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DEFECT S IN CRYSTALS
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absorption alloys arise associated assume band structure becomes behaviour bond Bravais lattice Brillouin zone calculation charge coefﬁcient conduction band conﬁned consider constant cubic deﬁned density determined diamagnetic dielectric difﬁcult diffraction direction dislocation effect electric ﬁeld elements empty energy band energy gap equation external ﬁeld Fermi energy Fermi level Fermi surface ferromagnetic ﬁlled ﬁlm ﬁnd ﬁnite ﬁrst ﬂux free atoms free electron gas frequency heat capacity hole impurity inﬂuence interaction ionic ions layer leading linear liquid low temperatures magnetic ﬁeld material modes molecule momentum N(EF neutron normal nuclear obtain occupied optical orbitals pair paramagnetic phase phonons Phys plane polarization potential primitive cell produce properties quantum rare earth reciprocal lattice reﬂection resonance sample scattering semiconductor shown in Fig signiﬁcant solid state physics space speciﬁc spin substances sufﬁciently superconducting symmetry thermal transition metals valence band valence electrons values vibrational wave function wave vector zero zone boundary