A visible colored chromium- and phosphorus-free conversion coating can be formed on a metal surface by contacting it with an aqueous liquid composition that comprises an alizarine dye and a product of chemical interaction between a first initial reagent component selected from the group consisting of fluoroacids of the elements titanium, zirconium, hafnium, boron, aluminum, silicon, germanium, and tin; and a second initial reagent component selected from the group consisting of titanium, zirconium, hafnium, boron, aluminum, silicon, germanium, and tin and all of oxides, hydroxides, and carbonates of all of titanium, zirconium, hafnium, boron, aluminum, silicon, germanium, and tin.
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