  We develop a dynamical model of the propagating nonlinear localized
excitations, supersonic kinks, in the cation layer in a silicate mica crystal.
We start from purely electrostatic Coulomb interaction and add the
Ziegler-Biersack-Littmark short-range repulsive potential and the periodic
potential produced by other atoms of the lattice. This approach allows the
construction of supersonic kinks which can propagate in the lattice within a
large range of energies and velocities. The interparticle distances in the
lattice kinks with high energy are physically reasonable values. The
introduction of the periodic lattice potential results in the important feature
that the kinks propagate with a single velocity and a single energy which are
independent on the excitation conditions. The found kinks are ultra-discrete
and can be described with the "magic wave number" $q\simeq 2\pi/3a$, which was
previously revealed in the nonlinear sinusoidal waves and supersonic kinks in
the Fermi-Pasta-Ulam lattice. The extreme discreteness of the supersonic kinks,
with basically two particles moving at the same time, allows the interpretation
of their double-kink structure. The energy of the supersonic kinks is between
the possible source of $^{40}$K recoil in beta decay and the energy necessary
for the ejection of an atom at the border as has been found experimentally.
