Peng Li,Milin Zhang,, *,Debin Ji,Min Qiu,Li Liu

1 Key Laboratory of Superlight Materials and Surface Technology,Ministry of Education,College of Materials Science and Chemical Engineering,Harbin Engineering University,Harbin 150001,China

2 College of Science,Heihe University,Heihe 164300,China

Keywords:Equilibrium Potential Electrolysis Molten salts Mathematical Grading rule Reduction

ABSTRACT The electrochemical behavior of lanthanide elements deposited on liquid zinc cathodes was studied using cyclic voltammetry(CV)and open circuit chronopotentiometry(OCP).We observed a“bimodal effect”in the equilibrium deposition potentials of zinc with lanthanides.A mathematic equation is derived to illustrate the relationship between the equilibrium potential of the intermetallic compounds formed by lanthanide elements and zinc and their atomic radius.This equation is not only applicable to lanthanide elements but also hold for other elements such as alkali metal lithium,alkaline earth metal magnesium,calcium and transition metal niobium,which have crucial theoretical significance for the electrolysis of intermetallic compounds,the separation,and extraction of metals.

1.Introduction

Lanthanide elements with atomic numbers from 57(lanthanum)to 71(lutetium)are a particular group in the periodic table of elements,as their 4f electrons are in an inner layer.In the previous studies,it was found that the“Bimodal Effect”causes the atomic radius of lanthanides or atomic volume changes with the atomic number[1].This study is based on the basic properties of lanthanide elements(Lens).Since Eu and Yb have a larger atomic radius than other rare earth elements,they have a weaker ability to form alloys and show more negative potentials during electrolysis.In the study,we found that the equilibrium potential of lanthanide deposition on the zinc electrode also has the phenomenon of“Bimodal Effect”.If we find a mathematical relationship between the equilibrium potential and the radius of the cathode metal,a mathematical equation can be established to predict the equilibrium potential of the electrolytic metal at the cathode[2].At present,the technology of single rare earth electrolysis is relatively mature in the world,but basic research on the formation rules of rare earth alloys is relatively lacking.This work can take the advantages of alloy electrolysis,the constitutional laws of alloy formation are identified and used to guide and predict alloy electrolysis'production.

In this work,we report the equilibrium potentials of Zn-rich Zn-Ln alloys,and among them,two peak values are at Eu and Yb,which indicates that there might be a close connection between the ability to form alloys and atomic radius.By sorting out and summarizing up the data,a mathematical equation,ELn-alloy=f(r1,r2)where r1represents the radius of the zinc atom,r2denotes the radius of lanthanide elements,was developed,which will play an essential role in the pyroprocessing of spent fuel,lanthanide alloy and electrolytic separation and purification of lanthanide and other elements.In the meantime,this equation is also applicable to other Zinc alloys,such as Zn-Li,Zn-Mg,Zn-Ca,Zn-Nb and so on.And this work has far-reaching strategic significance and essential practical significance,and can play a decisive role in promoting the development of the rare earth and other alloys.With the help of this equation,it is no longer necessary to waste human resources and material resources to explore the equilibrium voltage of an element forming an alloy with zinc,and the required voltage can be obtained by directly calculating by this equation.

2.Experimental

2.1.Preparation and purification of the melt

A mixture of anhydrous LiCl(45.0 g,Alfa Aesar,AR grade)and KCl(45.0 g,Alfa Aesar,AR grade)with the eutectic composition in a corundum crucible by mechanical stirring for more than 0.5 h was dried for more than 100 h at 473 K in the vacuum environment to remove the plethora water.Then the salt mixture in the corundum crucible was melted in an electric furnace under argon atmosphere in which the oxygen and moisture levels were below 1 ppm.

The solutions of lanthanides and Zn were brought into the melt by direct addition of anhydrous rare earth chlorides(3%)and ZnCl2(2%,Alfa Aesar,AR grade)powder.Anhydrous lanthanide chlorides were prepared in the following way:the well-distributed rare earth oxide(15 wt%)and NH4Cl(85 wt%)were heated at 803 K for 3 h in a vacuum furnace.For heavy lanthanides(gadolinium to lutetium),a mixture of well-scattered lanthanide oxide(10 wt%),NH4Cl(55 wt%)and KCl(35 wt%)was heated at 803 K for 3.5 h in a vacuum furnace[1].The reaction was monitored by X-ray diffraction and ICP-AES till the purity of the lanthanide chloride was more than 95%.

2.2.Electrochemical apparatus and electrodes

The three-electrode system investigated the electrochemical behavior of the system.The inert working electrode consisted of molybdenum wire of 1.0 mm diameter(Alfa Aesar 99.99%),and the surface area of the reactive working electrode was determined by the immersion depth of the electrode in the eutectic salts,which was 1.0 cm.The inert W electrode immersed in a melt containing lanthanide Elements(III)or Alkaline-earth metal elements(II)was prepared by freshly depositing a layer of Zn on the surface of W electrode at 0.9 V for 1 s before each electrochemical measurement.The counter electrode was a 6 mm diameter graphite rod(Alfa Aesar＞99.99%).The reference electrode consisted of a closed-end corundum tube filled with the LiCl-KCl eutectic salt and 1.0 wt.% AgCl,and an Ag wire of 0.5 mm diameter served as an electrical contact.All potentials were referred to the Ag(I)/Ag reference.All electrochemical data was collected using a PGSTAT 302 N potentiostat/galvanostat instrument(Autolab,Metrohm)with the Nova 1.11 software.

3.Results and Discussion

Although the electrochemical and thermodynamic properties of Zn-Ln(Ln=Dy,Nd,Tb)alloys in the molten LiCl-KCl system were known in the literature[2-4],the formation of Zn and other Lens has not been studied.In this work,we found that the mixture of these chlorides melts at a temperature much lower than any of their melting points,and the temperature needed to form the intermetallic compound is also lower than the theoretical value,which is shown in the binary phase diagram[5-7].These phenomena can be explained as follows:the blend of these chlorides outstrips the energy barrier which is the formation of the intermetallic compounds.About the composition of the crystal phase,metastable phase and amorphous phase with the above-mentioned underpotential deposition(UPD)method,the process involves the discharge of metal ions,about several eV,which measured regarding temperature,each atom is equivalent to experienced tens of thousands of degrees Celsius high temperature[8].As shown in Fig.1a,the ions in the melt exercise strenuously and irregular,so that some ions reduced to the metal atoms and combined into intermetallic compounds,while they didn't reach the energy barrier.Each ion was discharged to produce a high-temperature adsorption atom.Consequently,a certain amount of high-temperature adsorption atoms through surface diffusion mechanism to re-substrate surface diffusion,and ultimately formed a solid or liquid film(Fig.1a).

3.1.Nucleation principle and generation mechanism

The essence of forming intermetallic compounds is an electrolytic deposition.This process includes two aspects,the process of the reduction of metal ions on the cathode(precipitation of metal atoms)and the process of the crystallization(electron crystallization)of the new ecological metal atoms on the electrode surface[9,10].Fig.1 shows the schematic diagram of the atomic reduction and the formation of intermetallic compounds on the tungsten wire.In the course of this experiment,zinc was pre-deposited on a tungsten electrode to form a zinc cathode in advance and then reacted with other elements to create a metal piece compound.From Fig.1a,we can see that in the molten salt system,different metal ions were exercising and irregularly staggering;and when the cathode was formed on the tungsten wire,more active zinc atoms were adhered to form an adhesion layer first.Then the other metal ions accepted the electrons to form the corresponding metal atoms.As the concentration and temperature varied,different types of molecules formed different intermetallic compounds,as shown in Fig.1b.This growth of urchin-like particles also appeared in the formation of Sm-Zn alloys[11],and is similar to the creation of dendrites in a solid metal solution[12].

During the reduction process,sometimes it could be observed that a single atomic layer would be deposited when the electrode potential was significantly positive than the standard equilibrium potential of the deposited metal.Cyclic voltammogram indicates that the chemical potential of the deposited monolayer atoms on the surface of the dissimilar metal substrate is more harmful than that on the same metal surface,which corresponds to the so-called underpotential deposition(UPD)[13,14].In the other word,the interaction between the deposited atoms and the base atoms is stronger than that between the deposited atoms.

Fig.1.The schematic diagram showing the atomic reduction(a)and the formation of the Zn-Lns intermetallic compounds by molten salt electrolysis on the tungsten electrode(b)in the LiCl-KCl-ZnCl2(1.5 wt%)-LnCl3(2.0 wt%)melt.

As the applied potential is shifted to more negative values,the preformed Zn liquid membrane would offer a substrate for the diffusion of lanthanide elements.As the Lns diffuse into the Zn membrane,Lns-Zn intermetallic compounds would be formed in the solid state which would also be deposited on the inert electrode and grow larger.Similar phenomena were also found in the formation of Sm-Zn,Al-Gd,and La-Gd intermetallic compounds[11,15,16].

Fig.2.Cyclic voltammogram at tungsten electrode(S=0.322 cm2)of the LiCl-KCl-GdCl3(9.75×10-5 mol·cm-3)molten salt system at 923 K.Inserted Fig.I and II(enlarged pictures at B and B′).Inserted Fig.III,the evolutions of the peak potentials of peak B and peak B′as a function the scan rate.

Fig.3.Cyclic voltammogram at a tungsten electrode(S=0.322 cm2)of the LiCl-KCl-GdCl3,(9.75×10-5 mol·cm-3)molten salt system at scan rate=0.1 V·s-1.Inserted Fig.I:CVs of the same system with different experiment temperature from 923 to 1023 K.Inserted Fig.II:Peak voltages of the same system with different experiment temperature from 923 to 1023 K.

3.2.Electrochemical behavior

3.2.1.Cyclic voltammetry curve and the reversibility

Using cyclic voltammetry,the degree of reversibility of the electrode reaction,the possibility of the intermediate formation,phase boundary adsorption,or new phase formation can be judged from the shape of the curve[20].In this experiment,we used cyclic voltammetry to analyze the species and reversibility of alloy formation of rare earth elements and zinc.Firstly,we used cyclic voltammetry to study the optimum temperature and to scan speed for the experiment.The result was shown in Figs.2-4.The temperature and scan rate have huge impacts on the electrochemical behavior of Gd(III)on the W electrode in LiCl-KCl eutectic[21,22].

In Fig.2,the peaks A and A′correspond to the deposition and dissolution of Li metal,respectively.It is obvious that during the starting scan,peak B around-1.87 V represents the reduction of Gd(III)to Gd metal,and the peak B′at around-1.66 V is due to the dissolution of Gd metal when the scan direction was reversed.It is observed that the cathode potential will shift to more negative values with the increase of scan rate,and the accurate values of the peak potentials of peaks B and B′were marked in the inserted Fig.III in Fig.2.The influence of temperature on the peak potentials of B and B′ as shown in Fig.3 With the increase of the temperature,the cathode potential will shift to more negative values,and the accurate values of the peak potentials of the peaks B and B′were marked in the inserted Fig.II in Fig.3.

Fig.4 shows that every cyclic voltammogram has the redox peaks A and A′,and Z and Z′which means the redox of Li and Zn,respectively.The peaks between these two redox peaks indicate the formation of intermetallic compounds.It is evident that there are various intermetallic compounds of zinc and each kind of rare earth metal in the electron signal test.However,it was hard to get all of them out at one time by the method of electrolysis[16-18].

As shown in Figs.2-4,the amplitude of the reduction peaks is much weaker than the corresponding oxidation peaks.One possible reason is that the availability of deposited metal for the stripping[22].The reaction reversibility can be determined by the linear relationship of i(peak current density)vs.ν1/2(square root of scan rate).For the direct relationship,the reversibility of the cyclic voltammetry curve is based on the relationship between the peak current,peak voltage,and scan rate.It may be reversible,irreversible,or quasi-reversible[23,28].Reversibility can also be determined according to the following conditions:whether it works under equilibrium potential,or the products are stable compounds or ions.Previous research confirmed that the electrochemical behavior of intermetallic compounds of the lanthanum-cadmium system is reversible[15],while that in the lanthanum-zinc system is quasi-reversible[24].John et al.[25]indicated that the higher the scan rate,the smaller the amplitude of peak current.Michael et al.[26]reported that the scanning electrochemical microscope(SECM)allows a rigorous approach to the determination of the kinetic parameters of the process of reversible or quasi-reversible.Furthermore,John et al.[25]and Vandarkuzhai et al.[27]both conclude that a suitable scan rate(25≤ν≤150 mV⋅s-1)is vital for(obtaining?)the linear relationship.The experimental results show that,in the CV curves,the cathode and anode peaks are not symmetric,and the differences between them also vary.Also,the metal redox process occurs at the over potential rather than the equilibrium potential and the products are stable intermetallic compounds.Based on the above information,the reactions in the experiments are quasi-irreversible.

Fig.4.Cyclic voltammogram at a tungsten electrode(S=0.322 cm2)of the LiCl-KCl-ZnCl2(1.5 wt%)-LnCl3(Ln=La,Sm,Er,Gd,Yb)(2.0 wt%)molten salt system at 923 K(scan rate=0.1 V·s-1).

3.2.2.Open circuit chronopotentiometry

Open circuit chronopotentiometry(OCP)measures the different potentials when forming different intermetallic compounds.Figs.5 and 6 show the open circuit chronopotentiometry diagrams of LiCl-KCl-LnsCl3(2.0 wt%)-ZnCl2(1.5 wt%)at different temperatures after electrolyzing with a potential of-2.5 V for 10 s.While in the deposition of Zn and Lns,lots of different phases were generated as the potential shifted to more positive regions.In Ocps,different platforms mean different intermetallic compounds.

During the experiment,all OCP curves began at-2.4 V,which corresponds to the redox couple of Li(I)/Li(0)[29].And the highest platform of-0.6 V indicates the Zn(II)/Zn(0).The plateaus between these two show the formation of intermetallic compounds with different compositions.It worth noting that the plateaus of the same number,like the platform IX and(IX)in Fig.5(La),indicate the formation of the same intermetallic compound[12].Different reaction temperatures cause this difference in potential.From Fig.5,it can be seen that the type and stability of the formed alloy are relatively better at a temperature of 923 K.Therefore when studying the influence of factors other than temperature,we chose to experiment at 923 K.

Fig.5.OCPs of Zn and light rare earth elements:ZnCl3(1.5 wt%)-(I)LaCl3,(II)SmCl3,(III)ErCl3,(IV)GdCl3,(V)YbCl3(2.0 wt%)for 10 s in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)at different temperatures.

Fig.6.OCPs of the chloride of Zn and La,Sm,Er,Gd,Yb in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)for 10 s at 923 K,respectively.

From Fig.6,it can be seen that the longer the reaction time,the more types of alloys are formed.In contrast,light rare earth elements are more easily combined with zinc than heavy rare earth elements to form intermetallic compounds.And from Figs.5 and 6,for most experimental elements,it is possible to obtain as many intermetallic compounds as possible at 923 K.To ensure that the experimental variables are unique(different experimental elements),we selected the preliminary results at 923 K for comparative analysis.Fig.6 shows that at the same equilibrium potential and deposition time,the number of intermetallic compounds and the step time of each intermetallic compounds were not the same for different experimental elements[4].As we can see from the data when forming an alloy with zinc,an element with a larger atomic radius requires more negative potential.In other words,the influence of atomic radius on the formation of the alloy is similar to the impact of entropy.

Then we are curious whether the relationship between the atomic radius and the equilibrium potential can be expressed mathematically.After careful investigation,we chose the intermetallic compounds ZnxREyin which the proportion of x:y is 1:1,which is corresponding to the second platform nearest the zinc counterpart platform(the first platform from top to bottom)in the OCP curves,as these intermetallic compounds are the most stable ones.Also,the step of x:y that is 1:1 in the course of the experiment is called the rate-determining step(RDS)[30-32],which is often simplified by using this approximation of the rate determining step.In this experiment,the formula for the alloy formation is determined by the rate determining step.

Combined with the experimental data,we verified that the“Bimodal Effect”of Eu and Yb does exist in the radius and equilibrium potential of rare earth elements.The atomic radii of the lanthanides decreased from 18.7 pm in La to 173.4 pm in Lu,a total reduction of 14.3 pm,and the average reduction between every two adjacent elements was 14.3/14≈1 pm.Although the average difference is only 1 pm,the cumulative effect(14 pm total)is significant.However,the atomic radius does not decrease monotonically,but a phenomenon occurs at Eu and Yb,and a valley occurs at Ce.This is called the“Bimodal Effect”[33].In addition to the atomic radius,the atomic volume,density,coefficient of thermal expansion of the atom,the third ion energy,the sum of the first three ionization energies,the electronegativity of the atom,the melting point,and the boiling point of some compounds also occur.The results were shown in Figs.7 and 8.Comparing the above two figures,we can see that the element with a larger atomic radius is more negative in equilibrium potential,indicating that the atomic volume of lanthanide is inversely proportional to the equilibrium potential.Besides,the formation entropy of intermetallic compounds and entropy can be expressed as:(x1ln x1+x2ln x2).Where x1and x2represent the contribution of zinc and lanthanide to the alloy formation,respectively.We express x1and x2as r1/(r1+r2)and r2/(r1+r2),respectively,where r1is the radius of zinc and r2is the radius of the corresponding lanthanide.After analyzing the experimental results,the relationship between the atomic radius of different elements and the corresponding equilibrium voltage(E)of the intermetallic compounds can be expressed by the following equation:

Fig.7.The trend of the atomic radius with the atomic number of lanthanide elements.

Fig.8.Changes rule of The equilibrium potential of lanthanide elements on Zn cathode with atomic number.

Table 1 shows that the elements in the open circuit chronopotentiometry are the representation of the voltage corresponding to the alloys.When the data was plotted and fitted using a linear function,the slope and intercept were determined to be 6.58531 and 4.38501,respectively,as shown in Fig.9.The correlation coefficient and adjusted determination coefficient of the line are 0.99831 and 0.99625,respectively,which are both close to 1,indicating that there is a verystrong linear correlation between(x1ln x1+x2ln x2)and 1/(E×).Hence,formula 1 can be written as

Table 1 The equilibrium potential of Zn and rare earth elements for 10s in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)at 923 K

Fig.9.Linear plot of 1/(E×)vs.x1ln x1+x2ln x2of Zn and La,Sm,Gd,Er,Yb 10 s in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)at 923 K,respectively.

Fig.10.OCPs of Zn and alkali mental or transition mental elements:ZnCl2(1.5 wt%)-(I)MgCl3,(II)CaCl2,(III)NbCl3,(IV)LiCl,(V)PrCl3,(VI)CeCl3,(VII)DyCl3(2.0 wt%)for 10 s in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)at different temperatures.

where E means the formation potential of Zn1Lns1,r2indicates the radius of Lns,x1and x2are rZn/(rZn+r2)and r2/(rZn+r2),respectively.

4.Expansion of the Application of the Formula

To verify if formula 2 applies to other zinc alloys,we conducted experiments on other lanthanides(Ce,Pr,and Dy),alkali(Li,Mg and Ca)and transition(Nb)metals,and the results were shown below.

The OCP diagrams of ZnCl2(1.5 wt%)and CeCl3,PrCl3,DyCl3,CaCl2,MgCl2,NbCl5,LiCl(2.0 wt%)in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)for 10 s at different temperatures are shown in Fig.10.It is worth noting that although lithium can form intermetallic compounds with zinc,as shown in Fig.10(Li)(around-2.17 V,-1.95 V and-1.71 V),it is difficult to form a large amount Li-Zn alloys in the KCl-LiCl system.Furthermore,when other elements form alloys with Zn,it is difficult to detect the formation of Li-Zn alloys,even in the Li-rich system.It means that LixZnyis less stable than other intermetallic compounds and will undergo spontaneous decomposition while there were other metal elements.This is consistent with the system mentioned above that spontaneously forms more stable intermetallic compounds.

The open-circuit experiment results are shown in Fig.11.When forming alloys with zinc in the same deposition time,the needed time will be shortened with the increase of atomic number.We can call this phenomenon as“opposites attract”.Taxil[19]showed the relationship of the composition of electrolyte,which all indicate that the greater the difference in atomic structure,the more stable the binding process and the less energy required.This indirectly proves the theory of“opposites attract”.In the process of forming intermetallic compounds,atoms are bonded by metal bonds,the larger the difference between the atomic structure,the easier to combine to form the stable alloys.While at the same type of element atomic number difference is greater,the much difference between the atomic structure,the easier to form intermetallic compounds.

Fig.11.OCPs of the chloride of Zn and rare earth,alkali metal,transition metal elements for 10 s in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)at 923 K.

The precipitation potentials of Nd,Eu,Tb,Ho,Tm,Lu on Zn cathode are shown in Tables 2 and 3.Table 2 shows the atomic radius of Ce,Pr,Eu,Tb,Dy,Ho,Tm,Lu,Li,Mg,Ca,Nb and the corresponding x1,x2and x values.By bringing the data in Tables 1 and 2 into formula 2,respectively,we can know the differences between the calculated and experimental voltage values,as shown in Table.3.The differences are all close to 0.01 V,implying that formula 2 can predict the precipitation potential with great accuracy.The linear plot of the precipitation potential of all tested metals on the Zn cathode is shown in Fig.12.We can find that they almost overlap.To sum up,formula 2 can accurately predict the precipitation potential of zinc and other metal elements.

Table 2 The other atomic radius of the elements that can form alloys with zinc in the experiment

Fig.12.Linear ftited curve of 1/(E×)and x1ln x1+x2ln x2of zinc with rare earth,alkali metal and transition mental elements in the LiCl-KCl eutectic at the tungsten electrode after electrodepositing at-2.50 V(vs.Ag/AgCl)for 10 s at 923 K.

5.Conclusions

Zn forms the most stable intermetallic compounds with corresponding elements directly or indirectly.The reaction ions do not need to reach the theory temperature,because,during the reaction,the ions are likely to react at thousands of degrees at high temperature which is much higher than the energy barrier.And it is easier with light rare earth metals,while harder with heavy rare earth elements.There has a grading rule about the voltage value and atom radius of zinc and rare earth elements when they form intermetallic compounds.And the rule can be confirmed by the following formula 1/(E×)=6.5853(x1ln x1+x2ln x2)+4.3850.With such a model and equation,it is possible to provide the most basic theoretical basis of the alloy preparation,electrolytic separation,and purification between the potential value and the radius of the zinc and transitional or alkaline earth elements when they form alloys.Nevertheless,more deep researches are needed to separate the different intermetallic compounds of Zn at a different potential.

Acknowledgments

We want to thank Ke Ye for providing language help and writing assistance.