  In this work we study morphological characteristics of the critically-sized
crystalline nuclei at initial stage of the shear-induced crystallization of a
model single-component amorphous (glassy) system. These characteristics are
estimated quantitatively through statistical treatment of the non-equilibrium
molecular dynamics simulation results for the system under steady shear at
various (fixed) values of the shear rate $\dot\gamma$ and at different
temperatures. It is found that the sheared glassy system is crystallized
through nucleation mechanism. From analysis of a time-dependent trajectories of
the largest crystalline nuclei, the critical size $n_{c}$ and the nucleation
time $\tau_{c}$ were defined. It is shown that the critically-sized nuclei in
the system are oriented within the shear-gradient $xy$-plane at moderate and
high shear rates; and a tilt angle of the oriented nuclei depends on the shear
rate. At extremely high shear rates and at shear deformation of the system more
than $60$\%, the tilt angle of the nuclei tends to take the value
$\simeq45^\circ$ respective to the shear direction. We found that this feature
depends weakly on the temperature. Asphericity of the nucleus shape increases
with increasing shear rate, that is verified by increasing value of the
asphericity parameter and by the contour of the pair distribution function
calculated for the particles of the critically-sized nuclei. The critical size
increases with increasing shear rate according to the power-law,
$n_{c}\propto(\dot\gamma\tau_{c})^{1/3}$, whereas the shape of the
critically-sized nucleus changes from spherical to the elongated ellipsoidal.
We found that the $n_{c}$-dependencies of the nuclei deformation parameter
evaluated for the system at different temperatures and shear rates are
collapsed into unified master-curve.
