## 1 Introduction
The obtained results show that the wear rate was reduced by 24% and surface roughness by 21%, and the fatigue limit increased by 13%. Corrosion properties of various high-speed steels subjected to DCT are analyzed in [25]. The results show that microstructure, hardness, and corrosion resistance change to different extents depending on the chemical composition of the samples. A comprehensive review of DCT application is represented in [26]. Based on numerous studies, it was concluded that shallow cryogenic treatment, only up to \(-80\)\({}^{\circ}\)C, has less effect than DCT up to \(-196\)\({}^{\circ}\)C. Under both treatments, some steel grades showed reduced fatigue limit, while for other steels it increased. An optimal soaking time of about 36 h was noted for D2 steel. Precipitation of secondary carbides was considered the main factor of higher wear resistance due to the larger interface created with the matrix. A reduction in the wear rate of about 14% for AISI A8 subjected to DCT before tempering corresponded to a higher number of secondary carbides by 6%, and increased from 0.68% to 0.73% of the covered area [27]. Less represented in the literature, multistage cryogenic treatment (MCT) of X153 CrMoV12 cold work steel was tested in [28]. Both MCT and DCT produced similar changes in the microstructure, and increased the amounts of homogeneous refined carbides. The effects of multiple DCT and tempering on microstructure and properties of high carbon bearing steels are shown in [29]. Summarizing the metallurgical principles of microstructure formation in DCT [30], we can conclude that one of its primary objectives is the transformation of RA to martensite. This is one of the theoretically explained mechanisms for wear resistance increasing because the martensitic phase has much higher hardness than the initial austenite phase [31]. Typically, this phase transformation has been investigated and quantified via the X-ray diffraction (XRD) method [32; 33; 34; 35]. The authors of this work used such a method, along with an ultrasonic method and electron microscopy with a microanalyzer, to observe the transformations of RA. In addition to the RA transformation, another mechanism for wear resistance improvement by DCT is the secondary alloy carbides precipitated and uniformly distributed by the tempering [36; 37; 38; 39] or DCT itself [40]. In some studies of tool steels, it is stated that the DCT process promotes the diffusion of carbon atoms to dislocations [41; 42; 43; 44; 45; 46], and these cluster atoms contribute to an increase in the number of carbides during tempering. However, other authors believe that carbon atoms do not diffuse at the temperatures of DCT [47; 48], and that immobile carbon atoms are captured by gliding dislocations [49]. Another hypothesis for improved wear resistance is a higher dislocation density in the steel structure obtained after DCT. However, despite the repeated mention of this in the literature [48; 49; 50], quantitative analysis of the dislocation density is seldom possible. Hence, the question regarding the influence of DCT on the dislocation density of doped alloys remains unanswered; we set out to investigate it using the XRD method. Another important unresolved issue is the influence of a part's holding time in the coolant. It has been reported that DCT of martensitic steels conducted for a longer period has a better effect on the wear resistance [8; 40; 51]. However, according to a generally assumed theory of martensitic transformation, austenite to martensite transformation has to occur right after a certain level of temperature is reached, and additional time has no effect on martensite fraction volume. In addition, due to low diffusion rate, significant changes are not expected at such low temperatures [48]. On the other hand, most researchers use significant DCT exposure times (24 h or more) to obtain significant changes in the structure and distribution of carbides [8; 10; 13; 18; 33; 40; 51].