## 1 Introduction  
Slope farmland refers to the cultivated dry land distributed on a hillside. When the landform slope type is between 6 and 25\({}^{\circ}\) and it is cultivated, it can be called slope farmland. At present, the area of arable land in China is about 135 million ha, of which the area of slope farmland is about 30.9 million ha [1], accounting for over one-fifth. Due to the instability of slopes and uneven rainfall [2], slope farmland is prone to soil erosion, which carries soil, nitrogen, phosphorus, and other nutrients into water bodies, leading to siltation of rivers and lakes and eutrophication of water bodies. The slope farmland in the Three Gorges Reservoir area (TGRA) accounts for a high proportion (42%) [3], and it overlaps with the heavy rain area in the Yangtze River Basin [4], resulting in serious soil erosion in the area. According to the Soil and Water Conservation Bulletin, soil erosion areas accounted for 32.93% of the total TGRA in 2019 [5]; the TGRA is a key national-level soil and water conservation area. Calcareous soil, accounting for 34.1% of the total area of the reservoir area [6], is one of the main soil types in the TGRA, and one of the soils with a high risk of loss. Calcareous soil on slope farmland is a main source of soil erosion in the reservoir area.  
Excessive input of phosphorus via soil erosion is a key factor leading to eutrophication of water bodies [7; 8; 9]. There are two main transport mechanisms of phosphorus in slope farmland: one is the loss of particulate phosphorus via soil erosion, and the other is the loss of dissolved phosphorus via surface runoff and prompt subsurface flow. Studies have shown that the particulate phosphorus lost with soil erosion is the main form of phosphorus loss during migration, and its proportion can generally account for more than 80% of total phosphorus loss [3; 10]. Phosphorus lost via soil erosion enters the water system and undergoes migration and transformation [11; 12], resulting in reproduction of a large number of harmful algae and causing the eutrophication of water bodies. On the other hand, in the process of soil erosion, water, soil, and fertilizer are lost together, degrading soil quality [8] and declining the productivity of soil in the slope farmland; in order to maintain the level of productivity, a large number of chemical fertilizers are used, which will intensify the eutrophication of water bodies. Therefore, studying the fixation mechanism of phosphorus in the soil is of great significance to control the loss of phosphorus.  
Phosphorus in the soil is mainly fixed by minerals in the soil [12]. Soil minerals as the main constituents of soil generally account for 95% to 98% of the soil mass. Studies have shown that in calcareous soil, calcium carbonate, as the main substrate for phosphorus, binds to form calcium-bound phosphorus to fix phosphorus [13; 14; 15]. Other studies have shown that physical clays in calcareous soil [16; 17], especially the phyllosilicates [18], also have a strong effect of fixing phosphorus. The mineral composition of different particle size fractions varies greatly. Generally speaking, the minerals in the coarse fractions are mainly primary minerals (such as feldspar, calcite, muscovite, etc.), and in the fine fractions they are mainly clay minerals (such as kaolinite, montmorillonite, etc.) [19; 20], which make the fixing mechanism and phosphorus fractions differ in different particle size fractions of the soil [21].  
At present, there are relatively few studies on the effect of the particle size and mineral composition of calcareous soils on slope farmland on phosphorus fixation, and understanding this effect will improve the management of phosphorus loss from such soils. The objectives of this study were to determine (1) the phosphorus fractions and mineral components in different particle size fractions of calcareous soil on slope farmland; (2) their adsorption properties for phosphorus; and (3) the effect of mechanical and mineral composition on phosphorus fixation.