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Equation 5 · Part 10 · Materials Discovery and Degradation in Practice: An Advanced Technical Guide

subscript

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}},
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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