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Caption : figure s1. (a) xrd pattern of initial and washed practical caco<sub>3</sub> sludge, (b) the cr(vi) removal rate and leaching concentration of washed residues.

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Caption : figure s2. supercells output after calculation of (a) pure calcite, (b) cro<sub>4</sub><sup>2-</sup>-calcite, (c) hcro<sub>4</sub><sup>-</sup>-calcite, (d) cr<sub>2</sub>o<sub>7</sub><sup>2-</sup>-calcite, (e) pure vaterite, (f) cro<sub>4</sub><sup>2-</sup>-vaterite.

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Caption : figure s3. (a) carbonation and control experiments conducted in series liquid-solid ratio, (b) cr removal rate of residues during the reaction process.

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Caption : figure s4. ca and cr concentrations of the supernatants in different co2 pressure reaction, and the calculated ph value.

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Caption : figure s5. release coefficient l(t) equations of initial and treated samples.

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Caption : figure s6. (a) cr(vi) extraction efficiency and leaching toxicity of residues under various co<sub>2</sub> pressures; (b) xrd pattern and (c) sem imagine of treated residue; (d) comparison of initial and treated samples.