metals

Article Precipitates in Compact Strip Production (CSP) Process Non-Oriented Electrical

Jia-long Qiao 1,* , Fei-hu Guo 1, Jin-wen Hu 1,2, Li Xiang 1, Sheng-tao Qiu 1 and Hai-jun Wang 2

1 National Engineering Research Center of Continuous Casting Technology, China & Steel Research Institute Group, Beijing 100081, China; [email protected] (F.-h.G.); [email protected] (J.-w.H.); [email protected] (L.X.); [email protected] (S.-t.Q.) 2 School of Metallurgy and Resources, Anhui University of Technology, Maanshan 243002, China; [email protected] * Correspondence: [email protected]; Tel.: +86-188-0102-8675

 Received: 16 July 2020; Accepted: 18 September 2020; Published: 29 September 2020 

Abstract: Nitrogen and Sulfur in non-oriented electrical steel would form precipitates, which would severely affect its magnetic properties. Precipitates in compact strip production (CSP) process non-oriented electrical steel were investigated using a transmission electron microscope (TEM) and scanning electron microscopy (SEM). The precipitation mechanism and influence on grain growth were analyzed experimentally and theoretically. The results showed that the main particles in steel were AlN, TiN, MnS, Cu2S, and fine inclusions. The spherical or quasi-spherical of MnS and Cu2S were more liable to precipitate along grain boundaries. During the soaking process, the amount of MnS precipitated on the grain boundary was much larger than that of Cu2S. AlN and TiN in cubic shape precipitated inside grains or grain boundaries. Precipitates preferentially nucleated at grain boundaries, and TiN, MnS mainly precipitated during soaking. In the subsequent processes after soaking, AlN and Cu2S would precipitate unceasingly with the decrease in the average size. The distribution density, the volume fraction, and the average size of the precipitates in the annealed sheets were 9.08 1013/cm3, 0.06%, and 54.3 nm, respectively. Precipitates with the grain size of × 30–500 nm hindered the grain growth, the grains with 100–300 nm played a major role in inhibiting the grain growth, and the grains with the grain size of 70–100 nm took the second place.

Keywords: non-oriented electrical steel; CSP process; magnetic properties; precipitates; particle growth; driving force and pinning force

1. Introduction Non-oriented electrical steel is a kind of soft magnetic alloys, which desire high magnetic induction and low core loss [1]. On account of the small columnar crystals, which belong to the cubic ({100}<001>) of continuous cast slab that would inherit to the finished product, the magnetic induction intensity of compact strip production (CSP) process non-oriented electrical would be higher than the traditional products. However, the magnetic properties would be deteriorated by inclusions, which are difficult to float during the casting process, and the small size of precipitates through inhibiting grain growth [2–7]. As a result of the solubility fall of certain elements, the major residual elements or impurities of Cu, Ti, S, N, etc. would form nitride and sulfide precipitates [8]. AlN, TiN, MnS, Cu2S, etc. would obviously hinder the growth of crystal grains and strengthen γ-fiber texture components, leading to the decrease of magnetic properties of non-oriented electrical steel [1,5,9,10]. Many research works have been reported on the study of nitride and sulfide precipitates0 precipitation mechanism in non-oriented electrical steel [5–7,9–14]. The particle nucleation rate and

Metals 2020, 10, 1301; doi:10.3390/met10101301 www.mdpi.com/journal/metals Metals 2020, 10, 1301 2 of 15 Metals 2020, 10, x FOR PEER REVIEW 2 of 15 growth depend on the nucleation driving force, the diffusivity diffusivity of controlling element M in the the matrix, matrix, and the interfacial energy associated with the matrix [[8,15].8,15]. In In the the CSP CSP process’ process’ non-oriented non-oriented electrical electrical steel, the size of precipitates would grow more in the soaking process, but the precipitation contents are less [[5].5]. Meanwhile, models on the grain growth inhibiti inhibitionon by precipitates are presented with the hypotheses thatthat thethe grain grain growth growth will will stop stop by by the th pinninge pinning force force of particles of particles [12–14 [12–14,16,17].,16,17]. Studies Studies show showthat the that relationship the relationship between between grain sizes grain would sizes be stronglywould be inhibited strongly by increasinginhibited by the increasing interfacial areathe interfacialbetween grains area between and particles grains [ 18and–20 particles]. The e ff[18–20].ect of di Thfferente effect size of different of precipitates size of on precipitates the ferrite on grain the ferritegrowth grain is also growth different is also in non-oriented different in no electricaln-oriented steel electrical [7,10,14 ,steel21–26 [7,10,14,21–26].]. Given the above, the precipitation mechanism of precipitates in the CSP process’ non-oriented electrical steel has not been studiedstudied comprehensively, and most of these studies only simulate the qualitative relationship between precipitation and and grain grain growth growth theoretically. theoretically. In In the the present present study, study, by means of the thermodynamicsthermodynamics analysis, kinetics calculation, TEM, and SEM, the precipitation behavior of AlN, TiN, MnS, and Cu22S was studied. The The pinning pinning force force of of precipitates precipitates and driving force of grain growth were analyzed as we well,ll, with the aim to reduce the inhibition effects effects of precipitates on grain growth, thus enhancing the magnetic properties ofof CSPCSP process’process’ non-orientednon-oriented electricalelectrical steel.steel.

2. Materials and Methods The mainmain chemical chemical composition composition of compactof compact strip productionstrip production (CSP) process(CSP) non-orientedprocess non-oriented electrical electricalsteel used steel in theused present in the present study is study given is ingiven Table in1 Table. The 1. continuous The continuous casting casting billet billet with with 70 mm 70 mm in inthickness, thickness, which which was was soaked soaked at at about about 1373 1373 K, K was, was hot-rolled hot-rolled to to 2.3 2.3 mm mm inin thicknessthickness byby aa six-high rolling mill. The hot bands were cold rolled in 79% deformation to 0.5 mm in thickness by a six-high rolling mill. Then, the cold-rolled sheetssheets werewere annealedannealed atat 10931093 KK forfor 22 minmin inin NN22:H:H22 = 1:11:1 atmosphere atmosphere for recrystallizationrecrystallization andand grain grain growth. growth. The The heating heating rate rate and and cooling cooling rate rate of the of annealingthe annealing process process were were50 K/ s50 and K/s 25 and K/s, 25 respectively. K/s, respectively. The schematic The schema of thetic thermos-mechanicalof the thermos-mechanical cycle used cycle in used the present in the presentstudy is study shown is inshown Figure in1 .Figure 1.

Table 1. The main chemical composition of non-oriented electrical steel.

ElementsElements C C Si Si Mn Mn P PS Als NN CuCu Ti Ti Content,Content, wt% wt% 0.0030 0.0030 0.65 0.65 0.25 0.25 0.075 0.075 0.0040 0.0040 0.30 0.00350.0035 0.0300.030 0.00300.0030

2000

CSP process casting to 70mm 1600 Soaking: Annealing: 1373K+40min Initial rolling at 1323K 1093k+2min Heating rate:50K/s 1200 Hot rolling to 2.3mm Colding rate:25K/s

Coiling: 800 993K Temperature, K 400

Cold rolling to 0.5mm 0 Time Figure 1. SchematicSchematic of of the the thermos-mechanical thermos-mechanical cycle used in the present study.

The microstructure and and morphology morphology of of precipitates precipitates in in steel steel were were scientifically scientifically studied studied using using a transmissiona transmission electron electron microscope microscope (TEM; (TEM; JEM-2100F, JEM-2100F, JEOL, JEOL, Tokyo, Tokyo, Japan) Japan) and and scanning electron microscopy (SEM; Quanta 650FEG, FEI, Morristown, NJ, USA). Combining with energy dispersive spectrometer (EDS) and selected area electron diffraction (SEAD), the compositions and morphology of precipitates could be characterized.

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spectrometerMetals 2020, 10, x (EDS) FOR PEER and REVIEW selected area electron diffraction (SEAD), the compositions and morphology3 of 15 of precipitates could be characterized. TheThe carboncarbon extraction extraction replica replica test test sample sample for for TEM TEM was was prepared prepared into into a sample a sample with with a size a ofsize 8 mmof 8 (TD)mm (TD)10 mm× 10 (RD) mm by(RD) wire by cutting wire cutting and then and roughly then roughly and finely and ground. finely Theground. samples The weresamples prepared were × byprepared electro-polishing by electro-polishing at 90 mA in at 10% 90 mA AA electrolytein 10% AA for electrolyte 120 s. The for electrolyzed 120 s. The sampleselectrolyzed were samples coated withwere a coated layer of with carbon a layer film of with carbon a thickness film with of a aboutthickness 30 nm of about using 30 a vacuum nm using carbon a vacuum spray carbon instrument. spray Afterinstrument. dividing After the dividing carbon film the intocarbon a size film of into about a size 2 mm of about2 mm, 2 mm it was × 2 mm, placed it was in a placed 10% perchloric in a 10% × acidperchloric alcohol acid solution alcohol for solution electrolytic for electrolytic release, and release, then the and molybdenum then the molybdenum net with 3 net mm with in diameter 3 mm in wasdiameter used was to extract used to the extract carbon the film. carbon The film. samples The samples were also were prepared also prepared into SEM into samples, SEM samples, and then and electropolishingthen electropolishing and observation and observation with 100 with fields 100 in each fields sample in each were sample done at were 3000-10000 done magnificationat 3000-10000 undermagnification SEM. The under size andSEM. number The size of and precipitates number of were precipitates analyzed were using analyzed IPP (Image-Pro using IPP Plus, (Image-Pro MEDIA CYBERNETICS,Plus, MEDIA CYBERNETICS, Rockville, MD, Rockville, USA) software. MD, USA) software. MagneticMagnetic propertiesproperties of of the the core core losses losses (P 15(P/5015/50) were) were determined determined at theat the induction induction of 1.5of T1.5 and T and 50 Hz. 50 MagneticHz. Magnetic measurements measurements were were carried carried out for out final-annealed for final-annealed sheets sheets with with 30 mm 30 inmm width in width and300 and mm 300 inmm length, in length, both in both rolling in androlling transverse and transverse directions. directions. The measured The measured values were values averaged were to averaged parallelize to withparallelize the Epstein with the method. Epstein method.

3.3. ResultsResults andand DiscussionsDiscussions

3.1.3.1. MagneticMagnetic PropertiesProperties ResidualResidual elementselements (Nb,(Nb, V,V, Ti,Ti, Cu,Cu,etc.), etc.), carbon,carbon, nitrogen,nitrogen, andand sulfursulfur inin non-orientednon-oriented electricalelectrical steelsteel wouldwould formform finefine precipitatesprecipitates inin thethe productionproduction processprocess [1[1].]. PrecipitatesPrecipitates wouldwould hinderhinder graingrain growth,growth, whichwhich ultimatelyultimately increasesincreases thethe ironiron lossloss andand mechanicalmechanical properties.properties. Meanwhile,Meanwhile, precipitatesprecipitates wouldwould promotepromote the the formationformation of of thetheγ γ-fiber-fiber texturetexture andand reducereduce magneticmagnetic induction induction [ [27].27]. AnAn importantimportant purposepurpose ofof non-orientednon-oriented electricalelectrical steelsteel slabslab soakingsoaking isis toto coarsencoarsen precipitates,precipitates, therebythereby reducingreducing thethe hazardshazards ofof thethe precipitatesprecipitates [[5].5]. P TheThe variation tendency between between P P15/5015/ 50andand ∑ (C +(C N+ + NS ++ Ti)S is+ shownTi) is shown in Figure in Figure2. As the2. contents As the contentsof elements of elements (Si, Al, Mn, (Si, Nb, Al, V, Mn, Cu, Nb, etc.) V, and Cu, technology etc.) and technology for heating for processing heating processingwere nearly were equivalent, nearly equivalent,the statistical the results statistical showed results that showed P15/50 increased that P15/50 obviouslyincreased (increase obviously 0.22 (increase W/kg) 0.22with W an/kg) increase with an of P increase∑ (C + N of + S +(C Ti)+ inN 95–105+ S + Ti) ppm. in 95–105 It could ppm. be speculated It could be that speculated the increase that in the P15/50 increase was caused in P15/50 bywas the causedprecipitates by the formed precipitates by C, formed N, S, Ti, by etc. C, N, Therefore, S, Ti, etc. during Therefore, the duringproduction the production of non-oriented of non-oriented electrical electricalsteel, it is steel, necessary it is necessary to strictly to strictlycontrol controlthe conten the contentt of magnetic of magnetic harmful harmful elem elements.ents. Meanwhile, Meanwhile, it is itnecessary is necessary to study to study the the precipitation precipitation mechanism mechanism of ofthe the precipitates precipitates and and the the influence influence law ofof thethe precipitatesprecipitates onon thethe magneticmagnetic propertiesproperties of of non-oriented non-oriented electrical electrical steel. steel.

5.7

5.4 , W/kg

15/50 5.1

4.8

4.5

The core losses, P 95~105ppm 4.2 0.007 0.008 0.009 0.010 0.011 0.012 0.013 0.014 ∑(C+N+S+Ti), wt% . P Figure 2. The variation tendency between the core losses P (W/kg) and (C + N + S + Ti) (wt%). Figure 2. The variation tendency between the core losses 15P/15/5050 (W/kg) and ∑ (C + N + S + Ti) (wt%).

3.2. Morphology and Composition of the Precipitates During the smelting and continuous casting process of the CSP process’ non-oriented electrical steel, studies have shown that part of fine oxide inclusions could not grow and be absorbed by the ladle slag [28,29]. The fine oxide inclusions would remain in the slab, thereby worsening the magnetic

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3.2. Morphology and Composition of the Precipitates During the smelting and continuous casting process of the CSP process’ non-oriented electrical Metals 2020, 10, x FOR PEER REVIEW 4 of 15 steel, studies have shown that part of fine oxide inclusions could not grow and be absorbed by the ladle slag [28,29]. The fine oxide inclusions would remain in the slab, thereby worsening the magnetic properties. In addition, the precipitates would precipitate during production. Because of the rapid properties. In addition, the precipitates would precipitate during production. Because of the rapid cooling process, the CSP process would have a more uniform structure and a smaller degree of cooling process, the CSP process would have a more uniform structure and a smaller degree of segregation of continuous cast slab [1]. Therefore, the segregation in the slab center was ignored in segregation of continuous cast slab [1]. Therefore, the segregation in the slab center was ignored in this this article. In order to study various inclusions and precipitates in the CSP process’ non-oriented article. In order to study various inclusions and precipitates in the CSP process’ non-oriented electrical electrical steel, the species and size distribution of micro-inclusions and precipitates in samples were steel, the species and size distribution of micro-inclusions and precipitates in samples were analyzed analyzed by SEM and TEM. The morphology of typical inclusions and precipitates is shown in Figure by SEM and TEM. The morphology of typical inclusions and precipitates is shown in Figure3. 3.

Figure 3. Typical precipitates and inclusions in the annealing sheets. Figure 3. Typical precipitates and inclusions in the annealing sheets.

FigureFigure3 3 showsshows the typical precipitates precipitates and and incl inclusionsusions morphology morphology in inthe the annealing annealing sheets. sheets. The main precipitates were AlN, TiN, MnS, Cu2S, and the composite precipitates. Some fine oxide The main precipitates were AlN, TiN, MnS, Cu2S, and the composite precipitates. Some fine oxide inclusionsinclusions werewere alsoalso discovereddiscovered onon thethe graingrain boundary.boundary. Because sulfur is one of the surface-active elements, it tends to segregate to the grain boundary [14,30]. During the long time soaking, a number of sulfur atoms segregate along the grain boundary. The diffusion of and copper occurs simultaneously. When the solubility product of manganese, copper, and sulfur supersaturates, MnS and Cu2S would nucleate at the grain boundaries [31]. Hence, the spherical or quasi-spherical of MnS and Cu2S are more liable to precipitate along

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Because sulfur is one of the surface-active elements, it tends to segregate to the grain boundary [14,30]. During the long time soaking, a number of sulfur atoms segregate along the grain boundary. The diffusion of manganese and copper occurs simultaneously. When the solubility product of manganese, copper, and sulfur supersaturates, MnS and Cu S would nucleate at the grain Metals 2020,, 10,, xx FORFOR PEERPEER REVIEWREVIEW 2 5 of 15 boundaries [31]. Hence, the spherical or quasi-spherical of MnS and Cu2S are more liable to precipitate alonggrain boundaries. grain boundaries. As AlN As and AlN TiN and nucleation TiN nucleation mode mode is mainly is mainly heterogeneous heterogeneous nucleation nucleation [1,5,8], [1,5 the,8], thecubic cubic shape shape of AlN of AlN and and TiN TiN precipitates precipitates inside inside grains grains or grain or grain boundaries. boundaries. ItIt isis obviousobvious toto seesee thatthat thethe precipitatesprecipitates areare mainlymainly distributeddistributed inin thethe graingrain boundaryboundary oror inin thethe crystalcrystal inin FigureFigure4 .4. ManyMany tinytiny sphericalspherical andand blockyblocky precipitatesprecipitates lessless thanthan 6565 nmnm were were observed observed throughoutthroughout thethe grainsgrains andand graingrain boundariesboundaries ofof hot-rolledhot-rolled bandband andand annealedannealed sheets.sheets. AfterAfter countingcounting andand measuringmeasuring the size of precipitates observedobserved inin the fields,fields, thethe sizesize of precipitates inin thethe hot-rolled bandband andand annealedannealed sheetssheets waswas mainlymainly inin thethe rangerange ofof 30–50030–500 nm.nm. The precipitate size and densitydensity (number(number ofof precipitatesprecipitates inin thethe unitunit area)area) withinwithin 30–50030–500 nmnm inin allall thethe samplessamples areare shownshown inin FigureFigure5 .5.

Figure 4. Distribution of precipitates in the hot-rolled band ((aa)) andand annealedannealed sheetssheets ((bb)) (SEM).(SEM).

14 56 6x1014 0.08 Average size of precipitates, nm 3 Distribution density of precipitates, /cm 14 5x10 Volume fraction of precipitates, /% 52 0.06 14 4x1014

14 48 3x1014 0.04

14 2x1014 44 0.02 14 1x1014

40 0 0.00 Continuous Casting billet Hot rolled band Cold rolled sheet Annealed sheet Continuous Casting billet Hot rolled band Cold rolled sheet Annealed sheet Figure 5. Statistics of precipitates in Continuous Casting billet, hot-rolled band, cold-rolled sheet, and Figure 5. Statistics of precipitates in Continuous Casting billet, hot-rolled band, cold-rolled sheet, annealed sheet. and annealed sheet. As shown in Figure5, the precipitates in the CSP process’ non-oriented electrical steel tended to As shown in Figure 5, the precipitates in the CSP process’ non-oriented electrical steel tended to grow in the whole process. The distribution density and volume fraction of the precipitates before grow in the whole process. The distribution density and volume fraction of the precipitates before annealing also increased. After annealing, the precipitates further increased in size and volume fraction, annealing also increased. After annealing, the precipitates further increased in size and volume but the corresponding distribution density decreased. fraction, but the corresponding distribution density decreased. Because the cooling rate of the CSP process is fast and the time is short [32], a large number of Because the cooling rate of the CSP process is fast and the time is short [32], a large number of precipitates had precipitated in continuous casting slab. As precipitates are difficult to precipitate precipitates had precipitated in continuous casting slab. As precipitates are difficult to precipitate and grow adequately, the average size of precipitates in the continuous casting slab was small [1,5]. and grow adequately, the average size of precipitates in the continuous casting slab was small [1,5]. Precipitates would further precipitate and grow during the soaking and hot rolling process, so hot-rolled Precipitates would further precipitate and grow during the soaking and hot rolling process, so hot- rolled bands had fewer fine precipitates than the continuous casting billet. The final annealing process (820 °C, 2 min) provided thermodynamic and kinetic conditions for the precipitation and growth of precipitates. The average size, distribution density, and volume fraction further increased after annealing. The main sizes of the precipitates in the annealed sheet mainly distributed in 30–500 nm. The statistical results of the precipitates in the annealed sheets showed that the distribution density, the volume fraction, and the average size of the precipitates were 9.08 × 1013/cm3, 0.06%, and 54.3 nm, respectively.

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bands had fewer fine precipitates than the continuous casting billet. The final annealing process (820 ◦C, 2 min) provided thermodynamic and kinetic conditions for the precipitation and growth of precipitates. The average size, distribution density, and volume fraction further increased after annealing. The main sizes of the precipitates in the annealed sheet mainly distributed in 30–500 nm. The statistical results of the precipitates in the annealed sheets showed that the distribution density, the volume fraction, and Metalsthe average 2020, 10, sizex FOR of PEER the precipitatesREVIEW were 9.08 1013/cm3, 0.06%, and 54.3 nm, respectively. 6 of 15 × 3.3. Thermodynamic Thermodynamic Analysis Analysis of of Precipitates Precipitates Figure 66 showsshows thethe austeniteaustenite andand ferriteferrite phasesphases inin non-orientednon-oriented electricalelectrical steel,steel, whichwhich werewere calculated usingusing FactSage FactSage 7.2 software7.2 software (Thermfact (Thermfact/CRCT,/CRCT, Montreal, Montreal, QC, Canada QC, and Canada GTT-Technologies, and GTT- Technologies,Aachen, Germany). Aachen, The Germany). currently The investigated currently invest non-orientedigated non-oriented electrical steel electrical was within steel was the within single theaustenite single phaseaustenite during phase the during soaking the at aboutsoaking 1373 at K.ab Duringout 1373 the K. hot During rolling the process, hot rolling the initial process, rolling, the initialfinishing rolling, rolling, finishing and coiling rolling, were and within coiling the were austenite, within ferrite, the austenite, and ferrite, ferrite, respectively. and ferrite, The respectively. precipitates’ Theprecipitation precipitates’ temperature precipitation and temperature amount were and calculated amount were by FactSage7.2; calculated by the FactSage7.2; results are the shown results in areFigure shown6b. Itin can Figure be observed 6b. It can thatbe observed the main that precipitates the main were precipitates AlN, MnS, were and AlN, TiN. MnS, The and equilibrium TiN. The equilibriumprecipitation precipitation temperature temperature of them was of 1479 them K, was 1578 1479 K, and K, 1578 1588 K, K, and respectively. 1588 K, respectively. During soaking During at soakingabout 1373 at K,about the precipitation1373 K, the precipitation amounts of AlN, amounts MnS, andof AlN, TiN underMnS, and equilibrium TiN under conditions equilibrium were conditions0.0067%, 0.0099%, were 0.0067%, and 0.0031%, 0.0099%, respectively. and 0.0031%, The equilibriumrespectively. precipitation The equilibrium amount precipitation of MnS and amount TiN at ofthe MnS soaking and temperatureTiN at the soaking of 1373 temperature K basically reachedof 1373 K the basically upper limit, reached but thatthe upper of AlN limit, would but increase that of AlNgreatly would as the increase temperature greatly decreased. as the temperature Therefore, decrea the averagesed. Therefore, size of AlNthe average particles size would of AlN decrease particles in wouldthe subsequent decrease operationin the subsequent stage. On operation the contrary, stage. the On average the contrary, size of MnSthe average and TiN size would of MnS not decreaseand TiN wouldafter soaking. not decrease after soaking.

0.012 (b) FactSage7.2 calculated TiN 0.010 0.0099% MnS AlN 0.008

0.0067% 0.006

0.004 0.0031% Precipitates, wt%

0.002

1373K 0.000 1000 1100 1200 1300 1400 1500 1600 1700 T, K FigureFigure 6. Fe-Si-0.3Fe-Si-0.3 wt%Al-0.25 wt%Al-0.25 wt%Mn wt%Mn phase phase diagram diagram ( (aa)) and and precipitation precipitation curve curve of precipitates ( b).

The database of FactSage 7.2 does not figure figure out the relevant data of Cu2S,S, but it would race to precipitate with MnS [[1].1]. In this this experiment, experiment, because of the single γ phasephase during during the the soaking soaking at about about 1373 K,K, the the solution solution and and precipitation precipitation behavior behavior of the of Cu the2S andCu2 MnSS and in MnS austenite in austenite were mainly were discussed. mainly discussed.The equilibrium The equilibrium solid solubility solid product solubility formulas product of formulas Cu2S[33 of] and Cu2 MnSS [33] [ 34and] are MnS Equations [34] are (1)Equations and (2). (1) and (2).  lg [Mn] [S] γ = 9020/T + 2.929 ( 215/T + 0.097)[%Mn] (1) { · ⋅=−+} − −−+− − lg [MnS ] [ ]γ 9020 / T 2.929 ( 215 / T 0.097)[% M n] (1) n o lg [Cu]2 [S] = 26.31 44971/T (2) 2 γ lg{[][] Cu· ⋅= S} 26.31 −− 44971/ T γ (2) The equilibrium precipitation temperature of MnS and Cu2S was 1518.5 K and 1416.2 K, according to TableThe1 ,equilibrium as shown in Figureprecipitation7, and the temperature precipitation of temperatureMnS and Cu of2 MnSS was was 1518.5 very closeK and to the1416.2 result K, accordingcalculated to by Table FactSage7.2 1, as shown software. in Figure So, it 7, could and the be speculatedprecipitation that temperature Cu2S would of precipitate MnS was very after close MnS. to the result calculated by FactSage7.2 software. So, it could be speculated that Cu2S would precipitate after MnS.

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100 0.006

10-3

0.004 2 10-6 lg{[Cu] [S]}=26.31-44971/T

lg{[Mn][S]}=2.9-8966.3/T 0.0032

10-9 0.002 Solubility product Solubility Mass fraction, wt% 10-12

Mass fraction of Cu2S, wt%

1373K 1392K 10-15 0.000 1000 1200 1400 1600 1800 Temperature, K

Figure 7. Equilibrium solubility product of MnS and Cu2S and the precipitation curve of Cu2S. Figure 7. Equilibrium solubility product of MnS and Cu2S and the precipitation curve of Cu2S.

As shown in Figure7 7,, thethe decreasedecrease ofof equilibrium equilibrium solubility solubility productproduct of of Cu Cu22S with a decrease in temperature was much greater thanthan MnS.MnS. Hence,Hence, thethe equilibriumequilibrium precipitation temperature of MnS would gradually approach and and be be lower lower than than that that of of Cu Cu2S2 Sas as the the S content S content decreased. decreased. Calculation Calculation by byEquations Equations (1) and (1) and(2) showed (2) showed that the that solid the solidsolubility solubility products products of MnS of and MnS Cu and2S were Cu2 Sequal were at equal 1394.07 at 1394.07K. That K.is, ThatCu2S is,would Cu2S precipitate would precipitate below1394.07 below1394.07 K, and the K, andremaining the remaining sulfur was sulfur 0.00125%. was 0.00125%. As the soaking of the slab is the mainmain stage of precipitationprecipitation and growth of the precipitates,precipitates, the equilibrium precipitationprecipitation amountamount ofof each each precipitate precipitate under under soaking soaking is is shown shown in in Table Table2. As2. As shown shown in 2 Tablein Table2, the 2, the equilibrium equilibrium precipitation precipitation ratios ratios of of MnS, MnS, Cu Cu2S,S, AlN, AlN, and and TiNTiN atat thethe soakingsoaking temperature were 76.4%,76.4%, 37.2%, 37.2%, 65.2%, 65.2%, and and 99.3%, 99.3%, respectively. respecti Sincevely. theSince S element the S iselement a grain is boundary a grain segregation boundary elementsegregation [1,8 ,14element], the amount [1,8,14], of the MnS amount precipitated of MnS on theprecipitated grain boundary on the during grain the boundary soaking processduring wasthe 2 2 muchsoaking larger process than was that ofmuch Cu2 S.larger Meanwhile, than that AlN of and Cu CuS. 2Meanwhile,S precipitated AlN less and in the Cu soakingS precipitated phase. The less rest in 2 ofthe AlN soaking and Cuphase.2S would The rest be of finely AlN dispersed and Cu S inwould the grain be finely boundaries dispersed and in crystals the grain in boundaries the subsequent and heatcrystals treatment in the subsequent process, which heat seriously treatment aff process,ected the which grain seriously growth during affected the the annealing grain growth process. during the annealing process. Table 2. Equilibrium precipitation amount at the soaking temperature. Table 2. Equilibrium precipitation amount at the soaking temperature. MnS, wt% Cu2S, wt% AlN, wt% TiN, wt% MaxMnS, wt% Equilibrium Max Cu2S, Equilibriumwt% Max AlN, Equilibrium wt% Max TiN, Equilibrium wt% Max Equilibrium0.0081 Max Equilibrium0.00232 Max Equilibrium0.00473 Max Equilibrium0.00286 0.00106 0.00623 0.00725 0.00288 0.0081(76.4%) 0.00232(37.2%) 0.00473(65.2%) (99.3%)0.00286 0.00106 0.00623 0.00725 0.00288 (76.4%) (37.2%) (65.2%) (99.3%) 3.4. Kinetics Analysis of Precipitates 3.4. Kinetics Analysis of Precipitates During the production process of the CSP process’ non-oriented electrical steel, the soaking of the slabDuring is the the main production stage of precipitationprocess of the and CSP growth process’ of thenon-oriented precipitates. electrical The currently steel, the investigated soaking of 0.65the slab wt% is Si the non-oriented main stage electricalof precipitation steel was and within growth the of single the precipitates. austenite phase The currently during the investigated soaking at about0.65 wt% 1373 Si K, non-oriented as shown in electrical Figure6. Therefore,steel was within the model the issingle based austenite on the following phase during assumptions the soaking [ 8,14 at]: about 1373 K, as shown in Figure 6. Therefore, the model is based on the following assumptions 1.[8,14]: Assuming the nucleation mode is homogeneous nucleation and grain boundary nucleation; 2. Assuming the nucleus is spherical, and neglecting the misfit or the elastic strain energy between 1. Assumingthe new phase the nucleation and the matrix; mode is homogeneous nucleation and grain boundary nucleation;

3.2. AssumingAssuming the the nucleus interface is of spherical, austenite and and neglec the newting phase the misfit attain or the the partial elastic equilibrium strain energy during the betweenprecipitation the new and phase growth and process; the matrix; 3. Assuming the interface of austenite and the new phase attain the partial equilibrium during 4. Assuming the diffusion of chemical element M, forming the precipitates in the austenite, is the the precipitation and growth process; restrictive factor of precipitate’s growth. 4. Assuming the diffusion of chemical element M, forming the precipitates in the austenite, is the restrictive factor of precipitate’s growth.

3.4.1. Driving Force for the Nucleation

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3.4.1. Driving Force for the Nucleation The critical nucleus size, r *, and the activation energy for nucleation (or the free energy change of formation of the critical nucleus), ∆G*, can be obtained from the following Equations (3)–(5) [8,35–37]

4σ dHomogeneous∗ +Grain boundary nucleation = (3) − ∆GV

16πσ3 ∆G = (4) Homogeneous∗ nucleation 2 3(∆GV)

∆G∗ = A ∆G∗ (5) Grain boundary nucleation 1 ×   3 where A = 1 2 3σB + σB , σ is grain boundary energy (0.73 J/m2)[8], σ is the interfacial energy 1 2 − 2σ 2σ B between the new phase and the matrix, Vm is the molar volume of the new phase, ∆GV is the volume free energy reduction in creating a new phase from the matrix. The chemical driving power of nucleation and the precipitation process can be represented as Equation (6) [38–40]. [M]0, [X]0 are the initial concentrations of elements M and X, [M], [X] are the equilibrium concentrations of elements M and X. R is the gas constant, and T is the temperature.

RT [M]0 [X]0 ∆GV = [ln + ln ] (6) −Vm [M] [X]

Based on the above equations, the activation energies and the critical nucleus size for Cu2S, TiN, AlN, and MnS nucleation can be calculated in austenite during the soaking at about 1373 K. The parameter values for calculation are summarized in Table3.

Table 3. Parameter values for calculation [8,33].

Diffusion of M, D, Interfacial Energy, σ, Lattice Constant, Phases Solubility Product cm2/s J/m2 nm a = 0.3111, AlN 2.72–10062/T 5.9 exp( 241000/RT) 1.03504–0.3437 10 3T − ∗ − c = 0.4978 TiN 5.56–17205/T 0.15 exp( 251000/RT) 1.1803–0.5318 10 3T 0.4239 − ∗ − MnS 2.9–8966.3/T 1.7 exp( 222000/RT) 0.9225–0.4157 10 3T 0.52226 − ∗ − Cu S 26.31–4971/T 0.19exp( 272000/RT) 0.8 0.56286 2 −

The calculated activation energy and the critical nucleation radius for Cu2S, TiN, AlN, and MnS are shown in Figure8. The critical nucleus size decreased continuously with a decrease in temperature. The critical nucleus size of Cu2S, TiN, AlN, and MnS was on the same order of magnitude. The activation energy of each precipitate decreased monotonously with a decrease in temperature. TiN, AlN, and MnS were nucleated more easily than Cu2S in austenite. Cu2S, TiN, AlN, and MnS were preferentially nucleated at grain boundaries. Metals 2020, 10, 1301 9 of 15 Metals 2020, 10, x FOR PEER REVIEW 9 of 15

1650 1650 (a) (b)

1500 1500

1350 1350 TiN-Homogeneous nucleation TiN-Grain boundary nucleation AlN-Homogeneous nucleation TiN-Homogeneous nucleation 1200 1200 TiN-Grain boundary nucleation AlN-Grain boundary nucleation AlN-Homogeneous nucleation Temperature, K Temperature, Temperature, K Temperature, MnS-Homogeneous nucleation AlN-Grain boundary nucleation MnS-Grain boundary nucleation MnS-Homogeneous nucleation 1050 Cu S-Homogeneous nucleation 1050 MnS-Grain boundary nucleation 2 Cu2S-Homogeneous nucleation Cu2S-Grain boundary nucleation Cu2S-Grain boundary nucleation 900 900 0246810 0 50 100 150 200 * 20 Critical nucleation radius, nm Activation energy, ΔG , ×10 J FigureFigure 8. 8. CriticalCritical nucleation nucleation radius radius (a) (anda) and activation activation energy energy (b) (forb) fornew new phases phases nucleation nucleation vs. temperature.vs. temperature.

3.4.2.3.4.2. Nucleation Nucleation Rate Rate and and Precipitation-Time-Temperature Precipitation-Time-Temperature TheThe homogeneous homogeneous nucleationnucleation raterate in in the the matrix matrix and and the the heterogeneous heterogeneous nucleation nucleation rate onrate the on grain the grainboundary boundary were takenwere intotaken consideration into consideration in the present in the study.present The study. formula The forformula the relative for the nucleation relative nucleationrate (NrT) forrate the (NrT) homogeneous for the ho nucleationmogeneous and nucleation the heterogeneous and the hete nucleationrogeneous on grainnucleation boundary on grain could boundarybe calculated could by be Equations calculated (7) by and Equati (8), respectivelyons (7) and (8), [8]. respectively [8].

  Δ * + +  I * 1 1 GQ∆G∗ Q lg lg()I == 2lg2lgd d+−∗ +  (7)(7) K K Homogeneous nucleation kT Homogeneous nucleation ln10ln 10 −kT

* !   δ ΔGQ∆+G + Q I I =++−* δ 1 1 gg∗g g lg lg() = 2lg2lgdd∗ + lglg +  (8)(8) K K Grain boundary nucleation LkTL ln10 kT Grain boundary nucleation ln 10 − 23 where k is the Boltzmann constant (1.3806505 10−23 J/K), Q is the diffusion activation energy of where k is the Boltzmann constant (1.3806505 × ×10 −J/K), Q is the diffusion activation energy of the controlthe control element element M in M austenite in austenite (that (that is, the is, the diff diusionffusion activation activation energy energy of ofa asingle single atom), atom), δ δisis the the thicknessthickness of of crystal crystal interface interface (0.5 (0.5 nm), nm), LL isis the the average average grain grain diameter. diameter. TheThe formulaformula for for the the precipitation-time-temperature precipitation-time-temperature (PTT) (PTT) diagram diagram for the homogeneousfor the homogeneous nucleation nucleationand the heterogeneous and the hetero nucleationgeneous onnucleation grain boundary on grain is boundary calculated is by calculated Equation (9)by andEquation Equation (9) and (10), Equationrespectively (10), [8 respectively,41,42]. [8,41,42]. ! tGQ212.5 Δ * +  t0.050.05a a =−2 −* + × 1 ∆G∗ + 2.5Q lg lg = 1.289941.28994 2lg d 2lgd∗ + (9)(9) t tkT0a 3ln103 − − ln 10 × kT 0a HomogeneousHomogeneous nucleation nucleation

! * t t0.05g  1 A ΔGQ+  lg0.05g =− 2 1.28994 − 2lg d * + ×1 1 A1∆G∗ + Q lg rain boundary nucleation= 2 1.28994 2lgd∗ + (10)(10) t tkT0g  − − ln10 ln 10 ×  kT 0g GGrain boundary nucleation TheThe calculated calculated relative relative nucleation nucleation rate rate and and th thee precipitation-time-temperature precipitation-time-temperature (PTT) (PTT) diagram diagram forfor precipitates precipitates in in austenite austenite are are shown shown in in Figure Figure 99.. For the heterogeneousheterogeneous nucleation on the grain boundary,boundary, Cu Cu22S,S, TiN, TiN, AlN, AlN, and and MnS MnS had had low low relative relative nu nucleationcleation rates rates compared compared with with homogeneous homogeneous nucleation.nucleation. This This calculation calculation also also implied implied that that the the heterogeneous heterogeneous nucleation nucleation on on the the grain grain boundary boundary of of CuCu22S,S, TiN, TiN, AlN, AlN, and and MnS MnS migh mightt preferentially preferentially happen. happen. The precipitation-time-temperature (PTT) diagram of Cu2S, TiN, AlN, and MnS precipitation in the austenite region showed a C-shaped curve. The corresponding precipitation (5%) nose temperature of Cu2S, TiN, AlN, and MnS was about 1108 K, 1453 K, 1374 K, and 1243 K for homogeneous nucleation, 1065 K, 1593 K, 1584 K, and 1414 K for grain boundary nucleation, respectively. Hence, TiN, AlN, and MnS were mainly precipitated during the period of soaking at 1373 K, but Cu2S would precipitate slightly. Furthermore, combined with thermodynamic calculation (in Figures6 and7), the critical nucleation radius (in Figure8a), and the activation energy (in Figure8b) calculation results, it could be confirmed that TiN, MnS mainly precipitate during soaking and AlN, Cu2S would precipitate

Metals 2020, 10, 1301 10 of 15

unceasingly with the decrease in the average sizes in the subsequent processes after soaking. The tiny MetalsCu2S 2020 in the, 10, CSPx FOR process’ PEER REVIEW non-oriented electrical steel could also be better understood. 10 of 15

1650 1650 (a) (b)

1500 1500

1373K 1350 1350

1200 1200 TiN-Homogeneous nucleation TiN-Homogeneous nucleation TiN-Grain boundary nucleation TiN-Grain boundary nucleation AlN-Homogeneous nucleation Temperature, K Teemperature, K Teemperature, AlN-Homogeneous nucleation AlN-Grain boundary nucleation AlN-Grain boundary nucleation MnS-Homogeneous nucleation 1050 MnS-Homogeneous nucleation 1050 MnS-Grain boundary nucleation MnS-Grain boundary nucleation Cu S-Homogeneous nucleation Cu S-Homogeneous nucleation 2 2 Cu S-Grain boundary nucleation Cu S-Grain boundary nucleation 2 2 900 900 -60 -50 -40 -30 -20 20 40 60 80 100 Relative nucleation rate, lg(I/K) lg(t /t ) 0.05 0 FigureFigure 9. 9. NrTNrT ( (aa)) and and PTT PTT ( (bb)) curves curves of of new new phases phases pr precipitatedecipitated in in austenite. austenite.

3.4.3. Growth of Precipitates The precipitation-time-temperature (PTT) diagram of Cu2S, TiN, AlN, and MnS precipitation in the austeniteCu2S, AlN, region and TiNshowed control a elementsC-shaped of curve. Ostwald The ripening corresponding are Cu, Al, precipitation and Ti, respectively (5%) nose [8]. temperatureHowever, the of precipitation Cu2S, TiN, behaviorAlN, and of MnS MnS inwas non-oriented about 1108 electrical K, 1453 steelK, 1374 is more K, complicatedand 1243 K andfor homogeneousmust be determined nucleation, first. It1065 can beK, calculated1593 K, 1584 by Equation K, and (11)1414 [8 ].Kω for= AgrainMn/ AboundaryS is the ideal nucleation, chemical respectively.ratio of MnS, Hence, and AMn TiN,and AlN,AS are and the MnS relative were atomic mainly mass precipitated of Mn and during S, respectively. the period of soaking at 1373 K, but Cu2S would precipitate slightly. Furthermore, combined with thermodynamic calculation s (in Figures 6 and 7), the critical nucleationD radiusMn γω (in Figure 8a), andD theS γ activation energy (in Figure − 2.9 8966.3/T − 8b) calculation results, Mnit couldωS be= Econfirmed= that TiN,10 MnS− mainly( precipitate1) during soaking and(11) − DS γ · · DMn γ − − − AlN, Cu2S would precipitate unceasingly with the decrease in the average sizes in the subsequent processesThe calculationafter soaking. of MnS The controllingtiny Cu2S in elements the CSP in process’ the precipitation non-oriented process electrical of non-oriented steel could electrical also be bettersteel is understood. shown in Table 4. It can be seen that Mn- wS in non-oriented electrical steels was greater than E; hence sulfur would be the controlling element in the Ostwald ripening process of MnS. 3.4.3. Growth of Precipitates Table 4. Controlling element calculation of MnS in non-oriented electrical steel. Cu2S, AlN, and TiN control elements of Ostwald ripening are Cu, Al, and Ti, respectively [8]. However, the precipitation behaviorComputational of MnS Item in non-oriented electrical Values steel is more complicated and ω=A / A must be determined first. It can beMn- calculatedωS by Equation (11) 0.243146[8]. Mn S is the ideal chemical ratio of MnS, and AMn and AS are the relativeE atomic mass of Mn 0.026146 and S, respectively. Controlling element S ω DDMn−−γγ− S Mn−==ω S E ⋅102.9 8966.3/T ⋅ ( − 1) (11) DDSMn−−γγ According to the Fe–Si phase diagram in (Figure6a), it can be seen that the CSP process’ non-orientedThe calculation electrical of steelMnS was controlling in the austenite elements zone in duringthe precipitation the soaking process process of (about non-oriented 1373 K). electricalThe change steel of is the shown average in Table diffusivity 4. It can of be the seen kinetic that controlMn-wS in elements non-oriented for the electrical formation steels of eachwas greaterprecipitated than E; phase hence with sulfur temperature would be is the shown contro inlling Figure element 10. It in can the be Ostwald seen from ripening Figure 10process that theof MnS.diffusion coefficients of Al and S in the γ-phase were much larger than those of Ti and Cu. As the temperature decreased, the diffusion capacity of Al and S in the γ-phase decreased, and the rate of decline was linear.Table As4. Controlling the temperature element was calculation less than of MnS 1200 in K, non-oriented the diffusion electrical of Al, steel. S, Ti, and Cu in the γ-phase was almost negligible, and the precipitation kinetic conditions of each precipitate were poor. Computational Item Values Therefore, Cu2S, TiN, AlN, and MnS would mainly precipitate during soaking at 1373 K. Mn-ωS 0.243146 E 0.026146 Controlling element S

According to the Fe–Si phase diagram in (Figure 6a), it can be seen that the CSP process’ non- oriented electrical steel was in the austenite zone during the soaking process (about 1373 K). The change of the average diffusivity of the kinetic control elements for the formation of each precipitated phase with temperature is shown in Figure 10. It can be seen from Figure 10 that the diffusion coefficients of Al and S in the γ-phase were much larger than those of Ti and Cu. As the temperature decreased, the diffusion capacity of Al and S in the γ-phase decreased, and the rate of decline was linear. As the temperature was less than 1200 K, the diffusion of Al, S, Ti, and Cu in the γ-phase was

Metals 2020, 10, x FOR PEER REVIEW 11 of 15 Metals 2020, 10, x FOR PEER REVIEW 11 of 15 almost negligible, and the precipitation kinetic conditions of each precipitate were poor. Therefore, almost negligible, and the precipitation kinetic conditions of each precipitate were poor. Therefore, CuMetals2S, 2020TiN,, 10 AlN,, 1301 and MnS would mainly precipitate during soaking at 1373 K. 11 of 15 Cu2S, TiN, AlN, and MnS would mainly precipitate during soaking at 1373 K.

2.5x10-12 -12 /s 2.5x10 2 D /s Al 2 D 2.0x10-12 Al DTi 2.0x10-12 DTi DS -12 D 1.5x10 DS 1.5x10-12 Cu DCu

1.0x10-12 1.0x10-12

5.0x10-13 5.0x10-13

0.0 The diffusioncoefficients, D, cm 0.0 The diffusioncoefficients, D, cm 1500 1400 1300 1200 1100 1500 1400 1300 1200 1100 T, K T, K Figure 10. Variation of the diffusion coefficients of control elements with temperature. FigureFigure 10. 10. VariationVariation of of the the diffusion diffusion coefficients coefficients of of control control elements elements with with temperature. temperature. After nucleation, particles would mainly grow immediately. Lots of mathematical models have AfterAfter nucleation, nucleation, particles particles would would mainly mainly grow grow immediately. immediately. Lots Lots of of mathematical mathematical models models have have been developed to describe the particle growth in different situations. The theory of size change of beenbeen developed developed to to describe describe the the particle particle growth growth in in different different situations. situations. The The theory theory of of size size change change of of the precipitated phase in the dilute solution was first proposed by Ostwald. In the present paper, the thethe precipitated precipitated phase phase in in the the dilute dilute solution solution was was first first proposed proposed by byOstwald. Ostwald. In the In present the present paper, paper, the Ostwald ripening model of particles during the soaking process (about 1373 K) can be described by Ostwaldthe Ostwald ripening ripening model model of particle of particless during during the the soaking soaking process process (abo (aboutut 1373 1373 K) K) can can be be described described by by the following Equation (12) [8]: thethe following following Equation Equation (12) (12) [8]: [8]: 11 _  22 3 _ 88σσVVDCDC0 1 1 1 _ ≈⋅ 2P 0 3 3 rt 8σVDC  t1t 3 (12)(12) rt ≈⋅99VVCRTPC RT0  t 3 rt≈ BBPP · (12) 9VCRTBP where C0 isis the the equilibrium equilibrium concentration concentration of an element in the matrix (mol/mol); (mol/mol); CPP isis the the equilibrium equilibrium where C0 is the equilibrium concentration of an element in the matrix (mol/mol); CP is the equilibrium molar concentration of an elementelement in the precipitate (mol(mol/mol);/mol); VVP isis the the molar molar number number of of precipitate precipitate molar3 concentration of an element in the precipitate3 (mol/mol); VP is the molar number of precipitate (m3/mol);/mol); V BB isis the the molar molar number number of of austenite austenite (m (m3/mol);/mol); DD isis the the average average volume volume diffusion diffusion rate of (m3/mol); VB is the molar number of austenite (m3/mol); D is the average volume diffusion rate of atoms. alloy atoms. The calculated evolutionevolution ofof thethe particle particle size size with with time time at at 1373 1373 K K in in austenite austenite is shownis shown in Figurein Figure 11. The calculated evolution of the particle size with time at 1373 K in austenite is shown in Figure The11. The average average particle particle size size of of Cu Cu2S,2S, TiN, TiN, AlN, AlN, and and MnS MnS increased increased with with time. time. TheThe increasingincreasing velocity 11. The average particle size of Cu2S, TiN, AlN, and MnS increased with time. The increasing velocity of particles was great at the early stage, and the curvecurve of the increasing velocity tended to even flat flat of particles was great at the early stage, and the curve of the increasing velocity tended to even flat along with thethe reactionreaction proceedingproceeding continuously.continuously. Due Due to to the the higher higher di diffusionffusion coe coefficientfficient of of S andS and Al Al in along with the reaction proceeding continuously. Due to the higher diffusion coefficient of S and Al inaustenite austenite during during the the soaking soaking process, process, both both MnS MnS and AlNand grewAlN fastergrew thanfaster Cu than2S and Cu2 TiN.S and The TiN. growth The in austenite during the soaking process, both MnS and AlN grew faster than Cu2S and TiN. The growthrate and rate size and of AlN size andof AlN MnS and were MnS much were larger much than larger those than ofTiN those and of CuTiN2S, and as shown Cu2S, as in Figureshown 11in. growth rate and size of AlN and MnS were much larger than those of TiN and Cu2S, as shown in AfterFigure soaking 11. After for soaking 40 min, for the 40 sizes min, of the AlN, sizes MnS, of AlN, TiN, MnS, and CuTiN,2S and were Cu 105.022S were nm, 105.02 42.72 nm, nm, 42.72 5.42 nm, nm, Figure 11. After soaking for 40 min, the sizes of AlN, MnS, TiN, and Cu2S were 105.02 nm, 42.72 nm, 5.42and 9.74nm, nm,and respectively.9.74 nm, respectively. 5.42 nm, and 9.74 nm, respectively.

120 120 1373K AlN 100 1373K AlN 100 80 80 60 60 40 MnS 40 MnS 20 20 8 Cu S 2 8 Cu S 2 Radius of Particles, r/nm 4 TiN

Radius of Particles, r/nm 4 40min TiN 0 40min 0 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500 Soaking Time, t/s Soaking Time, t/s Figure 11. The growth potential of Cu 2S,S, TiN, TiN, AlN, and MnS in γ-Fe at 1373 K. Figure 11. The growth potential of Cu2S, TiN, AlN, and MnS in γ-Fe at 1373 K.

Metals 2020, 10, 1301 12 of 15

3.5. Grain Growth Behavior Grain size is controlled by the competition between the driving and pinning forces for grain growth, and grain growth would tend to occur as the driving force exceeds the pinning force [43]. Precipitates in the CSP process’ non-oriented electrical steel tended to be stable above the recrystallization temperature, as shown in Figure5. It can be judged that precipitates would play pinning or dragging action on the grain boundaries at the recrystallization temperature. The pinning force of precipitates and the driving force of grain growth were discussed in this study. The driving force for grain growth is provided by the reduction of grain boundary energy. The driving force provided by dislocation density on the grain growth could be negligible in non-oriented electrical steel. A theoretical equation modified by Gladman [44] could be used for calculating the driving force, Fd, for grain growth, as shown in Equation (13). The pinning effect of precipitates on grain growth is caused by the reduction in grain boundary areas. The pinning force, which was analyzed by Zener formula, rigid boundary model (RBM), and flexible boundary model (FBM), is shown by Equations (14) and (16) [14,45,46], with the hypotheses that the grain growth will stop by the pinning force of particles. 3 2  γ  F = (13) d 2 − Z R 3σ f F = · (14) Zener 2D 6σ f F = · (15) RBM π r · 3σ f 2/3 F = · (16) FBM π D · where Fd is the driving force, f is the volume fraction of particles, D is the average radius of the grains, Z is the size advantage (the ratio of the maximum grain size to the average grain size), and γ and σ are the grain boundary energy per unit area (taken as 0.8 J/m2)[47]. The values of the pinning force of precipitates and the driving force of grain growth were calculated and listed in Table5, and the trend of Fd with grain size (R-critical) is shown in Figure 12. The pinning forces were calculated by Zener formula, rigid boundary model (RBM), and flexible boundary model (FBM) and showed that the precipitates in the annealed sheet of 30–500 nm would pin grain growth at different grain sizes. The pinning force caused by 100–300 nm particles was the largest and by 70–100 nm was the second. Hence, the 100–300 nm particles played the main role in hindering grain growth, as shown in Figure 12. It can be concluded that a few finer grains, which have a much larger driving force, can grow up, and a large amount of grains is impeded by the precipitates.

Table 5. The calculated pinning forces (Fp) of precipitates-annealed sheet samples.

Size, nm D/nm Number/cm3 f/% Fp (Zener)/Pa Fp (RBM)/Pa Fp (FBM)/Pa 30–70 34 6.53 1013 1.88 10 3 6.64 104 8.45 104 3.42 105 × × − × × × 70–100 75 1.89 1013 5.85 10 3 9.36 104 1.19 105 3.31 105 × × − × × × 100–300 188 6.31 1012 3.07 10 2 1.96 105 2.50 105 3.99 105 × × − × × × 300–500 345 2.39 1011 7.19 10 3 2.50 104 3.19 104 8.26 104 × × − × × × 500–1000 702 3.42 1010 8.67 10 3 1.48 104 1.89 104 4.59 104 × × − × × × 1000–3000 1823 1.37 109 6.09 10 3 4.01 103 5.10 103 1.40 104 × × − × × × Metals 2020, 10, 1301 13 of 15 Metals 2020, 10, x FOR PEER REVIEW 13 of 15

25 5x105 R-critical (Zener) Main pinning sizes R-critical (FBM) 20 R-critical (RBM) 4x105

15 Fp (Zener) 3x105 Fp (FBM) Fp (RBM) 10 2x105 R-critical, μm

5 1x105 Pinning forces, Fp, Pa

0 0

30~70nm 70~100nm 0.1~0.3μm 0.3~0.5μm 0.5~1μm Figure 12. Relationship between Fd and R-critical. 4. Conclusions 4. Conclusions The precipitation behavior and effect on grain growth of precipitates in the CSP process’ The precipitation behavior and effect on grain growth of precipitates in the CSP process’ non- non-oriented electrical steel were characterized experimentally and theoretically. The conclusions oriented electrical steel were characterized experimentally and theoretically. The conclusions would would guide scholars, reducing the effects of precipitates and enhancing the magnetic properties of the guide scholars, reducing the effects of precipitates and enhancing the magnetic properties of the CSP CSP process’ non-oriented electrical steel. The following results were obtained: process’ non-oriented electrical steel. The following results were obtained:

1. As the contents of elements and technology for heating processing are nearly equivalent, P15/50 1. As the contents of elements and technologyP for heating processing are nearly equivalent, P15/50 increasesincreases obviously obviously with with an an increase increase in ∑ (C(C ++ NN ++ SS + +Ti)Ti) in in 95–105 95–105 ppm. ppm. 2. TEMTEM and and SEM SEM results results show show that that the the main main particles particles are are AlN, AlN, TiN, TiN, MnS, MnS, Cu Cu2S, 2andS, and fine fineoxide oxide inclusions.inclusions. The The distribution distribution density, density, the volume fraction, andand thethe averageaverage sizesize ofof thethe precipitates 13 3 in the annealed sheets are 9.08 10 /cm , 0.06%,13 and3 54.3 nm, respectively. precipitates in the annealed sheets× are 9.08 × 10 /cm , 0.06%, and 54.3 nm, respectively. 3. TheoreticalTheoretical calculations calculations show show that that precipitates precipitates are are preferential preferentiallyly nucleated nucleated at at grain grain boundaries. boundaries. DuringDuring the the soaking soaking process, process, TiN TiN and and MnS MnS are are the the main main precipitates, precipitates, and and AlN AlN and and Cu Cu2S2S would would precipitateprecipitate continuously, and thethe averageaverage particleparticle sizesize ofof AlNAlN andand Cu Cu22SS particlesparticles decreasesdecreases in in the thesubsequent subsequent process process after after soaking. soaking. 4. CombinedCombined with SEMSEM andand theoreticaltheoretical calculation calculation results, results, the the average average size size of AlNof AlN and and Cu 2CuS particles2S particleswould decrease would decrease after soaking, after soaking, but that ofbu MnSt that and of MnS TiN isand the TiN opposite. is the opposite. 5. TheThe precipitates precipitates in in 30–500 30–500 nm nm would would hinder hinder the grain the grain growth growth during during annealing, annealing, and the and 100– the 300100–300 nm particles nm particles played played the main the main role in role hindering in hindering the grain the grain growth. growth. Author Contributions: formal analysis, methodology, investigation, resources, data curation, and writing, J.- Authorl.Q.; validation, Contributions: L.X., F.-h.G.;Formal project analysis, administration methodology, and funding investigation, acquisition, resources, S.-t.Q.; data software, curation, J.-w.H. and All writing, J.-l.Q.;authors validation, have read L.X.,and agreed F.-h.G.; to project the published administration version and of the funding manuscript. acquisition, S.-t.Q.; software, J.-w.H., H.-j.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National key research and development plan, grant number Funding: This research was funded by the National key research and development plan, grant number2016YFB0300305. 2016YFB0300305. Acknowledgments: Financial supports from the National National key key research research and and development development plan plan (2016YFB0300305) (2016YFB0300305) and FactSage 7.2 software of Anhui University ofof TechnologyTechnology areare gratefullygratefully acknowledged.acknowledged.

ConflictsConflicts ofof Interest:Interest: The authors declare nono conflictconflict ofof interest.interest.

References

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