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Equation 5 · Part 11 · Materials Discovery and Degradation in Practice: An Advanced Technical Guide

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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}},
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.