Abstract:
The invention relates to apparatuses and methods for increasing energy efficiency and improving membrane robustness in primary metal production. In some aspects, the methods and apparatuses comprise interrupting a first current flow from the cathode to the anode and permitting a second current flow from the anode to the cathode. In some aspects, the methods and apparatuses comprise a solid oxygen ion-conducting membrane disposed in ion-conducting contact with the molten electrolyte, wherein the membrane has an electronic resistance less than about 200 ohms/cm 2

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of and priority to U.S. provisional patent application Ser. No. 61/899,013, filed Nov. 1, 2013, and entitled “Method to Remove Soluble Metal in the Flux (molten salt electrolytes), Increase Process Efficiency and Prevent Membrane Degradation,” the disclosure of which is hereby incorporated by reference in its entirety for all purposes. 
     
    
     GOVERNMENT SUPPORT 
       [0002]    This invention was made with government support under Grant Nos. DE-AR0000412 and DE-EE0005547, awarded by the Department of Energy. The government has certain rights in the invention. 
     
    
       [0003]    All publications, patent applications, patents, and other references mentioned herein are incorporated by reference in their entirety. The patent and scientific literature referred to herein establishes knowledge that is available to those skilled in the art. The issued patents, applications, and other publications that are cited herein are hereby incorporated by reference to the same extent as if each was specifically and individually indicated to be incorporated by reference. In the case of inconsistencies, the present disclosure will prevail. 
       FIELD OF THE INVENTION 
       [0004]    The invention relates to apparatuses and methods for increasing energy efficiency and improving membrane robustness in primary metal production. 
       BACKGROUND OF THE INVENTION 
       [0005]    In electrolytic cells for metal oxide reduction, use of a solid electrolyte, such as stabilized zirconia, between the molten salt and anode removes the anode requirement of anode chemical stability in contact with a molten salt. For reactive metals such as aluminum, magnesium, calcium, sodium, potassium and rare earth metals, the solid electrolyte improves current efficiency considerably by presenting a solid barrier between the metal produced at the cathode and oxidizing gases produced at the anode, preventing back-reaction (see, for example, U.S. Pat. Nos. 5,976,345 and 6,299,742; each herein incorporated by reference in its entirety). The process comprises a solid oxygen ion-conducting membrane (SOM) typically consisting of zirconia stabilized by yttria (YSZ) or other low valence oxide-stabilized zirconia, for example, magnesia- or calcia-stabilized zirconia (MSZ or CSZ, respectively). Operating temperatures between 750-1500° C. are employed for direct electrolysis of a desired oxide. In this process, the oxide is dissolved in a molten salt (e.g. fluoride melt). A cathode is placed in the salt (melt) and the anode is separated from the melt by the oxygen-ion conducting membrane. When the applied electric potential between the electrodes exceeds the dissociation potential of the metal oxide, the metal is reduced at the cathode and the oxygen ions migrate through the membrane and are oxidized at the anode. The anode is chosen to be either a liquid metal or a stable porous electronic ceramic oxide; at low temperature a porous solid metal can work as well. Since the membrane allows only oxygen ions to migrate, the ion cycling is prevented. In addition it is possible to use a reactant such as a carbon or a hydrocarbon source in the anode to decrease the dissociation potential of the oxide and further reduce the electrical energy consumption. The process has been used for producing a variety of metals from their respective oxides, such as: magnesium, aluminum, dysprosium, neodymium, titanium, tantalum, and silicon. 
         [0006]    Molten salt fluxes (such as CaF 2 —MgF 2 —MgO, CaCl 2 —MgCl 2 —CaO, etc.) used in solid oxide membrane (SOM)-based electrolysis process have a finite solubility for metals that are reduced at the cathode (such as Ca, Mg, Al, Dy, etc.) from their respective oxides dissolved in the flux. The soluble metal induces electronic conductivity in the flux; it decreases Faradaic efficiency of the electrolysis process and promotes membrane dissociation and degradation (Eric Gratz: “Solid Oxide Membrane (SOM) Stability in Molten Ionic Flux for the Direct Electrolysis of Magnesium Oxide,” Boston University Ph.D. Thesis, January 2013; herein incorporated by reference in its entirety). In solid oxide membrane (SOM) electrolysis one needs to therefore either lower metal concentration (which lowers electronic conductivity in the flux), or increase the electronic conductivity of the SOM, and lower degradation of the SOM. Lowering the electronic conductivity of the SOM would also increase current efficiency. This application describes a new process and apparatus for increasing the lifetime of the SOM by oxidizing the soluble metal in the flux mostly near the cathode or by increasing the electronic conductivity of the SOM. 
       BRIEF SUMMARY OF THE INVENTION 
       [0007]    In one aspect, a method for reducing a metal oxide comprising: providing a cathode in ion-conducting contact with a molten electrolyte, the molten electrolyte containing a metal oxide; providing an anode in ionic communication with the molten electrolyte; providing a power supply disposed between the cathode and the anode; using the power supply to cause a first current flow from the cathode to the anode, thereby reducing at least a portion of the metal oxide; and from time to time, interrupting the first current flow and electrically coupling the anode and the cathode, thereby permitting a second current flow from the anode to the cathode and thereby oxidizing at least a portion the metal in the molten electrolyte. In some embodiments, the method further comprises providing a solid oxygen ion-conducting membrane disposed to be in ion-conducting contact with the molten electrolyte and in electrical contact with the anode, the solid oxygen ion-conducting membrane separating the anode from the molten electrolyte. 
         [0008]    In another aspect, an apparatus for recovering a metal from a molten electrolyte is provided, comprising: a cathode in ion-conducting contact with the molten electrolyte; an anode in ionic communication with the molten electrolyte; a power supply and a first current switching device disposed between the cathode and the anode, wherein in a first state the first current switching device permits current flow between the anode and the cathode, and wherein in a second state the device interrupts said current flow; and a second current switching device disposed between the cathode and the anode, and disposed in parallel with the power supply and the first current switching device, wherein in a first state the second current switching device permits current flow between the anode and the cathode, and wherein in a second state the second current switching device interrupts said current flow. In some embodiments, the apparatus further comprises a solid oxygen ion-conducting membrane disposed to be in ion-conducting contact with the molten electrolyte; an anode in electrical contact with the solid oxygen ion-conducting membrane, the solid oxygen ion-conducting membrane electrically separating the anode from the molten electrolyte. 
         [0009]    In another aspect, an apparatus is provided comprising: a cathode in ion-conducting contact with the molten electrolyte; a solid oxygen ion-conducting membrane disposed to be in ion-conducting contact with the molten electrolyte, wherein the product of the membrane electronic resistance and its active area is less than about 200 ohms·cm 2 ; an anode in electrical contact with the solid oxygen ion-conducting membrane, the solid oxygen ion-conducting membrane separating the anode from the molten electrolyte; and a power supply disposed between the cathode and the anode. 
         [0010]    In another aspect, a method for recovering metal from a molten electrolyte is provided comprising: providing a cathode in ion-conducting contact with a molten electrolyte, the molten electrolyte containing the metal oxide; providing a solid oxygen ion-conducting membrane disposed to be in ion-conducting contact with the molten electrolyte, wherein the membrane has an electronic resistance less than about 200 ohms/cm 2 ; providing an anode in electrical contact with the solid oxygen ion-conducting membrane, the solid oxygen ion-conducting membrane separating the anode from the molten electrolyte; providing a power supply disposed between the cathode and the anode; and applying a current flow from the cathode to the anode. 
         [0011]    Still other objects and advantages of the invention will become apparent to those of skill in the art from the disclosure herein, which is simply illustrative and not restrictive. Thus, other embodiments will be recognized by the skilled artisan without departing from the spirit and scope of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    The following figures are illustrative only and are not intended to be limiting. 
           [0013]      FIG. 1 . An illustrative embodiment of an equivalent circuit of the SOM process for magnesium production. 
           [0014]      FIG. 2 . An illustrative embodiment of an apparatus for SOM electrolysis with switch A closed and switch B open. 
           [0015]      FIG. 3 . An illustrative embodiment of an apparatus for shorting the anode current collector with the cathode by keeping switch A open and switch B closed. 
           [0016]      FIG. 4 . A simplified equivalent circuit according to an illustrative embodiment of the invention. 
           [0017]      FIG. 5 . The SOM schematic as used in a representative embodiment of a SOM electrolysis according to an illustrative embodiment of the invention. 
           [0018]      FIG. 6 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0019]      FIG. 7 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0020]      FIG. 8 . Voltage versus time plot according to an illustrative embodiment of the invention. 
           [0021]      FIG. 9 . SOM cell impedance between the LSM anodic current collector and the bubbling tube cathode according to an illustrative embodiment of the invention. 
           [0022]      FIG. 10 . PDS between the inert anode current collector and bubbling tube cathode according to an illustrative embodiment of the invention. 
           [0023]      FIG. 11 . Current-time plot from pre-electrolysis at 2 V for 90 mins according to an illustrative embodiment of the invention. 
           [0024]      FIG. 12 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0025]      FIG. 13 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0026]      FIG. 14 . Voltage versus time plot according to an illustrative embodiment of the invention. 
           [0027]      FIG. 15 . Current versus time plot of a first electrolysis according to an illustrative embodiment of the invention. 
           [0028]      FIG. 16 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0029]      FIG. 17 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0030]      FIG. 18 . Potential versus time plot according to an illustrative embodiment of the invention. 
           [0031]      FIG. 19 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0032]      FIG. 20 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0033]      FIG. 21 . Potential versus time plot according to an illustrative embodiment of the invention. 
           [0034]      FIG. 22 . Current versus time plot of a first and second electrolysis according to an illustrative embodiment of the invention. 
           [0035]      FIG. 23 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0036]      FIG. 24 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0037]      FIG. 25 . Potential versus time plot according to an illustrative embodiment of the invention. 
           [0038]      FIG. 26 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0039]      FIG. 27 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0040]      FIG. 28 . Potential versus time plot according to an illustrative embodiment of the invention. 
           [0041]      FIG. 29 . Current versus time plot of all three electrolyses according to an illustrative embodiment of the invention. 
           [0042]      FIG. 30 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0043]      FIG. 31 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0044]      FIG. 32 . Potential versus time plot according to an illustrative embodiment of the invention. 
           [0045]      FIG. 33 . Electrochemical impedance spectroscopy (EIS) according to an illustrative embodiment of the invention. 
           [0046]      FIG. 34 . Current versus time plot according to an illustrative embodiment of the invention. 
           [0047]      FIG. 35 . Potential versus time plot according to an illustrative embodiment of the invention. 
           [0048]      FIG. 36 . Effect of R e(YSZ)  and R e(flux)  on maximum allowable applied potential E MAAP  according to an illustrative embodiment of the invention. 
           [0049]      FIG. 37 . Calculated current efficiency as a function of R e(flux)  for different values of R e(YSZ)  according to an illustrative embodiment of the invention. 
           [0050]      FIG. 38 . Effect of R e(YSZ)  and R e(flux)  on Mg production rate (current causing dissociation of MgO) according to an illustrative embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0051]    As used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the content clearly dictates otherwise. 
         [0052]    The term “about” is used herein to mean approximately, in the region of, roughly, or around. When the term “about” is used in conjunction with a numerical range, it modifies that range by extending the boundaries above and below the numerical values set forth. The term “about” is used herein to modify a numerical value above and below the stated value by a variance of 20%. 
         [0053]    In some embodiments, an electronic conductor is disposed in electrical contact with the anode. In some embodiments, an electronic conductor is disposed in electrical contact with the anode, the first switching device and the second switching device. 
         [0054]    In some embodiments, oxygen is provided to the anode. In some embodiments, the apparatus further comprises second solid oxygen ion-conducting membrane. In some embodiments, oxygen is provided through a second solid oxygen ion-conducting membrane. 
         [0055]    In some embodiments, the first current flow is run from about 3 to about 20 times as long as that of the second current flow. In some embodiments, the first current flow is run from about 3 to about 10 times as long as that of the second current flow. In some embodiments, the first current flow is run from about 3 to about 5 times as long as that of the second current flow. In some embodiments, the first current flow is run about 3 times as long as that of the second current flow. 
         [0056]    In some embodiments, the second current flow is run for about 1 second to about 30 seconds. In some embodiments, the second current flow is run for about 1 second to about 60 seconds. In some embodiments, the second current flow is run for about 10 seconds to about 60 seconds. In some embodiments, the second current flow is run for about 30 seconds to about 60 minutes. In some embodiments, the second current flow is run for about 30 seconds to about 30 minutes. In some embodiments, the second current flow is run for about 30 seconds to about 15 minutes. In some embodiments, the second current flow is run for about 30 seconds to about 5 minutes. In some embodiments, the second current flow is run for about 30 minutes to about 60 minutes. In some embodiments, the second current flow is run for about 30 minutes to about 30 minutes. In some embodiments, the second current flow is run for about 30 minutes to about 15 minutes. In some embodiments, the second current flow is run for about 30 minutes to about 5 minutes. 
         [0057]    In some embodiments, the product of membrane electronic resistance and its active area is less than about 200 ohms·cm 2 . In some embodiments, the product of membrane electronic resistance and its active area is less than about 150 ohms·cm 2 . In some embodiments, the product of membrane electronic resistance and its active area is less than about 50 ohms·cm 2 . In some embodiments, the product of membrane electronic resistance and its active area is less than about 20 ohms·cm 2 . In some embodiments, the product of membrane electronic resistance and its active area is less than about 10 ohms·cm 2 . In some embodiments, the product of membrane electronic resistance and its active area is less than about 5 ohms·cm 2 . In some embodiments, the product of membrane electronic resistance and its active area is between about 2 and about 5 ohms·cm 2 . In some embodiments, the product of membrane electronic resistance and its active area is between about 3 and about 4 ohms·cm 2 . 
         [0058]    In some embodiments, the solid oxygen ion-conducting membrane has a corrosion rate of less than about 1 micron per hour at current density of at least 0.1 amperes/sq. cm and at temperatures greater than about 700° C. In some embodiments, the solid oxygen ion-conducting membrane has a corrosion rate of less than about 0.5 micron per hour at current density of at least 0.1 amperes/sq. cm and at temperatures greater than about 700° C. 
         [0059]    In some embodiments, the solid oxygen ion-conducting membrane comprises a two-phase material. In some embodiments, the two-phase material is a two-phase oxide. In some embodiments, the two-phase material comprises cerium and strontium. In some embodiments, the two-phase material comprises samarium-doped cerium oxide, gadolinium-doped cerium oxide, samarium-doped zirconium oxide, or gadolinium-doped zirconium oxide. In some embodiments, the two-phase material comprises samarium-doped cerium oxide, or gadolinium-doped cerium oxide. In some embodiments, the two-phase material comprises samarium-doped zirconium oxide, or gadolinium-doped zirconium oxide. 
         [0060]    In some embodiments, the metal oxide comprises an oxide of magnesium, aluminum, silicon, calcium, titanium, copper, tantalum or a rare earth. In some embodiments, the metal oxide comprises magnesium oxide. 
         [0061]    In some embodiments, the molten electrolyte comprises a metal oxide. In some embodiments, the metal oxide comprises and oxide of magnesium, aluminum, silicon, calcium, titanium, copper, tantalum or a rare earth. In some embodiments, the metal oxide comprises and oxide of magnesium, aluminum, silicon, calcium, titanium, copper, or tantalum. In some embodiments, the metal oxide comprises and oxide of magnesium, aluminum, silicon, calcium, titanium, or copper. In some embodiments, the metal oxide comprises and oxide of magnesium, aluminum, or silicon. In some embodiments, the metal oxide comprises and oxide of magnesium or aluminum. In some embodiments, the metal oxide comprises aluminum oxide. In some embodiments, the metal oxide comprises magnesium oxide. 
         [0062]    In some embodiments, the apparatus further comprises an electrode disposed in ion-conducting contact with the molten electrolyte and not in physical contact with the cathode. 
         [0063]    In some embodiments, the current switching devices are independently selected from the group consisting of knife switches, relays, solid state relays, and sliding contacts. 
         [0064]    In some embodiments, the apparatus further comprises a control system for adjusting the first current switching device between the first state and the second state, and adjusting the second current switching device between the first state and the second state. 
         [0065]    In some embodiments, the solid oxygen ion-conducting membrane comprises zirconia, ceria, or copper oxide. In some embodiments, the solid electrolyte comprises zirconia or ceria. In some embodiments, the solid electrolyte comprises zirconia. In some embodiments, the solid electrolyte comprises ceria. In some embodiments, the solid oxygen ion-conducting membrane comprises copper oxide. 
         [0066]    In some embodiments, the solid oxygen ion-conducting membrane is doped with an n-type oxide. In some embodiments, the solid electrolyte comprises zirconia or ceria doped with an n-type oxide. In some embodiments, the solid electrolyte comprises zirconia doped with an n-type oxide. In some embodiments, the solid electrolyte comprises ceria doped with an n-type oxide. In some embodiments, the n-type oxide comprises CoO, MnO, Fe 2 O 3 , CeO 2 , TiO 2 , or Pr 2 O 3 . In some embodiments, the n-type oxide comprises Fe 2 O 3 . Other exemplary n-type oxides are found in T. Colomer and J. R. Jurado, “Mixed Conduction Mechanism in ZrO 2 —Y 2 O3-TiO 2 ”, Proceedings of the Second International Symposium on Ionic and Mixed, edited by T. A. Ramanarayanan, Wayne L. Worrell, Harry L. Tuller, p. 369, 1994, ECS Publication; herein incorporated by reference in its entirety. In some embodiments, the solid oxygen ion-conducting membrane is doped with an oxide of cobalt, manganese, iron, cerium, titanium, or praseodymium. In some embodiments, the solid oxygen ion-conducting membrane is doped with an oxide of cobalt, manganese, iron, cerium, or titanium. In some embodiments, the solid oxygen ion-conducting membrane is doped with an oxide of cobalt, manganese, iron, cerium, or titanium. 
         [0067]    In some embodiments, the solid oxygen ion-conducting membrane is doped with an oxide of lithium, sodium or potassium. In some embodiments, the solid electrolyte comprises zirconia doped with an alkali oxide such as Li 2 O, Na 2 O or K 2 O, which increase electronic conductivity as described in Y. Isobe, M. Fuse and K. Kobayashi, “Additive Element Effects on Electronic Conductivity of Zirconium Oxide Film,”  J. Nuc Sci Tech  81(6):546-551, 1994; herein incorporated by reference in its entirety. 
         [0068]    In some embodiments, the solid electrolyte further comprises an oxide such as, for example, gadolinium oxide or samarium oxide as dopants for ceria. In some embodiments, the solid electrolyte comprises copper oxide, for example in yttrium barium copper oxide (YBa 2 Cu 3 O 7 ), which has very high oxygen ion and electronic conductivity as described in W. Carrillo-Cabrera, H. D. Wiemhöfer and W. Göpel, “Ionic Conductivity of Oxygen Ions in YBa 2 Cu 3 O 7-x   ,” Solid State Ionics  32/33:1172-1178 (1989); herein incorporated by reference in its entirety. 
         [0069]    In some embodiments, the solid electrolyte comprises a two-phase material, in which one phase has high oxygen ion conductivity and the other has high electronic conductivity. In some embodiments, the two-phase material is a two-phase oxide. In some embodiments, the two-phase oxide comprises ceria in the oxygen ion conductor. In some embodiments, the two-phase oxide comprises strontium titanate in the electronic conductor. In some embodiments, the two-phase oxide comprises zirconia in the ionic conductor, for example in yttria-stabilized zirconia. In some embodiments, the two-phase oxide comprises manganese oxide in the electronic conductor, for example in a mixture of yttria-stabilized zirconia and strontium-doped lanthanum manganite (LSM). In some embodiments, the two-phase oxide comprises tin oxide or zinc oxide in the electronic conductor. In some embodiments, the two-phase material comprises a metal in the electronic conductor. In some embodiments, the two-phase material comprises liquid silver in the electronic conductor. 
         [0070]    Development of the solid oxide membrane (SOM) electrolysis process has provided an alternative method for refinement of metal oxides (see, e.g, U.S. Pat. Nos. 5,976,345, and 6,299,742; each herein incorporated by reference in its entirety). The process as applied to metal production consists of a metal cathode, a molten salt electrolyte bath that dissolves the metal oxide that is in electrical contact with the cathode, a solid electrolyte oxygen ion conducting membrane (SOM) typically consisting of zirconia stabilized by yttria (YSZ) or other low valence oxide-stabilized zirconia, for example, magnesia- or calcia-stabilized zirconia (MSZ or CSZ, respectively) in ion-conducting contact with the molten salt bath, an anode in ion-conducting contact with the SOM, and a power source for establishing a potential between the cathode and anode. Because it has been used most often in development of the SOM process, in this disclosure, YSZ is often used as short hand to describe any solid electrolyte used as an oxygen ion conducting membrane between the liquid electrolyte and anode. 
         [0071]    During SOM electrolysis, the desired metal is produced at the cathode and depending on its solubility some of it also dissolves in the flux. The process of metal dissolution begins to induce electronic conductivity in the flux and the current (process) efficiency begins to fall. Current efficiency is defined as the ratio of faradic current to total current or the fraction of total current used for metals production. In other words, the process efficiency is: 
         [0000]    
       
         
           
             
               
                 
                   
                     Total 
                      
                     
                         
                     
                      
                     moles 
                      
                     
                         
                     
                      
                     of 
                      
                     
                         
                     
                      
                     metal 
                      
                     
                         
                     
                      
                     produced 
                     × 
                     valence 
                      
                     
                         
                     
                      
                     of 
                      
                     
                         
                     
                      
                     the 
                      
                     
                         
                     
                      
                     metal 
                     × 
                   
                 
               
               
                 
                   
                     Faraday 
                      
                     
                         
                     
                      
                     Constant 
                   
                 
               
             
             
               Total 
                
               
                   
               
                
               Integral 
                
               
                   
               
                
               of 
                
               
                   
               
                
               Current 
                
               
                   
               
                
               over 
                
               
                   
               
                
               Time 
             
           
         
       
     
         [0072]    The numerator in the above expression is the Faradaic Current or the Current equivalent of the metal produced. During electrolysis, it is possible to determine the rate of actual metal produced by analyzing and measuring the output rate of the anodic product gas. Thus, current or process efficiency can be monitored during electrolysis. Process electrical energy usage is approximately inversely proportional to current efficiency; for example, a process with 80% current efficiency uses approximately 9/8 times as much electrical energy as a process with 90% current efficiency. In an actual electrolytic process, as the metal dissolves in the flux it increases its electronic conductivity and, as a result, the electronic (non-faradaic) portion of the total current increases, which in turn decreases the process efficiency. In addition to the decrease in the process efficiency, the membrane also begins to dissociate because the flux with electronic conductivity acts as an extension of the cathode and dissociates the zirconia. This is explained herein using an equivalent circuit and applying it to the membrane-based electrolysis of MgO as an example, though this can apply to reduction of many other oxides, illustratively (but not exclusively) including Al 2 O 3 , SiO 2 , CaO, TiO 2 , CuO, Ta 2 O 5 , and rare earth oxides. 
         [0073]    Zirconia-Membrane-Based Electrolysis of MgO: In the SOM electrolysis, the oxides that could be dissociated include Fe 2 O 3  (from the reaction chamber), ZrO 2 , and MgO when an electric potential of ˜3V is applied between the inert anode current collector and the cathode. The standard Nernst potential for Fe 2 O 3 , ZrO 2 , and MgO dissociations during SOM electrolysis with an inert anode current collector were calculated using Equation 1, and the values are shown in Table 1. In Equation 1, E N   0  is the standard Nernst potential, ΔG N   0  is the standard Gibbs free energy of the reaction, n is the number of electrons per mole of oxide dissociated, and F is the Faraday constant (96,485 C mol −1 ). The standard Gibbs free energy change values were obtained from HSC Chemistry 5.11™ Database (A. Roine, “HSC Chemistry 5.11.” 2002; herein incorporated by reference in its entirety). 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     N 
                     0 
                   
                   = 
                   
                     
                       - 
                       
                         ΔG 
                         N 
                         0 
                       
                     
                     
                       n 
                        
                       
                           
                       
                        
                       F 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Standard Nernst potentials for relevant SOM reactions at 1150° C. 
               
             
          
           
               
                 Reaction 
                 Temperature (K) 
                 ΔG N   0  (kJ) 
                 n 
                 E N   0  (V) 
               
               
                   
               
             
          
           
               
                 Fe 2 O 3  →2Fe + 3/2O 2 (g) 
                 1423 
                 454 
                 6 
                 −0.784 
               
               
                 MgO →Mg(g) + 1/2O 2 (g) 
                 1423 
                 439 
                 2 
                 −2.275 
               
               
                 ZrO 2  →Zr + O 2 (g) 
                 1423 
                 831 
                 4 
                 −2.153 
               
               
                   
               
             
          
         
       
     
         [0074]    As shown in Table 1, the absolute value of the standard Nernst potential for Fe 2 O 3  dissociation is much smaller than those for MgO and ZrO 2 ; that is, the dissociation of Fe 2 O 3  is the most favorable, assuming that all the three species behave ideally and given the same anode conditions in the SOM process. In actual SOM experiments, the dissociation of Fe 2 O 3 , and/or other more electronegative impurities such as SiO 2 , Cr 2 O 3 , and Al 2 O 3 , contributes to the leakage current. A pre-electrolysis is usually performed to dissociate these oxides by applying a DC electric potential, higher than their dissociation potentials but lower than the dissociation potential of MgO. 
         [0075]    From Table 1, the dissociation of ZrO 2  is more favorable than the dissociation of MgO, assuming that both species behave ideally and given the same anode conditions in the SOM process. During the SOM process, however, the YSZ membrane is protected from electrochemical ZrO 2  dissociation due to the electric potential drop across the flux. Even when the flux has some electronic conductivity, the electric potential drop across the flux is such that the zirconia does not experience the full applied potential across the entire electrolysis cell. However, if the electronic conductivity in the flux and the applied potential across the electrolysis cell are both sufficiently high, then the potential drop across the YSZ membrane can be large enough to dissociate the zirconia. 
         [0076]    Equivalent Circuit of the SOM Electrolysis Process: Based on current understanding of the SOM electrolysis process, an equivalent circuit of the SOM electrolysis process is presented as shown in  FIG. 1 . The symbols used in  FIG. 1  are defined in Table 2. 
         [0000]    
       
         
               
             
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Definitions of symbols in the SOM 
               
               
                 equivalent circuit shown in FIG. 1. 
               
             
          
           
               
                 Symbol 
                 Definition 
               
               
                   
               
               
                 R i(YSZ)   Fe     2     O     3     
                 Ionic resistance of YSZ membrane involved for Fe 2 O 3   
               
               
                   
                 dissociation 
               
               
                 R i(YSZ)   MgO   
                 Ionic resistance of YSZ membrane involved for MgO 
               
               
                   
                 dissociation 
               
               
                 R i(YSZ)   ZrO     2     
                 Ionic resistance of YSZ membrane involved for ZrO 2   
               
               
                   
                 dissociation 
               
               
                 R i(flux)   Fe     2     O     3     
                 Ionic resistance of flux (between the YSZ membrane and 
               
               
                   
                 the cathode) involved for Fe 2 O 3  dissociation 
               
               
                 R i(flux)   MgO   
                 Ionic resistance of flux (between the YSZ membrane and 
               
               
                   
                 the cathode) involved for MgO dissociation 
               
               
                 R mt(a, c)   Fe     2     O     3     
                 Mass transfer resistance at the anode and cathode for Fe 2 O 3   
               
               
                   
                 dissociation 
               
               
                 R mt(a, c)   MgO   
                 Mass transfer resistance at the anode and cathode for MgO 
               
               
                   
                 dissociation 
               
               
                 R ct(a, c)   Fe     2     O     3     
                 Charge transfer resistance at the anode and cathode 
               
               
                   
                 for Fe 2 O 3  dissociation 
               
               
                 R ct(a, c)   MgO   
                 Charge transfer resistance at the anode and cathode 
               
               
                   
                 for MgO dissociation 
               
               
                 R ct(a, c)   ZrO     2     
                 Charge transfer resistance at the anode and cathode 
               
               
                   
                 for ZrO 2  dissociation 
               
               
                 R e(YSZ)   
                 Electronic resistance of the YSZ membrane 
               
               
                 R e(flux)   
                 Electronic resistance of the flux between the YSZ 
               
               
                   
                 membrane and the cathode 
               
               
                 R cc   
                 Resistance of the anode current collector 
               
               
                 R ex   
                 Resistance of external circuit elements 
               
               
                 E N   Fe     2     O     3     
                 Nernst potential for Fe 2 O 3  dissociation 
               
               
                 E N   MgO   
                 Nernst potential for MgO dissociation 
               
               
                 E N   ZrO     2     
                 Nernst potential for ZrO 2  dissociation 
               
               
                 E applied   
                 Applied potential 
               
               
                 I i   Fe     2     O     3     
                 Ionic current for Fe 2 O 3  dissociation 
               
               
                 I i   MgO   
                 Ionic current for MgO dissociation 
               
               
                 I i   ZrO     2     
                 Ionic current for ZrO 2  dissociation 
               
               
                 I e(YSZ)   
                 Electronic current passing the YSZ membrane 
               
               
                 I T   
                 Total current 
               
               
                   
               
             
          
         
       
     
         [0077]    The equivalent circuit ( FIG. 1 ) first shows that impurity oxides with greater cation electronegativity than magnesium (such as Fe 2 O 3 ), will dissociate before MgO. A pre-electrolysis is usually conducted to remove the Fe 2 O 3 . After the pre-electrolysis, an electric potential exceeding the dissociation potential of MgO is applied. Once the MgO dissociates, magnesium is produced at the cathode. Some of the magnesium produced dissolves in the flux, and at the operating temperature of 1150° C., the rest evolves as vapor and is carried away by the forming gas or argon. The dissolved magnesium subsequently increases the electronic conductivity of the flux. The YSZ membrane has electronic conductivity at the operating temperature and the other prevailing experimental conditions. A flux with electronic conductivity essentially serves as an extended cathode, and it allows for electronic current to pass through the flux and the membrane, decreasing the current efficiency. If the flux had no electronic conductivity, then the current passing through the flux would be purely ionic, and all of the current input to the cell would be used in the process of dissociating MgO. 
         [0078]    The presence of an electronic current acts as an internal short circuit in the SOM process. As more magnesium dissolves into the flux, the electronic conductivity of the flux will further increase. The increased electronic conductivity also decreases the electronic potential drop across the flux (since R e(flux)  decreases), and then the potential drop across the YSZ membrane will correspondingly increase while a constant DC electric potential is applied across the entire cell. The increased potential drop across the YSZ can cause the dissociation of zirconia, which will degrade the YSZ membrane. To avoid ZrO 2  dissociation, the electronic potential drop across the YSZ membrane should not exceed the dissociation potential of ZrO 2 . Maintaining high R e(flux)  by removing dissolved magnesium from the flux can thus be used to enhance zirconia stability. Furthermore, it is also evident from the equivalent circuit that if the electronic resistance of the YSZ (R e(YSZ) ) decreases, the total resistance and the potential drop across the entire membrane will decrease. This strategy can also be used to enhance zirconia stability. 
         [0079]    Method and apparatus for Removing Soluble Metallic Magnesium in the Flux to Increase R e(flux) : A method of removing the magnesium dissolved in the flux is presented.  FIGS. 2 and 3  show the schematics for the process. The apparatus comprises a reaction chamber ( 101 ) containing a molten flux ( 102 ). During electrolysis, switch A ( 103 ) is closed, and switch B ( 104 ) is open ( FIG. 2 ). Potential from a power supply ( 105 ) is applied between the inert oxygen anode current collector ( 106 ) containing liquid silver ( 107 ) inside the YSZ membrane ( 108 ) and the cathode ( 109 ) to dissociate MgO in the flux. Magnesium will be produced at the cathode and oxygen at the anode ( FIG. 2 ). The SOM process has been shown to have high current efficiencies at the beginning because there is no dissolved magnesium and the flux is essentially ionic. However, as the process runs and produces metallic magnesium, that magnesium dissolves, and the current efficiency drops significantly due to electronic current in the flux caused by the increase in the dissolved metallic magnesium. In order to improve the current efficiency, the inert oxygen anode current collector inside the YSZ membrane can be electrically shorted with the cathode by opening switch A and closing switch B ( FIG. 3 ). The P O     2    above the liquid silver anode encased within the YSZ membrane is around 1 atm, much greater than the P O     2    in the flux; this difference in P O     2    drives oxygen ions to flow from the silver to the flux. However, without shorting, there is no current path to provide electrons to oxygen atoms to convert them to ions, nor to remove electrons from the metallic magnesium dissolved in the flux. 
         [0080]    With each shorting, the oxygen dissolved in the liquid silver will reduce their valence to become oxygen ions, which will migrate through the YSZ tube and oxidize the soluble metallic magnesium at the cathode/flux interface ( FIG. 3 ). The half-cell reactions involved and the overall reaction are shown below (Equations 2-4). 
         [0000]      Liquid silver anode/YSZ interface: O(Ag)+2 e   − →O 2−   (Eq. 2)
 
         [0000]      Cathode/flux interface: O 2− +Mg(flux)→MgO(flux)+2 e   −   (Eq. 3)
 
         [0000]      Overall reaction: Mg(flux)+O(Ag)→MgO(flux)  (Eq. 4)
 
         [0081]    This will reduce the concentration of the soluble metallic magnesium near the cathode/flux interface (increase the electronic resistance of the flux and decrease the electronic transference number), and thereby increase the current efficiency of the subsequent electrolysis. Therefore a programmed periodic interruption of the electrolysis and shorting of the electrodes will remove the dissolved magnesium from near the cathode by oxidizing it back to MgO and thereby create an electron blocking layer near the cathode/flux interface, which will aid in increasing the process efficiency and prevent zirconia dissociation/degradation. 
         [0082]    In this system, there is a minimum and maximum useful time for shorting the cell. The maximum useful time is established by the lower of the oxygen availability at the anode, or the dissolved magnesium content in the flux. That is, if one opens switch A and closes switch B for a longer time than is necessary to oxidize all of the dissolved metal in the flux, this would release excess oxygen into the flux and reduction chamber. This excess oxygen could oxidize metals such as iron in contact with the flux, or could enter the gas phase and oxidize product metal elsewhere. 
         [0083]    Similarly, if all of the available oxygen at the anode leaves through the zirconia as described above, then the magnesium in the flux can create a driving force for extracting oxygen from the zirconia itself, damaging the membrane. For this reason, some embodiments of the invention would provide addition of oxygen to the anode. Some embodiments would add one or more SOM tubes to the flux, and provide additional oxygen for oxidizing metal through that tube or set of tubes. 
         [0084]    The minimum useful time is established by the quantity of product metal, such as magnesium bubbles, in electrical connection to the cathode-flux interface. When the dissolved metal is depleted, the shorting current falls to zero. In some embodiments, re-oxidation of at least a portion of attached metal and at least a portion, but not all, of dissolved metal is advantageous. Shorting the cell will likely lead to oxidation of that cathode-connected metal before metal dissolved in the flux, as cathode-connected metal is likely at higher activity. Therefore, it is particularly advantageous to operate with switch A open and switch B closed for longer than the time required to oxidize cathode-attached metal, in order to oxidize dissolved metal, and then oxidize metal in the flux in order to increase R e(flux) . 
         [0085]    In some embodiments, the minimum useful time for shorting is on the order of 1-30 seconds, and the maximum useful time is on the order of 1-60 minutes. In some embodiments, the minimum useful time for shorting is on the order of 10-30 seconds, and the maximum useful time is on the order of 1-60 minutes. Furthermore, brief shorting time leads to high process utilization, but relatively little dissolved metal oxidation. In addition, long electrolysis time, leading to low R e(flux) , would result in low process efficiency and likely partial reduction of the zirconia SOM. Therefore, optimal operation may involve alternately shorting the cell (with switch A open and B closed) for just above the minimum useful time as described above, and running electrolysis (with switch A closed and B open) for some multiple of this minimum useful shorting time, illustratively 3-20 times as long as the minimum useful shorting time. In some embodiments, electrolysis is run 1-20 times as long as shorting time. In some embodiments, electrolysis is run 3-20 times as long as shorting time. In some embodiments, electrolysis is run 1-10 times as long as shorting time. In some embodiments, electrolysis is run 3-10 times as long as shorting time. In some embodiments, electrolysis is run 1-10 times as long as shorting time. In some embodiments, electrolysis is run 1-5 times as long as shorting time. 
         [0086]    The shorting process changes the initial roles of the anode and cathode in the electrolytic process, which is appreciated by those of ordinary skill in the art. 
         [0087]    This consideration regarding cathode-attached metal means that useful operation of this mechanism requires that only a relatively small amount of product metal be in contact with the cathode. For example, if a solid metal is produced at the cathode, then that metal will likely all oxidize before oxidizing metal in the flux. This would dramatically reduce the current efficiency of the cell. Likewise, if a liquid metal is produced at the cathode while switch A is closed and B is open, one would need to remove most or all of that liquid metal product away from contact with either the cathode or flux before opening switch A and closing switch B, in order to avoid re-oxidizing large amounts of product metal before oxidizing metal dissolved in the flux. For example, rare earth production cells often use a cathode which enters the cell from the top, and the metal produced on the cathode drips downward off of the cathode and falls to a collection well or cup below the cathode. This effectively separates most of the liquid metal product away from electrical contact with the cathode, such that short circuiting would first oxidize the small amount of product metal at the cathode, then would oxidize dissolved metal in the flux, but the large majority of the product metal in the collection well would not be oxidized. 
         [0088]    Lowering of the electronic resistance of YSZ (R e(YSZ) ) to increase membrane stability: It is to be noted that lowering of the electronic resistance advantageously should not impact the low ionic (oxygen ion) resistance of the membrane, and the material is advantageously stable under reducing conditions that exist in the SOM reactor. Such a membrane might involve doping n-type oxides to zirconia such as CoO, MnO, Fe 2 O 3 , CeO 2 , TiO 2 , Pr 2 O 3 , etc. (T. Colomer and J. R. Jurado, “Mixed Conduction Mechanism in ZrO 2 —Y 2 O 3 —TiO 2 ”, Proceedings of the Second International Symposium on Ionic and Mixed, edited by T. A. Ramanarayanan, Wayne L. Worrell, Harry L. Tuller, p. 369, 1994, ECS Publication; herein incorporated by reference in its entirety). One might also use an entirely different membrane material, such as one based on ceria, for example ceria doped with gadolinia or samaria, which has comparable or higher oxygen ion conductivity to zirconia but much higher electronic conductivity (lower electronic resistance) than zirconia. For zirconia-based or ceria-based membrane materials, one might use an alkali oxide dopant such as Li 2 O, Na 2 O or K 2 O, which increase electronic conductivity as described in Y. Isobe, M. Fuse and K. Kobayashi, “Additive Element Effects on Electronic Conductivity of Zirconium Oxide Film,”  J. Nuc Sci Tech  81(6):546-551, 1994; herein incorporated by reference in its entirety. Alternatively, one may employ two-phase material, such as a two-phase oxide, one phase promoting oxygen conduction and the other promoting electronic conduction. An example could include a composite of ceria and strontium titanate. The former would promote oxygen ion conduction with some electronic conduction and the later will promote electronic conduction. These oxides may be doped with other oxides such as those of gadolinium or samarium to further enhance their respective transport properties. List of possible materials having these properties are available in the literature (S. Gopalan, U. B. Pal, A. Karthikeyan, and H. Cui, “Composite Mixed Oxide Ionic and Electronic Conductors for Hydrogen Separation,” U.S. Pat. No. 7,588,626; herein incorporated by reference in its entirety). The two-phase material may use a metal as the electronic conductor, for example liquid silver can infiltrate a porous oxide ion conductor. 
         [0089]    Estimating threshold membrane conductivity:  FIG. 4  shows the equivalent circuit of  FIG. 1 , but simplified to remove the mixed ionic-electronic current labeled I i   ZrO2 . If the potential in the electronic circuit across the zirconia is below its dissociation potential E N   ZrO2 , then the current I i   ZrO2  will be zero, resulting in the equivalent circuit shown in  FIG. 4 . This condition will prevent the degradation of zirconia, resulting in much longer lifetime of the membrane. This condition also greatly simplifies analysis, as the equivalent circuit of  FIG. 4  is much simpler than that of  FIG. 1 . It should be noted that “zirconia” here is used in an illustrative manner; if the membrane comprises ceria then its dissociation potential should be used in place of zirconia, likewise with copper oxide or other oxide ion conducting membrane materials. 
         [0090]    Typical silicon or aluminum cells operate at 3-4 V total voltage (E applied ), magnesium or rare earth cells operate at 4-6 V. The external resistance labeled R cc  is about 0.4-0.8 V. The net potential range across the flux and membrane electronic resistances is therefore 2.2-3.6 V in silicon or aluminum cells, 3.2-5.6 V in magnesium or rare earth cells. A goal is to operate at 0.3-1 A/cm 2  current density at the anode. Subtracting a representative target metal dissociation potential of 2 V from the operating voltage ranges, and dividing by target anode current density, leads to ionic product of total resistance and anode area in the range of 0.2-5.3 Ω·cm 2  for silicon or aluminum, 1.2-12 Ω·cm 2  for magnesium or rare earths. Assuming about half of this value is in the flux leads to flux ionic resistance-area product R i(flux)  of 0.1-2.7 Ω·cm 2  for silicon or aluminum, 0.6-6 Ω·cm 2  for magnesium or rare earths. 
         [0091]    Typical electronic transference number is very low in aluminum and silicon cells, around 0.1-0.03, that is, 90-97% of the current is productive ionic current. In magnesium or rare earth cells, that number can be as low as 0.3-0.5. This means that flux electronic resistance is about 9-30 times higher than ionic resistance for silicon or aluminum, about 1-2 times higher in magnesium or rare earths. The product of flux electronic resistance and anode area is thus in the range 0.9-86 for aluminum or silicon, and 0.2-9.3 for magnesium or rare earths. This and the range of in-cell voltages gives electronic current density in the range of 0.025-4 A/cm 2  for aluminum or silicon, 0.22-9.3 for magnesium or rare earths. 
         [0092]    With this electronic current density at the anode, keeping the zirconia or other membrane material overpotential below its dissociation potential, illustratively 2.15 V for zirconia, requires that the product of membrane electronic resistance and anode area R e(YSZ) ·A be below about 0.5-85 Ω·cm 2  for aluminum or silicon, about 0.2-9.4 for magnesium or rare earths. An advantageous product is therefore less than about 200 Ω·cm 2 , with 20 Ω·cm 2  being particularly advantageous. 
         [0093]    It will be recognized that one or more features of any embodiments disclosed herein may be combined and/or rearranged within the scope of the invention to produce further embodiments that are also within the scope of the invention. 
         [0094]    Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. Such equivalents are also intended to be within the scope of the present invention. 
       EXAMPLES 
       [0095]    The examples provided below facilitate a more complete understanding of the invention. The following examples illustrate exemplary modes of making and practicing the invention. However, the scope of the invention is not limited to specific embodiments disclosed in such examples, which are illustrative only, since alternative methods can be utilized to obtain similar results. 
       Example 1 
       [0096]    A SOM electrolysis experiment was performed to demonstrate the feasibility of removing the soluble magnesium in the flux by shorting the circuit. The experimental setup employed was as described in  FIGS. 2 and 3 . The SOM schematic is shown in  FIG. 5 . The reaction chamber ( 501 ) contains flux ( 502 ), the inert anode current collector ( 506 ), a liquid silver anode ( 507 ), which are disposed in the YSZ SOM ( 508 ), alumina spacers ( 510 ), a venting tube ( 511 ) and a bubbling tube ( 512 ) (See, e.g., U.S. Patent Publication No. 2013/0192998; herein incorporated by reference in its entirety). The reaction chamber is disposed above a condensing chamber ( 513 ) (See, e.g., U.S. Patent Publication No. 2013/0152734; herein incorporated by reference in its entirety). Flow rates in cc/min are as follows: stirring tube—180, stirring tube annulus—300, SOM annulus—0, current collector—20. The flux was 470 g, composed of (45 w % MgF 2 -55 w % CaF 2 )-5 w % MgO-2 w % YF 3 . Hot zone temperature was 1150° C. Periodic shorting the circuit was performed to remove soluble Mg from the flux. It used a ¼″ stainless steel tube to bubble argon-5% hydrogen forming gas through the flux at 180 SCCM flow rate. The starting magnesium oxide concentration in the flux was 5 wt %. 
         [0097]    At the beginning of the SOM experiment, the electronic transference number of the flux was measured to be 0.032, indicating the flux conductivity was dominated by ionic species. The measurement procedure involves measuring the total resistance between the bubbling tube electrode (cathode) and the steel crucible (anode) employing Electrochemical Impedance Spectroscopy (EIS) and then measuring the DC electronic resistance between the same electrodes by applying a very small potential between the electrodes.  FIG. 6  shows the EIS plot indicating total resistance. R flux,T =0.222Ω.  FIG. 7  shows the current versus time plot.  FIG. 8  shows that 0.1 V was applied to measure the electronic resistance of the flux; such that voltage and the current in  FIG. 7  indicate that R flux,e =6.978Ω. From these, R flux,i =0.229Ω is calculated, as well as the electronic transference number (see, e.g., A. Roine, “HSC Chemistry 5.11.” 2002; Xiaofei Guan, “Novel Process for Recycling Magnesium Alloy Employing Refining and Solid Oxide Membrane Electrolysis,” Boston University Ph.D. Thesis, September 2013; each herein incorporated by reference in its entirety). Thus, t flux,e =R flux,i /(R flux,i+ R flux,e )=0.032. SOM cell impedance between the LSM anodic current collector and the bubbling tube cathode in the beginning was also measured at 0.36Ω ( FIG. 9 ). 
         [0098]    A potentiodynamic scan (PDS) between the inert anode current collector and bubbling tube cathode showed 2 dissociation potentials: one around 2.2 V and another at round 1 V ( FIG. 10 ). Based on this, to remove any electronegative impurity oxides in the flux such as Fe 2 O 3 , Cr 2 O 3 , SiO 2  or Al 2 O 3 , pre-electrolysis ran at 2 V (below the MgO dissociation potential of 2.2 V) for 90 mins; the resulting current-time plot is shown in  FIG. 11 . That plot indicates that most of the impurity oxides were likely reduced in the first ten minutes of the pre-electrolysis. 
         [0099]    Electronic transference after pre-electrolysis was measured to be 0.037. This is based on EIS in  FIG. 12 , which shows R flux,T =0.186Ω; current versus time and potential versus time in  FIGS. 13 and 14  show R flux,e =4.960Ω such that R flux,i =0.193Ω. Thus, t flux,e =R flux,i /(R flux,i+ R flux,e )=0.037. 
         [0100]    Electrolysis was performed thrice, each for 2 hours at 2.5 V, which is above the dissociation potential of MgO (see  FIG. 2 ). Between and after these electrolysis runs, the cell was shorted to oxidize magnesium metal dissolved in the flux.  FIG. 15  shows the current-time plot of the first electrolysis run. After this electrolysis,  FIG. 16  shows impedance spectroscopy indicating R flux,T =0.156Ω; current versus time in  FIG. 17  and potential versus time in  FIG. 18  indicate that R flux,e &gt;0.177Ω; and R flux,i &lt;1.289Ω. Thus, after the first electrolysis t flux,i =R flux,i /(R flux,i+ R flux,e )&lt;0.879: nearly 90% of the current was carried by electrons. 
         [0101]    Following the first electrolysis, the inert anode current collector inside the YSZ membrane was electrically shorted with the bubbling tube cathode for 1 hour (see  FIG. 3 ).  FIG. 19  shows impedance spectroscopy indicating R flux,T =0.134Ω; current versus time in  FIG. 20  and potential versus time in  FIG. 21  indicate R flux,e =1.420Ω; thus R flux,i =0.148Ω. Thus, after shorting the circuit t flux,e =R flux,i /(R flux,i+ R flux,e )=0.094, indicating that less than 10% of current was carried by electrons. 
         [0102]      FIG. 22  shows the current-time plot of both the first and second electrolysis.  FIG. 23  shows EIS indicating R flux,T =0.124Ω; current versus time in  FIG. 24  and potential versus time in  FIG. 25  indicate R flux,e =0.415Ω; thus R flux,i =0.177Ω. Thus, after the second electrolysis t flux,e =R flux,i /(R flux,i+ R flux,e )=0.299. After shorting for one hour,  FIG. 26  shows EIS indicating R flux,T =0.165Ω; current versus time in  FIG. 27  and potential versus time in  FIG. 28  indicate R flux,e =2.323Ω; thus R flux,i =0.177Ω. Thus, shorting the circuit after the second electrolysis shows t flux,e =R flux,i /(R flux,i+ R flux,e )=0.071, which is again lower than after the second electrolysis. 
         [0103]      FIG. 29  shows the current-time plot of all three electrolyses. Steady state current decreases at first due to MgO depletion from the flux, then increases as more Mg metal dissolves into the flux.  FIG. 30  shows EIS after the third electrolysis, indicating R flux,T =0.122Ω; current versus time in  FIG. 31  and potential versus time in  FIG. 32  indicate R flux,e =0.232Ω; thus R flux,i =0.259Ω. Thus, after the third electrolysis t flux,e =R flux,i /(R flux,i+ R flux,e )=0.528. After one hour of shorting,  FIG. 33  shows EIS indicating R flux,T =0.133Ω; current versus time in  FIG. 34  and potential versus time in  FIG. 35  indicate R flux,e =1.754Ω; thus R flux,i =0.144Ω. Thus, shorting the circuit after the third electrolysis leads to t flux,e =R flux,i /(R flux,i+ R flux,e )=0.076, which is again lower than after the third electrolysis. 
         [0104]    Table 3 summarizes electronic transference numbers of the flux (t flux,e ) measured before and after shorting the circuit. The electronic transference number decreased each time to less than 0.1 as a result of shorting the circuit. It shows that shorting the circuit is an effective method of reducing the amount of soluble magnesium in the flux and also improving the performance of the SOM electrolysis. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Electronic transference numbers of the flux 
               
               
                 (t flux, e ) before and after shorting the circuit 
               
             
          
           
               
                   
                 t flux, e  before shorting 
                 t flux, e  after shorting 
               
               
                   
                 the circuit 
                 the circuit 
               
               
                   
                   
               
             
          
           
               
                 After the 1 st  electrolysis 
                 0.879 
                 0.094 
               
               
                 After the 2 nd  electrolysis 
                 0.299 
                 0.071 
               
               
                 After the 3 rd  electrolysis 
                 0.528 
                 0.076 
               
               
                   
               
             
          
         
       
     
         [0105]    Better performance may result if shorting is performed between the inert anode current collector and the tube cathode (excluding the steel reaction chamber). 
         [0106]    A negative correlation between the electronic transference number of the flux and the current efficiency of the SOM electrolysis has been observed (Xiaofei Guan, “Novel Process for Recycling Magnesium Alloy Employing Refining and Solid Oxide Membrane Electrolysis,” Boston University Ph.D. Thesis, September 2013; herein incorporated by reference in its entirety). Dissolved magnesium metal is responsible for imparting electronic conductivity to the flux. The electronic transference number of the flux was measured to assess the magnesium dissolution in the flux during SOM electrolysis. As more magnesium metal was produced during SOM electrolysis, the electronic transference number increased and the current efficiency of the SOM electrolysis decreased. A method of removing the soluble magnesium in the flux and mitigating the effects of electronic current is presented, and proof-of-concept experiment has been performed to demonstrate its feasibility. 
       Example 2 
       [0107]    The equivalent circuit model was used to determine the effect of the electronic resistance, on membrane stability (maximum allowable applied potential without reducing the zirconia membrane, E MAAP ) and the production rate of Mg in the experimental magnesium oxide reduction cell shown in  FIG. 5 . 
         [0108]    As more magnesium dissolves into the flux, the electronic conductivity of the flux will increase. The dissolved magnesium provides a pathway for the electronic current in the flux. There are both electronic and ionic current passing through the flux and the YSZ membrane (see the equivalent circuit in  FIG. 1 ). As described above, the increased electronic conductivity of the flux decreased the electronic potential drop across the flux and increased the potential drop across the YSZ membrane while a constant DC electric potential is applied across the entire cell. To avoid ZrO 2  dissociation, the potential drop across the YSZ membrane (I e(YSZ) ·R e(YSZ) ) should not exceed the electric potential for ZrO 2  dissociation, which is also the absolute value of the Nernst potential for ZrO 2  dissociation, |E N   ZrO     2   |. When the potential drop across the YSZ membrane is equal to |E N   ZrO     2   |, as expressed by Equation (5), the ionic current for ZrO 2  dissociation, I i   ZrO     2    becomes zero. In this case, the applied potential is defined as the maximum allowable applied potential (E MAAP ) to avoid ZrO 2  dissociation. 
         [0000]        I   e(YSZ)   ·R   e(YSZ)   =|E   N   ZrO     2   |  (Eq. 5)
 
         [0109]    To calculate the E MAAP , it is necessary to simplify the equivalent circuit in  FIG. 1 . According to the polarization modeling, the mass transfer resistances for MgO dissociation are negligible at the current range of 0 A to 1.7 A. At the point when magnesium dissolves in the flux and imparts electronic conductivity to the flux, all the Fe 2 O 3  must have already been removed. Therefore, the circuit branch for Fe 2 O 3  dissociation can be eliminated. The simplified equivalent circuit is shown in  FIG. 35 . The contact ohmic resistance associated with the interfaces for ionic species transport (R contact ) is incorporated into the simplified equivalent circuit. 
         [0110]    According to the Kirchhoff&#39;s Current Law (KCL), 
         [0000]        I   T   =I   i   MgO   +I   e(YSZ)   (Eq. 6)
 
         [0111]    The Kirchhoff&#39;s Voltage Law (KVL) applied to the closed circuits in the simplified equivalent circuit gives 
         [0000]        E   MAAP   =I   T   ·R   cc   +I   e(YSZ) ·( R   e(YSZ)   +R   e(flux) )  (Eq. 7)
 
         [0000]        E   MAAP   =I   T   ·R   cc   +I   i   MgO ·( R   contact   +R   i(YSZ)   MgO   +R   i(flux)   MgO   +R   ct(a,c)   MgO )+| E   N   MgO |  (Eq. 8)
 
         [0112]    Equations 5-8 are independent and they form a system of equations in the four unknown parameters: I e(YSZ) , I T , I i   MgO , and E MAAP . 
         [0113]    The current efficiency when the applied potential is E MAAP  can be represented as 
         [0000]        CE=I   i   MgO   /I   T   (Eq. 9)
 
         [0114]    To quantify the E MAAP  for the SOM experiment, the values of the parameters in Equations 5-8 need to be either measured during the experiment or calculated based on the literature findings. 
         [0115]    Given the geometric similarities, the values of the electronic and ionic resistances of the flux between the bubbling tube and the reaction chamber are approximately equal to the electronic and ionic resistances of the flux between the YSZ membrane and the reaction chamber (R e(flux)  and R i(flux)   MgO ) (Xiaofei Guan, “Novel Process for Recycling Magnesium Alloy Employing Refining and Solid Oxide Membrane Electrolysis,” Boston University Ph.D. Thesis, September 2013; herein incorporated by reference in its entirety). The absolute value of the Nernst potential for MgO dissociation, |E N   MgO |, was measured to be approximately 2.08V. E N   ZrO     2    can be calculated according to the Nernst equation as shown in Equation 10. In Equation 10, E N   0,ZrO     2   =−2.153V is the standard Nernst potential for ZrO 2  dissociation at T=1150° C.; a ZrO2(s)  and a Zr(s)  are the activities of the solid ZrO 2  and Zr at the cathode side of the YSZ membrane, and they are both equal to unity; and a O2(g),anode/YSZ  is the activity of oxygen at the anode/YSZ interface, and it was equal to 1.747. Therefore, |E N   ZrO     2   | is equal to 2.17V. 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     N 
                     
                       ZrO 
                       2 
                     
                   
                   = 
                   
                     
                       E 
                       N 
                       
                         0 
                         , 
                         
                           ZrO 
                           2 
                         
                       
                     
                     + 
                     
                       
                         RT 
                         
                           4 
                            
                           F 
                         
                       
                        
                       
                         ln 
                          
                         
                           ( 
                           
                             
                               a 
                               
                                 ZrO 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                   ( 
                                   s 
                                   ) 
                                 
                               
                             
                             
                               
                                 a 
                                 
                                   Zr 
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                               
                                
                               
                                 a 
                                 
                                   
                                     O 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                       ( 
                                       g 
                                       ) 
                                     
                                   
                                   , 
                                   
                                     anode 
                                     / 
                                     YSZ 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
         [0116]    The ohmic resistance of the LSM-Inconel current collector having a 27.6 mm×4.4 mm×4.1 mm LSM bar was measured to be ˜0.125Ω. The current collector used in the SOM experiment had a smaller LSM bar (16.5 mm×3.4 mm×2.9 mm). The cell constants of the two LSM bars are close. Therefore, the ohmic resistance of the LSM-Inconel current collector (Rcc) used in SOM experiments is estimated to be 0.125Ω. 
         [0117]    The charge transfer resistance at the cathode for MgO dissociation (R ct,c   MgO ) is the gradient of the activation polarization (Xiaofei Guan, “Novel Process for Recycling Magnesium Alloy Employing Refining and Solid Oxide Membrane Electrolysis,” Boston University Ph.D. Thesis, September 2013; herein incorporated by reference in its entirety) with respect to the ionic current, as expressed by Equation 11. R ct,c   MgO  depends on the ionic current for MgO dissociation (I i   MgO ), an unknown parameter to be solved. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                             
                         
                          
                         
                           
                             R 
                             
                               ct 
                               , 
                               c 
                             
                             MgO 
                           
                           = 
                           
                             
                                
                               
                                 η 
                                 at 
                               
                             
                             
                                
                               i 
                             
                           
                         
                          
                       
                        
                       
                         ? 
                       
                     
                     = 
                     
                       
                         RT 
                         F 
                       
                        
                       
                         1 
                         
                           
                             
                               
                                 ( 
                                 
                                   I 
                                   i 
                                   MgO 
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             
                               
                                 ( 
                                 
                                   2 
                                    
                                   
                                     i 
                                     o 
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
         [0118]    The ionic resistance of the YSZ membrane (R i(YSZ) ) depends on the ionic conductivity (σ i(YSZ) ), the cross-sectional area (A(x)), and the thickness of the YSZ membrane (L YSZ ) as shown in the following equation: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         R 
                         
                           i 
                            
                           
                             ( 
                             YSZ 
                             ) 
                           
                         
                       
                       = 
                       
                         
                           ? 
                         
                          
                         
                           1 
                           
                             σ 
                             
                               i 
                                
                               
                                 ( 
                                 YSZ 
                                 ) 
                               
                             
                           
                         
                          
                         
                           
                              
                             x 
                           
                           
                             A 
                              
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         ? 
                       
                        
                       
                         indicates text missing or illegible when filed 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     12 
                   
                   ) 
                 
               
             
           
         
       
     
         [0119]    Filal et al. have reported the ionic conductivities of the YSZ membrane with different amounts of Y 2 O 3  (3 mol % and 9.5 mol %) ( Solid State Ionics,  1995, 80, 27-35; herein incorporated by reference in its entirety). In this work, 6 mol % YSZ membrane was employed, and its ionic conductivity at 1150° C. was estimated to be 21.88 S/m by interpolation from the literature data ( Solid State Ionics,  1995, 80, 27-35; herein incorporated by reference in its entirety). The ionic resistance of the YSZ membrane was calculated to be 0.0711Ω. 
         [0120]    The total ohmic resistance of the SOM cell (R ohm ) was measured to be 0.54Ω before any magnesium was dissolved in the flux (Xiaofei Guan, “Novel Process for Recycling Magnesium Alloy Employing Refining and Solid Oxide Membrane Electrolysis,” Boston University Ph.D. Thesis, September 2013; herein incorporated by reference in its entirety). Knowing the ionic resistance of the YSZ membrane (R i(YSZ) ), the contact resistance associate with the interfaces for ionic species transport (R contact ) was calculated to be around 0.14Ω by subtracting R i(YSZ)  (0.0711Ω), R i(flux)   MgO  (˜0.2Ω), and R cc  (0.125Ω) from R ohm  (0.54Ω). 
         [0121]    The electronic resistance of the YSZ membrane (R e(YSZ) ) depends on the electronic conductivity (σ e(YSZ) ), the cross-section area (A(x)), and the thickness of the YSZ membrane (L YSZ ) as shown in the following equation: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         R 
                         
                           i 
                            
                           
                             ( 
                             YSZ 
                             ) 
                           
                         
                       
                       = 
                       
                         
                           ? 
                         
                          
                         
                           1 
                           
                             σ 
                             
                               i 
                                
                               
                                 ( 
                                 YSZ 
                                 ) 
                               
                             
                           
                         
                          
                         
                           
                              
                             x 
                           
                           
                             A 
                              
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         ? 
                       
                        
                       
                         indicates text missing or illegible when filed 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     13 
                   
                   ) 
                 
               
             
           
         
       
     
         [0122]    Park et al. ( J. Electrochem. Soc.  1989, 136, 2867-2876; herein incorporated by reference in its entirety) have studied the electronic transport in 8 mol % YSZ, and empirical equations were derived for the electron and hole conductivities, (σ e(8YSZ) ) and (σ h(8YSZ) ), as a function of temperature (800° to 1050° C.) and oxygen partial pressure: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       σ 
                       
                         e 
                          
                         
                           ( 
                           
                             8 
                              
                             YSZ 
                           
                           ) 
                         
                       
                     
                     = 
                     
                       1.31 
                       × 
                       
                         10 
                         7 
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               
                                 - 
                                 3.88 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 k 
                                 B 
                               
                                
                               T 
                             
                           
                           ) 
                         
                       
                        
                       
                         ? 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     14 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         σ 
                         
                           h 
                            
                           
                             ( 
                             
                               8 
                                
                               YSZ 
                             
                             ) 
                           
                         
                       
                       = 
                       
                         2.35 
                         × 
                         
                           10 
                           2 
                         
                          
                         
                           exp 
                            
                           
                             ( 
                             
                               
                                 
                                   - 
                                   1.67 
                                 
                                  
                                 
                                     
                                 
                                  
                                 eV 
                               
                               
                                 
                                   k 
                                   B 
                                 
                                  
                                 T 
                               
                             
                             ) 
                           
                         
                          
                         
                           ? 
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         ? 
                       
                        
                       
                         indicates text missing or illegible when filed 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     15 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where kB is the Boltzmann constant (1.38×10 23  J/K), P O2,YSZ  is the local oxygen partial pressure in the YSZ membrane. Based on the knowledge of σ e(8YSZ)  and σ h(8YSZ) , it is possible to estimate the electron and hole conductivities, σ e(6YSZ)  and σ h(6YSZ) , of 6 mol % YSZ as follows (Xiaofei Guan, “Novel Process for Recycling Magnesium Alloy Employing Refining and Solid Oxide Membrane Electrolysis,” Boston University Ph.D. Thesis, September 2013; herein incorporated by reference in its entirety): 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       σ 
                       
                         e 
                          
                         
                           ( 
                           
                             6 
                              
                             YSZ 
                           
                           ) 
                         
                       
                     
                     = 
                     
                       1.31 
                       × 
                       
                         10 
                         7 
                       
                        
                       
                         exp 
                          
                         
                           ( 
                           
                             
                               
                                 - 
                                 3.88 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 k 
                                 B 
                               
                                
                               T 
                             
                           
                           ) 
                         
                       
                        
                       
                         
                           ( 
                           
                             6 
                             8 
                           
                           ) 
                         
                         
                           
                             - 
                             1 
                           
                           / 
                           2 
                         
                       
                        
                       
                         ? 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     16 
                   
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         σ 
                         
                           h 
                            
                           
                             ( 
                             
                               6 
                                
                               YSZ 
                             
                             ) 
                           
                         
                       
                       = 
                       
                         2.35 
                         × 
                         
                           10 
                           2 
                         
                          
                         
                           exp 
                            
                           
                             ( 
                             
                               
                                 
                                   - 
                                   1.67 
                                 
                                  
                                 
                                     
                                 
                                  
                                 eV 
                               
                               
                                 
                                   k 
                                   B 
                                 
                                  
                                 T 
                               
                             
                             ) 
                           
                         
                          
                         
                           
                             ( 
                             
                               6 
                               8 
                             
                             ) 
                           
                           
                             1 
                             / 
                             2 
                           
                         
                          
                         
                           ? 
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         ? 
                       
                        
                       
                         indicates text missing or illegible when filed 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     17 
                   
                   ) 
                 
               
             
           
         
       
     
         [0123]    The electronic conductivity in YSZ is primarily n-type at low oxygen partial pressures below 1.28×10 −6  atm, but p type at higher oxygen partial pressures. The local electronic conductivity of the YSZ membrane depends on the local oxygen partial pressure. To calculate the electronic resistance of the YSZ membrane, it is necessary to obtain the oxygen partial pressure distribution in the YSZ membrane. In the SOM experiment with an inert anode current collector, it has been evaluated that the oxygen partial pressure at the anode/YSZ interface, P O2,anode/YSZ , was 1.747 atm. The oxygen partial pressure at the flux/YSZ interface was fixed by the equilibrium reaction: 2Mg(g)+O 2 (g)=2MgO(flux) inside the reaction chamber. The equilibrium constant of this reaction at 1150° C. is obtained from HSC Chemistry 5.11™ Database (A. Roine, “HSC Chemistry 5.11,” 2002; herein incorporated by reference in its entirety) as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       K 
                       = 
                       
                         
                           ? 
                         
                         = 
                         
                           1.729 
                           × 
                           
                             10 
                             32 
                           
                         
                       
                     
                      
                     
                       
 
                     
                      
                     
                       
                         ? 
                       
                        
                       
                         indicates text missing or illegible when filed 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     18 
                   
                   ) 
                 
               
             
           
         
       
     
         [0124]    The magnesium partial pressure inside the reaction chamber, P Mg(g) , was determined by the magnesium evolution rate (˜19.4 cm 3 /min at 1150° C.) and the argon flow rate (˜2331 cm 3 /min at 1150° C.), and was calculated to be 0.0083 atm. Five percent of MgO was dissolved in the flux, and the activity of MgO in the flux must be between 0.1 and 1. Therefore, the oxygen partial pressure at the flux/YSZ interface is calculated to be around 10 −29  atm. Having known the oxygen partial pressure on the two sides of the YSZ membrane, it is possible to calculate the oxygen partial pressure distribution in the membrane assuming there is no oxygen partial pressure change across the interfaces (Yuan et al.,  J. Electrochem. Soc.  1996, 143, 3214-3222; herein incorporated by reference in its entirety). However, Virkar has shown that generally there are abrupt changes in oxygen partial pressure across the electrode/membrane interfaces (Virkae et al.,  J. Power Sources.  2005, 147, 8-31; herein incorporated by reference in its entirety). The role of the interfaces on affecting the oxygen partial pressure distribution inside the YSZ membrane during the SOM electrolysis is still unknown. That said, the minimum combined value of σe(YSZ) from equations 16 and 17 above is on the order of 10 −5  S/cm, and to achieve 200 or 20 Ω·cm 2  resistance-area product would require approximately 20 or 2 μm maximum YSZ solid electrolyte thickness respectively. This is too thin to be practical, particularly in a highly corrosive molten salt environment, so higher electronic conductivity is strongly preferred. 
         [0125]    Instead of calculating R e(YSZ)  using the above analysis, it is therefore more realistic to take a series of trial values (4Ω, 45Ω, and 100Ω) of R e(YSZ) , in order to understand what value for an alternate material leads to industrially advantageous process operation. With approximately 20 cm 2  active anode area in this setup, those trial values correspond to 80, 900, and 2000 Ω·cm 2  respectively. Those trial values are chosen to obtain current efficiencies in the range that is experimentally observed (70-95%) and also the ionic currents for MgO dissociation when the applied potential is E MAAP . The values of the parameters used to calculate the unknown parameters (I e(YSZ) , I T , I i   MgO , and E MAAP ) are given in Table 4 below. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Parameters used in the equivalent circuit for calculating the influence 
               
               
                 of R e(YSZ)  on the membrane stability and Mg production. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Trial value 
                 Electronic resistance of the YSZ 
                 4Ω, 45Ω, and 
               
               
                   
                 membrane (R e(YSZ) ) 
                 100Ω 
               
               
                 Calculated 
                 Ionic resistance of the YSZ membrane 
                 0.0711Ω 
               
               
                 parameters 
                 (R i(YSZ)   MgO ) 
               
               
                   
                 Resistance of the anode current collector 
                 0.1Ω 
               
               
                   
                 (R cc ) 
               
               
                   
                 Contact resistance associated with the 
                 0.14Ω 
               
               
                   
                 interfaces for ionic species transport 
               
               
                   
                 (R contact ) 
               
               
                   
                 Potential for ZrO 2  dissociation (|E N   ZrO     2   |) 
                 2.17 V 
               
               
                 Measured 
                 Potential for MgO dissociation 
                 2.08 V 
               
               
                 parameters 
                 producing magnesium vapor at the 
               
               
                   
                 cathode (|E N   MgO |) 
               
               
                   
                 Ionic resistance of the flux (R i(flux)   MgO ) 
                 0.164Ω(1 st ), 
               
               
                   
                   
                 0.158Ω(2 nd ), 
               
               
                   
                   
                 0.200Ω(3 rd ), 
               
               
                   
                   
                 0.144Ω(4 th ). 
               
               
                   
                 Electronic resistance of the flux(R e(flux) ) 
                 5.857Ω(1 st ), 
               
               
                   
                   
                 3.110Ω(2 nd ), 
               
               
                   
                   
                 1.048Ω(3 rd ), 
               
               
                   
                   
                 1.001Ω(4 th ). 
               
               
                   
               
             
          
         
       
     
         [0126]      FIG. 36  shows the calculated E MAAP  as a function of R e(flux)  for different values of R e(YSZ) . The calculated E MAAP  decreases as R e(flux)  decreases for each value of R e(YSZ) . As more magnesium dissolves into the flux, R e(flux)  becomes smaller, and thus E MAAP  becomes smaller as well. During the SOM experiment, R e(flux)  can be monitored, and applied potential can be adjusted accordingly to avoid ZrO 2  dissociation. In addition, E MAAP  can be increased by increasing R e(flux) . This can be accomplished by operating the SOM electrolysis cell at low total pressures which is an effective method of removing magnesium dissolved in the flux and reducing the electronic conductivity of the flux (E. Gratz, “Solid Oxide Membrane (SOM) Stability in Molten Ionic Flux for the Direct Electrolysis of Magnesium Oxide,” Boston University (Ph.D. Dissertation), 2013; herein incorporated by reference in its entirety). 
         [0127]      FIG. 36  also shows that the calculated E MAAP  increases as R e(YSZ)  decreases for each value of R e(flux) . It suggests that E MAAP  can be increased by decreasing R e(YSZ) , with 4Ω—i.e. 80 Ω·cm 2 —being by far the best resistance of this series for operating at industrially useful voltage and cell productivity. This can be realized by reducing the thickness of the YSZ membrane and/or increasing the electronic conductivity of the YSZ membrane. 
         [0128]      FIG. 37  shows the calculated current efficiency as a function of R e(flux)  for different values of R e(YSZ) . The calculated current efficiency decreases as R e(flux)  decreases. It should be noted that the applied potential is E MAAP  in this modeling, which varies as a function of R e(flux) .  FIG. 37  also shows that the current efficiency decreases as R e(YSZ)  decreases for same R e(flux) . Therefore, R e(YSZ)  cannot be too small in order to maintain a high current efficiency of the SOM electrolysis. In addition to current efficiency, the performance of the SOM electrolysis can also be evaluated by the production rate of magnesium and oxygen, which is linearly proportional to the ionic current for MgO dissociation (I i   MgO ). 
         [0129]      FIG. 38  shows the calculated I i   MgO  as a function of R e(YSZ)  for different values of R e(YSZ)  when the applied potential is E MAAP . Overall, a high R e(flux)  and a relatively low R e(YSZ)  are required to achieve ZrO 2  stability, high current efficiency, and high production rate of magnesium and oxygen. With about 20 cm 2  active anode area in this setup, operating at industrially useful current density of above 0.3 A/cm 2  requires operation above 6 A current. Again, 4Ω—i.e. 80 Ω·cm 2 —is by far the best value here, and 10Ω—i.e. 200 Ω·cm 2 —is a maximum industrially usable resistance, with 20 Ω·cm 2  being a practical value in case R e(flux)  falls due to high reactive metal dissolution. 
         [0130]      FIGS. 36 and 38  show that a high R e(flux)  and a relatively low R e(YSZ)  are required to achieve ZrO 2  stability, high current efficiency, and high production rate. 
         [0131]    As will be apparent to one of ordinary skill in the art from a reading of this disclosure, further embodiments of the present invention can be presented in forms other than those specifically disclosed above. The particular embodiments described above are, therefore, to be considered as illustrative and not restrictive. Those skilled in the art will recognize, or be able to ascertain, using no more than routine experimentation, numerous equivalents to the specific embodiments described herein. Although the invention has been described and illustrated in the foregoing illustrative embodiments, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the invention can be made without departing from the spirit and scope of the invention, which is limited only by the claims that follow. Features of the disclosed embodiments can be combined and rearranged in various ways within the scope and spirit of the invention. The scope of the invention is as set forth in the appended claims and equivalents thereof, rather than being limited to the examples contained in the foregoing description.