Elastic properties of binary crystals in neutron stars and white dwarfs

Abstract

Elastic properties play an important role in neutron stars and white dwarfs. They are crucial for modeling stellar oscillations and different processes in magnetars and in degenerate stars which enter compact binary systems. Using electrostatic energy of deformed lattices, we calculate elastic moduli of ordered binary body-centered cubic (sc2) and face-centered cubic (fc2) lattices. We use two methods to determine the effective shear modulus µ eff . We show that µ eff calculated as an average of the shear stiffness over all possible wavevectors (for polarization vectors perpendicular to the wave vector) agrees with the results obtained from the linear mixing rule. For the sc2 lattice, our calculations are also consistent with the results of numerical simulations of disordered binary body-centered cubic lattice.

Electrostatic properties and stability of Coulomb crystals

“…For arbitrary c 1 and c 2 fcob ( , c 1 , c 2 ) is not fitted, at small |c 1 -1| and |c 2 -1| it could be obtained from the elastic moduli. 36 For any fixed in consideration the minimal value of fcob ( , c 1 , c 2 ) always achieves at c 2 = c 1 , but it is not necessary that this happens at c 1 = 1. For c 2 = c 1 and for some values of fcob ( , c 1 , c 2 ) − fccb is plotted in Figure 1, where fccb = fcob ( , 1, 1).…”

“…The binary body-centred orthorhombic and other deformed sc2 lattices were studied in Ref. 36 Instead of the fccb lattice, the deformed sc2 lattice has the global minimum of energy at its cubic configuration at any fixed Z 1 and Z 2 .…”

Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus

“…It perfectly agrees with the result by Baiko (2011), where the coefficient 0.1194572 was given. For two-component ordered crystals, tensor was calculated by Kozhberov (2019) and = 0 (within this calculation's accuracy). 5 Similarly, the equation ( 13) can be straightforwardly applied to calculate V eff for multicomponent lattice structures, whose energies were calculated by Chamel & Fantina (2016); Kozhberov (2018), but V eff was not studied previously.…”

“…If there is only one type of atomic nuclei at a given layer, they form a crystal with a body-centered cubic (bcc) lattice (Hamaguchi et al 1997;Baiko 2002;Kozhberov 2018). However, in multicomponent models (e.g., Fantina et al 2020;Carreau et al 2020a,b) more complicated lattices are possible (e.g., Ogata et al 1993;Chamel & Fantina 2016;Kozhberov 2019). Solidification into amorphous structure is discussed elsewhere (e.g., Jones 1999;Sauls et al 2020).…”

“…Electron screening was considered by Baiko (2012); Kobyakov & Pethick (2015); Baiko (2015). Elastic properties of multicomponent crystals were studied by Kozhberov (2019).…”