## 3 Results and Discussion
### Microstructural Evolution and Transformation Kinetics
It has been confirmed in various studies [23, 24, 28] that with an increasing vanadium content, the rate of perlite transformation slows and the steel hardness increases by increasing the vanadium content. Vanadium in solution seems to affect the mobility of the carbon atoms [10, 25, 26, 27, 28, 29, 30]. Using Thermo-Calc software we performed the thermodynamic analysis, showing that the type of stable carbides in the matrix changes from cementie to M\({}_{6}\)C and M\({}_{7}\)C\({}_{3}\) carbides. The formation of these carbides is due to the uphill diffusion of elements such as cerium and molybdenum [31]. Therefore, the formation kinetics of these carbides will be slower than cementie, and at low temperatures of transformation,  
Figure 4: Dilatometric test results of the silicon-modified alloy (1.6511 Si2), silicon-modified alloy after adding vanadium (1.6511 Si2V), and silicon-modified alloy after adding a rare earth alloy (1.6511 Si2M) at a continuous cooling rate of 4 \({}^{\circ}\)C/s. Figure 5: **(a)** Optical microscopy and **(b)** SEM metallography of sample 1.6511 Si2V; **(c)** optical microscopy and **(d)** SEM metallography of sample 1.6511 Si2M. SEM metallography shows that the microstructure of both alloys is granular bainite. Note: 1.6511 Si2V is CFB while 1.6511 Si2M is containing carbides. the possibility of their formation is very low. The presence of cerium and lanthanum in a chemical composition similar to vanadium increases the probability of obtaining bainite, and especially martensite, at lower cooling rates. The reason for this manner in different studies has been stated as the deposition of this element in the interface of ferrite and austenite, which prevents the diffusion of carbon [30; 31; 32; 33]. Preventing or disrupting the diffusion of carbon by vanadium and cerium can be the main reason for the delay in forming the perlite (or ferrite). However, in general, the behaviors of the two elements are different. Vanadium retains carbon in austenite, while cerium prevents the diffusion of trapped carbon in ferrite into austenite. Thus, the probability of cementite formation in the sample containing cerium is much higher than the sample containing vanadium. This issue will be discussed in further discussions. Isothermal dilatometry at 300 \({}^{\circ}\)C was used to investigate the effect of vanadium and cerium on the transformation in the isothermal condition (Figure 6). Time was measured till the dilatation stopped. In this respect, vanadium leads to an earlier cessation of transformation, and cerium delays its cessation by a different behavior; therefore, in similar conditions, the specimen that contains the vanadium parent phase should have a greater effect on the isothermal transformation than a specimen that contains rare earth elements. This point is confirmed by other examinations in the present study. Microscopic images in Figure 7 show that the substructure resulting from the isothermal transformation in both samples is carbide-free bainite. The retained austenite phase percentage change with increasing vanadium and rare earth elements was investigated using the EBSD phase map. According to the phase map (Figure 8), the face-centered cubic (FCC) phase corresponding to austenite is shown in a different color from the body-centered cubic (BCC) phase corresponding to the ferrite phase. Image analysis showed the volume percent of retained austenite in sample 1.651i2 is about 16%. The sample containing vanadium and cerium have 20 and 12% volume fractions of austenite, respectively. As expected, the retained austenite volume fraction is higher in the sample where the bainite transformation stopped earlier (1.6511 Si2V sample), and the volume fraction of the retained austenite is lower in the sample where the transformation stopped posteriorly (1.6511 Si2M sample). Figure 6: Isothermal dilatometry graph of 1.6511 Si2, 1.6511 Si2V, and 1.6511 Si2M at 300 \({}^{\circ}\)C. Note: Transformation cessation is delayed by adding rare earth elements, but vanadium caused it to occur sooner.