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The impact on the electric field distribution of a non-uniform concentration of polarizable species within cross-linked polyethylene insulation for High Voltage Direct Current (HVDC) cable is investigated. Two case studies are considered where the species are diffusing from the bulk of the insulation towards the interfaces or from the interfaces to the bulk. The first case is associated with diffusion of cross-linking byproducts that are known to be permanent dipoles. The second case is associated with diffusion of polarizable species from the interfaces (semi-conducting screens in the case of cables). A diffusion model is applied and used to derive a general expression for the polarization charge. Diffusion of by-products leads to the formation of "hetero" polarization charges adjacent to the electrodes whereas diffusion of polarizable species from the interfaces leads to the formation of "homo" polarization charge. Overall, the impact on the field distribution of a non-uniform concentration of polarizable species is weak when compared to space charge measurements. This suggests that inhomogeneous distribution of dipoles is unlikely the dominant phenomenon behind the heterocharges build-up in non-fully degassed XLPE samples.