Direct observation of the formation of polar nanoregions in   Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ using neutron pair distribution function   analysis
  Using neutron pair distribution function (PDF) analysis over the temperature range from 1000 K to 15 K, we demonstrate the existence of local polarization and the formation of medium-range, polar nanoregions (PNRs) with local rhombohedral order in a prototypical relaxor ferroelectric Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$. We estimate the volume fraction of the PNRs as a function of temperature and show that this fraction steadily increases from 0 % to a maximum of $\sim$ 30% as the temperature decreases from 650 K to 15 K. Below T$\sim$200 K the PNRs start to overlap as their volume fraction reaches the percolation threshold. We propose that percolating PNRs and their concomitant overlap play a significant role in the relaxor behavior of Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$. 
I.-K. Jeong, T. W. Darling, J. K. Lee, Th. Proffen, R. H. Heffner, J.   S. Park, K. S. Hong, W. Dmowski, T. Egami