Energy resolution of triple-axis spectrometer

In summary, the energy resolution comes from the wavelength distribution of the incoming neutrons together with the accuracy of the analyzer. The total resolution comes from the wavelength distribution of the incoming neutrons multiplied with the corresponding energy uncertainty.
  • #1
revbrapok
1
0
Hi,
I have encountered the problem of energy resolution of neutron triple-axis spectrometer, which we haven't covered during our solid state physics lectures.
11tts8n.jpg

262mdcg.jpg

I don't know where do we get the equation for the energy resolution from and even the numerical calculations in the solution seem odd to me as I am unable to get the same results. Can someone give me an insight into this or better suggest me some literature covering this problem?
 
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  • #2
The total resolution comes from the wavelength distribution of the incoming neutrons together with the accurary of the analyzer - that looks fine. The given uncertainties are relative values, so the energy uncertainty gets multiplied with the corresponding energy.
I would expect a quadratic sum (##\sqrt{a^2+b^2}## instead of a+b) and I don't understand the prefactors of 2, but that could be some (conservative) convention.

I can confirm the neutron energy, I have no idea where the 5 meV come from.
The intermediate step in the final calculation looks completely wrong, but the result of 37µeV agrees with the formula.
 
  • #3
http://en.wikipedia.org/wiki/Propagation_of_uncertainty, look at sections "Simplification" and "Example". With this you should be able to figure out where the "2" comes from.

The intermediate step should probably read 2 x (13.06 + 8.06) x 10^-3, using the simplification that delta lambda/lambda is pretty much the same for the monochromator and the analyzer.

I agree with mfb that one should probably use a quadratic sum.

The 5 meV is just an example of the excitation one might measure with this inelastic neutron scattering experiment.
 
  • #4
M Quack said:
http://en.wikipedia.org/wiki/Propagation_of_uncertainty, look at sections "Simplification" and "Example". With this you should be able to figure out where the "2" comes from.
The only "2" I see there is related to a correlation between two uncertain parameters, something we do not have here. And we don't have squared parameters either.
 
  • #5
E is quadratic in k and thus lambda, and the error propagation is (or should be)

(delta E)^2 = (delta lambda_0)^2 (d E_0/d lambda_0)^2 + ...

= (delta lambda_0)^2 (-2 hbar^2 /(2m lambda_0^3)^2 + ...

= (delta lambda_0/lambda_0 2 E_0)^2 + ...

correct me if I am wrong. (I have 1/2 bottle of wine as excuse :-))
 
  • #6
Oh right...
Okay, that explains the factor of 2.
 

What is the energy resolution of a triple-axis spectrometer?

The energy resolution of a triple-axis spectrometer refers to its ability to distinguish between different energy levels of particles or waves. It is typically measured in units of energy, such as meV, and is an important factor in determining the accuracy and precision of the data collected by the spectrometer.

How is the energy resolution of a triple-axis spectrometer determined?

The energy resolution of a triple-axis spectrometer is determined by several factors, including the quality of the instrument's components, such as its monochromator and analyzer, and the geometry of the instrument. Additionally, the energy resolution can be improved by using techniques such as double focusing or by increasing the length of the spectrometer's collimation system.

Why is energy resolution important in scientific research?

Energy resolution is important in scientific research because it allows for the accurate measurement of subtle energy differences between particles or waves. This can provide valuable insights into the properties and behavior of materials, such as their electronic structure and magnetic properties.

What are some methods for improving the energy resolution of a triple-axis spectrometer?

Some common methods for improving the energy resolution of a triple-axis spectrometer include using higher quality components, optimizing the geometry of the instrument, and implementing specialized techniques such as double focusing or using a monochromator with multiple crystals. Additionally, the energy resolution can be improved by carefully calibrating the instrument and minimizing sources of noise.

Are there any limitations to the energy resolution of a triple-axis spectrometer?

Yes, there are some limitations to the energy resolution of a triple-axis spectrometer. These may include instrumental limitations, such as the maximum energy range that the spectrometer can measure, as well as practical limitations, such as the need for longer data collection times to achieve higher resolution. Additionally, the energy resolution may be affected by external factors such as temperature fluctuations or sample quality.

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