Formation and Growth Mechanism of Clusters in Liquid REM-alloyed Stainless Steels

Abstract

REM-oxide clusters extracted from 253MA stainless steel grade samples from a pilot trial were investigated using a 2%TEA electrolyte. The samples were taken from liquid steel at different holding times after an addition of an appropriate amount of mischmetal. Thereafter, SEM in combination with EDS was deployed for three dimensional (3D) investigations of the characteristics of the extracted REM-oxide clusters. A reliable cluster size distribution (CSD) was obtained by improving the observation method and it was used to explicate the formation and growth mechanism of REM-oxide clusters. A correlation between morphology of clusters and their growth rate was found. This was used to divide the clusters into two different groups, which form and grow in accordance to different mechanisms. The results also show that the growth of clusters is governed by different types of collisions dependent up on size of the clusters. It has been concluded that for REM-oxide clusters turbulent collisions are the main controlling mode for the growth rate.

1. Introduction

It is well known that inclusions and clusters, which are formed in liquid steel during ladle treatment, have harmful effects on the casting process (clogging problems) as well as on the final mechanical properties of a steel product. Especially, steels deoxidized or alloyed with rare earth metals (REM) are difficult to produce due to the high tendency of REM-oxides to form cluster and clog the nozzle during casting.^1,2) It was reported^1,3) that the main part of the nozzle accretion in stainless steels is caused by agglomeration of Ce inclusions and clusters in the nozzle. Therefore, much attention is paid to control the formation and growth of inclusions and clusters in liquid steel during ladle treatment of stainless steels.

Lindborg et al.⁴⁾ showed that collisions play the most important role in the growth of inclusions after the very rapid initial nucleation and diffusion growth. Different kinds of collisions play larger role for growth of inclusions over different size ranges: Brownian collisions are effective for the inclusions in the size range 0.1–1 μm; Brownian and Turbulent collisions - for 1–10 μm and Turbulent and Stokes` collisions - for inclusions larger than 10 μm.^5,6,7) These conclusions have been drawn on the basis of mathematical modeling done for spherical aluminum oxide inclusions.⁵⁾ However, REM-oxide clusters mostly observed in molten stainless steels have irregular shapes and larger densities (6500–7200 kg/m³) in comparison to the spherical Al₂O₃ inclusions. Therefore, REM-oxide clusters shall have a different behavior and growth rate than the Al₂O₃ inclusions.

Appelberg et al.⁸⁾ used a Confocal Laser Scanning Microscope (CSLM) to study REM inclusions. They reported that there exists a strong attraction force between REM particles which results in an agglomeration of inclusions and clusters. Bi et al.⁹⁾ studied the characteristics of REM clusters in stainless steel after electrolytic extraction. An increase in the number of large sized clusters per cubic millimeter, at an expense of smaller clusters, with an increased holding time was observed. However, the mechanism of clusters growth was not considered in details.

This study is focused on the three dimensional (3D) investigation of REM clusters in 253MA stainless steel at different holding times after an addition of misch-metal during a pilot trial. The cluster size distributions in steel samples taken at different holding time were used for consideration of the mechanism of formation and growth of REM-oxide clusters in liquid steel.

2. Experimental

In this study, steel samples were taken during a pilot trial (350 kg) from liquid 253MA stainless steel after alloying by rare earth metals. The composition of 253MA stainless steel was the following (in wt%): 17–19% Cr, 7–9% Ni, 1.3–1.4% Si and 1.3–1.4% Mn. The pilot trial was carried out in an induction furnace under an Ar atmosphere. Double thickness lollipop samples (LP4/12 having 4 and 12 mm thickness) were taken from liquid steel at 3 (sample S1), 6 (S2) and 9 (S3) minutes of holding time after an addition of 1.49 kg of misch-metal. The misch-metal contained about ~50% Ce, ~35% La and ~15% of the other REM elements.

According to recommendations obtained in a previous study,¹⁰⁾ one half of a horizontal slice (Fig. 1) was cut from each sample and used for electrolytic extraction (EE). The electrolytic extraction was carried out by using a 2%TEA electrolyte (2 v/v% triethanol amine – 1 w/v% tetramethylammonium chloride - methanol) and using the following parameters: current – 40–60 mA and voltage – 3.6–3.8 V. The weight of the steel dissolved during the extractions, W_dis, varied between 0.11 and 0.19 g.

Fig. 1.

Typical lollipop LP4/12 sample taken from the liquid steel and the specimen used for electrolytic extraction.

The electrolyte after electrolytic extraction was filtrated through a polycarbonate (PC) film filter with an open pore size of 0.4 μm. The extracted non-metallic inclusions and clusters were investigated in three dimensions (3D) on a surface of a film filter by using a SEM at magnifications of 300–5000. The total observed area and total number of investigated clusters on film filters were varied from 30 to 75 mm² and from almost 400 to 1100, respectively.

To investigate the cluster characteristics, the two following observation methods were used:

Method 1: All clusters were observed on an A₁ unit area (A₁=3 mm²) of a film filter at a magnification of 500 times. Five different zones on each film filter were investigated and an average value of the results obtained by the SEM was calculated. Also, the total area observed by Method 1 was 15 mm² for each sample.

Method 2: Only large size clusters (larger than 5 μm for samples S1 and S2 and larger than 10 μm for sample S3) were observed on an A₂ unit area (A₂=15 mm²) of a film filter in each zone at a magnification of 300 times. The total area observed by Method 2 varied from 15 to 75 mm², due to different number of clusters present in the different samples.

The number of clusters per unit volume of steel sample (N_V) in different size intervals was calculated as follows:   

$$N_V=n\cdot \frac{A_f}{A_{obs}}\cdot \frac{{\rho }_m}{W_{dis}}$$(1)

where n is the number of clusters in the given size interval. The parameters A_f and A_obs are the total area of the film filter (~1200 mm²) with inclusions and clusters after filtration and the area of the filter observed by SEM. The parameter ρ_m is the density of the steel (~0.0078 g/mm³).

The maximum length (L_C), area (A_C) and circularity factor (CF) of each cluster on the SEM images were measured by using the “ImageJ” software. In this study, the circularity factor was used as a quantitative parameter of the morphology of cluster and calculated by using the ImageJ software as follows:   

$$CF=\frac{4\pi \cdot A_C}{P_C^2}$$(2)

where P_C is the perimeter of the cluster image determined by the ImageJ software.

3. Results and Discussion

3.1. Characteristics of Clusters in Different Samples

In this study, agglomerations consisted of three and more inclusions are considered as a cluster. Some typical small and large clusters, which were observed on a surface of film filter after electrolytic extraction, are shown in Fig. 2. For each sample, characteristics of clusters such as the number, size and morphology were determined. The cluster size distributions were obtained by the 3D investigations of 400–1100 clusters on a surface of filters after electrolytic extraction of the steel samples.

Fig. 2.

Typical small (a) and large (b) clusters observed on a surface of film filters after electrolytic extraction and filtration.

A typical cluster size distribution (CSD) obtained by observing 147 clusters on 3 mm² on film filter of the sample S3 is shown in Fig. 3(a) in terms of N_V with constant size step (ΔLc=1 μm). In addition, the obtained CSD value is also presented as a relationship between the cluster length (L_C) and log(W_C), where W_C is the weight of the steel sample containing only one cluster in the given size range, Fig. 3(b). The value of W_C can be calculated as follows:   

$$W_c=\frac{{\rho }_m}{N_V}$$(3)

In other words, the W_C value represents the weight of steel sample which must be dissolved to find one cluster in a given size range. As can be seen in Fig. 3(b), some part of this relationship for the CSD values (in the size range from 4 to 10 μm) can be well described by a linear function (correlation coefficient R is 0.961). In this case, the small sized clusters (<4 μm) are not considered for determination of this linear function (hereafter called “CSD function line”). However, the data points for clusters larger than 10 μm are very scattered and do not correspond to the obtained CSD function line. The main possible reasons for this big deviation can be the following:

Fig. 3.

Typical size distribution of clusters (a) and the weight of steel sample (W_C) containing only one cluster in the given size range (b) in sample S3.

1) number of investigated large size clusters (>10 μm) are not enough for getting a reliable smooth CSD function line, due to a limited observed area of the film filter;

2) the compositions of clusters are different due to the different sources and/or formation mechanisms;

3) the growth rate of clusters in different size ranges are significantly different.

The above mentioned possible reasons are discussed below.

The number of large size clusters (>10 μm) in the CSD was increased by gradually increasing the observed area on a filter from 3 mm² (A₁) to 6 (2A₁), 9 (3A₁), 12 (4A₁) and 15 (5A₁) mm² (Method 1). The obtained CSD function lines for 3, 9 and 15 mm² of the observed areas are shown in Fig. 4(a) for the S3 sample. It was found that the slopes of the CSD function lines are not significantly changed by increasing the observed area from 9 (3A₁) to 15 mm² (5A₁). The R value for these function lines is varied from 0.953 to 0.978. Therefore, the 5A₁ function line was used as a reference CSD function line to estimate the deviations of the other CSD function lines obtained at lower observed areas. In this study, this deviation of log(W_C(i·A1)) value for i-th CSD function line was calculated in percentage as follows:   

$$\mathrm{\Delta }log(W_C{\hspace{0.17em}}_{(i\cdot A\mathit{1})})=100\%\cdot \left|log(W_C{\hspace{0.17em}}_{(i\cdot A\mathit{1})})-log(W_C{\hspace{0.17em}}_{(5A\mathit{1})})\right|/log(W_C{\hspace{0.17em}}_{(5A\mathit{1})})$$(4)

An effect of number of observed clusters in one size step on average deviation from 5A₁ function line is shown in Fig. 4(b). Error bars represent the arithmetic standard deviation of obtained values in the respective size step. It can be seen that the deviation of the log(W_C(i·A1)) values decreases drastically with an increased number of observed cluster per size step and can reach the value less than 3% at 5 and more observed clusters per size step. Therefore, in this study, the reliable CSD function lines, which deviate from the 5A₁ reference function line with less than 3%, were obtained based on data points having at least 5 clusters per size step.

Fig. 4.

CSD function lines for different observed areas for sample S3 (a) and the effect of the cluster number per size step on the deviation from the 5A₁ reference function line (b).

Figure 5 shows the CSD function lines for all three samples obtained by observation of clusters on 15 mm² of filters (5A₁). It can be seen that several data points (open marks) representing clusters with larger length significantly deviate from the obtained CSD function lines. These data points contain less than 5 measured clusters per size step, due to the limited observed area of the film filter. Based on the results obtained by an estimation of largest size of inclusions in rolled steels,¹¹⁾ it was found that the linear distribution of SEV (statistics of extreme value) can be significantly improved with an increased number of measurements, especially in the size ranges of large size inclusions. Therefore, in this study, the number of observed clusters in the respective size ranges was increased by increasing of observed area on each film filter (Method 2).

Fig. 5.

CSD function lines of different samples obtained by observation of clusters on a 15 mm² of film filter (Method 1).

It was found that the deviation of log(W_C) values for larger clusters (≥15 μm) from the 5A₁ reference function line tends to decrease with an increased observed area till 30 mm², as shown in Fig. 6(a) for S3 sample. A value of this deviation was calculated by using a similar Eq. (4). However, it can be seen that a further increase of the observed area from 30 to 75 mm² decreases this deviation for larger size clusters only insignificantly despite that the number of measured clusters in these size ranges are larger than 5 (from 5 to 23). Figure 6(b) shows the CSD function lines for all three samples obtained at increased observed areas (Method 2). It should be pointed out that all data points shown in this figure include at least 5 measured clusters. The total observed area on the film filter and numbers of measured clusters for each sample are given in Table 1. Despite the drastic increase of the observed area and measured clusters, it was found that the data points representing larger size clusters (open marks) for samples S2 and S3 tend to lie on new function lines (FL2). However, this was not observed in the sample S1 due to the absence of large sized clusters. The equations of the CSD function lines for small (FL1) and large (FL2) sized clusters and their correlation coefficient (R) are given in Table 2. The R values for all obtained function lines varied from 0.982 to 0.999, which indicates a good correlation between the measured data and the function lines.

Fig. 6.

Relationships between the observed area and deviations of the log(W_C) values for larger size clusters from a 5A₁ reference function line (a) and CSD function lines for different samples obtained at increased observed areas using Method 2 (b).

Table 1. Observed area and total number of measured cluster in different samples.

Sample	Observed area (mm2)			Total number of measured clusters
	Method 1	Method 2	Total area
S1	15	15	30	399
S2	15	45	60	669
S3	15	60	75	1087

Table 2. Equations of obtained CSD functions lines for different samples.

Sample	CSD function line 1 (FL1)	R	CSD function line 2 (FL2)	R
S1	y=0.352·x−5.986	0.999	–	–
S2	y=0.273·x−5.936	0.989	y=0.196·x−5.394	0.982
S3	y=0.154·x−5.504	0.996	y=0.073·x−4.446	0.982

The bilinear representation of cluster distributions in samples S2 and S3 indicates the presence of two different types of clusters. According to Bretta and Murakami,¹²⁾ the SEV distributions of inclusions having different compositions are presented by a bilinear graph on the probability plot. Similar tendencies for the SEV lines were reported by Kanbe et al.¹¹⁾ by investigating non-metallic inclusions in stainless steels. However, in this study it was found that the composition of inclusions in clusters in all size ranges are very similar and corresponds to REM-oxides. For instance, the clusters corresponding to the FL1 line contain on average 59.4% La and 33.1% Ce and the clusters corresponding to the FL2 line contain 58.8% La and 32.8% Ce. The remaining parts of the compositions for inclusions in clusters were Nd and Pr in both cases. Therefore, it can safely be assumed that the observed clusters have the same source and formation mechanisms.

Zhou et al.¹³⁾ reported that inclusions having the same composition but different 3D structure also show different distributions. In this study, the morphology of inclusions in the investigated clusters was very similar. However, it was found that the circularity factor (CF) of clusters, which corresponds to a quantitative characteristic of the cluster morphology, significantly decreases with an increased length of clusters, as is shown in Fig. 7(a) for S3 sample. The average CF values for all clusters presented on the FL1 and FL2 lines in different samples are compared in Fig. 7(b). It can be seen that the average CF values for small size clusters (FL1 lines) are significantly higher than those for large size clusters (FL2 lines). This indicates that the clusters from these two different CSD function lines might have different growth mechanisms and, as a result, different morphologies. In this study the value of CF=0.15 was selected as a critical value for quantitative separation of observed clusters into two different groups, small size clusters (CF≥0.15) and large sized clusters (CF<0.15) which correspond to the FL1 and FL2 lines, respectively.

Fig. 7.

Average values of circularity factors (CF) of observed clusters in different size ranges in the S3 sample (a) and from different CSD function lines (FL1 and FL2) in various samples (b).

From the above discussion it can be inferred that the deviation observed in Fig. 3(b) is due to the difference in growth rate of clusters with different sizes and circularity factor.

3.2. Mechanism of Formation and Growth of Clusters

The formation and growth mechanism of clusters in the liquid steel can be conditionally divided into the following steps: Step 1- formation of small clusters due to collision of separate inclusions; Step 2 – growth of cluster by collision with separate inclusions (Mechanism 1) and Step 3 – growth of cluster by collision with other clusters (Mechanism 2).

It is apparent that the formation and growth of clusters is proportional to the number of collisions. The number of collisions of inclusions/clusters in the liquid steel per unit time (“collision rate”) can be calculated according to following relationship¹⁴⁾   

$$\frac{d{n}_{i,j}}{dt}={\beta }_{ij}{n}_i{n}_j$$(5)

where β_ij is the collision volume (m³/s), n_i and n_j are the numbers of inclusions/clusters of certain size ranges and t is time (s). There are three main types of collisions, which occur during interaction of inclusions/clusters: i) Brownian collisions ( ${\beta }_{ij}^B$ ) due to random movement of inclusions in molten steel, ii) Stokes` collisions ( ${\beta }_{ij}^S$ ) due to flotation of inclusions/clusters having smaller density in comparison with liquid steel and iii) turbulent collisions ( ${\beta }_{ij}^T$ ), which take place due to movement of inclusions/clusters along with molten steel flow. The collision volume for each type can be expressed as follows:^5,6)   

$${\beta }_{ij}^B=\frac{2kT}{3\mu }\frac{{(r_i+r_j)}^2}{r_i{r}_j}$$(6)

  

$${\beta }_{ij}^S=\frac{2g\pi ({\rho }_f-{\rho }_{ox})}{9\mu }{(r_i+r_j)}^3\left|r_i-r_j\right|$$(7)

  

$${\beta }_{ij}^T=1.3\alpha \sqrt{\pi {\rho }_f\epsilon /\mu }{(r_i+r_j)}^3$$(8)

where k is Boltzman constant (J/K), T is temperature (K), μ is the dynamic viscosity of steel (kg/m.s), g is gravitational acceleration (m/s²), ρ_f and ρ_ox are the densities of the steel and oxide particle respectively (kg/m³), α is the collision efficiency, ε is the turbulent energy dissipation (m²/s³) and r_i and r_j are the radii of the two colliding inclusions/clusters.

All three types of collisions contribute to the total number of collisions that occur. However, not all of them have same contribution. The β_ij values were calculated for each type of collisions by using the parameters given in Table 3. Figure 8 represents the calculated values of different collisions volumes for an inclusion having diameter of 1 μm (r_i=0.5 μm) that collides with other inclusions. As can be seen, the magnitudes of ${\beta }_{ij}^B$ and ${\beta }_{ij}^S$ are drastically smaller than that of ${\beta }_{ij}^T$ over all studied ranges of r_j. For small inclusions up to 1 μm, the Stokes` collisions have no significant influence whereas the Brownian collisions have some effect on the collision volume of small size particles. For large size inclusions/clusters (2r<sub>j</sub>=2–50 μm), the turbulent collisions have much higher impact on growth rate compared to the Stokes` collisions. This is due to that the ${\beta }_{ij}^T$ values are 24–590 times higher than the ${\beta }_{ij}^S$ values. The too small effect of the Stokes` collisions on the growth of REM-oxide inclusions/clusters in the liquid steel can be explained by the small difference between densities of steel and REM-oxides in Eq. (7).

Table 3. Data used in the calculations of the collision volumes.

α	ε (m2/s3)	μ (kg/m·s)	ρf (kg/m3)	ρox （㎏/m3）	T (K)	k (J/K)	g (m/s2)
0.3	0.01	0.005	7000	6900	1923	1.38×10−23	9.81

Fig. 8.

Collision volume for an inclusion with a diameter of 1 μm (r_i=0.5 μm) that collides with other inclusions of different sizes.

Thus, the suggested mechanism of formation and growth of REM-oxide clusters and its correlation to experimental results can be summarized as follows:

Step 1. Brownian and turbulent collisions are involved in the formation of clusters in the liquid steel.

Step 2. These clusters tend to grow by Mechanism 1 due to the turbulent collisions resulting in growth of small sized clusters (CF≥0.15) according to the FL1 line

Step 3. Large sized clusters (CF<0.15), which corresponds to the FL2 line, grow by Mechanism 2 due to turbulent collisions and partially by Stokes` collisions.

However, it is important to mention that the collision volumes have been derived considering spherical particles whereas clusters have irregular shape. Therefore, an estimation of the collision volume of clusters by using the equivalent diameter (d_eq= $\sqrt{4A_C/\pi }$ ) might lead to an underestimation of the results. This is because the irregular cluster has a significantly larger surface area in comparison to an equivalent spherical inclusion. For instance, Fig. 9(a) shows a cluster which has the maximum length L_C=25.2 μm and the equivalent diameter d_eq=11.8 μm. The calculated β_ij for L_C are 2–3 times larger than those for d_eq value, as shown in Fig. 9(b). Therefore, the equation for calculation of β_ij value for clusters should be modified by introducing some coefficient for shape factor, which will be considered in a separate article. In this study, it was assumed that a cluster in the liquid steel can rotate around its center due to the fluid flow and can collide with inclusions/clusters within rotational region, whose maximum diameter equals to the maximum length of this cluster, as illustrated in Fig. 9(a). Therefore, the maximum length of clusters was used to estimate the maximum possible collision volume of inclusions/clusters in the liquid steel.

Fig. 9.

(a) Illustration of how the L_C and d_eq values of an observed cluster were determined, (b) a comparison of the collision volumes for a cluster with L_C=25 μm and d_eq=12 μm.

The growth rate of different clusters is proportional to the rate of the number of collisions (“collision rate”), which depends on the collisions volume (β_ij) and numbers of clusters (n_i and n_j). The CSD in different samples obtained by Method 2 are shown in Fig. 10(a). The total collision rates for clusters corresponding to the FL1 and FL2 lines were calculated by using Eq. (5). The obtained results are shown in Fig. 10(b). The values of r_i and r_j for different samples were determined from the obtained cluster size distributions and given in Fig. 10(b). It should be pointed out that the selected r_i values correspond to the CSD peak values for each sample. The n_i and n_j values correspond to the N_V values for clusters of i and j size ranges. As can be seen in Fig. 10(b), the total collisions rate of clusters $\left(=\sum \frac{d{n}_{i,j}}{dt}\right)$ increases with time for both the FL1 and FL2 function lines. However, this increase is substantially higher for the FL2 values compared to the FL1 values. For instance, the total collisions rate in sample S3 (9 min of holding) calculated for FL1 is almost 2 times larger than that in sample S2 (6 min of holding), whereas that corresponding value for FL2 is more than 5 times larger. Therefore, it can be concluded that after 6 minutes of holding time the large size clusters represented by the FL2 line grow at a much faster rate than the small clusters shown by the FL1 line.

Fig. 10.

(a) Cluster size distribution (CSD) of all the three samples obtained at increased observed areas by using Method 2, and (b) the total rate of collisions for all three samples calculated for selective values of r_i.

4. Conclusions

The cluster size distributions (CSD) in REM alloyed stainless steel have been investigated using a three dimensional (3D) method to elucidate the mechanism of formation and growth of clusters. Steel samples were taken during a pilot plant trial. Then, electrolytic extraction followed by filtration was used for investigations of inclusion/cluster characteristics by using SEM. Finally the morphologies were determined using SEM. Based upon the presented experimental results following conclusions can be made:

(1) At least 5 clusters per size step in the CSD should be investigated to obtain reliable CSD function lines with deviations that are less than 3%.

(2) Turbulent collisions are the dominant collision mode in the growth of REM-oxide clusters compared to the Brownian and Stokes` collisions.

(3) The collision volume of clusters (β_ij) in the melt should be calculated by considering the shape factor. The maximum possible β_ij value for clusters can be determined by using the maximum length of clusters, instead of the equivalent diameter of spherical inclusions having the same volume as the investigated cluster.

(4) The growth rate of REM clusters increases exponentially with an increased size of clusters.

(5) Different growth rates of small and large size REM clusters can be explained by the collisions of clusters with individual inclusions (Mechanism 1) and with other clusters (Mechanism 2). After a 6 minutes holding time, Mechanism 2 is dominant for REM clusters in REM alloyed stainless steel.

(6) Circularity factor (CF) can be used for classification of REM clusters into two groups, small clusters (CF≥0.15) and big clusters (CF<0.15), which form and grow in accordance to different mechanisms.

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