Regularities of Crystallization Heat Release During Solidification of Alloyed Cast Irons

The chemical composition of alloys plays an important role at their crystallization and influences the solid phase formation, and thus, microstructure and properties. The present paper studies the release of the heat of crystallization of alloyed wear-resistant cast irons in order to determine the quantitative patterns of the chemical composition influence to the kinetics of crystallization. The differential thermal analysis was applied to get the data of heat release, its rate at cast iron temperature decrease. The normalized dependence of the amount of crystallization heat over time was obtained. The main temperature parameters were analyzed and four stages at irons crystallization were established and characterized with their duration and released heat. The multiple correlation analysis allowed considering a numerous physical and chemical factors and distinguishing their role at crystallization of irons. As a result, the quantitative regularities are determined of influencing the content of alloying elements, impurities and carbides on a heat and time of crystallization at the different stages of solidification, which are of great importance in developing alloyed irons with required quality and properties.


Introduction
It is known that the influence of the chemical composition of metals and alloys on their crystallization is mainly associated with a change in the thermophysical properties of the melt and the conditions of the solid phase formation [1][2][3].It was previously shown that the solid phase grows under concentration supercooling, determined by the content and diffusion of the dissolved elements, the energy of the boundary between liquid and solid phases of the melt, and the temperature field in front of the growing solid phase [4,5].A change in the temperature field can not only enhance or weaken the concentration supercooling, but also completely eliminate it at a negative temperature gradient in front of the moving crystallization front [5].The temperature distribution in the casting after melt pouring into the mold is determined by the conditions of heat removal and the release kinetics of heat of overheating and crystallization.
One of the effective methods to study the crystallization process of metals and alloys is the differential thermal analysis (DTA) [6][7][8].It allowed particularly to investigate the graphitization ability of spheroidal graphite cast iron processed by Al, Zr, Ca-FeSi [9], solidification influence in the control of inoculation effects in ductile cast irons [10], solidification pattern of Si-alloyed, inoculated ductile cast irons [11], the influence of final inoculation on the metallurgical quality of nodular cast iron [12] and an increasing precision and yield at casting production by simulation of the solidification process based on realistic material data evaluated from thermal analysis [13].
The kinetics of heat of superheating release is studied and given in the numerous works [1][2][3][4][5]14], while the regularities of the release of the heat of crystallization of multicomponent metal systems have not been studied enough.
The aim of the present work is to study the release of the heat of crystallization of alloyed wear-resistant cast irons in order to determine the quantitative patterns of the chemical composition influence to the kinetics of crystallization.

Methodology
The alloyed wear-resistant cast irons of different grades were used in the study (Table 1).The temperatures of liquidus (tl) and solidus (ts), heat (L) and time () of crystallization of the irons at cooling in helium at a rate of 20 K/min, as well as regularities of change in the rate of crystallization heat release were determined by the method of differential thermal analysis (DTA) with thermoanalyzer GDTD-24AV (SETARAM, France) on the samples with a diameter of 3 mm and a length of 6 mm.
The surface of solidified samples was etched with 2-4 wt.% nitric acid solution to analyze microstructure.It was done by MIM-10 optical microscope, JEOL JSM-35CF electron microscope and INCA Energy 350 (Oxford Instruments) energy dispersion analyzer.
For a more accurate comparison of the crystallization heat release kinetics of the alloys with different chemical composition, analytical dependences were plotted in relative time coordinates (the ratio of the current time to the total solidification time) and crystallization heat (the ratio of the current value of the crystallization heat to the one released till complete solidification of the sample).The values were changed from 0 to 1, where 0 means the beginning of the process, whereas 1 means its end.
These regularities were determined by analyzing the polynomial in the form were: Y -rate of crystallization heat release, A0, A1, …Anpolynomial coefficients, xtime.
This equation approximated the experimental data on the rate changes in crystallization heat release.
After determining the coefficients Equation 1 was integrated in the range from 0 to 1 and the normalized dependence of the amount of crystallization heat (L) over time () was obtained as below: The coefficients (Ai) of the regression Equation 1, multiple correlation (Ri) and the relative approximation error () were determined according to the method described in [15].

Results and discussion
The chemical composition, the temperatures of liquidus (tl,) and solidus (ts), heat of crystallization (L) and solidification time () of the studied cast irons are presented in Table 1 and the rates of crystallization heat release of alloyed cast irons are shown in Figure 1.
The Table 2 shows the parameters of Equation 1 and the regularities of crystallization heat release calculated by Equation 2in relative and absolute values shown in Figure 2.
Correlation analysis showed that the polynomial of degree 16 of Equation 1 describes the data shown in Fig. 1 with a sufficient degree of reliability.The correlation coefficient (R) varies from 0.992 to 0.999, and the average approximation error () -from 3.9 to 9.2%.When the number of variables is less than 16 the degree of reliability decreases and the approximation error increases.When the number of variables exceeds 16, Equation 1 becomes more complicated.
The data analysis of the Figures 1 and 2 shows that the crystallization process of the studied irons consists of the following stages: 1.
The beginning of the austenite precipitation process with an increase in the rate of crystallization heat release to a local maximum, 2.
Completion the process of austenite precipitation with a decrease in the rate of crystallization heat release to a local minimum, 3.
The beginning of the eutectic precipitation process with an increase in the rate of crystallization heat release to a maximum, 4.
Completion of the eutectic precipitation process with a decrease in the rate of crystallization heat release to zero at the moment of the end of solidification.
The results of determining the duration of the above stages and the amount of crystallization heat release in this case are shown in Table 3.
Analysis of the data in Figure 2 and Table 3 shows that, depending on the chemical composition of cast irons, the duration of the first stage of solidification is from 11 to 22% of the total solidification time, the second -20 -60%, the third -17 -35%, and the fourth -12 -27%.The amount of released crystallization heat at the first stage varies from 7 to 13% of the total heat of crystallization, at the second -from 14 to 46%, at the third -from 29 to 55% and at the fourth -from 17 to 29%.* the relative and absolute values of the parameters are respectively given in the numerator and denominator.
It is known [4,5] that the value of the crystallization heat of an alloy is directly proportional to the number of atoms passed from a liquid solution to a solid state.Consequently, the accumulation of the elements and mainly carbide phases at the interface between the liquid and solid phases during solidification should affect the crystallization heat of the alloys.From one hand solid carbides act like obstacles for atoms to pass from a liquid solution to a solid state and though decrease the crystallization heat.From another hand increase in solid carbides areas lead to crystallization heat increase.
The accumulation of the elements at the interface between the liquid and solid phases is possible both due to a change in solubility and the occurrence of adsorption and desorption processes.At the same time, at the initial moment of crystallization, the content of the element (i) in the liquid ahead of the flat crystallization front (Cli) due to the change in solubility is determined by the following dependence [4]: where K0 -equilibrium distribution coefficient; Ci is the volumetric content of the i-th element in the melt, %.
The values of equilibrium distribution coefficients in austenite are given in Table 4.The accumulation efficiency of elements at the interface between the liquid and solid phases as a result of adsorption processes (Гi) is determined by Gibbs equation: where T is the temperature of the melt, K; Runiversal gas constant (R = 8.32 J/(Kmol); i/C i -partial derivative of the energy of the boundary between liquid and solid phases with respect to the content of the i-th element in the melt, mN/%; i -the energy of the boundary between liquid and solid phases, which is determined by the equation given in [19]: where  l-s is the energy of the boundary between liquid and solid phases, N/m.
The quantitative regularity of the influence of the chemical composition on the energy of the boundary between liquid and solid phases of iron-carbon melts was determined according to the experimental data in [20][21][22].
The established regularity has the following form: where C, Si, Mn, Cr, Ni, P, S, Mo are the content of these elements in the melt, respectively, %; t is the temperature of the melt, С; Rp -correlation coefficient;  -relative approximation error, %.
It was shown in [23][24][25] that at the ratio of the concentrations Cr/C=3-10, the crystallization of cast irons begins with the formation of austenite, and the eutectic is formed with the formation of austenite and carbides of (Cr, Fe)7C3 type, which contain from 50 to 70% chromium [23].
The regularity of the influence of elements on the amount of carbides (K) of (Cr, Fe)7C3 type in cast irons containing from 1.96 to 3.03% C; 0.3 to 0.75% Si; 0.64 to 4.6% Mn; 12.7 to 36% Cr; up to 11.4% Ni; up to 2.6% Mo, were determined from the experimental data given in [23].
The results of the mathematical analysis showed that the equation has the following form: Rp=0.999; =0.31%.
The results of calculating the total content of elements in a liquid at the interface between the liquid and solid phases at the initial moment of crystallization due to the different solubility of elements in the liquid and austenite (Сil-a), as a result of adsorption at temperatures of liquidus (Гil), solidus (Гis) and in the middle of the solidification interval (Гil-s), as well as the amount of carbides (K) are given in Table 5. Carbides amount (30.98%) calculated by Equation ( 7) in 300Kh22 cast iron, for which a significant increase in the heat of crystallization was observed, is compared to the experimental values (32.7%) (Fig. 3).Analysis showed that the difference is of 1.7% that is acceptable at modeling of the structure.Analysis of elements content in carbides (Fig. 4 a), between carbides (Fig. 4 b) and in solid solution (Fig. 4 c) showed that chromium in carbides varies from 25.6 to 46.43 % wt.(average 37.9%), silicon from 0.12 to 0.54% (0.219%), manganese from 3.2 to 3.8% wt.(3.52%) (Table 6).An assessment of carbides influence on crystallization heat shows that their increase from 18 to 21% correlates with a decrease in the crystallization heat (correlation coefficient r = 0.983).Further carbides increase from 21 to 31% opposite trend is observed (correlation coefficient r = 0.793) Taking as independent factors the amount of carbides (K) formed during the eutectic formation, the total content of elements in the liquid at the interface between the liquid and solid phases at the initial moment of crystallization due to the different solubility of elements in the liquid and austenite (Сil-a) and as a result of adsorption at temperatures of liquidus (Гil), solidus (Гis) and in the middle of the solidification interval (Гil-s), the effectiveness of their combined effect on the kinetics of heat of crystallization release of high-alloy cast irons at various stages of solidification was investigated.
Multiple correlation analysis with the 1st degree polynomial showed that the efficiency of accumulation of the elements on the surface of crystallization centers and growing austenite crystals as a result of adsorption at the liquidus temperature (Гil) and in the middle of the solidification interval (Гil-s) determines the duration of stages I and II of crystallization, respectively.In the transition to the eutectic crystallization, an additional significant factor is the release of carbides, the amount of which (K) simultaneously with the efficiency of accumulation of elements on the surface of growing crystals as a result of adsorption at a solidus temperature (Гis) determines the duration of stages III and IV of crystallization.
At eutectic crystallization austenite and carbides serve as accumulators, since the solubility of elements in them is less than in the melt.
An analysis of the regularities representing by this table shows that the accumulation of elements and phases ahead of the crystallization front slows down its progress and leads to an increase in the crystallization time.Evaluation of the effectiveness of the influence of factors according to the Student's criterion (tSt) showed that the influence of elements adsorbed on the interface of the liquid and solid phases is 2.2-3.6 times higher than the influence of carbides.It is seen that at the beginning of the precipitation of austenite and eutectic (stages I and III), the amount of heat depends on the duration of the stages (і).At the final stages of austenite and eutectic separation (stages II and IV), an additional influence is exerted by the accumulation of the elements in the liquid at the interface between the liquid and solid phases, which is formed as a result of different solubility of elements in the melt and austenite (Сil-a).
The coefficients (Ai -Аі, АСil-a) of the regression of the 1st degree polynomial at A0 = 0, multiple correlation (Ri) and relative approximation error () are shown in Table 8. Analysis of the data given in Table 8 shows that the amount of heat of crystallization released at all stages depends on the duration of the process.
The experimental results and analysis show that the release of crystallization heat depends mainly, according with Student's criterion (tSt), on the efficiency of accumulation of alloying elements, impurities and carbides on the interfacial surface.

Conclusions
The study of the crystallization kinetics for different grades of alloyed wear-resistant cast irons revealed four stages at their solidification with subsequent austenite and eutectic precipitation, which are distinguished by the duration and released heat.
The chemical composition of irons influences to the crystallization kinetics and increase of heat release through the concentrations gradient of the elements at the solid-liquid interface and their accumulation on the surface of growing crystals.The impurities and precipitated carbides are found to play an important role in the intensification of crystallization heat release due to their barrier effect on the advancement of growing austenite crystals.
The quantitative regularities determined in this study could be useful at the development of alloyed cast irons of required quality and properties.Particularly, they can be used for modeling the process of alloyed cast irons solidification and predicting the development of casting defects in castings.

1 .
Influence of the chemical composition on the rate of heat of crystallization release of alloyed cast irons.a) 240Kh16; b) 260Kh28; c) 300Kh12G3M; d) 300Kh12G5; e) 300Kh12M; f) 300Kh22; solid linesexperiment; dotted lines -calculation.a) b) Fig. 2. Kinetics of the release of heat of crystallization of alloyed cast irons in relative (a) and absolute (b) values

Table 1 .
The chemical composition, liquidus (tl) and solidus (ts) temperatures, heat of crystallization (L) and solidification time () of cast irons

Table 2 .
Coefficients (Ai) of the regression Equation 1, multiple correlation (Ri) and relative approximation error () for determining the rate of release of heat of crystallization of alloy cast irons

Table 3 .
The duration of the stage (i) and the amount of released heat of crystallization (Li) during the solidification of alloy cast irons*

Table 7 .
The parameters of the 1st degree polynomial calculated at different stages of irons solidification

Table 8 .
The parameters of the 1st degree polynomial calculated at different stages of solidification of the irons