Reference Intensity Ratio (RIR) method for quantitative analysis

The so-called "Reference Intensity Ratio" (RIR) method presented by de Wolff and Visser [1] is used automatically for (semi-) quantitative analysis if at least two entries have been selected as matching. The quantity (weight %) of each selected phase/entry is displayed in the "Quant.(%)" column of the match list and of course also in the report.

The RIR analysis is based on intensity scale factors that are calculated automatically for all entries/phases in the match list. For this, the intensity differences between reference entry peaks as well as their correlated experimental counterparts are minimized using a least-squares refinement. In addition, the difference between the profile calculated from the match list entry peaks and the experimental profile is also minimized by least-squares refinement.

The second component of the RIR method (in addition to the intensity scale factors just mentioned) are so-called "I/Ic values". These values indicate the intensity ratio of the strongest peak (given in counts) between a certain phase X ("I") and Corundum as standard material ("Ic"), or, as a formula,

I/Ic = I(strongest peak of phase X) / I(strongest peak of Corundum)

I/Ic values can be determined experimentally from the intensities of the strongest peaks in two diffraction patterns, one of the pure phase X and another one of the pure Corundum standard. Both diffraction patterns have to be measured under the same experimental conditions (e.g. counting times).

As an alternative, I/Ic can also be calculated from the known crystal structure (see below).

As a rule of thumb for X-ray diffraction, compounds/phases that contain heavy elements with a lot of electrons have large I/Ic values and vice versa.

What you can do if I/Ic values are missing

The RIR analysis can only be carried out if all matching entries contain I/Ic values. If only one of the selected entries does not contain an I/Ic value, the values for the remaining selected entries cannot be calculated as well.

All entries in the COD reference database that is installed automatically along with Match! contain I/Ic values that have been calculated from the crystal structure data. However, there may be entries e.g. in ICDD PDF databases (especially the PDF-2) that do not contain any I/Ic value or at least crystal structure data that could be used to calculate I/Ic.

Hence, you should check if an entry contains an I/Ic value before selecting it, by taking a look at the column "I/Ic" in the candidate list in which a corresponding value must be given.

If you select one (or more) entries without I/Ic value as "matching", "No I/Ic" will be displayed in the "Quant.(%)" column of the match list. In this situation, "n.a." is displayed for "Quant.(%)" for the remaining entries even if they contain I/Ic values.

Here is what to do in this situation to obtain a quantitative analysis result:



[1] P.M. de Wolff, J.W. Visser, "Absolute intensities", Rep. 641.109 Technische Physische Dienst, Delft 1964.