A method for producing a mainly crystalline solidified steel slag, which method comprises the steps of: - producing a liquid steel slag on top of molten steel, which liquid steel slag is composed to contain at least CaO, SiO 2 , MgO and Al 2 O 3 and to have a first basicity ( B 1 ), defined as the weight ratio between the CaO content of said liquid steel slag and the SiO 2 content thereof, which is higher than 1.2; - separating said liquid steel slag from said molten steel; - lowering the basicity of the liquid steel slag separated from the molten steel from said first basicity ( B 1 ) to a second basicity ( B 2 ) at least partially by dissolving at least one low basicity material in the liquid steel slag, which low basicity material contains at least 50 wt% of SiO 2 and has a further basicity, defined as the weight ratio between its CaO content and its SiO 2 content, which is equal to zero when it is free of CaO or which is smaller than 0.30 when it contains CaO; and - solidifying the liquid steel slag having said second basicity ( B 2 ) by cooling it down to produce said mainly crystalline solidified steel slag, characterised in that the difference between said first basicity ( B 1 ) and said second basicity ( B 2 ) is comprised between 0.02 and 0.2 and the liquid steel slag which is solidified to produce said solidified steel slag is composed to contain A wt.% of Al 2 O 3 , with A being defined by the following equation : A ≥ -5.51 * ( B 2 - M * 0.022 - F * 0.011) 2 + 26.67 * ( B 2 - M * 0.022 - F * 0.011) - 23 wherein: A is the Al 2 O 3 content, expressed in weight percent, of the solidified steel slag; M is the MgO content, expressed in weight percent, of the solidified steel slag; F is the CaF 2 content, expressed in weight percent, of the solidified steel slag, with F being equal to zero when the solidified steel slag is free of CaF 2 ; and B 2 is said second basicity of the solidified steel slag. - producing a liquid steel slag on top of molten steel, which liquid steel slag is composed to contain at least CaO, SiO 2 , MgO and Al 2 O 3 and to have a first basicity ( B 1 ), defined as the weight ratio between the CaO content of said liquid steel slag and the SiO 2 content thereof, which is higher than 1.2; - separating said liquid steel slag from said molten steel; - lowering the basicity of the liquid steel slag separated from the molten steel from said first basicity ( B 1 ) to a second basicity ( B 2 ) at least partially by dissolving at least one low basicity material in the liquid steel slag, which low basicity material contains at least 50 wt% of SiO 2 and has a further basicity, defined as the weight ratio between its CaO content and its SiO 2 content, which is equal to zero when it is free of CaO or which is smaller than 0.30 when it contains CaO; and - solidifying the liquid steel slag having said second basicity ( B 2 ) by cooling it down to produce said mainly crystalline solidified steel slag, A is the Al 2 O 3 content, expressed in weight percent, of the solidified steel slag; M is the MgO content, expressed in weight percent, of the solidified steel slag; F is the CaF 2 content, expressed in weight percent, of the solidified steel slag, with F being equal to zero when the solidified steel slag is free of CaF 2 ; and B 2 is said second basicity of the solidified steel slag. <EOS>