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Equation 5 · Part 13 · Materials Discovery and Degradation in Practice: An Advanced Technical Guide

Denominator: sum_i w_i (y_i^obs)^2

Rwp=∑iwi(yiobs−yicalc)2∑iwi(yiobs)2,R_{wp} = \sqrt{\frac{\sum_i w_i \left(y_i^{\mathrm{obs}} - y_i^{\mathrm{calc}}\right)^2}{\sum_i w_i \left(y_i^{\mathrm{obs}}\right)^2}},
∑iwi(yiobs)2\sum_i w_i \left(y_i^{\mathrm{obs}}\right)^2

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

sumim_i wiw_i (yioy_i^obs)^2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Modern practice fits the whole pattern simultaneously — peak positions, intensities, widths, and background — against a structural model, a procedure called Rietveld refinement. Software packages such as GSAS-II implement this as a nonlinear least-squares problem that minimizes the weighted residual between an observed and a calculated pattern across every measured point [ 6 ] . Refinement quality is reported as a weighted profile R-factor, Rwp=∑iwi(yiobs−yicalc)2∑iwi(yiobs)2R_{wp} = \sqrt{\frac{\sum_i w_i \left(y_i^{\mathrm{obs}} - y_i^{\mathrm{calc}}\right)^2}{\sum_i w_i \left(y_i^{\mathrm{obs}}\right)^2}}. alongside a goodness-of-fit statistic that compares RwpR_{wp} to the value expected from counting statistics alone. A low RwpR_{wp} is necessary but not sufficient evidence of a correct structure: a wrong space group with enough adjustable…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

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