Ammoniacal System Mechanisms for Leaching Copper from Converter Slag

: In pyrometallurgical processes reﬁning copper, the main source of loss in the conversion stage is from slag. This paper reports on research work treating converter slag containing high percentages of copper (36 wt%) using ammonium hydroxide at room temperature. Variables analyzed are solution pH, agitation, temperature, NH 4 OH concentration and particle size. Results showed that the hydronium ion resulting from ammonium hydroxide dissociation was the main oxidant of copper compounds in slag, such as CuO, Cu 2 O and Cu, with the exception of CuFeO 2 . The particles contain a large amount of microcracks (porosity) in their refractory structure (analyzed by compositional image capture (BSE)). Thus, the di ﬀ usion of the leaching solution through the microcracks making contact with the copper oxides would be allowed. Leaching mechanisms were corroborated by X-ray di ﬀ raction and scanning electron microscopy analysis. Increasing temperature and NH 4 OH concentration while decreasing particle size obtained higher copper recoveries, reaching values of 84.8%. Under the same conditions, the main impurity (iron) was minimal ( < 2%). Solution pH also a ﬀ ected slag leaching. Agitation of the solution positively a ﬀ ected the rate of copper extraction. Leaching kinetics of the leaching solution through the porosity formed in the slag was analyzed under the intraparticle di ﬀ usion model. The reaction order was 1.2 with respect to the concentration of ammonium hydroxide and the model was inversely proportional to the square of the particle radius. The activation energy obtained was 42.3 kJ / mol for temperature range 283 to 333 K.


Introduction
Metallurgical treatment of metallic sulfides is generally carried out by means of high temperature methods, usually pyrometallurgy. Conversion stage, there are two sequential stages-the elimination of iron and some other impurities in the so-called "slag blow" stage; and the subsequent stage to convert white metal (Cu 2 S) to metallic copper (Cu), known as the "copper blow" stage. During the conversion process, highly uncontrolled oxidation occurs, causing chemical copper losses through direct contact of metallic copper with gaseous oxygen (reaction (1)), as well as through direct contact of the white metal with the main constituent of slag, iron oxide (FeO) (reaction (2)).
Thermodynamically, reaction (1) is very favorable; however and although reaction (2) should not occur because the activity of copper oxide in a slag is on the order of 4.25 × 10 −7 , there is ample such as malachite in ammonia/ammonium carbonate system [12], oxidized copper ore in ammonium chloride solution [13], complex copper in ammonia-ammonium chloride solution [14], malachite ore in ammonium nitrate solutions [15], tenorite and cuprite in ammonium media [16,17]. Ammonia leaching has not been carried out for converter slags.
Therefore, the main objective of this research work is to leach a slag from a Peirce-Smith converter using ammonium hydroxide (NH 4 OH) under different working conditions as an alternative to leaching with sulfuric acid (or any other acid).

Experimental Design
Codelco Chile's Ventanas Division provided converter slag specifically from their conversion process in a Peirce-Smith Furnace. In brief, slag is cooled with industrial water to reduce temperature from 1373 K to 293 K, is then crushed, ground and classified into several size fractions, (most frequently −210 + 149, −149 + 105, −105 + 74 and −74 + 53 µm, with average particle sizes of 180, 127, 90 and 64 µm, respectively). Chemical analysis was performed on samples obtained at average sizes of 180 and 64 µm, showing 36% Cu, 19% Fe and the remaining insoluble parts. Converter slag here presented a very high concentration of copper, higher than bibliographically recorded (0.68-9.13% Cu). Therefore, hydrometallurgical treatment of waste (slag) was of interest.
Chemical analyses of the solutions were made by Atomic Absorption Spectroscopy (AAS) with a Hitachi Z-8100 Zeeman kit (Hitachi High-Technologies Corporation, Tokyo, Japan). For the slag characterization in scanning electron microscopy (SEM), the sample was covered with coal to be conductive. Chemical analysis (EDS) and compositional image capture (BSE) and morphological (SEM) were performed using a Tescan ® Vega LSH electron microscope, equipped with an EDS Bruker ® 6030 detector (TESCAN, Brno, Czech Republic). Solids were determined by X-ray diffraction (XRD), using a Bruker ® D4 Endeavor kit, operated with Cu radiation and a Kβ Ni radiation filter (Bruker AXS Advance D8, Bruker, Billerica, MA, USA).
In order to know the chemical species and/or elements present in converter slag, an XRD of the original sample was performed, obtaining the results observed in Figure 1. Here, peaks indicate delafossite (CuFeO 2 ), cuprite (Cu 2 O), tenorite (CuO), metallic copper (Cu), chalcocite (CuS), magnetite (Fe 3 O 4 ) and fayalite (Fe 2 SiO 4 ) compounds-in short, copper present in the converter slag is mainly oxidized.
Metals 2020, 10, x FOR PEER REVIEW 3 of 18 chloride solution [13], complex copper in ammonia-ammonium chloride solution [14], malachite ore in ammonium nitrate solutions [15], tenorite and cuprite in ammonium media [16,17]. Ammonia leaching has not been carried out for converter slags. Therefore, the main objective of this research work is to leach a slag from a Peirce-Smith converter using ammonium hydroxide (NH4OH) under different working conditions as an alternative to leaching with sulfuric acid (or any other acid).

Experimental Design
Codelco Chile's Ventanas Division provided converter slag specifically from their conversion process in a Peirce-Smith Furnace. In brief, slag is cooled with industrial water to reduce temperature from 1373 K to 293 K, is then crushed, ground and classified into several size fractions, (most frequently −210 + 149, −149 + 105, −105 + 74 and −74 + 53 μm, with average particle sizes of 180, 127, 90 and 64 μm, respectively). Chemical analysis was performed on samples obtained at average sizes of 180 and 64 μm, showing 36% Cu, 19% Fe and the remaining insoluble parts. Converter slag here presented a very high concentration of copper, higher than bibliographically recorded (0.68-9.13% Cu). Therefore, hydrometallurgical treatment of waste (slag) was of interest.
Chemical analyses of the solutions were made by Atomic Absorption Spectroscopy (AAS) with a Hitachi Z-8100 Zeeman kit (Hitachi High-Technologies Corporation, Tokyo, Japan). For the slag characterization in scanning electron microscopy (SEM), the sample was covered with coal to be conductive. Chemical analysis (EDS) and compositional image capture (BSE) and morphological (SEM) were performed using a Tescan® Vega LSH electron microscope, equipped with an EDS Bruker® 6030 detector (TESCAN, Brno, Czech Republic). Solids were determined by X-ray diffraction (XRD), using a Bruker® D4 Endeavor kit, operated with Cu radiation and a Kβ Ni radiation filter (Bruker AXS Advance D8, Bruker, Billerica, MA, USA).
In order to know the chemical species and/or elements present in converter slag, an XRD of the original sample was performed, obtaining the results observed in Figure 1. Here, peaks indicate delafossite (CuFeO2), cuprite (Cu2O), tenorite (CuO), metallic copper (Cu), chalcocite (CuS), magnetite (Fe3O4) and fayalite (Fe2SiO4) compounds-in short, copper present in the converter slag is mainly oxidized.  The 180 µm sample was analyzed by SEM to determine the degree of fracture and morphology of the converter slag particles ( Figure 2). The particles show an important degree of fracture or porosity (indicated by arrows in the images). This fracturing, called microcracks, could help diffuse leaching solutions through the particle.
Metals 2020, 10, x FOR PEER REVIEW 4 of 18 The 180 μm sample was analyzed by SEM to determine the degree of fracture and morphology of the converter slag particles ( Figure 2). The particles show an important degree of fracture or porosity (indicated by arrows in the images). This fracturing, called microcracks, could help diffuse leaching solutions through the particle. Leaching experiments began by placing 1 dm 3 of ammonium hydroxide leaching solution into a 2 dm 3 capacity reactor. This reactor consisted of a heating blanket, condenser (to decrease the evaporation rate), mechanical agitator of the digital type (with a teflon impeller), thermocouple and a tube to extract the liquid samples. Then, 1 × 10 −3 kg of converter slag sample was introduced. For experiments run at elevated temperature, the solution was first heated to the desired temperature. During the experimental time, liquid samples were extracted and analyzed by AAS for Cu and Fe analysis. In some cases, solid samples were obtained by washing and drying residues and they were analyzed by X-ray diffraction to get the qualitative phase analysis and BSE was used for cross sections of particle morphology.

Solution pH
The converter slag dissolution zone in ammonia media at different solution pH values was analyzed. The pH values were 6.0, 10.5 and 14.0. The tests were performed at NH4OH concentration of 0.7 mol/dm 3 , temperature 298 K, particle size 64 m, agitation speed 500 rpm and liquid/solid ratio of 1000/1. To maintain the pH value of the solution, sulfuric acid (98% purity) or sodium hydroxide (98.5% purity) was added, as appropriate. Figure 3 shows the results obtained for leaching times up to 2700 s. Leaching experiments began by placing 1 dm 3 of ammonium hydroxide leaching solution into a 2 dm 3 capacity reactor. This reactor consisted of a heating blanket, condenser (to decrease the evaporation rate), mechanical agitator of the digital type (with a teflon impeller), thermocouple and a tube to extract the liquid samples. Then, 1 × 10 −3 kg of converter slag sample was introduced. For experiments run at elevated temperature, the solution was first heated to the desired temperature. During the experimental time, liquid samples were extracted and analyzed by AAS for Cu and Fe analysis. In some cases, solid samples were obtained by washing and drying residues and they were analyzed by X-ray diffraction to get the qualitative phase analysis and BSE was used for cross sections of particle morphology.

Solution pH
The converter slag dissolution zone in ammonia media at different solution pH values was analyzed. The pH values were 6.0, 10.5 and 14.0. The tests were performed at NH 4 OH concentration of 0.7 mol/dm 3 , temperature 298 K, particle size 64 µm, agitation speed 500 rpm and liquid/solid ratio of 1000/1. To maintain the pH value of the solution, sulfuric acid (98% purity) or sodium hydroxide (98.5% purity) was added, as appropriate. Figure 3 shows the results obtained for leaching times up to 2700 s.  It can be seen in the figure that as the experimental time increases, the extraction of copper from the converter slags increases. Thus, for a pH of 10.5, an extraction of 29.9% Cu was obtained at a time of 600 s, while at 2700 s, extraction reached 69.6%. It should also be noted that copper extractions were lower for pH values of 6.0 and 14.0, reaching extractions of only 7.3% and 15.1%, respectively. This decrease in extraction will be discussed later.

Effect of Agitating the Solution
The agitation of the leaching solution was varied between a range of 100 and 950 rpm. In addition, an agitation-free test was added. The working conditions used were for pH value 10.5, an ammonium hydroxide concentration of 0.7 mol/dm 3 , particle size 64 m, temperature 298 K and a liquid/solid ratio of 1000/1. Figure 4 shows time-dependent copper extractions for the stirring ranges used on the solution.  It can be seen in the figure that as the experimental time increases, the extraction of copper from the converter slags increases. Thus, for a pH of 10.5, an extraction of 29.9% Cu was obtained at a time of 600 s, while at 2700 s, extraction reached 69.6%. It should also be noted that copper extractions were lower for pH values of 6.0 and 14.0, reaching extractions of only 7.3% and 15.1%, respectively. This decrease in extraction will be discussed later.

Effect of Agitating the Solution
The agitation of the leaching solution was varied between a range of 100 and 950 rpm. In addition, an agitation-free test was added. The working conditions used were for pH value 10.5, an ammonium hydroxide concentration of 0.7 mol/dm 3 , particle size 64 µm, temperature 298 K and a liquid/solid ratio of 1000/1. Figure 4 shows time-dependent copper extractions for the stirring ranges used on the solution.
As can be seen in the figure, a low stirring speed (100 rpm) copper extraction was achieved close to 38.3%. As stirring speed increased, copper extraction increased to 84.8% (at stirring rate 950 rpm). Above 500 rpm, the amount of copper extracted is not highly influenced. This phenomenon is due to the role of mass transfer. Thus, the mass transfer would not be relevant to the flow of ions through the slag particles. It was thus concluded that future experiments would be set at 500 rpm agitation.
It should be noted that working without agitation (0 rpm) an extraction value of 11.1% was achieved. This value is important because copper extraction from converter slag still occurs, even without stirring the solution. This is mainly due to the leaching solution diffusing throughout the slag via microcracks (pores) [18]. These microcracks are produced by the sudden cooling of the slags in the pyrometallurgical process, when water (at 293 K) makes contact with molten slag (1373 K).
Partially leached samples (0 rpm, 2700 s) were analyzed by BSE, which are shown in Figure 5. It can be seen in this figure that the particles contain a large amount of microcracks in their structure, even subdivided inside them generating a greater amount of porosity in the particle. Thus, the diffusion of the leaching solution through the microcracks by contact with the copper oxides would be allowed.
For future work, the study of more detailed analyzes could be evaluated through the use of techniques such as the B.E.T. (Brunauer, Emmett and Teller), which would allow to determine the specific surface area of the solid.  As can be seen in the figure, a low stirring speed (100 rpm) copper extraction was achieved close to 38.3%. As stirring speed increased, copper extraction increased to 84.8% (at stirring rate 950 rpm). Above 500 rpm, the amount of copper extracted is not highly influenced. This phenomenon is due to the role of mass transfer. Thus, the mass transfer would not be relevant to the flow of ions through the slag particles. It was thus concluded that future experiments would be set at 500 rpm agitation.
It should be noted that working without agitation (0 rpm) an extraction value of 11.1% was achieved. This value is important because copper extraction from converter slag still occurs, even without stirring the solution. This is mainly due to the leaching solution diffusing throughout the slag via microcracks (pores) [18]. These microcracks are produced by the sudden cooling of the slags in the pyrometallurgical process, when water (at 293 K) makes contact with molten slag (1373 K).
Partially leached samples (0 rpm, 2700 s) were analyzed by BSE, which are shown in Figure 5. It can be seen in this figure that the particles contain a large amount of microcracks in their structure, even subdivided inside them generating a greater amount of porosity in the particle. Thus, the diffusion of the leaching solution through the microcracks by contact with the copper oxides would be allowed. For future work, the study of more detailed analyzes could be evaluated through the use of techniques such as the B.E.T. (Brunauer, Emmett and Teller), which would allow to determine the specific surface area of the solid.

Effect of Temperature
The effect of temperature on the leaching rate of converter slag was studied for a range of 283 to 333 K, with NH4OH concentration constant at 0.7 mol/dm 3 , particle size at 64 m and liquid/solid ratio at 1000/1. Figure 6 shows the results of the temperature effect.

Effect of Temperature
The effect of temperature on the leaching rate of converter slag was studied for a range of 283 to 333 K, with NH 4 OH concentration constant at 0.7 mol/dm 3 , particle size at 64 µm and liquid/solid ratio at 1000/1. Figure 6 shows the results of the temperature effect.
As temperature increases, copper extraction is faster. Thus, at time 2700 s and temperature 293 K, copper extraction reached 50%; increasing temperature 1.1 times (323 K), the same extraction was obtained after only 660 s, a reduction of 75.5%.
To determine converter slag leaching mechanisms, samples obtained at a temperature of 298 K, 0.7 mol/dm 3 NH 4 OH and at times of 2700 and 7200 s (i.e., partially and completely leached) were analyzed. Solid samples were analyzed by XRD. Results for both samples (2700 and 7200 s) were similar. Therefore, only analysis performed for the sample obtained at 7200 s are presented in Figure 7.

Effect of Temperature
The effect of temperature on the leaching rate of converter slag was studied for a range of 283 to 333 K, with NH4OH concentration constant at 0.7 mol/dm 3 , particle size at 64 m and liquid/solid ratio at 1000/1. Figure 6 shows the results of the temperature effect. As temperature increases, copper extraction is faster. Thus, at time 2700 s and temperature 293 K, copper extraction reached 50%; increasing temperature 1.1 times (323 K), the same extraction was obtained after only 660 s, a reduction of 75.5%.
To determine converter slag leaching mechanisms, samples obtained at a temperature of 298 K, 0.7 mol/dm 3 NH4OH and at times of 2700 and 7200 s (i.e., partially and completely leached) were analyzed. Solid samples were analyzed by XRD. Results for both samples (2700 and 7200 s) were similar. Therefore, only analysis performed for the sample obtained at 7200 s are presented in Figure  7. Copper compounds can be seen in Figure 7, with strong peaks identifying compound delafossite and a slight presence of cuprite. However, tenorite was not identified in this sample neither metallic copper (Cu). These results indicate that ammonia leaching occurred for oxidized copper species such as Cu2O and CuO as well as for Cu. Conversely and as confirmed by XRD, CuFeO2 was not dissolved by NH4OH. These results are analogous to previous studies [5], in which recoveries over 85% of copper were not possible due to the presence of copper ferrite (CuFeO2), a ferromagnetic ceramic compound which is very difficult to leach due to its refractory properties.

Converter Slag Leach Mechanism
Ammonium hydroxide incorporated into the solution was immediately decomposed down to form an ammonium ion (NH3) and a hydronium ion (H3O + ), following reaction (3). In this and previous work [16,17], it was demonstrated that H3O + is responsible for leaching copper oxides through physical and electrochemical processes, while NH3 created copper complexes to maintain cupric ions in the alkaline solution system (constant dissociation of ammonia = 1.77 × 10 −5 to 298 K).
2θ, degree Copper compounds can be seen in Figure 7, with strong peaks identifying compound delafossite and a slight presence of cuprite. However, tenorite was not identified in this sample neither metallic copper (Cu). These results indicate that ammonia leaching occurred for oxidized copper species such as Cu 2 O and CuO as well as for Cu. Conversely and as confirmed by XRD, CuFeO 2 was not dissolved by NH 4 OH. These results are analogous to previous studies [5], in which recoveries over 85% of copper were not possible due to the presence of copper ferrite (CuFeO 2 ), a ferromagnetic ceramic compound which is very difficult to leach due to its refractory properties.

Converter Slag Leach Mechanism
Ammonium hydroxide incorporated into the solution was immediately decomposed down to form an ammonium ion (NH 3 ) and a hydronium ion (H 3 O + ), following reaction (3). In this and previous work [16,17], it was demonstrated that H 3 O + is responsible for leaching copper oxides through physical and electrochemical processes, while NH 3 created copper complexes to maintain cupric ions in the alkaline solution system (constant dissociation of ammonia = 1.77 × 10 −5 to 298 K).
Therefore, the leaching mechanism for oxide slags (Cu 2 O and CuO) in the presence of ammonium hydroxide is given by the following semi-reactions [16,17]: In the case of the reaction (4), the hydronium ion provides protons necessary for the dissolution of CuO (the dissolution of this compound follows a physical process). Reaction (5), in contrast, has the hydronium ion in an electrochemical process to provide the necessary electrons to generate the oxide/reduction pair (using reaction (6)) and thus dissolve the Cu 2 O.
Copper ions released into the solution (reactions (4) and (5)) are complexed by the ammonium ion to generate copper tetra-amine (Cu(NH 3 ) 4 2+ ) according to reaction (8). It should be noted that the tetra-amine formation process is allowed through previous generation of Cu(NH 3 ) 2 2+ ; however, that ion is thermodynamically unstable in basic systems [13,15].
To corroborate the formation of copper tetra-amine, a Pourbaix stability diagram (E H -pH) was constructed for the Cu-NH 4 OH-H 2 O system for temperature 293 K, copper concentration 0.00236 mol/dm 3 and ammonium hydroxide concentrations of 0.1, 0.35 and 0.7 mol/dm 3 . The thermodynamic data used for the construction of the diagram were extracted from the HSC Chemistry program database [19]. This diagram ( Figure 8) shows that solution pH was preponderant vs. potential in obtaining the copper tetra-amine. Thus, for NH 4 OH concentration 0.1 mol/dm 3 , Cu(NH 3 ) 4 2+ was maintained in solution at pH ranging from 7 to 14 for the entire potential range.
Outside those pH ranges, copper precipitated as an oxide (CuO), decreasing copper concentration in solution and inhibiting further purification/concentration of this metal. Thus pH effect is shown, here, as in Figure 3. In addition, were copper oxide to form, NH 3 consumption (reaction (8)) would stop, NH 4 OH would not decompose and H 3 O + would not be generated (reaction (3)). In short, CuO production directly and negatively affects Cu 2 O and CuO leaching from the slag. Tests with NH 4 OH concentrations (0.35 and 0.70 mol/dm 3 ) show that as concentration of ammonium hydroxide increases, the stability zone of the copper tetra-amine was reduced, yielding for NH 4 OH 0.7 mol/dm 3 a pH range from 8.3 to 13.4. effect is shown, here, as in Figure 3. In addition, were copper oxide to form, NH3 consumption (reaction (8)) would stop, NH4OH would not decompose and H3O + would not be generated (reaction (3)). In short, CuO production directly and negatively affects Cu2O and CuO leaching from the slag.
Tests with NH4OH concentrations (0.35 and 0.70 mol/dm 3 ) show that as concentration of ammonium hydroxide increases, the stability zone of the copper tetra-amine was reduced, yielding for NH4OH 0.7 mol/dm 3 a pH range from 8.3 to 13.4.  The formation of the copper tetra-amine generated an imbalance between reactions (4) and (5) (i.e., Cu 2+ concentration decreased), thus causing a higher dissolution rate for the two copper oxides CuO and Cu 2 O. These two compounds delivered a greater amount of copper ions to the basic solution, given by reactions (9) and (10).
It should be noted that if the concentration of ammonia in the solution is reduced, it could lead to the formation of copper oxide.
On the other hand, metallic copper can be dissolved by hydronium ions (coming from the disiation of NH 4 OH) by an electrochemical process. Then, the dissolution mechanism would be given by the expression 11. Figure 9 shows the results of converter slag copper extraction as a function of NH 4 OH concentration. The working temperature was 298 K; particle size, 64 µm; and liquid/solid ratio, 1000:1.

Effect of NH 4 OH Concentration
The Figure shows that increased concentration of ammonium hydroxide increased dissolution of converter slag. Thus, at concentration of 0.2 mol/dm 3 , 36.1% was obtained at a time of 7200 s; at concentration 0.8 mol/dm 3 , a recovery of 71.3% was obtained after the same amount of time. At the minimum NH 4 OH concentration tested (0.1 mol/dm 3 ), copper extraction was 15.6%. Stoichiometric concentrations from reactions (9) and (10) are calculated at 0.5 and 1.0 mol/dm 3 of NH 4 OH, respectively; however, concentrations 5 to 10 times lower than the above still gave significant copper extractions. Figure 9 shows the results of converter slag copper extraction as a function of NH4OH concentration. The working temperature was 298 K; particle size, 64 m; and liquid/solid ratio, 1000:1.  (9) and (10) are calculated at 0.5 and 1.0 mol/dm 3 of NH4OH, respectively; however, concentrations 5 to 10 times lower than the above still gave significant copper extractions.

Particle Size Analysis
Four different converter slag particle sizes were compared: 64, 90, 127 and 180 µm. Working conditions were similar to previous experiments. The copper extraction curves are given in Figure 10. It is clear that particle size is largely determinant of dissolution rate. For size 180 µm, a recovery of 11.3% was obtained after time 1800 s, while for particle size 64 µm, copper extraction reached 69.9% for the same time. This phenomenon is likely due to two situations, that is, as particle size decreased: 1) useful metal was released from the slag and 2) surface area increased. Four different converter slag particle sizes were compared: 64, 90, 127 and 180 m. Working conditions were similar to previous experiments. The copper extraction curves are given in Figure 10. It is clear that particle size is largely determinant of dissolution rate. For size 180 m, a recovery of 11.3% was obtained after time 1800 s, while for particle size 64 m, copper extraction reached 69.9% for the same time. This phenomenon is likely due to two situations, that is, as particle size decreased-1) useful metal was released from the slag and 2) surface area increased.

Examination of the Solid/liquid Ratio
The ratio between leaching solution and slag was examined with the aim of obtaining the highest copper extraction with the lowest amount of solution. Working conditions were similar to those indicated in the previous points. The amount of solution was varied from 0.1 to 1.4 dm 3 with amount of slag constant at 1 × 10 −3 kg. Results are shown in Figure 11.

Examination of the Solid/liquid Ratio
The ratio between leaching solution and slag was examined with the aim of obtaining the highest copper extraction with the lowest amount of solution. Working conditions were similar to those indicated in the previous points. The amount of solution was varied from 0.1 to 1.4 dm 3 with amount of slag constant at 1 × 10 −3 kg. Results are shown in Figure 11. As the liquid/solid ratio decreased, copper extraction decreased. At 100 dm 3 /kg, an extraction of 9.3% was achieved; at 400 dm 3 /kg, 60.8%. The highest Cu extractions were at ratio 1000 dm 3 /kg, which marks the most efficient reaction between diffusion medium NH4OH and CuO-Cu2O-Cu.

Converter Slag Leaching Kinetics
Although and as previously mentioned, converter slag particles have microcracks, Figure 6 shows that slag leaching could also be described by the intraparticle diffusion model, that is, solution leaching through slag porosity. Assuming that constant reactant concentrations and diffusion rate through porous layer of radius ro, the rate equation, described by the shrinking core model, is given by the following expression [20]: In Equation (11), x CS is the converted (reacted) fraction of the converter slag; apparent rate constant (kapp) is a function of temperature, NH4OH concentration and particle size. Constant kapp is directly related to the intrinsic rate constant of the system, given by expression (13): where k is the intrinsic rate constant, C NH 4 OH n , is the concentration of ammonium hydroxide and n is the reaction order of NH4OH. Finally, ro is the initial radius of the slag particle.
A graph of 1 − 3(1 − x CS ) 2 3 + 2(1 − x CS ) versus time was constructed for the experimental data obtained in Figure 6 for temperature range 283 to 333 K and for particle size 64 m. Results are shown in Figure 12. The same data treatment method was used for the results obtained on the effects of ammonium hydroxide concentration ( Figure 9) and particle size ( Figure 10). As the liquid/solid ratio decreased, copper extraction decreased. At 100 dm 3 /kg, an extraction of 9.3% was achieved; at 400 dm 3 /kg, 60.8%. The highest Cu extractions were at ratio 1000 dm 3 /kg, which marks the most efficient reaction between diffusion medium NH 4 OH and CuO-Cu 2 O-Cu.

Converter Slag Leaching Kinetics
Although and as previously mentioned, converter slag particles have microcracks, Figure 6 shows that slag leaching could also be described by the intraparticle diffusion model, that is, solution leaching through slag porosity. Assuming that constant reactant concentrations and diffusion rate through porous layer of radius r o , the rate equation, described by the shrinking core model, is given by the following expression [20]: In Equation (11), x CS is the converted (reacted) fraction of the converter slag; apparent rate constant (k app ) is a function of temperature, NH 4 OH concentration and particle size. Constant k app is directly related to the intrinsic rate constant of the system, given by expression (13): where k is the intrinsic rate constant, C n NH 4 OH , is the concentration of ammonium hydroxide and n is the reaction order of NH 4 OH. Finally, r o is the initial radius of the slag particle.
A graph of 1 − 3(1 − x CS ) 2 3 + 2(1 − x CS ) versus time was constructed for the experimental data obtained in Figure 6 for temperature range 283 to 333 K and for particle size 64 µm. Results are shown in Figure 12. The same data treatment method was used for the results obtained on the effects of ammonium hydroxide concentration ( Figure 9) and particle size ( Figure 10).
Metals 2020, 10, x FOR PEER REVIEW 13 of 18 Figure 12. Leaching kinetics of converter slag using the data in Figure 6.
The regression lines shown in Figure 12 fit very well to experimental data over the entire temperature range (0.95 > R 2 > 0.99) These results demonstrate the applicability of this kinetic model for diffusion in a porous layer of radius ro (Equation (12)).
Similarly to the above, though to quantify reaction order n, a graph was constructed using kinetic data on the effect of NH4OH concentrations. Results are shown in Figure 13, where experimental data on all ammonium hydroxide concentrations measured fit very well to Equation (12). Afterwards, the slopes of each adjustment were used for Equation (13) and a graph of ln kapp versus ln C NH 4 OH was constructed, with initial particle radius and temperature constant, as shown in Figure 14. The regression lines shown in Figure 12 fit very well to experimental data over the entire temperature range (0.95 > R 2 > 0.99) These results demonstrate the applicability of this kinetic model for diffusion in a porous layer of radius r o (Equation (12)).
Similarly to the above, though to quantify reaction order n, a graph was constructed using kinetic data on the effect of NH 4 OH concentrations. Results are shown in Figure 13, where experimental data on all ammonium hydroxide concentrations measured fit very well to Equation (12). Afterwards, the slopes of each adjustment were used for Equation (13) and a graph of ln k app versus ln C NH 4 OH was constructed, with initial particle radius and temperature constant, as shown in Figure 14. The regression lines shown in Figure 12 fit very well to experimental data over the entire temperature range (0.95 > R 2 > 0.99) These results demonstrate the applicability of this kinetic model for diffusion in a porous layer of radius ro (Equation (12)).
Similarly to the above, though to quantify reaction order n, a graph was constructed using kinetic data on the effect of NH4OH concentrations. Results are shown in Figure 13, where experimental data on all ammonium hydroxide concentrations measured fit very well to Equation (12). Afterwards, the slopes of each adjustment were used for Equation (13) and a graph of ln kapp versus ln C NH 4 OH was constructed, with initial particle radius and temperature constant, as shown in Figure 14.   This figure shows the linear adjustment of the seven kapp values (over the whole NH4OH concentration range) with R 2 of 0.90. Reaction order n was then calculated using slope values, which resulted in a reaction order n of 1.2 for NH4OH concentration in the solution.
Looking at Equation (13), particle radius squared varied inversely with the apparent kinetic constant. To corroborate this relationship, experimental data obtained from Figure 10 were used and adjusted according to Equation (12), yielding Figure 15. Controlled diffusion through porous layer of radius ro (Equation (13)), requires that 1/(ro 2 ) must vary linearly with ln kapp. Figure 16 shows such variation, where it can be seen that the ln kapp data have a very good linear fit to experimental data, R 2 of 0.98, indicating that the heterogeneous kinetic model (Equation (12)) models converter slag dissolution very well. This figure shows the linear adjustment of the seven k app values (over the whole NH 4 OH concentration range) with R 2 of 0.90. Reaction order n was then calculated using slope values, which resulted in a reaction order n of 1.2 for NH 4 OH concentration in the solution.
Looking at Equation (13), particle radius squared varied inversely with the apparent kinetic constant. To corroborate this relationship, experimental data obtained from Figure 10 were used and adjusted according to Equation (12), yielding Figure 15. Controlled diffusion through porous layer of radius r o (Equation (13)), requires that 1/(r o 2 ) must vary linearly with ln k app . Figure 16 shows such variation, where it can be seen that the ln k app data have a very good linear fit to experimental data, R 2 of 0.98, indicating that the heterogeneous kinetic model (Equation (12)) models converter slag dissolution very well.    To calculate the activation energy (Ea), the intrinsic rate constant (modifying Equation (13)) was first calculated using apparent rate constants (given in Figure 11), at temperature range 283 to 333 K, NH4OH concentration 0.7 mol/dm 3 , reaction order n of 1.2 and particle size 67 m (ro = 33.5 m). Table 1 shows the k-values as a function of the temperature range used in this study. To calculate the activation energy (E a ), the intrinsic rate constant (modifying Equation (13)) was first calculated using apparent rate constants (given in Figure 11), at temperature range 283 to 333 K, NH 4 OH concentration 0.7 mol/dm 3 , reaction order n of 1.2 and particle size 67 µm (r o = 33.5 µm). Table 1 shows the k-values as a function of the temperature range used in this study. After the k-values had been obtained, an Arrhenius graph (ln k versus 1/T) was constructed ( Figure 17). A good linear adjustment (R 2 > 0.85) of the ln k data can be appreciated. The calculated activation energy was 42.3 kJ/mol for the temperature range 283 to 333 K, which is a typical value for a particle diffusion model (Equation (12)). Finally, then, the dissolution rate of converter slag in an ammonia system (NH 4 OH) can be represented by the following expression: ( Figure 17). A good linear adjustment (R 2 > 0.85) of the ln k data can be appreciated. The calculated activation energy was 42.3 kJ/mol for the temperature range 283 to 333 K, which is a typical value for a particle diffusion model (Equation (12)). Finally, then, the dissolution rate of converter slag in an ammonia system (NH4OH) can be represented by the following expression: Here, R = 8.314 J/mol / K, ro is given in microns, C NH 4 OH is in mol/dm 3 , t is s, T is Kelvin and k = 2.52 × 10 7 µm 2 ۰mol/(dm 3 ۰s).

Conclusions
Converter slag can be leached with NH4OH at a concentration of 0.7 mol/dm 3 , 298 K, pH 10.5 and agitation of 500 rpm. By increasing the temperature and concentration of ammonium hydroxide and decreasing the particle size, it was possible to obtain a high recovery of copper, reaching a value of 84.8%.
The particles contain a large amount of microcracks in their refractory structure. Thus, the diffusion of the leaching solution through the microcracks making contact with the copper oxides would be allowed. Thus, converter slag leaching can be described by the intraparticle diffusion model because of slag porosity. Here, R = 8.314 J/mol/K, r o is given in microns, C NH 4 OH is in mol/dm 3 , t is s, T is Kelvin and k = 2.52 × 10 7 µm 2 ·mol/(dm 3 ·s).

Conclusions
Converter slag can be leached with NH 4 OH at a concentration of 0.7 mol/dm 3 , 298 K, pH 10.5 and agitation of 500 rpm. By increasing the temperature and concentration of ammonium hydroxide and decreasing the particle size, it was possible to obtain a high recovery of copper, reaching a value of 84.8%. NH 4 OH directly leached copper oxides like Cu 2 O, CuO and Cu but not, however, delafossite (CuFeO 2 ). This was corroborated by XRD analyzes.
The particles contain a large amount of microcracks in their refractory structure. Thus, the diffusion of the leaching solution through the microcracks making contact with the copper oxides would be allowed. Thus, converter slag leaching can be described by the intraparticle diffusion model because of slag porosity.
The model that best represented slag dissolution is given by the following expression: 1 − 3(1 − x CS ) 2 3 + 2(1 − x CS ) = k app t, with calculated activation energy is 42.3 kJ/mol. The reaction order was 1.2 for the concentration of ammonium hydroxide and inversely proportional to the square of the particle radius.

Conflicts of Interest:
The authors declare no conflict of interest.