Question

in tem, we can obtain a diffraction pattern of a thin sample through the use of objective apertures that act as a barrier for incoming electron radiation in the microscope column. due to the small angle that the beam makes as it transmits through the crystal planes of tem samples, the bragg condition can be modified to: if electrons of wavelength (3.40x10^-12) m are transmitted through a thin cu film with a lattice parameter of (3.1600x10^-10) m and the distance r between the transmitted and diffracted spots is (6.5000x10^-4) m, what is the bragg's angle ( ) to obtain a tem diffraction spot for the first order (111) plane of cu? express your a

Answer 1

To find the Bragg's angle for the first order diffraction of the (111) plane in a thin Cu film using the given electron wavelength and lattice parameter, we utilize the Bragg's Equation and a geometric relationship involving the camera length and the diffraction spot distance on the photographic plate.

Step-by-step explanation:

The Bragg's angle is the angle at which constructive interference occurs due to electron diffraction in a crystal lattice, resulting in a diffraction pattern. According to the Bragg's condition, this occurs when the path length difference (PLD) between the waves reflected from successive crystal planes is a whole number of wavelengths. The Bragg Equation which expresses this condition is nλ = 2d sin θ, where n is the order of the diffraction, λ is the wavelength of the electrons, d is the spacing between planes in the crystal, and θ is the Bragg's angle. Given an electron wavelength of 3.40x10^-12 m, a lattice parameter (d-spacing) of 3.1600x10^-10 m, and using the small angle approximation, we can calculate the Bragg's angle for the first order diffraction of the (111) plane in a thin Cu film.

Using a geometrical relation involving the camera length (L) and the distance (r) between the transmitted and diffracted spots on the photographic plate, we can express sin θ as r / (2L), where L is the distance between the sample and the photographic plate. Thus, by manipulating the Bragg Equation and substituting known values, we can solve for the Bragg's angle θ.