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Equation 9 · Part 5 · Materials Discovery and Degradation in Practice: An Advanced Technical Guide

Symbol T_use

AF=exp⁡ ⁣[EakB(1Tuse−1Ttest)],AF = \exp\!\left[\frac{E_a}{k_B}\left(\frac{1}{T_{\mathrm{use}}} - \frac{1}{T_{\mathrm{test}}}\right)\right],
TuseT_{\mathrm{use}}

What this part means

TuT_use occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

TuT_use 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

…acceleration factor no longer describes what happens at service temperature. A first-order approximation for a single, unchanged mechanism follows AF=exp⁡ ⁣[EakB(1Tuse−1Ttest)]AF = \exp\!\left[\frac{E_a}{k_B}\left(\frac{1}{T_{\mathrm{use}}} - \frac{1}{T_{\mathrm{test}}}\right)\right]. where EaE_a is the mechanism’s activation energy, TuseT_{\mathrm{use}} and TtestT_{\mathrm{test}} are absolute temperatures, and kBk_B is Boltzmann’s constant. This is a genuine, useful model — it is also only as good as the assumption that EaE_a and the mechanism are constant over the interval being extrapolated, an assumption every accelerated-aging program…

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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.

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