Crystal diffraction using Bragg's Law

In summary, the question is asking for the longest possible wavelength of an X-ray source that can reveal the (211) Bragg peak of a cubic crystal with three orthogonal sides of length 0.3nm. Using Bragg's Law and the formula for d, the wavelength can be calculated to be 2.44A, but the angle θ is needed to solve the equation. The question is also asking for help with calculating the d value of a crystal compound using Bragg's Law, with the unknown variable of n in the equation.
  • #1
frederer
1
0

Homework Statement



You wish to study a material with a cubic crystal structure with
three orthogonal sides of length a = 0.3nm. What is the
longest possible wavelength of the X-ray source you could use
to reveal the (211) Bragg peak of the crystal?


Homework Equations



nλ = 2dSinθ (Bragg's Law)

d = a/sqrt(h^2 + k^2 + l^2)

The Attempt at a Solution



Hi. Ok so i think i need the two formulae above to solve this question.

You can figure out d simply enough by slotting in the numbers,
giving λ = 2.44Asinθ
but the trouble I am having is how to calculate the angle θ. If you draw out the
cube in question you can see the angles formed between in the plane but
I am not sure which angle, if one of these angles at all is required to solve
the question. Any help would be much appreciated.
 
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  • #2
Dear all
i am struggling on a question regarding powder XRD. Can anybody please help me on this.

Question: I have lambda(X-ray wavelength used) and 2theta(100% intense peak) value of a crystal compound; with that data can anyone calculate the "d(distance between two planes)" value of that crystal using braggs law(i.e. nλ = 2 d sinΘ) theoritically. If so please explain me with an example.
Note: What is the n value we need to apply in that formula.
 

FAQ: Crystal diffraction using Bragg's Law

What is crystal diffraction?

Crystal diffraction is a phenomenon in which a beam of light, electrons, or other particles is scattered by the regular arrangement of atoms in a crystal. This scattering pattern can be analyzed to determine the structure and properties of the crystal.

What is Bragg's Law?

Bragg's Law is a mathematical relationship between the wavelength of incident radiation, the angle of incidence, and the distance between crystal planes. It is used to calculate the angles at which diffraction peaks will occur in a crystal diffraction pattern.

How does crystal diffraction using Bragg's Law work?

When a beam of radiation is directed at a crystal, it will interact with the regular arrangement of atoms and produce a diffraction pattern. The angles at which the diffraction peaks occur can be calculated using Bragg's Law, which takes into account the wavelength of the radiation and the distance between crystal planes.

What types of radiation can be used for crystal diffraction?

Crystal diffraction can be performed using a variety of radiation sources, including X-rays, electrons, and neutrons. Each type of radiation has its own unique properties and is suited for different types of crystal structures and research purposes.

What is crystallography and how is it related to crystal diffraction using Bragg's Law?

Crystallography is the branch of science that deals with the study of crystals, their structure, and properties. Crystal diffraction using Bragg's Law is a fundamental technique used in crystallography to analyze the diffraction patterns produced by crystals and determine their structure and properties.

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