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Caption : fig. s1 (a) influence of current density on the generation rate of ce(oh)3. (b) the ph changes of catholyte and anolyte during electrolysis with current densities of 100~300 ma cm−2.

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Caption : fig. s2 xps spectra of the as-electrolyzed powders prepared at the current density of (a) 100, (b) 150, (c) 200, (d) 250 and (e) 300 ma cm−2. (f) the proportion of ce3+ in the as-electrolyzed powders prepared at current densities of 100~300 ma cm−2.

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Caption : fig. s3 sem images of the ceo2 nanopowders obtained at the current densities of (a) 100, (b) 150, (c) 200, (d) 250 and (e) 300 ma cm–2 after calcination at 450 ℃ with (f) the corresponding xrd patterns.

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Caption : fig. s4 sem images of the ceo2 nanopowders calcined at (a) 550, (b) 650, (c) 750 and (d) 850 °c. (e) xrd patterns of the ceo2 nanopowders obtained after calcination at various temperatures.

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Caption : fig. s5 (a) n2 gas adsorption–desorption isotherms and (b) the barret-joyner-halenda pore size distribution for ceo2 nanopowders calcinated at various temperatures.

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Caption : fig. s6 xps spectra of ceo2 nanopowders after calcination at (a) 450, (b) 550, (c) 650, (d) 750 and (e) 850 °c (electrolysis conditions: 0.3 mol l⁻1 cecl3, 200 ma cm–2).

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Caption : fig. s7 current efficiencies of the her process at current densities of 100~300 ma cm–2.