  Atomic spectroscopy is used to search for the space-time variation of
fundamental constants which may be due to an interaction with scalar and
pseudo-scalar (axion) dark matter. In this letter, we study the effects which
are produced by the variation of the nuclear radius and electric quadrupole
moment. The sensitivity of the electric quadrupole hyperfine structure to both
the variation of the quark mass and the effects of dark matter exceeds that of
the magnetic hyperfine structure by 1-2 orders of magnitude. Therefore, the
measurement of the variation of the ratio of the electric quadrupole and
magnetic dipole hyperfine constants is proposed. The sensitivity of the optical
clock transitions in the Yb$^+$ ion to the variation of the nuclear radius
allows us to extract, from experimental data, limits on the variation of the
hadron and quark masses, the QCD parameter $\theta$ and the interaction with
axion and scalar dark matter.
