Engin 45 Lab 2x Ray Diffraction And Crystallography Turn-In

Question

Engin 45 Lab 2x Ray Diffraction And Crystallographyturn In The Lab Wi Engin 45 Lab #2 X-Ray Diffraction and Crystallography Turn in the lab with all of your answers written on a separate sheet of paper. During a lunar exploration, an unknown metallic crystalline substance is discovered. The external morphology indicates that it is a cubic material. A diffraction pattern of this material, using an X-ray of wavelength 1.54 Å, provides the following data (shown here as a graph and in a table): Diffraction Peak | Bragg Diffraction angle (θ) #1: 19.1° #2: 22.2° #3: 32.2° #4: 38.8° #5: 40.85° There are three options for the crystalline structure: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). We are asked to calculate the lattice parameter (a) for each angle for each crystalline structure. Each crystalline structure has different sets of planes that produce diffraction peaks. The goal is to determine which structure fits the experimental data by calculating a consistent lattice parameter (a) across all peaks for each structure, based on the Bragg law and diffraction data.

Dr. Jack HW Helper · Accepted Answer

The question involves analyzing X-ray diffraction data to identify the crystalline structure of an unknown cubic metallic substance. Using Bragg's Law, we will calculate the lattice parameter (a) for each peak and structure type, to see which structure yields a consistent a value across multiple diffraction peaks. Bragg's Law relates the diffraction angle (θ), the wavelength (λ), and the interplanar spacing (d) as: nλ = 2d sin θ where n is the order of diffraction, typically taken as 1 for initial calculations. For cubic crystal systems, the interplanar spacing d is related to the lattice parameter a and Miller indices (h, k, l) as: d = a / √(h² + k² + l²) Given the diffraction peaks at specific angles θ and the wavelength λ = 1.54 Å, we will proceed to find the corresponding interplanar spacings, then determine the lattice parameter a for each structure type based on the appropriate set of (h, k, l) planes for each structure. For the Simple Cubic structure, the allowed reflections are where h, k, and l are all odd or all even, with no restrictions. The BCC structure allows reflections with h + k + l even, and FCC allows h, k, l all either odd or even, but with specific selection rules. Each structure has different allowed sets of planes, which influence the calculation of a from the measured diffraction peaks. Calculations of Crystalline Structure and Lattice Parameter a Step 1: Calculate d for each peak using Bragg’s Law: d = λ / (2 sin θ) where λ = 1.54 Å and θ is the diffraction angle in degrees. Step 2: Determine the Miller indices (h, k, l) for each peak based on the structure type. Commonly for FCC, the first few peaks correspond to (111), (200), (220), (311), etc. For BCC, peaks are attributed to (110), (200), (211), (220), etc. For SC, the reflections are (100), (110), (111), (200), etc. Step 3: Calculate lattice parameter a for each peak using the equation: a = d × √(h² + k² + l²) Step 4: Check consistency of a across all peaks for each structure; the corr

Engin 45 Lab 2x Ray Diffraction And Crystallography Turn-In

Engin 45 Lab 2x Ray Diffraction And Crystallographyturn In The Lab Wi

Paper For Above instruction

Calculations of Crystalline Structure and Lattice Parameter a

Step 1: Calculate d for each peak using Bragg’s Law:

Step 2: Determine the Miller indices (h, k, l) for each peak based on the structure type.

Step 3: Calculate lattice parameter a for each peak using the equation:

Step 4: Check consistency of a across all peaks for each structure; the correct structure will yield approximately the same a value for all peaks.

Example calculations:

Analysis and Identification of Element

Problem 1: Platinum FCC Crystal Analysis

Solution:

Problem 2: Tungsten BCC Crystal

Conclusion

References