Accuracy, Precision and Detection Limits
Accuracy refers to the “truth” of the analysis. It depends on the standards used and the spectral processing and corrections applied to the raw data. It is an absolute description.
Precision refers to the reproducibility of the measurement of the X-ray counts in the EDS spectrum. It depends on the number of X-rays in the spectrum and the statistics related to that number. Measurement of precision allows comparison of analyses from different grains, different analysis sessions or different studies. It is a relative description.
The minimum detection limit is the concentration corresponding to a peak that can just be distinguished statistically from background fluctuations. This is generally taken to be a peak height equal to three times the standard deviation of the background count. This will vary between different elements and analytical lines, and for the same element in different matrixes. For routine EDS analysis, the detection limits are about 1000 ppm or 0.1 wt%.
Figure: Detection limits for EDS and WDS microanalysis.
Random and systematic errors
Experimental uncertainty is due to random and systematic errors.
Random errors are statistical fluctuations, in either direction, in the measured data due to the limitations of the measurement device.
Systematic errors are reproducible inaccuracies that are consistently in the same direction and are likely to be caused by an error in the experimental setup, e.g., incorrect reading of accelerating voltage or beam current.
In EDS analysis, sources of error may be related to the sample, the microscope, the EDS detector and the data reduction software.
Errors related to the sample include
- The sample is not homogeneous – only one phase should be intersected in the interaction volume
Figure: How a non-homogeneous sample can affect quantitative analysis.
- The sample is not stable in the microscope – sample outgassing, melting or volatility of some elements, e.g. clay minerals, Na in glass.
- The sample is not well polished or is porous.
- The sample is not conductive – charging can affect the effective energy of the primary-beam electrons.
Figure: The build-up of electrons on the surface of a non-conducting sample can deflect the primary electron beam and change the effective kV of the analysis system.
- For insulating samples, a conductive path must be made from the surface of the sample to electrical ground.
Figure: An insulating sample can be made conductive by coating the surface with a conductive material and by creating a conductive path from the surface of the sample to ground with either conductive paint or conductive tape.
- The sample is not clean – there may be fingerprints, dust or lint on the surface.
Figure: Contamination of the surface of the sample can result in inaccurate analyses as X-rays are generated from both the sample and surface contaminants.
- For light-element analysis, inappropriate standards or inappropriate correction procedures.
Errors related to the microscope include
- Incorrect reading of accelerating voltage.
- Instability of the beam – the beam current must be stable while the X-ray spectrum is being collected.
- Incorrect setting of working distance.
Errors related to the EDS detector system include
- Incorrect setting of takeoff angle.
- Incorrect setting of detector-sample geometry.
- Instability of detector electronics.
- Build up of ice or contamination on the detector window.
Errors related to data processing
- Insufficient counts in the X-ray spectrum to overcome statistical fluctuations.
- Background subtraction routines.
- Matrix correction models.
- Correction of spectral artifacts.
- Correction for overlapping peaks, i.e. spectral deconvolution.
Accuracy and precision
Care must be taken to minimize the potential errors in the analysis system. The accuracy of the analysis depends on the sum of all the errors. It can only be defined by reference to standards. A well-characterized standard should be analysed in every analysis session to verify the analysis conditions.
It is difficult to quantify all sources of errors for EDS analysis. The combined errors limit the precision of EDS analysis to ±2% relative for major components.