Recent DFT (density functional theory) simulations showed that metals have a hitherto overlooked symmetry termed hidden scale invariance [Hummel {em et al.}, Phys. Rev. B {bf{92}}, 174116 (2015)]. According to isomorph theory, this scaling property implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics are invariant to a good approximation when given in properly reduced units. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. This paper investigates consequences and implications of the isomorph theory in six metallic crystals; Au, Ni, Cu, Pd, Ag and Pt. The data are obtained from molecular dynamics simulations employing many body effective medium theory (EMT) to model the atomic interactions realistically. We test the predictions from isomorph theory for structure and dynamics by means of the radial distribution and the velocity autocorrelation functions, as well as the rather dramatic prediction of instantaneous equilibration after a jump between two isomorphic points. Many properties of crystals tend to be dominated by defects and many of the properties associated with these defects are expected to be isomorph invariant as well. This is investigated in this paper for the case of vacancy diffusion. We find the predicted invariance of structure and also of dynamics, though less rigorous. We show results on the variation of the density scaling exponent $gamma$, which can be related to the Gruneisen-parameter, for all six metals. We consider large density changes up to a factor of two, corresponding to very high pressures. Unlike systems modelled using the Lennard-Jones potential where the density scaling-exponent $gamma$ is almost constant, it varies substantially when using the EMT potential and is also strongly material dependent.
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