Braggs law: lattice constant

In summary, the conversation discusses using x-ray diffraction with a wavelength of 1.6\dot{A} to determine the lattice constant for a simple cubic lattice. The (222) peak at 32 degrees is used to find the spacing of the (222) planes using Braggs law, and the value of n is 1 for the first order diffraction lobe. The conversation also mentions that higher order peaks are not visible in a standard diffractometer and a Laue pattern may be needed to see them. The (422) peak is also mentioned as an example, but it is not needed for the calculation.
  • #1
vebbie
4
0
need help working out this problem. if you have a simple cubic lattice characterised using x-ray diffraction with a wavelegth of 1.6[tex]\dot{A}[/tex]. The main peak in the scan is (222) and the angle is 32 degrees. By using braggs law to find the lattice constant do you just sub in the values and solve for d? (n[tex]\lambda[/tex]=dSin[tex]\theta[/tex]. If so what value do you use for "n".
 
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  • #2
It is the diffraction order, use 1 for the first order diffraction lobe.
 
  • #3
but does the peak have any use for the calculation. suppos it was the 422 peak
 
  • #4
d is the spacing of the (222) planes. If you were looking at the (422) reflection, then d would be the spacing of the (422) planes. You might have to do some geometry to get the lattice spacing from the data.
 
  • #5
"but does the peak have any use for the calculation. suppos it was the 422 peak"

The index n is a consequence of the fact that reflections occur when (k - k') = G. Braggs Law diffraction condition is a simplification of the Laue Condition for diffraction: (k - k') = G. The higher order peaks are forward scattering instead of backwards scattering so you won't be able to see them in a standard diffractometer. You would nee to generate a Laue pattern to see these peaks. To answer your question you don't need these peaks.

modey3
 

1. What is Braggs law and how does it relate to lattice constant?

Braggs law is a fundamental principle in crystallography that describes the relationship between the wavelength of X-rays and the spacing of atomic planes in a crystal lattice. It states that when X-rays are diffracted by a crystal, the resulting diffraction pattern will be strongest when the X-rays have a wavelength that is twice the distance between the atomic planes, also known as the lattice constant.

2. How is lattice constant measured?

Lattice constant is typically measured using techniques such as X-ray diffraction or electron diffraction. These methods involve directing a beam of X-rays or electrons at a crystal and analyzing the resulting diffraction pattern to determine the distance between atomic planes. Other methods, such as atomic force microscopy, can also be used to measure lattice constant.

3. What factors can affect the lattice constant of a crystal?

The lattice constant of a crystal can be influenced by a variety of factors, including temperature, pressure, and the presence of impurities or defects in the crystal structure. These factors can cause the atomic planes to expand or contract, resulting in a change in the lattice constant.

4. How does lattice constant impact the properties of a crystal?

The lattice constant of a crystal plays a crucial role in determining its physical and chemical properties. It affects the crystal's density, melting point, electrical and thermal conductivity, and mechanical strength. Changes in the lattice constant can also lead to phase transitions, where the crystal structure transforms into a different arrangement of atoms.

5. Can lattice constant be altered or controlled?

Yes, lattice constant can be altered or controlled through various methods, such as changing the temperature or applying external pressure to the crystal. In some cases, it is also possible to intentionally introduce impurities or defects to manipulate the lattice constant and, consequently, the properties of the crystal.

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