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The problem to be solved when choosing an appropriate dilution for a transmission sample is to balance the total absorption, the edge step and an appropriate amount of material to make a pellet. In an ideal world, we want an edge step between 0.5 and 1.5 absorption units, whilst keeping the total absorption within reasonable limits, i.e. approximately ideally below 1.5 absorption units, though perhaps relaxing that constraint to 2.5 absorption units or below for more difficult samples. There are two motivation motivations for keeping total absorption at ~2<2.5 absorption units:
the avoidance of "thickness effects". The optically thicker a sample is, the more the measured energy-dependent absorption will be affected by imperfections in sample homogeneity. At a total absorption of 5 absorption units, 1 photon in 150 will make it through the sample. If regions of the sample illuminated by the beam have varying absorption, because your sample was poorly mixed, or worse, there are areas where the element of interest is absent, the measured absorption signal will be dominated by the contributions from those regions. More information can be found in the following papers:
Stern, E. A. & Kim, K. (1981). Thickness effect on the extended-x-ray-absorption-fine-structure amplitude. Physical Review B23, 3781–3787.
Heald, S. M. (1988). Design of an EXAFS experiment. In: Koningsberger, D. C. & Prins, R. (eds) X-Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES. John Wiley & Sons, 119–162.
optimal signal to noise. See here for further explanation.
In addition, we need a mass of material that is large enough to reliably press into pellets. For many materials, the optimal mass for a 7 mm pellet will be in the single figure milligram range, a mass too small to reliably press high quality pellets. Thus, we must dilute the material of interest with an inert dilutant, preferably a material that has low atomic number (and thus has low absorption) and that also forms good pellets. The material of choice at the MEX beamline is microcrystalline cellulose, C6H10O5. A good mass for a 7 mm pellet is 40 mg of sample; for a 13 mm pellet, 90 mg is a good mass.
Diluting the material of interest with cellulose changes both the total absorption and the edge step. Thus, the problem to be solved is to choose a dilution that gives reasonable values for total absorption, edge step and mass of material to be pressed into a pellet. For many real-world samples, optimum values for all three parameters cannot be achieved. Thus, the task for the user is to use tools like XAFSmass to explore the parameter space to find the least worst compromise.
Example 1 - tungsten metal powder
Using XAFSMass, enter W as the compound, µtd (total absorption) as 21.5, S (area of the pellet) as 0.37 3848451 (the area of a 7 mm diameter pellet expressed in cm2). Choose the energy from the drop down list to be the W L3 edge (+50 eV):
XAFSMass reports that the edge step will be 10.57, which is almost within 942, in the middle of the ideal range of 0.5-1.5, but the mass required is very small, 32.94 46 mg. It is unlikely that it will be possible to successfully press a 7 mm pellet of this mass, particularly of a hard material like W. Thus, it will be necessary to dilute the W metal with cellulose. The python version of XAFSmass has a much more featureful parser than the older version, and allows us to easily express dilutions. Let's start with investigating a 50-50 mix of W metal and cellulose. Change the compound to W%50(C6H10O5) and click calculate:
XAFSMass automatically converts our expression for dilution into a molecular formula, W0.882C6H10O5, and returns a slightly smaller edge step of 10.55 928 absorption units. However, the mass required is still far less than the optimal 40 mg for a 7 mm pellet. Lets try diluting the W to 10%5%, by entering W%10W%5(C6H10O5):
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This result is much closer to what we want. The edge step is within our optimal range at 10.38 73 absorption units, and the mass required is 3438.6 1 mg, close enough to 40 mg that a successful pellet will be possible. Enthusiastic users can optimise further and find that a 40 mg pellet requires a dilution of 84.45 68 wt% W, and gives an edge step of 10.35718:
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Comparison with the "simple" method
A simpler way of using XAFSmass is to enter only the material formula and a µtd (total absorption). XAFSmass will then return a mass and edge step. That mass of material can then be mixed with a dilutant such as cellulose to a pre-defined final mass, known to make robust pellets, such as 40 mg for 7 mm OD pellets:
In the example above, 42.1 46 mg of W would be mixed with 3537.9 54 mg of cellulose. Let us include cellulose in the calculation. 42.1 46 mg of W diluted with 3537.9 54 mg of cellulose corresponds to a concentration of 106.25 15 wt%. This can be entered into XAFSmass via the following formula W%10W%6.2515(C6H10O5):
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If we inspect the XAFSmass window, we can see that the mass required for the total absorption we specified (21.5 abs units) is 3532.2 4 mg. This is not equivalent to the pellet we made above, and we can confirm that by looking at the absorptance step box, where is reports that the mass of W is 31.61 99 mg and the edge step is 10.38764. To calculate 42.1 46 mg of W mixed with 3537.9 54 mg of cellulose we must manually increase the value of µtd (total absorption) until the mass is 40.0 mg AND the absorptance step box report 42.1 46 mg W and an edge step of 10.57942:
After changing the value a few times we find that the total absorption of the W + cellulose mix is 21.839685. This is a little higher than the 21.5 abs. units we specified in the "simple" calculation, and probably would not have too much impact on the final result.
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