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1.1.AtomicDisplacements
21
a)
c)
b)
d)
Figure1.7.DisorderedTi/Nbatoms:(a)cubic;(b)tetragonal;(c)orthorhombic;(d)rhombo-
hedral.Theblackdotmarkstheunitcellcenter.Thearrowsmarkthedirectionofspontaneous
polarization.
produceplanesofdifusesheetsperpendicularto<100>.Whatthismeans
isthatlocallythestructureisnotcubicbutactuallyrhombohedral,since
withineachshort-rangeorderedregiontheTiatomsaredirectedalongin-
dividual3-foldaxes:thusatthelocalscaleofafewnanometers,thecrystal
isactuallypolar,withthepolarizationefectivelyaveragedtozeroover
allunitcells.InthetetragonalphaseIItheTiatomsoccupyfourpossible
<111>sitessothattheyaverageouttogivearesultantpolarizationalong
the[001]direction.Inthiscaseonesetofdifuseplanesvanishesleaving
twosetsperpendicularto[100]and[010].IntheorthorhombicphaseIII,
theTiatomsoccupyjusttwoofthe<111>sitestogivearesultantaverage
polarizationalong[110]andthenonlyonesetofdifuseplanesisleft.
Finally,intherhombohedralphaseIVthedifusescatteringisabsentalto-
getherandthestructureisfullyorderedwiththeTidisplacedalong[111].
Thisisaverybeautifulmodelwhichhasbeenstudiedformanyyears,but
withconflictingviewsonwhetheritisactuallycorrectornot.Forexample