Diamonds in Neptune? In this publication from 1981, was shown that Neptune is raining diamonds:


  Many of the current models of Uranus and Neptune postulate a three-layer structure, consisting of an inner rocky core, a middle ‘ice’ layer of fluid, $\rm H_2\rm O$, $\rm{CH}_4$, $\rm{NH}_3$ and an outer hydrogen–helium layer of solar composition. The estimated pressures and temperatures of the ice layer range from about 6Mbar and 7,000K at the inner core-ice boundary to $\approx$ 0.2 Mbar and 2,200K at the outer ice/hydrogen–helium boundary. I point out here, that shockwave experiments on these liquids, as well as theoretical studies, imply that the $\rm H_2\rm O$ and $\rm{NH}_3$ in the ice layer are almost totally ionized, and the $\rm{CH}_4$ has been pyrolysed to carbon, possibly in the metallic or diamond form.


Question: In the decades since this work was published in 1981 have these predictions been addressed further, or even proven or disproven?

If this turns out to be true, would these diamonds have different physical properties than those on Earth because of the different formation mechanism?
People have demonstrated high-pressure diamond formation using laser-driven shocks, much in line with the original idea. The diamond rain idea seems to be doing well (popular science article about it, with references). 

However, it is quite likely that the diamonds could have different properties because of formation mechanisms. There are a lot of unusual allotropes of carbon, and local conditions of formation (not to mention impurities) may cause the carbon to turn into these forms rather than the standard diamond lattice. 

Simulations show that beyond 1000 GPa diamond has a BC8 structure. However, this is a pressure unlikely to occur inside Neptune's atmosphere: it occurs deep in the mantle, so sinking diamonds may shift crystal form.