Lab Report

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Results and discussions: The structure of the prepared material was investigated employing many techniques such as X-rays diffraction, SEM and TEM electron microscopy. In order to scrutinize the crystal structure of the samples X-rays diffraction was carried out using diffractometer XPERT-MPDUG, Philips PW3040. Figure (1) depicts the X-ray diffraction of the as synthesized samples. It can be seen that the nature of the sample is formed in poly crystalline form. The most important peaks are displayed. The most intense peaks were indexed to be 201, 011, 111, 400, 311, 102, 020, and 112. The indexed peaks correspond to single pure orthorhombic phase according to ICDD card 83-1758 (75-2115). The reflection planes, regarding the ICDD card, are…show more content…
Regarding the data in Table (1), the crystallite size based on Scherrer equation is smaller than that based on the other two methods. Obviously this can be attributed to the contribution of strain to line profile broadening which is neglected in Scherrer equation and can be approved as follow: The sample broadening contribution BT can be written, for Scherrer consideration, as [9]: BT = Bsc (1) where Bsc, the Sherrer broadening, is given by the widely used expression Bsc = K.λ / [Dsc cosθ] (2) where Dsc is the Sherrer domain size and the other symbols have their usual meaning. For Williamson-Hall treaty, BT can be written as [10]: BT = BS + BST (3) where BS is the broadening domain size contribution and BST represents the strain broadening contribution. BS = K.λ / [DWH cosθ] (4) BST = 4 η tanθ (5) where DWH is the Williamson-Hall domain size and η is the micro-strain. From (1), (2), (4) and (5) in (3) then K.λ / [Dsc cosθ] = K.λ / [DWH cosθ] + 4 η tanθ, Finally 1/ Dsc = 1/ DWH + 4 η sinθ / Kλ. (6) According to equation (6), Dsc must be less than DWH. The domain size calculated by Scherrer equation must also be less than that based on Warren- Averbach method. Another criterion should be
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