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Equation 9 · Part 8 · How Materials Discovery and Degradation Actually Work

subscript

δ(t)≈δ0+kt\delta(t) \approx \delta_0 + k\sqrt{t}
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

Diffusion-limited SEI thickening is commonly modeled with a square-root-of-time growth law, δ(t)≈δ0+kt\delta(t) \approx \delta_0 + k\sqrt{t}. where δ(t)\delta(t) is film thickness, δ0\delta_0 an initial thickness, and k a rate constant set by species diffusivity through the existing film — a direct consequence of assuming the rate-limiting step is diffusion across a film whose own thickness is the barrier [ 2 ] . This is a model, not a universal law : the review is explicit that mixed kinetic-and-transport regimes, porous or cracked SEI, and side reactions all produce departures from a clean square-root trend, and reconciling model and experiment remains an open problem [ 2 ] .

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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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Sources cited in the surrounding passage

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