  We study the effect of impurities on the two types of spin-dimers in the
hybrid chain/ladder spin 1/2 quantum magnet Sr$_{14}$Cu$_{24}$O$_{41}$. Four
different impurities were used, namely, the non-magnetic Zn (0.0025 and 0.01
per Cu) and Al (0.0025 and 0.01 per Cu), and magnetic Ni (0.0025 and 0.01 per
Cu) and Co (0.01, 0.03, 0.05 and 0.1 per Cu). These impurities were doped in
high-quality single-crystals synthesized by the floating zone method. The
magnetic susceptibility of pristine Sr$_{14}$Cu$_{24}$O$_{41}$ is analyzed
rigorously to confirm that at low temperatures (T $<$ 5 K), the "free" spins in
the chains undergo a long-distance dimerization as proposed in a recent study
[Sahling et al. Nature Phys., \textbf{11}, 255 (2015)]. The effect of impurity
on these dimers is analyzed by measuring the specific heat down to T = 0.06 K.
We found that even at the lower impurity concentration, the long-distance
dimers are significantly severed, but the quantum entangled spin dimerized
state of the chains persists. On the other hand, the other type of spin dimers
that forms at relatively higher temperatures via an intervening Zhang-Rice
singlet are found to be practically unaffected at the lower impurity
concentration; but at 1\% doping, even these are found to be considerably
severed. The effect of Co impurity turned out to be most unusual displaying a
strongly anisotropic response, and with a dimerization gap that suppresses
faster along the chain/ladder direction than perpendicular to it as a function
of increasing Co concentration.
