  Recently, the bi-layer Kagome lattice material Ca$_{10}$Cr$_7$O$_{28}$ has
been shown to be a quasi-two-dimensional quantum spin liquid (QSL) where the
frustration arises from a balance between competing ferromagnetic and
antiferromagnetic exchange within a bi-layer. In an attempt to understand what
happens when this balance is disturbed, we present a magnetic dilution study.
Specifically, we have synthesized Ca$_{10}$(Cr$_{1-x}$V$_x$)$_7$O$_{28}$ (0
$\leq$ x $\leq$ 0.5) where magnetic Cr$^{5+}$ ($S = 1/2$) is partially replaced
by non-magnetic V$^{5+}$ ($S = 0$). We also synthesized the fully non-magnetic
isostructural material Ca$_{10}$V$_7$O$_{27.5}$. We report a detailed
structural, magnetic and heat capacity study on these materials. A monotonic
increase in the unit cell parameters is found for the
Ca$_{10}$(Cr$_{1-x}$V$_x$)$_7$O$_{28}$ materials with increasing $x$. An order
of magnitude decrease in the Curie-Weiss temperature from $4$ to $0.5$~ K is
found for the partial V substituted samples, which indicates a relative
increase in antiferromagnetic exchange with increase in V content. However,
despite this change in the relative balance in the exchange interactions and
the large disorder introduced, no magnetic ordering or spin-glass state is
observed down to $2$~K in the V substituted samples. The QSL state of the
parent compound thus seems surprisingly robust against these large
perturbations.
