tag:blogger.com,1999:blog-13869903.post6593863764736155491..comments2024-03-28T04:15:44.459-05:00Comments on nanoscale views: What is (dielectric) polarization?Douglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-13869903.post-56360298186805878012018-08-13T11:21:33.713-05:002018-08-13T11:21:33.713-05:00Hi Don, see, that's what I'd thought befor...Hi Don, see, that's what I'd thought before, too - that one really has to worry about surfaces and their termination. The problem is apparently much worse than that, though. See page 3-4 of the Vanderbilt article (http://physics.rutgers.edu/~dhv/pubs/local_preprint/dv_fchap.pdf). Seems like it should be possible to define the bulk dielectric response of a 3d solid without worrying about surfaces. If you do DFT and look at Si both with and without an external electric field, and all you do is integrated up some apparently sensibly-defined polarization, you end up underestimating \(\kappa_{\mathrm{dc}}\) by an order of magnitude from the correct value. The Berry phase approach gives sensible definitions for the polarization in ferroelectrics as well, without regard to precise surface termination. Of course, I'm with you on the idea that one should always be able to talk about internal electric fields within materials (based on the motion of a gedanken or experimentally inserted "test charge"), and clearly surface termination can strongly affect that, depending on the geometry of the material.Douglas Natelsonhttps://www.blogger.com/profile/13340091255404229559noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-57636412262655776632018-08-13T10:48:53.518-05:002018-08-13T10:48:53.518-05:00Interesting, thanks.
Of course, the ambiguity abo...Interesting, thanks.<br /><br />Of course, the ambiguity about polarization can arise in much simpler situations, for example an ionic crystal like sodium chloride. Different ways of defining the unit cell give completely different dipole moments for the cell. And although (change in) induced polarization is easier to measure, there is a real thing that is the internal field in a salt crystal. <br /><br />I believe that everything ends up depending in principle on how the crystal is terminated (e.g. cations or anions as the last layer). I vaguely remember that there have been III-V structures (which are somewhere between ionic and pure covalent) grown by molecular-beam epitaxy that showed the expected sensitivity to the termination.<br />I would have expected that a complete theory of polarization would need to incorporate surface states as well. Don Monroehttp://www.donmonroe.infonoreply@blogger.com