## 1 Introduction  
Steel slag is an industrial solid waste generated in the steel-making process, but it is rich in dicalcium silicate (C\({}_{2}\)S) and tricalcium silicate (C\({}_{3}\)S) in mineral compositions, which is similar to cement clinker [1; 2; 3; 4]. Based on its mineral compositions, steel slag has great potential for application as supplementary cementitious materials (also known as mineral admixture) of cement and concrete [5; 6; 7; 8]. Generally, only after being ground into powder, could steel slag have hydration activity and be used as supplementary cementitious materials [9; 10]. The smaller the particle size of steel slag powder, the higher its hydration activity [11; 12]. However, the grfindability of steel slag is much worse than that of other mineral admixtures such as fly ash and granulated blast-furnace slag, seriously impeding the preparation efficiency of steel slag powder and its application performance in building materials. Therefore, its grinding property is an important consideration in the application of steel slag. In the grinding process of a solid, particles characteristics such as size, distribution, bulk density, and dispersion are in constant change on a macroscopic scale, and the internal chemical bonds of particles are constantly broken on a microscopic scale [13; 14; 15]. Steel slag has poor grindability because of a large amount of iron oxides and continuous solid solution composed of some divalent metal oxides, which form a dense structure in the steel slag [16; 17]. Currently, the researches on improvement of grinding efficiency for steel slag mainly focus on the optimization of grinding equipment--such as vertical mill and roller mill, while there are few researches on other measures, such as removal of hardly grinding phases (HGP) or the use of chemical admixtures. Although vertical mills have been applied in grinding of steel slag, many application researches indicate that steel slag powder prepared by vertical mills have poor particle morphology--such as flat, needle, and irregular shapes, resulting in the ball mill still being chosen by many manufacturers to prepare steel slag powder in China. Meanwhile, some studies indicate that metallic iron in steel slag is one main reason causing its poor grinding property. However, in different grinding periods, the factors influencing grinding efficiency usually change due to different grinding characteristics [18; 19; 20], but to date these factors have not been yet been fully studied. Some researches also show that the split-phase phenomenon occurs in the grinding process of steel slag, resulting in ground steel slag powder having some differences in chemical and mineral compositions during different grinding periods [21; 22]. So, it is necessary to reveal the factors influencing the grinding efficiency of steel slag from studying grinding characteristics, hardly grinding phases, and split-phase phenomenon during different grinding periods. Moreover, in the grinding process of a solid, other phenomena such as agglomeration of fine particles and re-healing of particle fracture surfaces result in a lower grinding efficiency and higher energy consumption [23; 24; 25; 26]. In recent years, grinding aids, most of which are polar organic compounds, are extensively applied to weaken agglomeration of fine particles and improve grinding efficiency of cement [27]. Therefore, the use of grinding aids is also an important way to improve preparation efficiency of steel slag powder. Based on the abovementioned discussion, the hardly grinding phases of converter steel slag were revealed from the proportion, morphology, mineral, and chemical compositions. Then the grinding characteristics of untreated and pretreated (i.e., magnetic separation) steel slag were compared from the proportion of iron phases, grinding efficiency, particle size, and particle distribution and morphology.