## 2 Experimental
### The Chemical Reaction Mechanism and an Analysis of the Use of a Dry Battery to Prepare Ferrite  
Waste batteries were used as the raw material to produce Mn-Zn ferrite. The waste batteries and the waste solution form a metallic ion solution, which is neutralized and precipitated using NaOH. After passing through air to allow oxidation and to remove the salt, the product is sintered at a high temperature to produce [Mn\({}_{x}\)Zn\({}_{1-x}\)]Fe\({}_{2}\)O\({}_{4}\) ferrite. MnO\({}_{2}\) in the dry battery and ferrous sulfate and sulfuric acid in the steel acid cleaning waste solution react to form MnO\({}_{4}\), FeSO4 and water. Fe in dry the battery reacts with the FeSO\({}_{4}\) that is dissolved in steel acid cleaning waste solution to form ferrous sulfate, and then forms ferric sulfate and hydrogen. Zn in the dry battery reacts with  
Figure 1: The synthesis of [Mn\({}_{x}\)Zn\({}_{1-x}\)]Fe\({}_{2}\)O\({}_{4}\) ferrite from waste battery.  
sulfuric acid in the steel acid cleaning waste solution to form ZnSO\({}_{4}\) and hydrogen. Finally, Hg in the dry battery reacts with ferrous sulfate in the steel acid cleaning waste solution to form HgSO\({}_{4}\) and ferric sulfate. The formulae for these reactions are:  
\[\mathrm{MnO}_{2}+2\mathrm{FeSO}_{4}+3\mathrm{H}_{2}\mathrm{SO}_{4}\rightarrow \mathrm{MnSO}_{4}+\mathrm{Fe}_{2}(\mathrm{SO}_{4})_{3}+2\mathrm{H}_{2}\mathrm{O}, \tag{1}\]  
\[\mathrm{Fe}+\mathrm{Fe}_{2}(\mathrm{SO}_{4})_{3}\rightarrow 3\mathrm{FeSO}_{4}, \tag{2}\]  
\[\mathrm{Fe}+\mathrm{H}_{2}\mathrm{SO}_{4}\rightarrow\mathrm{FeSO}_{4}+\mathrm{ H}_{2}, \tag{3}\]  
\[\mathrm{Zn}+\mathrm{H}_{2}\mathrm{SO}_{4}\rightarrow\mathrm{ZnSO}_{4}+\mathrm{ H}_{2}. \tag{4}\]  
When the dry battery is dissolved in steel acid cleaning waste solution, four metallic ion solutions that contain sulfate are obtained. Waste iron powder is added into HgSO\({}_{4}\) to displace Hg, and three metallic ion solutions of Mn, Zn and Fe are formed. Based on the stoichiometric ratio, one mole of MnO\({}_{2}\), Fe and Zn requires a total of five moles of acid to dissolve completely. It is generally ensured that the reaction is complete by adding excess acid. NaOH is added to neutralize the sulfate, and the product was precipitated to yield hydroxide.  
\[(1-x)\mathrm{MnSO}_{4}+x\mathrm{ZnSO}_{4}+2\mathrm{FeSO}_{4}+8\mathrm{NaOH} \rightarrow(1-x)\mathrm{Mn}(\mathrm{OH})_{2}+x\mathrm{Zn}(\mathrm{OH})_{2}+2 \mathrm{Fe}(\mathrm{OH})_{2}+4\mathrm{Na}_{2}\mathrm{SO}_{4} \tag{5}\]  
Air is passed over the metal hydroxide to oxidize it and to produce Mn\({}_{1-x}\mathrm{Zn}_{x}\mathrm{Fe}_{2}\mathrm{O}_{4}\). The reaction formula is  
\[(1-x)\mathrm{Mn}(\mathrm{OH})_{2}+x\mathrm{Zn}(\mathrm{OH})_{2}+2\mathrm{Fe}( \mathrm{OH})_{2}\stackrel{{\mathrm{air}}}{{\rightarrow}}\mathrm{ Mn}_{1-x}\mathrm{Zn}_{x}\mathrm{Fe}_{2}\mathrm{O}_{4}+4\mathrm{H}_{2}\mathrm{O}. \tag{6}\]  
An inductively coupled plasma (ICP) was used to measure the metal ion content in the battery solution. There was a large excess of Fe ions so the solution was supplemented with Mn and Zn. The solution was adjusted according to that was required for different Mn-Zn compositions. The entire reaction uses a waste battery and steel acid cleaning waste solution as raw materials, and the battery is dissolved into ionic solution. After the displacement reaction, impurities such as Cu, Hg and Cd in ionic solution are removed and NaOH solution is used to precipitate the metallic ion. Air is passed over the product and heat is introduced to oxidize the metallic solution that carries the OH root, which slowly forms into ferrite with a spinel structure. The recovery rate of useful materials for waste batteries was 83.92 wt %. This method can save the cost of MnO\({}_{2}\), Fe, Zn and Fe raw materials, and solve the problem of waste batteries and waste acid pollution.