  There are two general ways to compress the cuprates, by external pressure or
by internal pressure as induced by isovalent-ion substitution. Paradoxically,
they have the opposite effect on the superconducting transition temperature.
This thesis seeks to understand the salient difference between these two
pressures.
  We study three families of cuprates where the ion size can be systematically
altered; Bi$_2$(Sr$_{1.6-x}$A$_x$)Ln$_{0.4}$CuO$_{6+ \delta}$, ACuO$_2 $ and
LnBa$_{2-x} $Sr$_x $Cu$_3 $O$_{7-\delta} $ where Ln is a Lanthenide or Y and
A=\{Mg,Ca,Sr,Ba\}. We use a variety of techniques to explore our paradox, for
example; Raman spectroscopy to measure the antiferromagnetic exchange energy
and energy gaps, Density Functional Theory to calculate the density of states,
Muon Spin Relaxation to measure the superfluid density as well as a variety of
more conventional techniques to synthesize and characterise our samples.
  Our Raman studies show that an energy scale for spin fluctuations cannot
resolve the different effects of the two pressures. Similarly the density of
states, while an important property, does not clearly resolve the paradox. Our
superfluid density measurements show that the disorder resulting from
isovalent-ion substitution is secondary in importance for the superconducting
transition temperature.
  Instead, we find that the polarisability is a key property of the cuprates
with regard to superconductivity. This understanding resolves the paradox! It
implies that electron pairing results from either (i) a short-range interaction
where the polarisability screens repulsive longer-range interactions and/or
(ii) the relatively unexplored idea of the exchange of quantized, coherent
polarisation waves. More generally, we have also demonstrated the utility of
studying ion-size effects to further our collective understanding of the
cuprates.
