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Figure below shows the first four peaks of the x-ray diffraction pattern for copper, which has an FCC crystal structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used. 1 40.0 Intensity (relative) Peak 1: Peak 2: Peak 3: 50.0 Peak 4: (a) Index (i.e., give h, k, and I indices) for each of these peaks. < 70.0 Diffraction angle 20 > 60.0 Diffraction pattern for polycrystalline copper. 80.0 90.0

Figure below shows the first four peaks of the x-ray diffraction pattern for copper, which has an FCC crystal structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used. 1 40.0 Intensity (relative) Peak 1: Peak 2: Peak 3: 50.0 Peak 4: (a) Index (i.e., give h, k, and I indices) for each of these peaks. < 70.0 Diffraction angle 20 > 60.0 Diffraction pattern for polycrystalline copper. 80.0 90.0

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### X-ray Diffraction Pattern Analysis for Copper The figure illustrates the first four peaks of the x-ray diffraction pattern for copper, which has a face-centered cubic (FCC) crystal structure. The analysis was carried out using monochromatic x-radiation with a wavelength of 0.1542 nm. #### Graph Explanation - **Title:** Diffraction pattern for polycrystalline copper. - **X-Axis:** Diffraction angle \( 2\theta \) ranging from 40.0° to 90.0°. - **Y-Axis:** Intensity (relative), representing the strength of the diffraction signal. - **Peaks:** Four distinct peaks are visible in this range, indicating the angles at which diffraction occurs for the copper crystal. #### Task (a) **Indexing Peaks:** Determine the corresponding Miller indices (h, k, l) for each peak in the diffraction pattern. - **Peak 1:** - **Peak 2:** - **Peak 3:** - **Peak 4:** These indices are crucial for understanding the planes in the crystal lattice that contribute to the x-ray diffraction.
Transcribed Image Text:### X-ray Diffraction Pattern Analysis for Copper The figure illustrates the first four peaks of the x-ray diffraction pattern for copper, which has a face-centered cubic (FCC) crystal structure. The analysis was carried out using monochromatic x-radiation with a wavelength of 0.1542 nm. #### Graph Explanation - **Title:** Diffraction pattern for polycrystalline copper. - **X-Axis:** Diffraction angle \( 2\theta \) ranging from 40.0° to 90.0°. - **Y-Axis:** Intensity (relative), representing the strength of the diffraction signal. - **Peaks:** Four distinct peaks are visible in this range, indicating the angles at which diffraction occurs for the copper crystal. #### Task (a) **Indexing Peaks:** Determine the corresponding Miller indices (h, k, l) for each peak in the diffraction pattern. - **Peak 1:** - **Peak 2:** - **Peak 3:** - **Peak 4:** These indices are crucial for understanding the planes in the crystal lattice that contribute to the x-ray diffraction.
(b) Determine the interplanar spacing for each of the peaks. - **Peak 1:** [Input Box] nm - **Peak 2:** [Input Box] nm - **Peak 3:** [Input Box] nm - **Peak 4:** [Input Box] nm (c) For each peak, determine the atomic radius for Cu and compare these with the value presented in the Table "Atomic Radii and Crystal Structures for 16 Metals." - **Peak 1:** [Input Box] nm - **Peak 2:** [Input Box] nm - **Peak 3:** [Input Box] nm - **Peak 4:** [Input Box] nm
Transcribed Image Text:(b) Determine the interplanar spacing for each of the peaks. - **Peak 1:** [Input Box] nm - **Peak 2:** [Input Box] nm - **Peak 3:** [Input Box] nm - **Peak 4:** [Input Box] nm (c) For each peak, determine the atomic radius for Cu and compare these with the value presented in the Table "Atomic Radii and Crystal Structures for 16 Metals." - **Peak 1:** [Input Box] nm - **Peak 2:** [Input Box] nm - **Peak 3:** [Input Box] nm - **Peak 4:** [Input Box] nm
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