## 1 Introduction  
Of the numerous toxic elements that can be leached from waste, chromium appears to be of greatest concern when it comes to human health. The hexavalent oxidation state of Cr is toxic, and several of the chromates are classified as carcinogenic by the WHO (World Health Organization) [1]. The main risk associated with Cr leaching is the contamination of ground water, generally used as public water supplies. For this reason, Cr concentration in drinkable water is restricted to very low limits, i.e., 0.1 mg/L in the US [2] or 50 \(\upmu\)g/L in the European Union [3]. Specific studies on the leaching behavior of Cr in slag started in the US over 30 years ago. The role of slag binary basicity (BI\({}_{2}\): CaO/SiO\({}_{2}\)), MgO concentration and slag processing after slagging were investigated by [PERSON] and [PERSON] [4]. When BI\({}_{2}\) is above 2.0, Cr is present as calcium chromite (CaO-Cr\({}_{2}\)O\({}_{3}\)), regardless of the MgO content, and the slag are prone to high Cr leachability. Leaching can be minimized if basicity is well below 2, with enough MgO to form insoluble picrochromite (MgO-Cr\({}_{2}\)O\({}_{3}\)), the hypothetical Mg-Cr end-member of the spinel series. These results were confirmed about 20 years later by [PERSON] et al. [5] and [PERSON] et al. [6] who studied the thermodynamics of the SiO\({}_{2}\)-CaO-MgO-Cr\({}_{2}\)O\({}_{3}\) system. Both studies confirmed the role played by BI\({}_{2}\) in the formation of Ca-chromite, especially in a low-MgO-slag system. In our opinion, the use of a simply binary basicity index (BI\({}_{2}\)) could not address the leaching behavior of Cr-spinels when formed in low Al\({}_{2}\)O\({}_{3}\)-MgO slag [7; 8]. For instance, in slag with low concentration of the above-mentioned chemical species, the spinels risk being over saturated in Cr, with potential risk of Cr leaching [8]. For this reason, in the present paper, BI\({}_{4}\) was used, thus also taking Al\({}_{2}\)O\({}_{3}\) and MgO into account. Other basicity indexes are available, i.e., optical basicity (\(\Lambda\)) [9]. \(\Lambda\) is a good index because it considers the whole chemical composition of a slag but its computation requires a long time and its interpretation is not practical; since it is always below 1, it is difficult to understand if a slag is acidic or alkaline [10]. In addition, for certain oxides more optical basicity values are available in literature [11; 12; 13; 14] and this results in a different interpretation of the behavior of an oxide with respect its capacity to donate or receive an oxygen anion. A strong contribution to defining the positive effects of spinel formation was given by [PERSON] et al. [15], who delineated a simple but reliable index with which to forecast the Cr leachability in stainless steel EAF slag: The so-called sp-factor. However, the effectiveness of this parameter has been recently disproved in terms of predicting the leaching of Cr in carbon steel slag [7]. Recent investigations have focused on the dissolution of silicates and aluminates, since in high basicity slag, Cr tends to remain in solution in silicates complex instead of forming spinels [16; 17]. In this regard, [PERSON] et al. [18] defined a new index, called cs-factor, which accounts for the Cr bound in calcium silicates, more solvable in water than spinels. Currently, a recently published paper explained a method to favor the migration of Cr from an unstable silicate-matrix to spinels: The key is the solidification pattern from liquid to solid that allows Cr to migrate from silicates to enrich spinels [19]. Other than the formation of Ca-chromite, which releases Cr due to oxidation to CaCrO\({}_{4}\), one of the effects of high basicity seems to be the formation of unstable spinels, that feature a non-negligible content of impurities (Ca, Si) and irregular shape [8; 20; 21]. As stated by [PERSON] et al.