The breaking strain of neutron star crust Page: 3 of 11
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tween them, and the electron screening length Ar = strained by moving a boundary layer of frozen ions on top
lrl/2/2e(3rr2ne)1/a with ne the electron density. The to- and bottom against each other . We cutoff the po-
tal potential energy is given by the sum over all pairs tential at the large distance rent = 10Ae resulting in each
>1<1 k(r'Z). Charge neutrality insures that ne = Zn ion interacting with about 5400 neighbors; for smaller
where n is the ion density. The ions are assumed to form values of rout the results depend on rcut  (Figs. S1
a classical one component plasma that can be character- and S2). 
ized by the Coulomb parameter I', Figure 1 shows the shear stress versus strain for body-
Z2c2 centered cubic (bcc) crystals as it is the equilibrium struc-
T = a . (2) ture at the given density and F; some results for the
face-centered cubic (fcc) structures are added as some
This is the ratio of a typical Coulomb energy to thermal metastable fcc phase might be present in the crust as
energy and the ion sphere radius a = [3/(4irn)]1/3 is a well. For all investigated crystallographic shear systems
typical distance between ions. the perfect crystals all show a BS well above 0.1, and
We calculate at a reference density of n = 7.18 x 10-5 break in a rather abrupt fashion with only a very small
fm-3 using Z = 29.4 and an atomic mass number A = 88 region where plasticity, i.e. deviation from a linear stress-
(1 x 1013 g/cm3) . Results can be scaled to other strain relation, is present. The multi-million ion systems
densities at constant F and approximately scaled to other were strained at a rate of 4x 10-- c/fm. As we cannot
Z at constant F, which involves only a small change in Ae. simulate the very large time and length scales associated
Most of our simulations are for a temperature T = 0.1 with NSC we have to rely on estimates based on a series
MeV. This corresponds to F = 834. We ignore the effects of simulations that suggested basically no size effects for
of free neutrons that are present in the inner crust. the single crystal simulations presented here (Fig. S3)
and a converging result at low shear rates (Fig. S4). We
also note that tripleing the temperature only reduces the
000014 a '"" maximum stress by about 25% and does not significantly
0m1\ r--'-- -t alter the BS.
bccil0 0; nnj] of Ct-
0.00012 - - As very little is known about the defect structure, grain
tcc (ti1 )t11perfect - ',sizes, and associated grain boundaries of NSC that po-
S o.ooo1 tentially can reduce the strength, we also consider poly-
crystalline materials that are generated using a Voronoi
ae-os - -construction in which grain centers and orientations are
picked at random and each ion belongs to the grain center
se-os - -that is closest . After this initialization, the system is
' 'equilibrated by heating it from 0.1 to 0.3 MeV and back
4e-os , I - to 0.1 MeV over a total simulation time of 275000 fm/c.
The system is then sheared at a strain rate of 4 x 10 7
2e-05 .--' c/fm. Figure 2 shows one system with 12.8 million ions
at strains of 0.0, 0.05, 0.1, and 0.15 (for stress-strain
o 'I curve see Fig.i). The radial distribution functions ex-
0 o.os o.1 oss 02 hibit characteristic peaks of the bcc structure for strains
Shear strain up to 0.1. After failure, at 0.15 strain some degree of
FIG. 1: Shear stress versus strain for perfect and defective amorphization might be possible. The system starts to
bcc and fcc single crystals containig about 2 million ions for deform plastically near the grain boundaries in a collec-
different shear systems -as given by the shear plane and tive manner without exhibiting signs of dislocations or
direction- are shown. In addition a polycrystalline sample other more localized events (Fig.2 and movie S5). How-
containing 12.8 million ions and 8 randomly oriented grains ever, at large strains the samples are plastically deformed
with an average grain diameter of 3962 fm is shown. Results and the mode of failure seems to be a reorientation of
were obtained at a strain rate of 4x10-7 c/fm. local regions -possibly associated with some degree of
amorphization (Fig.2)- to accommodate the shear. This
collective, rather than more localized dislocation-based,
We perform large-scale MD simulations of shearing mode of plasticity makes the crystal stronger and break
NSC material as we believe that this is the most im- at larger strains than terrestrial metals, where the elec-
portant mode of failure in the crust. Tension simu- tronic density can have a localized structure to accom-
lations at constant volume, had a breaking strain and modate local defects. This failure mechanism also does
strength that was smaller by 2.5 and 2, respectively. not allow for voids or fracture to appear as these local-
We use two independent MD codes: YukawaMD is a se- ized defects would possibly heal under the influence of the
rial MD code where the system is strained by deforming high pressure. In fact, simulations that started out with
the periodic boundary conditions.  SPaSM  is a a cylindrical hole with a diairieter of 2.5x the nearest
high-performance parallel MD code where the system is neighbor distance initialized into the otherwise perfect
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Kadau, Kai & Horowitz, C J. The breaking strain of neutron star crust, article, January 1, 2009; [New Mexico]. (https://digital.library.unt.edu/ark:/67531/metadc934137/m1/3/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.