Measuring Inter-planar Spacing using X-Ray Diffraction – P15

X-ray diffraction was explored as an analysis technique in different materials. X-rays were used to identify an unknown crystal, calculate the Plank constant, and find the inter-planar spacing’s of aluminium.

In the experiment Leybold Didactic Systems x-ray apparatus was used. The X-Ray apparatus was connected to a data logging computer, which recorded the count rate of x-rays at different angular spacing’s. In the apparatus, x-rays are produced by accelerating electrons into a Molybdenum target which produced a Bremsstrahlung continuum containing the Kα and Kβ transitions from Molybdenum. These transitions occur at wavelengths, Kα = 0.7107 × 10−10 nm and Kβ = 0.6310 × 10−10 nm. By altering the potential difference used to accelerate the electrons, the energy of the produced x-ray is changed. Initially, the minimum wavelength of x-rays produced was compared to the electron accelerating voltage, in order to determine Plank’s constant. A NaCl crystal was used to separate the different wavelengths of x-rays to different angular separations, where the count rate of each could be recorded. The shift in position of the Kα and Kβ lines from NaCl to an unknown FCC crystal was recorded. Because different crystals have different inter-planar spacing’s and therefore different lattice constants, the x-rays were diffracted to different angles depending on the crystal.

X-rays were shown to be a useful tool in the analysis of crystals, allowing the lattice constant and therefore type of crystal to be identified. An un- known crystal was analysed and found to have a lattice constant of 0.409 ± 0.009 pm. From this result the crystal was identified as LiF, which has a lattice constant of 0.403 pm [2]. It was then found that zirconium could be used to filter out wavelengths up to Kα. Using this filtered radiation, the inter-planar spacing of aluminium was determined. X-Ray diffraction was proved to be a useful technique as all the literature values of inter-planar spacing’s of aluminium were within the measured results uncertainties.

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