What crystal structures are predicted for the crystalline phase of matter inside crystalizing white dwarfs? Does it depend on the carbon/oxygen ratio?

Question

The abstract of Venner et al. (2023) A Crystallizing White Dwarf in a Sirius-Like Quadruple System includes the following:

The location of HD 190412 C on the 𝑇_eff − mass diagram implies it is undergoing crystallization, making this the first confirmed crystallizing white dwarf whose total age can be externally constrained. Motivated by the possibility that a cooling delay caused by crystallization can be directly detected for this white dwarf we employ a variety of methods to constrain the age of the system; however, our empirical age anomaly of +3.1 ± 1.9 Gyr is ultimately too imprecise to reach statistical significance, preventing us from making strong constraints to models of white dwarf crystallization. Our results are nonetheless compatible with the recent hypothesis that ²²Ne phase separation is responsible for the excess cooling delay of crystallizing white dwarfs.

The "pile-up" of white dwarfs in the 𝑇_eff − mass plot suggests temporary halt in the rate of apparent cooling and this is interpreted as an exothermic phase change. The phase change is further interpreted to be from a dense ionized plasma(?) to a very dense solid of primarily carbon with perhaps oxygen. If I understand correctly the solid phase is considered to be an actual crystal. Sciencealert.com's White Dwarf Star Enters Its Crystallization Era, Turning Into A 'Cosmic Diamond' puts the density at of the order of 10⁶ kg/m³ (which would make the interatomic distances of the order of only 0.5 Angstroms¹) so these crystals will not be something found or even reproducible on Earth.

Whether or not that white dwarf crystal is diamond is unknown; the density of white dwarfs is over around 1 million kilograms per cubic meter, while the density of diamond is about 3,500 kilograms per cubic meter. Denser allotropes of carbon do exist; on the other hand, there's plenty of diamond floating around out there in space.

¹per ProfRob's comment the density should be another 10³ higher still, making the interatomic spacing more like 0.05 Angstroms!

Question: What kind of crystal structures are predicted for the crystalline phase of matter inside crystalizing white dwarfs? Does it depend on the carbon/oxygen ratio?

note: I'm looking for the crystallographic primitive unit cell as well as the conventional cell, but if it's for example diamond cubit then that term covers both.

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Further reading:

• Wikipedia's White dwarf; Radiation and cooling

Answer 1

Finding an answer in the literature was a little vexing, perhaps because astrophysicists are not really interested in just what the crystal structure might be.

For instance, Horowitz et al. have a nice Physical Review Letter on "Crystallization of Carbon-Oxygen Mixtures in White Dwarf Stars" and ... never ... say what the crystal structure is. But, it does have a good overview of how the problem might be treated:

The electrons are assumed to be a degenerate Fermi gas. The ions interact with screened Coulomb interactions:

$v_{i,j}(r) = Z_i Z_j e^2 e^{-r/\lambda} / r$

Where $\lambda$ is the Thomas Fermi screening length.

A paper in Physical Review E by J. Hughto et al. uses a similar formalism for the ion-ion interaction. They define a ratio

$\kappa = a_e / <Z>^{1/3} \lambda $

where $a_e$ is the electron sphere radius in the degenerate gas. Their claim is that for their mixtures (carbon, oxygen, neon), $\kappa < 0.4$ and they expect the ground state to be body-centered cubic.

The reference for that claim is a paper in the Journal of Chemical Physics by S.S. Hamaguchi et al., titled "Phase diagram of Yukawa systesm near the one-component-plasma limit revisited". Although Hamaguchi is on one-component plasmas, the methodology is all very similar, and the phase diagram (Fig. 2 in the paper) shows that bcc is the only solid until $\kappa > 1$ is encountered, and then the low 'temperature' (its complicated) phase becomes fcc, with bcc remaining at higher temperature/energy.

So, the expected crystal structure in white dwarfs is body-centered cubic.