Crystallography and Precipitation Kinetics of Copper Sulfide in Strip

ISIJ International, Vol. 44 (2004), No. 9, pp. 1560–1567

Crystallography and Precipitation Kinetics of Copper Sulﬁde in Strip Casting Low Carbon Steel

Zhongzhu LIU, Yoshinao KOBAYASHI and Kotobu NAGAI

Steel Research Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047 Japan. (Received on February 10, 2004; accepted in ﬁnal form on June 23, 2004 )

Copper and sulfur are the major residual elements or impurities in scrap steel. The direct near net shape casting is an attractive process for scrap recycling. In the present paper, the precipitation and orientation relationship with matrix of copper sulfide in a strip casting steel were investigated by transmission electron microscopy. Nano-scale copper sulfides less than 50 nm with a face-centered cubic structure (Digenite) were found precipitating throughout the grains. These tiny copper sulfides have a cube–cube orientation relationship with the body-centered cubic a-Fe matrix, which is (001) //(001) and [110] //[110] . Cu2S a-Fe Cu2S a-Fe Thermodynamic and kinetic analysis was conducted to compare the Cu2S precipitation to the MnS precipitation in g-Fe and a-Fe. The calculation shows the nucleation of Cu2S is dominant in the g-Fe at low temperature and in the a-Fe compared with that of MnS. The high cooling rate during strip casting and the complete coherent relationship with the matrix result in the present nano-scale copper sulfides. KEY WORDS: copper sulfide; manganese sulfide; orientation relationship; nucleation; particle growth; precipitation; strip casting.

to form the defect compound Cu S, which is stable up to 1. Introduction 2x 780 K at 36.60 at%S and down to 345 K at 35.65 at% S. Copper is one of the major residual elements in steel be- Therefore, the high Digenite is the most probable phase that cause it is difficult to remove during the steelmaking is expected in steel at high temperature. process. Although copper causes hot shortness at high tem- The high digenite has an anti-fluorite cF12 (Fm3¯m) peratures since it is harder to oxidize than the iron matrix, structure with sulfur atoms arranged in a face-centered copper could be used as an alloying element in some steels cubic (f.c.c.) lattice and copper atoms occupying all the to improve the corrosion resistance and to enhance the me- tetrahedral interstitial sites, as shown in Fig. 1. Alternatively, chanical properties.1–3) such a structure can be viewed as a simple cubic lattice of A lot of attention has been given to the strengthening ef- Cu atoms with S atoms occupying half of the centers of the fects from the copper solid solution or the copper particle cubes. Experiments have also shown the existence of a non- 1–3) precipitates in steel. Recently some papers reported that stoichiometric digenite Cu2xS phase (x 0–0.25) due to the copper sulfide particles could also increase the strength and large vacancy content.11) The clustering of vacancies and work hardening ability of steel.4,5) Much earlier there were Cu atoms produces several types of digenite superstruc- reports on the existence of copper sulfides in steel/iron6–8); tures. The lattice parameters have some fluctuation with the however, only a few papers have discussed the structure and the formation mechanism of copper sulfide in detail. Table 1. Compositions, structures, and stabilities of copper On the other hand, mineralogists have carried out exten- sulfide minerals.9,10) sive investigations on the thermodynamics and phase rela- tions in the Cu–S system. The results show that the copper bearing sulphides are very complex in this system, as shown in the Cu–S system phase diagram.9) The composition, structure and stabilities of copper sulfide minerals were summarized by Posfai10) and are shown in Table 1. Several metastable phases also exist such as low digenite, protodjurleite, tetragonal, hexagonal-tetragonal CuxS, Blaubleibender covellite (I, II), and CuS2. According to the phase diagram of the Cu–S system,9) the high Digenite (Dg) has a broad phase field, with the Cu- rich boundary approximately at the Cu2S stoichiometry between 708 and 1 403 K. The Cu-deficient boundary extends

num grids, and a beryllium specimen holder was used to avoid the possible detection of Cu from the grid and the specimen holder. TEM observation was performed with a JEM-2000FXII microscope operating at 200 kV and cou- pled to an energy dispersion spectrometer (EDS).

3. Experimental Results 3.1. Morphology and Composition of Sulfides Many tiny spherical copper sulfides were observed throughout the grains in the present strip steel, as shown in Fig. 2. These copper sulfides are less than 50 nm with a mean size of about 15 nm. The density of these tiny sulfides is estimated to be roughly 1020 m3. The EDS analysis Fig. 1. Anti-fluorite unit cell, which the digenite system is based shows that these tiny sulfides consist mainly of Cu and S on. Empty circles: f.c.c. unit cell of sulphur; Full circles: tetragonal sites, partially filled by copper. and include a little Fe. Manganese sulfides are usually larger than 100 nm and Table 2. The chemical composition of the cast strip, mass%. contain some Cu and Fe as shown in Fig. 3. 3.2. Crystal Structure of Tiny Copper Sulfide The electron diffraction patterns from the same tiny particle are shown in Fig. 4, which clearly demonstrates that the tiny copper sulfide is a f.c.c copper sulfide phase (Digenite). These results are consistent with the reports by Harbottle,12) who reported that an f.c.c copper sulfide phase x value. They are 0.5735 and 0.556 nm for Cu2S and Cu1.8S, in the range of 10–30 nm is formed in a weld specimen of a respectively. mild steel. The direct near net shape casting is an attractive process Superlattice reflections are observed in the diffraction for scrap recycling, since the fine microstructure produced pattern along a zone axis [011] as shown in Fig. 5. These by high solidification and cooling rate may cover up the results are consistent with the reports by Conde,13) Dyck14) detrimental effects caused by impurities/residual elements and Pierce,15) who conducted detailed investigations of the in the scraps. In the present paper, the crystal structure and superstructures in naturally forming or synthetic digenite the orientation relationship of the copper sulfide with the minerals. matrix in strip casting strips were investigated by transmission electron microscopy (TEM). Based on the classical nu- 3.3. Orientation Relationship between Tiny Copper Sulfide Particles and Matrix cleation theory, the precipitation kinetics of Cu2S in g-Fe and a-Fe were analyzed by comparing them to those of Selective area electron diffraction (SAED) study was car- MnS. ried out with TEM to clarify the orientation relationship (OR) between the tiny copper sulfides and the matrix (a- Fe). Figure 6(a) shows the [001] SAED pattern of an a-Fe 2. Experimental Procedures matrix. A lot of diffraction spots are seen in addition to the 2.1. Materials and Casting Conditions matrix spots. If we assume that the particles have a cube- Table 2 shows the chemical composition of the test steel cube relationship with the matrix, the spots that do not be- produced by the twin drum caster at the Mitsubishi Heavy long to the matrix correspond very well to those of f.c.c. Industries Ltd., Hiroshima R&D Center. The casting speed Cu2S with the zone axis being parallel to [001]. was 0.333 m/s, the casting temperature was 1 84620 K, Figure 6(b) shows the [011] SAED pattern of an a-Fe the casting weight was 200 kg, and the mold width was matrix for the same specimen. It is difficult to determine 600 mm. The drum supporting force controlled the thick- the relationship between the particles and the matrix from ¯ ness of the cast strip to about 3.6 mm. The strip was air this pattern. However, the spots those are marked 200 and cooled on the transportation roller tables and coiled at in Fig. 6(a) also appear in Fig. 6(b). In addition, by consid- about 1 073 K. ering the superstructural phenomenon shown in Fig. 5, the spots that do not belong to the matrix correspond to those 2.2. Analysis Methods of Cu2S. Here the zone axis is also parallel to the [011] of Precipitates in the strips were observed by TEM. Thin Cu2S. Thus, the assumption that the tiny copper sulfides sliced specimens for TEM observation were cut from the have a cube–cube relationship with the matrix is reason- bulk with a thickness of 0.2 mm and mechanically ground able, and the OR can be represented as (001) //(001) Cu2S a-Fe to 80 mm. Foil samples of f3 mm were finally prepared by and [110] //[110] . Cu2S a-Fe electro-polishing at 50 V in an electrochemical solution Usually the orientation relationships between the f.c.c. containing 5 vol% perchloric acid and 95 vol% methanol. and the b.c.c. phase (particle is B1-type) are cube–cube or Carbon extraction replicas were also prepared through the cube-on-edge, as summarized by Furuhara17–19) in Fig. 7 standard procedures. The replicas were floated on molybde- and Table 3. The OR has a close correlation with the lattice

Fig. 2. Morphology and composition of tiny copper sulfides. (a) bright field, thin foil; (b) dark field, thin foil; (c) bright field, extraction replica; (d) EDS.

Fig. 3. Typical manganese sulﬁde in the present steel. parameter ratio between the particles and the matrix (austenite or ferrite). If the ratio of the lattice parameters is about 1.0 or 2.0, a cube–cube OR is expected, such as a VC with austenite; while a cube-on-edge is expected, such — as a VC with ferrite with a ratio of about √2 . The Fig. 4. Diffraction patterns obtained from the same tiny particle Baker–Nutting (B–N) orientation relationship, which is with (a) zone axis [001] and (b) zone axis [112]. (001)f.c.c.//(001)b.c.c. and [100]f.c.c.//[110]b.c.c., is a cube-on- edge OR.

The present OR between the Cu2S and the matrix can be is about 1.55–1.60, so a near cube-on-edge OR and the for- predicted from the above theoretical analysis based on the mation of a Cu2S with a plate like shape in austenite are ex- disregistry between the particles and the matrix, even pected; while the lattice parameter ratio between Cu2S and though there seems no experiment report so far to show that ferrite is about 1.94–2.0, so a cube–cube OR and the for- the C1-type f.c.c. and the b.c.c phases have a cube–cube mation of a Cu2S with a spherical shape in ferrite are ex- OR. The lattice parameter ratio between Cu2S and austenite pected, which is the same as that in the present case.

Fig. 5. Diffraction pattern of copper sulﬁde along the [011] zone

corresponding to the structures 2a0. Where a0 is the {111} spacing of the cubic close packed sulfur sublattice.

Fig. 7. The relation between the OR and the lattice parameter ratio.17–19) (det | IA1 | is a parameter representing the misﬁt between two phases.)

Table 3. The disregistry between the particles and the g-Fe/a- Fe matrix.17–19)

Fig. 6. Orientation relationship between tiny copper sulﬁdes and

the a-Fe matrix. (a) Zone axis: a-Fe [001], Cu2S [001]; (b) Zone axis: a-Fe [011], Cu2S [011].

The complete coherent OR between the tiny copper sulfides and the a-Fe suggests that these tiny copper sulfides may precipitate from the a-Fe instead of the g-Fe. Furthermore, the coherent OR may greatly influence the interfacial energy between the particle and the matrix as well as the nucleation process of the particles.

4. Thermodynamic and Kinetic Analysis of Precipita- tion The present strip was coiled at 1 073 K, the temperature at which both g-Fe and a-Fe phases may exist in the present steel. Therefore, in addition to the comparison between the precipitation behaviors of MnS and Cu2S, the precipitation behaviors in g-Fe and a-Fe can also be compared to each other. 4.1. Supersaturation Degree and Driving Force for the Nucleation Assuming that the nucleus is spherical and neglecting the the following equations20): misﬁt or the elastic strain energy between the new phase 2sV and the matrix, the critical nucleus size, r*, and the activa- r* m ...... (1) tion energy for nucleation (or the free energy change of for- DGV mation of the critical nucleus), DG*, can be obtained from

16ps 3V 2 DG* m ...... (2) 2 3DGV where Vm is the molar volume of the new phase, DGV is the volume free energy reduction in creating a new phase from the matrix, and s is the interfacial energy between the new phase and the matrix. From Eq. (2), one of the main factors controlling DG* is the driving force for nucleation (DGV). The driving force for nucleation can be roughly calculated using Eq. (3)21):

DT DGQV ...... (3) Te Fig. 8. The driving force for nucleation of MnS and Cu2S vs. where Te is the equilibrium temperature that can be calcu- temperature. lated from the new phase solubility in the matrix, DT is the undercooling below T and Q is the free energy of the solu- e Table 4. Interfacial energy between the matrix and some par- tion that can be evaluated from the new phase solubility ticles. product in the matrix.21) The solubility of MnS in d/a and g iron are as follows22,23): log([%Mn][%S])9 020/T2.929(215/T 0.097)[%Mn] for the g-iron log([%Mn][%S])10 590/T4.092 for the d/a-iron Therefore, based on the present steel composition, we g a have QMnS 85 200 J/mol (for [%Mn] 0.54), and QMnS 101 300 J/mol. Unfortunately, there is not much data for copper sulﬁde solubility in steel. Only Shimazu24) was able to report the Cu2S solubility in silicon steel with a composition of 0.05%C–2.9%Si–0.08%Mn–0.03%S–(0.010.044%)Cu: log([%Cu]2[%S])4 4971/T26.31

The above Cu2S solubility is assumed to be suitable for the present steel. In addition, since there is only a little dif- ference in the MnS solubility between the g-Fe and the a- boundary energies for the three types of planar interfaces as Fe in the range of 973 and 1 173 K, the above Cu S solubili- follows: 2 s is about 0.05–0.2 J/m2 for a coherent interface. ty is also used for a-Fe between 973 and 1 173 K. So we 2 have Qg Qa 286 900 J/mol. s is about 0.2–0.8 J/m for a semicoherent interface. Cu2S Cu2S 2 Based on the present steel composition, the equilibrium s is about 0.8–2.5 J/m for an incoherent interface. Figure 9 is the schematic representation of the interface precipitation temperature in g-Fe for MnS and Cu2S are between Cu2S and ferrite. It is reasonable to estimate calculated to be 1 731 and 1 469 K respectively. 2 s Cu S/a-Fe to be about 0.05–0.2 J/m since the interface is co- The calculated volume free-energy change, DGV, for 2 herent between Cu2S and ferrite, while the interface be- MnS and Cu2S nucleation in both g-Fe and a-Fe are shown MnS Cu2S tween Cu2S and austenite is a rough semi-coherent one in Fig. 8. At high temperature, both DGV and DGV are MnS Cu2S since the lattice parameter ratio a Cu S/a g-Fe is 1.55–1.6 and low, and DGV is a slightly larger than DGV . However, — 2 Cu2S MnS far from the value of √2 . Therefore based on the experi- DGV increases more quickly than DGV with decreas- ing temperature. When the temperature is below 1 373 K, mental interfacial data of MnS and the disregistry data listed Cu2S MnS in Table 3, the interfacial energy s Cu S/g-Fe and s Cu S/a-Fe are DGV is larger than DGV , which means that Cu2S has a 2 2 2 2 larger driving force for nucleation and supersaturation com- estimated to be 0.83 J/m and 0.2 J/m , respectively, in the pared to those for MnS at low temperature in both g-Fe and present paper. a-Fe. Based on the above interfacial energy data, we can calcu- late the activation energies and the critical radii for solid 4.2. Interfacial Energy between Matrix and Sulﬁdes MnS and Cu2S nucleation in g-Fe and a-Fe. The parameter The precipitation activation energy DG* is also related to values for calculation are listed in Table 5. the interfacial energy between the new phase and the ma- The calculated activation energy and the critical nucle- trix, s. The related experimental and calculated data of ation radius for MnS and Cu2S are shown in Fig. 10. From MnS and Cu2S are listed in Table 4. Unfortunately there are this ﬁgure, we can see that MnS is nucleated more easily in no data for the s between Cu2S and austenite or ferrite. g-Fe than in a-Fe. Howe27) presented the ranges of the solid–solid interface In g-Fe, the activation energy and the critical nucleation

Fig. 9. Schematic representation of the two possible interfaces between Cu2S and ferrite.

Table 5. Parameter values for calculation.

Fig. 10. Activation energy and critical nucleation radius for MnS

and Cu2S nucleation vs. temperature.

heterogeneous nucleation rate on grain boundary are taken into consideration in the present paper. The activation energy for the homogeneous nucleation and the heterogeneous nucleation are calculated by Eqs. (2) and (8) respective- ly30,31): radius of Cu2S is only slightly lower or smaller than that of 3 2 16pxs()Vm MnS. But in a-Fe, Cu2S has much lower activation energy DG* ...... (8) 2 and a critical nucleation radius compared to those for Cu2S 3DGV in g-Fe and MnS in either of the iron phases, which partly Here is a modiﬁer of when a high-energy site like explains the formation of tiny copper sulﬁdes well in the x s grain boundary is the nucleation site. For the heterogeneous present steel. nucleation on grain boundary, x is set to 0.7 in the present 4.3. Nucleation Rate calculation.

According to the classical nucleation theory, the nucle- The calculated nucleation rates for MnS and Cu2S in g- ation rate (I) of a new phase in the solid state is given by Fe and a-Fe are shown in Fig. 11. For the heterogeneous the general nucleation equation28): nucleation on grain boundary (Fig. 11(a)), both MnS and Cu2S have low nucleation rates at high temperature in g-Fe; Ê DG* ˆ however, the nucleation rate of Cu2S increases quickly with II0 expÁ ˜ ...... (4) Ë kTB ¯ a decrease in temperature and becomes higher than that of MnS below 1 300 K. In a-Fe, the nucleation rate on grain 23 where kB is the Boltzmann constant (1.38 10 J/K) and T boundary of MnS is very low due to the high interfacial en- is temperature. I0 is the pre-exponential factor, which ergy with a-Fe; while the nucleation rate of Cu2S is much means the distribution density of embryo, depending on the higher due to the low interfacial energy with a-Fe. number of nucleation sites, the content of solute elements For the homogeneous nucleation in the matrix (Fig. and so on. Assuming 20 elements of S in the nucleus, I0 is 11(b)), the precipitation of MnS in both g-Fe and a-Fe as 24 3 1 29) ﬁxed as 10 /m ·s in present calculation. well as Cu2S in g-Fe seems to be impossible since the nu- The homogeneous nucleation rate in the matrix and the cleation rate is too low. Only the homogeneous nucleation

Table 6. Diffusion coefﬁcient of Cu, Mn and S in d/a and g iron, 104 m2·s1.

Fig. 11. Nucleation rate of MnS and Cu2S vs. temperature. (a) Heterogeneous nucleation on grain boundary; Fig. 12. The growth potential of MnS and Cu2S in g-Fe and a- (b) Homogeneous nucleation in the matrix. Fe at 1 073 K. of Cu2S in a-Fe is quite probable since the nucleation rate diffusion coefficient on the particles growth process. is almost in the same range with that of Cu2S nucleation on The Ostwald ripening model can be described by the fol- grain boundary in a-Fe. lowing Eq. (9): This calculation implies the heterogeneous precipitation of MnS may happen either at high temperature in 8sDV[]M rr3 3 m ◊t ...... (9) slower cooling or without enough concentration of Cu. t 0 9RT Furthermore, the calculation strongly suggests the domi- where, rt is the particle radius at time t, r0 is the particle ra- nant precipitation of Cu2S in a-Fe and in g-Fe at low temperature with some concentration of Cu when the MnS dius at initial time, s is the surface energy of the particle- precipitation in g-Fe is suppressed by rapid cooling. matrix interface, D is the diffusivity of the relevant atomic Accordingly, combined with the activation energy and the species, [M] is the concentration of the relevant atomic critical nucleation radius calculation results, there is a great species in the matrix, Vm is the particle molar volume, R is possibility that we can understand the tiny copper sulfide the gas constant, and T is the temperature. We can observe precipitate from the a-Fe. either a low s or low diffusion coefficients results in a low growth rates. 4.4. Growth of Particles The diffusion coefficient of Cu, Mn and S in g-Fe and a- After nucleation, some particles will grow immediately Fe are listed in Table 6.36,37) Table 6 shows that at high tem- and other particles may dissolve into the matrix again. A lot perature (in the d phase), Cu has a slightly higher diffusion of mathematical models have been developed to describe coefficient than that of Mn. In the g phase, both Mn and Cu the particle growth in different situations.32–34) Suzuki35) re- have low diffusion coefficients with Cu having the lowest cently applied four different mathematical models to pre- diffusion coefficient among the three elements. At low tem- dict the size distribution of particles in stainless steel during perature (in the a phase), Cu has almost the same diffusion solidification and reported that the Ostwald ripening model coefficient as that of Mn. provided the best correlation with the experimental results. The calculated evolution of the particle size with time at In the present paper, assuming the particles have the spheri- 1 073 K in both g-Fe and a-Fe are shown in Fig. 12. Both cal shape in both g and a phases, the Ostwald ripening MnS and Cu2S grow faster in a-Fe than in g-Fe, which is model is used to estimate the effect of interface energy and due to the higher diffusion coefficient of Mn and Cu in a-

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