Can a material made of a heavier isotope of an element become harder or stronger? I was wondering if any experiments have been done to measure if there is a change in the hardness or strength of a material made solely of a heavier isotope of an element which is a constituent of the material. Or if the strength or hardness increases with the increase in proportion of heavier isotopes of the atoms of a particular element jn the material.
 A: The nuclear force is a contact force, with potential energy curve
$$
V \propto \frac{e^{-r/r_0}}{r}.
$$
The range parameter $r_0$ is roughly one femtometer.  Nuclei in a solid are typically $10^5\rm\,fm$ apart, so the nuclear interaction between nuclei from different atoms is astoundingly suppressed.
If you think of a solid as a lattice of atoms connected by springs with Hooke constant $k$, the natural frequencies of these oscillators, 
$$ \omega_0 = \sqrt{k/m}, $$ will be different for crystals of different isotopes.  For instance the mass difference between carbon-12 and carbon-13 is about 8%, so compared to a C-12 diamond a C-13 diamond would have about 4% smaller resonant frequency.  My naive expectation is that this would probably change heat capacity, and possibly change thermal conductivity, but I don't know very much about hardness or other mechanical properties.
A: There is one small effect that has not yet been covered in the other answers.  When we solve Schrodinger's equation for the electron orbitals we use the so called reduced mass $$\mu=m_e m_n/(m_e+m_n)$$ so the solutions for the orbitals will be slightly different for the case where extra neutrons are added to the nucleus. The electron mass is so much smaller than the nuclear mass that this is a really minuscule effect and likely will not be experimentally observable for the properties that you are considering.
A: Drawing on my chemistry background and asking a few of my Ceramic Engineering friends, the answer is "No".  We had the consensus that the nucleus does not impart any physical property on the hardness or strength but the "electron cloud" and its interactions. The electrons are not affected in any way by the different in isotopes.  
