Fair value measurements and financial instruments - Additional Information (Details) - Kronos Worldwide - EUR (€)	Jun. 30, 2025	Dec. 31, 2024	Feb. 12, 2024
9.50% Senior Secured Notes due 2029
Fair value measurements and financial instruments
Interest rate			9.50%
9.50% Senior Secured Notes due 2029 | Kronos International, Inc
Fair value measurements and financial instruments
Interest rate	9.50%	9.50%
Estimated market price of the notes	€ 1,079
Principal amount of debt instrument	€ 1,000
3.75% Senior Secured Notes due 2025 | Kronos International, Inc
Fair value measurements and financial instruments
Interest rate	3.75%	3.75%
Estimated market price of the notes	€ 999
Principal amount of debt instrument	€ 1,000