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1 9 / . 4. 1/ the d i e l e c t r i c function e(m) of the transmitted substance. This interesting aspect needs a more detailed discussion of the procedure. In an energy loss spectrum of electrons we measure the intensity of electrons (number per second): I(AE,~) having lost the energy AE and being scattered into the direction ~; ~ means a vector with i~l = 0 the scattering angle against the primary beam. 3) with I(AE,~), is important for the quantitative v e r i f i c a t i o n of the physical assumptions of the d i e l e c t r i c theory; i t shall be sketched b r i e f l y .

G . , for p-terphenyl in Fig. 8. 15/. The loss i n t e n s i t y at low energies indicates whether we have to do with a metal or an i n s u l a t o r : In metals the loss function starts with zero at AE = 0 and increases l i n e a r l y with AE as can be calculated from the free electron loss function, whereas in substances with a band gap the loss function is zero up to the energy at which AE equals the gap energy. j2- -? 5 0 b) 0 Graphit / \ j ~ Irn-I ~,, / I I I t 10 20 30 eV 40 Fi 9. 6a,b. The loss function of an uniaxial crystal (graphite); (a) Im(-1/~): q• axis; (b) Im(-1/~): qll c axis.

Full l i n e / 5 . 8/ . 5. 5- a) I I b) o 10 20 30 eV Fig. 5a,b. Dielectric function of gold. 7/. 8/ lihe from optical measurements. 10/ 48 e) In anisotropic crystals the spectrum depends on the d i r e c t i o n of ~ inside the c r y s t a l , e . g . , i f in graphite the d i r e c t i o n of q is oriented p a r a l l e l to the c axis or to the a axis d i f f e r e n t loss functions and ~ values are measured, see Figs. 7. The s i t u a t i o n is more complex in b i a x i a l crystals where the d i e l e c t r i c tensor has three d i f f e r e n t s values in the main axes.