ELNES at magic angle conditions

If one needs to cancel the effects of the anisotropy of the sample in a EELS experiment in the TEM, a particular couple of values for the collection and convergence angle must be used, called magic angle conditions (MAC). Recent developments in the theory have shown that a full relativistic treatment is mandatory to correctly describe this effect and that the MAC are strongly dependent on the acceleration voltage. We show how the analytical formula can be derived and give the exact analytical solution for the MAC which can then be easily applied to every practical case. We show the consequences of the energy dependence of the magic angle and that the parallelity of the beam will be the limiting factor for high acceleration voltages while for low acceleration voltages the contribution coming from Bragg spots may make it impossible to reach MAC.