction carried across, though I may be wrong about how it arose.

On the earlier question of which flinabe: I couldn't get past the paywall on FST 68(3) 669-673, so I can't confirm which composition that paper uses. For what it's worth, the commonly quoted ones are 31-31-38 and 33-33-33, and Grimes et al. 1958 used 35-27-38 (Serrano-López et al., arXiv:1307.7343: "The usually suggested composition for ternary FLiNaBe in recent papers is (0.31-0.31-0.38) or (0.33-0.33-0.33)"). None of them is 35.5-35.5-29, which is what makes me think something has slipped. Putting the mol definition in the comment would make it checkable at a glance.

The FLiNaK numbers do check out exactly, for the record. Table 12-1 on p. 571 of Chapter 12 of Fluid Fuel Reactors lists LiF-NaF-KF (46.5-11.5-42), m.p. 454 °C under a "Composition, mole %" heading, and Fig. 12-1 on p. 570 is the ternary diagram with the 454 °C eutectic (free scan: https://moltensalt.org/references/static/downloads/pdf/FFR_chap12.pdf, p. 571 is PDF page 3). Also, on the description table: in any LiF-NaF-KF mixture the fluorine is exactly 50 at.% because all three cations are monovalent, so 50% holds whatever the ratios are.

One last low priority thought. The library tests do build every material (test_dictionary_of_materials_makes_openmc_materials), so a formula that parses will pass CI even if the numbers are off. A small check on the resulting element fractions for these two entries would catch this class of slip, though that's happily a separate PR.

Thanks again for digging out the references, the FLiNaK correction alone is well worth having.