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Published equation contexts

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}}

Why this formula appears here

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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ii

Symbol i

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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yiobsy_i^{\mathrm{obs}}

Symbol y_i^obs

yioy_i^obs is one of the signed contributions combined to compute the quantity on the left.

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yicalcy_i^{\mathrm{calc}}

Symbol y_i^calc

yicy_i^calc occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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∑iwi(yiobs−yicalc)2\sum_i w_i \left(y_i^{\mathrm{obs}} - y_i^{\mathrm{calc}}\right)^2

Numerator: sum_i w_i (y_i^obs - y_i^calc)^2

The complete quantity above the fraction bar.

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∑iwi(yiobs)2\sum_i w_i \left(y_i^{\mathrm{obs}}\right)^2

Denominator: sum_i w_i (y_i^obs)^2

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

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ii

Starting index or lower bound: i

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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ii

Starting index or lower bound: i

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Read this term in its guide →

How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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}},

Equation 5 · Materials Science

Materials Discovery and Degradation in Practice: An Advanced Technical Guide

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Meanings in this article

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