X-Ray Diffraction Equation (Mineralogy HW)

In summary, the conversation is about requesting assistance with a Mineralogy problem involving X-Ray Diffraction. The question asks for a derivation of a diffraction equation relating reflection angle (theta) to wavelength (lambda) and d spacing (d). The person has been struggling with the problem for two days and is looking for help. The conversation also includes a discussion about the conditions for constructive vs. destructive interference of reflected waves in relation to the given diagram.
  • #1
Maxilen
1
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Homework Statement


Okay so, I was hoping someone out there might be able to assist me with a Mineralogy problem I have. The concept is based around X-Ray Diffraction.

The question:

Derive a diffraction equation from the illustration below that relates the reflection angle (theta) to the wavelength (lambda) and the d spacing (d). Show all of your work so that it is clear that you understand the physics and the math in this important derivation.

Here is a picture of the diagram given...sorry for the poor quality :)
http://yfrog.com/5m0331102025j

I've been banging my head against this for two days now, and I just don't seem to be getting anywhere with this...Ive tried google, my book, everything at my disposal, I just can't seem to figure this out at all...I am at a stand still because there are 5 other questions related to this problem, but i need to solve this first...can anyone help...Thanks in advance for your time! :)
 
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  • #2
I guess it is not for any theta, but for a specific value of theta? One that gives some observable effect? For that effect to happen - is there anything you can tell about FG?

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  • #3
Start with one of the fundamental considerations:
in terms of that diagram, what are the conditions for constructive vs. destructive interference of the reflected waves?
 

1. What is the X-Ray Diffraction Equation?

The X-Ray Diffraction Equation, also known as the Bragg Equation, is a mathematical formula used to determine the spacing between crystal lattice planes in a mineral sample. It is expressed as nλ = 2dsinθ, where n is the order of the diffraction peak, λ is the wavelength of the X-ray beam, d is the spacing between crystal lattice planes, and θ is the angle of diffraction.

2. How is the X-Ray Diffraction Equation used in mineralogy?

The X-Ray Diffraction Equation is used in mineralogy to identify and characterize mineral samples based on their crystal structure. By analyzing the diffraction peaks produced by a mineral sample, the spacing between its crystal lattice planes can be calculated and compared to known values for different minerals, allowing for identification.

3. What factors can affect the accuracy of the X-Ray Diffraction Equation?

Several factors can affect the accuracy of the X-Ray Diffraction Equation, including instrument calibration, sample preparation, and the quality of the X-ray beam. Inadequate sample preparation, such as uneven grinding or incorrect orientation, can lead to inaccurate diffraction patterns. Additionally, instrument settings must be carefully calibrated to ensure proper measurement of the diffraction angles and intensity of the peaks.

4. Can the X-Ray Diffraction Equation be used to determine the composition of a mineral sample?

No, the X-Ray Diffraction Equation cannot be used to determine the composition of a mineral sample. It only provides information about the crystal structure and spacing of the mineral's lattice planes. Other analytical techniques, such as electron microprobe analysis, must be used to determine the chemical composition of a mineral sample.

5. How has the X-Ray Diffraction Equation impacted the field of mineralogy?

The X-Ray Diffraction Equation has had a significant impact on the field of mineralogy. It has greatly improved the ability to identify and characterize minerals, allowing for more accurate and efficient mineralogical analysis. This has also led to advancements in other fields, such as material science and geology, where X-ray diffraction is used to study the structure and properties of various materials.

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