Search & Match

How it works

QualX performs a multi-step search:

1. Strongest peaks filter: for each database card, only the N strongest reference peaks are compared against the experimental peak list (fast pre-filter).
2. FOM calculation: a weighted Figure of Merit combines peak-position matching and intensity matching.
3. Ranking: cards are sorted by descending FOM; only cards above Min. FOM are shown.

Figure of Merit

At the end of the search–match step a list of plausible database crystalline phases are ranked according to the decreasing values of a FoM. The FoM includes four contributions, three of them suitably weighted, according to the following formula:

\[ \mathrm{FoM}=\sqrt{\frac{\mathrm{FoM}_{db}\cdot\left(w_{\theta}\,\mathrm{FoM}_{\theta} +w_{I}\,\mathrm{FoM}_{I}+w_{ph}\,\mathrm{FoM}_{ph}\right)}{w_{\theta}+w_{I}+w_{ph}}} \]

where FoM_θ takes into account the average difference between the 2θ values of the observed and matched database peaks; FoM_I is related to the average difference between the intensity values of the observed and matched database peaks; FoM_ph depends on the percentage of the matched experimental peaks and on their intensity; and FoM_db depends on the percentage of the matched database peaks and on their intensity.

FoM_θ is the contribution coming from the 2θ differences between the experimental and the associated database peaks:

\[ \mathrm{FoM}_{\theta} = 1 - \dfrac{\displaystyle\sum_{i}^{N_{db}^{ass}} \left|2\theta_i^{\mathrm{exp}} - 2\theta_i^{db}\right|}{N_{db}^{ass}\cdot\Delta} \]

where the summation is over the associated database peaks (a database peak is considered associated if its 2θ distance from the experimental peak is less than Δ), 2θ^exp and 2θ^db are the positions of the experimental and database peaks, respectively.

FoM_I is the contribution due to the differences between the intensities of the experimental and the associated database peaks:

\[ \mathrm{FoM}_{I} = 1 - \dfrac{\displaystyle\sum_{i}^{N_{\mathrm{exp}}^{ass}} \left|I_i^{\mathrm{exp}} - I_i^{db}\right|}{N_{\mathrm{exp}}^{ass}} \]

where I^exp and I^db are the experimental and database intensity respectively, the summation is over the associated experimental peaks.

FoM_ph is the contribution due to the intensities of the associated experimental peaks and their percentage:

\[ \mathrm{FoM}_{ph} = \sqrt{\dfrac{\displaystyle\sum_{i=1}^{N_{\mathrm{exp}}^{ass}} I_i^{\mathrm{exp}}}{\displaystyle\sum_{i=1}^{N_{\mathrm{exp}}} I_i^{\mathrm{exp}}} \cdot\dfrac{N_{\mathrm{exp}}^{ass}}{N_{\mathrm{exp}}}} \]

where N_exp is the total number of experimental peaks.

FoM_db is the contribution due to the intensities of the associated database peaks and their percentage:

\[ \mathrm{FoM}_{db} = \sqrt{\dfrac{\displaystyle\sum_{i=1}^{N_{db}^{ass}} I_i^{db}}{\displaystyle\sum_{i=1}^{N_{db}} I_i^{db}} \cdot\dfrac{N_{db}^{ass}}{N_{db}}} \]

where I_db is the database intensity and the summation at the numerator is over the associated database peaks; N_db is the total number of the database peaks.

The weighting factors w_θ, w_I, w_ph and Δ (default heuristic values are set for them) can be adjusted directly by the user via the graphical interface. w_ph is related to the number of expected phases.

The default value of the weights w_θ, w_I, and w_ph is 0.5, but it can be changed by the dialogue window in Figure 1 (via the "2θ", "Intensity" and "Phases" trackbars).

Search Options

Open Search → Search & Match Options:

Option	Description
Min. FOM	Discard cards below this threshold
2θ / d weight	Contribution of peak-position agreement to FOM
Intensity weight	Contribution of intensity agreement to FOM
Phases weight	Bias towards single-phase vs. multi-phase solutions
Δ2θ	Peak matching tolerance in degrees (Auto = calculated from peak widths)
Max. entries	Maximum number of results to display
Check strongest peaks	Use only the N strongest peaks for the pre-filter
Check deleted cards	Include cards marked as deleted in the database
Residual searching	After accepting a phase, automatically re-search on residual peaks

Accepting a Phase

1. Select a card in the Results List.
2. Click Accept (✓). The card is moved to the Quantitative dock.
3. If Residual searching is enabled, QualX subtracts the accepted phase contribution and repeats the search on the remaining peaks.