Computational design of Mg alloys with minimal galvanic corrosion

Krishnamohan Thkkpat,Hyun-Sop Han,Ji-Won Choi,Sun-Chol L,Eul Sik Yoon,Guanzh Li,Hyun-Kwan Sok,f,Yu-Chan Kim,f,***,Ja-Hun Kim,Pil-Ryun Cha,*

a Indo-Korea Science and Technology Center,Jakkur,Bangalore 560065,India

b Division of Nano & Information Technology,KIST School,Korea University of Science and Technology,Seoul 02792,Republic of Korea

c Electronic Materials Research Center,Korea Institute of Science and Technology,Seoul 02792,Republic of Korea

d Center for Biomaterials,Biomedical Research Institute,Korea Institute of Science and Technology,Seoul 02792,Republic of Korea

eDepartment of Plastic and Reconstructive Surgery,Korea University College of Medicine,Seoul 02841,Republic of Korea

fDivision of Bio-Medical Science and Technology,KIST School,Korea University of Science and Technology,Seoul 02792,Republic of Korea

g School of Advanced Materials Engineering,Kookmin University,Seoul 02707,Republic of Korea

Abstract Formation of galvanic cells between constituent phases is largely responsible for corrosion in Mg-based alloys.We develop a methodology to calculate the electrochemical potentials of intermetallic compounds and alloys using a simple model based on the Born-Haber cycle.Calculated electrochemical potentials are used to predict and control the formation of galvanic cells and minimize corrosion.We demonstrate the applicability of our model by minimizing galvanic corrosion in Mg-3wt%Sr-xZn alloy by tailoring the Zn composition.The methodology proposed in this work is applicable for any general alloy system and will facilitate efficient design of corrosion resistant alloys.

Keywords:Galvanic corrosion;First-principles;Cluster expansion;Thermodynamics;Modeling;Magnesium alloys.

1.Introduction

In recent years,magnesium and its alloys have attracted great attention as degradable materials for cardiovascular and orthopedic implants owing to their biocompatibility,degradability and high strength-to-weight ratio[1–21].However,rapid corrosion of Mg alloys and the hydrogen gas by-product could have detrimental effects on the host tissue,thereby limiting their clinical application.Corrosion of Mg alloys mainly occurs due to galvanic coupling between the constituent phases.The potential difference between the two phases acts as a driving force for this spontaneous electrochemical process when it comes in contact with an electrolyte.The phase with the lower potential(anodic phase)gets preferentially corroded and this preferential corrosion can be minimized by reduction of the potential difference between the two phases or by aligning them.

Fig.1.Standard Born-Haber cycle for a redox reaction of a pure element.The plots(i–iii)demonstrate the correlation between the total sum of energy at sublimation,ionization and solvation steps with the experimentally obtained value of standard electrode potential(SEP).

A galvanic series shows which metal(or semi-metal)phase is noble or active,and it can be experimentally determined by constructing electrochemical cells.The standard electrode potential(SEP)or standard reduction potential,is a measure of the thermodynamic oxidizing and reducing ability of a pure elemental metal at a standard state,and it conventionally determines the galvanic series[22].SEP values have been well documented for pure metals for many years,and they can be used to determine which metal(phase)is noble or active within galvanic couples.A galvanic series measured in a standard state can also be applied to various different corrosion environments.However,for binary or multi-component metal alloys,a limited amount of data on such potentials have been reported in literature due to numerous possible combinations to create different alloy phases.Therefore,the prediction of galvanic coupling in metal alloys and their associated corrosion tendency,would greatly benefit from a computational methodology that calculates their electrochemical potential values in accordance with the SEP.

Herein,we propose a simple model to estimate the standard electrochemical potential of pure metals using the Born-Haber cycle and extend it to estimate the electrochemical potentials of intermetallic compounds and solid solutions.The proposed model is then applied to the Mg-Sr-Zn ternary alloy system.Thermodynamic free-energy calculations were carried out to estimate the solubility of Zn in the multiphase alloy system under equilibrium conditions via cluster-expansion hamiltonians which were parametrized using density functional theory(DFT)total energies.Subsequently,in order to minimize the galvanic corrosion within the system,the amount of Zn to be added to the Mg-3wt%Sr alloy system is determined.Lastly,we carry out experimental verification of our theoretical predictions.

2.Material and methods

Material Preparation:Commercially pure Mg(99.98%)ingots and Sr(99.95%)metal grains were melted in a stainless still crucible under an Ar atmosphere at 700 °C for 120 min.The chemical composition of the alloy was confirmed by ICP-AES(Inductively Coupled Plasma-Atomic Emission Spectrometry).Each specimen was polished with sandpaper of grit size #4000 to 3 μm,1 μm,and 0.3 μm thickness.FE-SEM(Inspection F)and EDS(Energy Dispersive X-ray Spectroscopy)were used to confirm the distribution and existence of different phases.

Immersion Test:1 mm thick,Φ8 mm coin shape specimens were polished with sandpaper of grit size #2000.After the polishing,ultrasonic cleaning was performed using ethanol and acetone,followed by drying.The specimen was immersed in the Hank’s Balanced Salt Solution(HBSS)to measure the amount of hydrogen gas generated by the corrosion of Mg(1 mol of Mg generates 1 mol of hydrogen gas).HBSS contains the following components in g/L(Calcium Chloride 0.1396,Magnesium Sulfate 0.09767,Potassium Chloride 0.4,Potassium Phosphate Monobasic 0.06,Sodium Chloride 8.0,Sodium Phosphate Dibasic 0.04788,D-Glucose 1.0).The temperature was maintained at 37±0.5 °C to achieve a similar environment to that of the human body.In addition,the homeostasis effect of the human body was applied to replace about 55% of the total solution with a fresh HBSS solution every 24 h.

Fig.2.Schematic of the extended Born-Haber cycle for an intermetallic compound/alloy.ΔGTot is calculated using the Born-Haber cycle in Fig 1.

Weight loss Test:1 mm thick,Φ8 mm coin shape specimens were polished with sandpaper of grit size #2000.After the polishing,ultrasonic cleaning was performed using ethanol and acetone,followed by drying.The specimen was immersed in HBSS to measure the total weight loss after 24 h and 62 h.The corrosion products were washed away in chromic acid(CrO3:250 g,distilled water:1000 ml)for 20 min before the measurement.The temperature was maintained at 37±0.5 °C to achieve a similar environment to the body.In addition,the homeostasis effect of the human body was applied to replace about 55% of the total solution with a fresh HBSS solution every 24 h.

Electrochemical Test:The surface of the specimen was polished with sandpaper of grit size #2000.The electrochemical experiments were carried out using an electrochemical cell with a conventional three-electrode system and a potentiostat(CHI 760C,CH Instruments,Inc.)at 37 °C in a constant temperature bath with 300 ml of HBSS.Platinum(Pt)was used as a counter electrode of the working electrode,and a silver/silver chloride(Ag/AgCl)electrode was used as a reference electrode.Open circuit potential(OCP)tests were performed for 2500 s immediately after the samples were immersed in the solution.The polarization curves were measured at a rate of 0.001 mV/s.

Material Characterization:The immersed specimens were washed with distilled water to remove ions and substances in the solution that could remain on the specimen surface and dried.The cross section was polished with sandpaper of grit size # 4000 until its thickness was 3 μm and 1 μm.Components and behavior of the corrosion layer were analyzed using FE-SEM(Field Emission Scanning Electron Microscopy,Inspect F)and EDS.The size of the electron beam and the current was 3.5 and 15.00 kV,respectively.

3.Theory

3.1.Modified Born-Haber cycle

The Born-Haber Cycle is a simple approach to calculate reaction energies.A schematic of the Born-Haber cycle of a redox reaction

is shown in Fig.1.Gibbs free energy is a state function that has no dependency on the path of the reaction,but depends only on the initial and final states of the reaction.Therefore,the redox reaction where a bulk solid transforms into a hydrated ion can be represented as a 3 step process comprising of 1)sublimation of the solid to gas phase,2)ionization of the gaseous phase and 3)solvation of the ions.The change in free energy of this redox reaction can be calculated as

whereΔGSubdenotes the sublimation or cohesive energy of the solid,ΔGIonizationdenotes the ionization energy of the gaseous atoms andΔGSolvationdenotes the solvation energy of the ion.The change in free energy can be linked to the SEP(E)by the equation wherenis the charge of the solvated ion andFis the Faradays constant.We collected the experimentally measured SEP and accurate energies of sublimation,ionization and solvation of 40 elements readily available in literature[22–24].The plots in Fig.1(i-iii)show the correlation between summation of energies(normalized by n)at the end of each step in the cycle and SEP of these 40 elements.The plots after the sublimation and ionization steps(Fig.1 i and ii respectively)look scattered with no clear correlation.After the inclusion of solvation energy in the 3rd step(Fig.1 iii),a linear correlation can be observed for all the elements,as is also evident from Eq.(2).This clearly demonstrates that the thermodynamic Born-Haber cycle can be successfully applied for the estimation of SEP,if the cohesive,ionization,and solvation energy values for the element are available.

In practical corrosion applications,the galvanic series by SEP is well established and agrees with the galvanic series obtained using experimentally measured OCPs;therefore,when a galvanic couple is constructed,it is easy to determine which phase is active or noble.However,only a limited number of experimentally obtained OCP values are currently available and it is not possible to define the electrochemical potential for metal alloys and intermetallic compounds.Therefore,we propose extension of the Born-Haber cycle to estimate the redox potential in accordance with standard potentials for binary,ternary,and higher multicomponent metal alloys and compounds.For any intermetallic compound or alloy(Am1Bm2Cm3Dm4…),the formation energy(ΔGFormation)and mixing energy(ΔGMix)terms need to be considered in addition to Eq.(1)(see Fig.2).This’extended’Born-Haber cycle can be considered as a set of parallel and independent cycles for all constituent elements in the alloy/intermetallic compound,after a decomposition step where it decomposes into its constituent pure elementsA,B,C,D.etc.before sublimation.The modified equation is

whereaiis the activity of ion of elementiin solution.If we assume that the interactions between solvated ions is negligible(ideal solution approximation)the equation can be written as

For alloys,ΔGFormation+ΔGMixcan be calculated directly by ensemble averaging configurations sampled using cluster expansion hamiltonians.

3.2.Free energy calculations

Our calculations are based on first-principles DFT as implemented in the Vienna Ab-initio Simulation Package(VASP)[25].We use the Projector Augmented Wave(PAW)method[26]to model the interaction between ionic cores and valence electrons,and a plane wave basis for representing wavefunctions is truncated using a 500 eV cutoff.We use 6×6×6 and 12×12×7 meshes of k-points in sampling the Brillouin zone integrations for Sr2Mg17and Mg phases respectively.The lattice parameters of Mg after structural optimization area=3.19?A,c/a=1.62and the lattice parameters of Sr2Mg17after structural optimization area=10.52?A,c/a=0.9769.

For alloys due to a large number of possible configurations,ensemble averaging of energies is required for each composition.Since DFT calculations cannot be carried out for thousands of possible configurations(per composition),cluster expansion method[27–29]can be used to sample the energetics of many configurations.Total energy of alloys configurations is calculated by constructing cluster expansion hamiltonians of both Mg+Zn and Sr2Mg17+Zn systems independently.Cluster expansion hamiltonians containing 2-site clusters are trained using the evolutionary genetic algorithm implemented in-house package LACOS.The energy of an alloy configurationσis calculated by

whereE0represents the empty site energy andJ1andJ2,irepresent the effective cluster interactions(ECI)of 1-site and 2-site clusters respectively.∏1and∏2,irepresent the cluster correlation for the 1-site and 2-site clusters respectively,and are calculated by

Fig.3.Comparison of total energies of alloy configurations calculated using DFT and cluster expansion hamiltonians.

Fig.4.Plot of electrochemical potential calculated using the extended Born-Haber cycle along with the experimentally measured corrosion potentials.

where,σidenotes the site occupation variable which takes a value+1 if the site is occupied by Zn and-1 when occupied by Mg.A total of 180 and 130 configurations were used to select and train the ECI’s of Mg+Zn and Sr2Mg17+Zn systems respectively.The final model of the Mg+Zn and Sr2Mg17+Zn systems have seven and five 2-site clusters respectively.Selection of the final model was based on minimizing the RMS error below 1 meV/atom and keeping the number of clusters as low as possible,for rapid sampling.The accuracy of our model is further verified by comparing the energies from DFT and cluster expansion for a set of structures not used for training(see Fig.3).The total energy of 100,000 configurations(NCal)were calculated using the cluster expansion Hamiltonian for different compositions of Zn and used to calculate the free energy.

Free energies are calculated using the GQCA[30,31]method.The free energyG(x,T)at a compositionxof alloying element Zn and temperatureTis:

The entropy termS(x,T)is calculated using

The probability distribution functionpiat temperatureTis

whereZrepresents the partition function

The above summations run over all the alloy configurations sampled(Ncal)with energyEi.NRealis the total number of possible alloy configurations for a given composition.

Finally,the internal energyU(x,T)is calculated by

The vibrational contribution to free energy is not included in this work.

4.Results and discussion

4.1.Theoretical predictions

Fig.5.The calculated electrochemical potential of(a)Mg and(b)Sr2Mg17 phase as a function of Zn concentration.

We first demonstrate the extended Born-Haber cycle on Mg intermetallic compounds.The calculated electrochemical potentials for some select intermetallic compounds is plotted in Fig.4 against its experimentally measured corrosion potential[32].Our calculated values differ significantly from experimentally measured values,but correctly reproduces the trend in ordering(i.e.,same order of activity).The difference in magnitude is largely due to non-ideal experimental conditions.The potential of pure Mg is-2.36 V in pure water(under standard conditions),whereas it is-1.65 V in 0.1 M NaCl solution.Other real-time factors like the formation of surface films in the specimen during OCP measurements is also responsible for this difference.The success of our model is in reproducing the correct trend in the activity.In a multicomponent alloy system with Mg and Mg2Zn or Mg and Mg17Al12,the Mg phase will get selectively corroded whereas for a system with Mg and Mg2Ca the intermetallic phase will get selectively corroded.The Mg2Ca phase has been shown to be selectively corroded in Mg-Ca alloys from previous studies[33].Hence,we can use our extended Born-Haber cycle approach to estimate and construct a database of potentials for any intermetallic phase by calculating the formation energy from first-principles,if the structure is known.Such a database can be useful in predicting formation of galvanic couples in alloys.

After predicting the possibility of formation of galvanic cells,we demonstrate how galvanic corrosion can be eliminated by aligning the potentials of both the phases.From our database,we found that the Sr2Mg17intermetallic phase has an electrochemical potential of-2.387 V,which is very close to that of pure Mg matrix(E=-2.36 V).It is possible to align the electrochemical potential of the phase by alloying with Zn.As shown previously,galvanic corrosion in Mg-Ca-Zn alloys can be controlled by optimizing the concentration of Zn[33].A similar approach can be used for Sr2Mg17phase whose potential is closer to the Mg phase than that of the Mg2Ca phase.Hence,Mg-Sr-Zn ternary alloy was selected as our model system.Mg-3wt%Sr alloy microstructure primarily consists of Sr2Mg17intermetallic phase in Mg matrix[34].Due to the lower potential of the Sr2Mg17phase,it acts as the anode and gets preferentially corroded.The potential was expected to align close to the Mg phase by addition of Zn into the phase.The added Zn can dissolve either into the matrix phase or the intermetallic phase.In this study two different solid solutions were modeled.The free energy of the Mg+Zn and Sr2Mg17+Zn solid solutions,calculated using the GQCA method is shown in Fig.1a in the supplementary information.The free energy of the Sr2Mg17+Zn phase is lower than that of the Mg+Zn solid solution at all temperatures considered,indicating a higher solubility of Zn in the intermetallic phase during processing.The electrochemical potential of the intermetallic phase increases linearly with Zn concentration(see Fig.5).At a Zn concentration of 1.8% the potential of this phase in aligned with that of the Mg phase.A similar linear increase in the electrochemical potential can be observed for the Mg solid solution.Therefore,alloying with Zn is an effective method to align the potentials.Next,we tailor the exact amount of Zn that should be alloyed with the system to effectively compare with experimental results.

Fig.6.(a)Equilibrium concentration of Zn in Mg and Sr2Mg17 phases as a function of total Zn concentration in the system(c),obtained from both theory and experiments.b)The electrochemical potential of both Mg and Sr2Mg17 phases as a function of total Zn concentration in the system.It can be clearly seen that at c=0.42%,the potentials of both the phases are balanced.Microstructure of c)Mg-3wt%Sr,d)Mg-3wt%Sr,e)Mg-3wt%Sr-0.3wt%Zn and f)Mg-3wt%Sr-1wt%Zn alloys after immersion in HBSS.The microstructure was imaged using FE-SEM.

Fig.7.The SEM micrographs of Mg-5wt%Ca-xZn samples imaged after immersion in HBSS a)x=0 wt% b)x=0.5 wt% d)x=1 wt% e)x=1.5 wt%.c)The electrochemical potential of both Mg and Mg2Ca phases as a function of total Zn concentration in the system.It can be clearly seen that at c=1.07%,the potentials of both the phases are balanced.s

The equilibrium concentrations of an element in various phases of a multiphase alloy can be estimated using a simple thermodynamic analysis.For the case of an element Zn added to a multiphase system consisting of Mg and Sr2Mg17phases,the total free energy of the system can be expressed as

wherefis the phase fraction of the Sr2Mg17phase and,denotes the composition of Zn in Mg and Sr2Mg17phases respectively.Assuming all Sr atoms form the intermetallic phase in an Mg-3wt%Sr alloy,the phase fraction is 0.08.Minimizing the above equation with the following constraint on the total concentration of Zn

yields

The above equation indicates that the system is in equilibrium when the chemical potentials of both the phases are the same.Therefore,for any amount of Zn added to the system,the composition in individual phases can be estimated using this method.The chemical potentials were calculated from the derivative of free energies(see Fig.1(b)in supplementary information).The chemical potentials are lower for the intermetallic phase and the trend in the equilibrium concentration of Zn(see Fig.6a),shows that it is more soluble in the intermetallic phase.This is also evident from the higher free energies of solid solutions of Zn in the matrix compared to that of Zn in the intermetallic phase.To achieve the critical concentration of 1.8% in the intermetallic phase,the total Zn added to the system should be approximately 0.38%.Since Zn also modifies the potential of the Mg phase,the actual concentration will be slightly higher.The electrochemical potential of both the phases(see Fig.6b)calculated using the equilibrium concentrations are found to be similar at a total Zn concentration of 0.42%.At concentrations above 0.42%the Mg phase will get preferentially corroded instead of the intermetallic phase.Experimental validation of our predictions is demonstrated in the next section.

Additionally,we also applied this method on the previously proposed Mg-Ca-Zn alloy system[33,35].Mg-5wt%Ca-1wt%Zn alloy was shown to be a good candidate for applications as biodegradable implants.The microstructure of Mg-5wt%Ca has 2 phases,Mg2Ca and Mg(see Fig.7).As shown earlier in Fig.4,the Mg2Ca phase has an electrochemical potential of-2.42 V.Similar to the case of Sr2Mg17,the potential increases as a result of alloying with Zn and aligns with the Mg phase.Our calculation of equilibrium concentration predicts that a total Zn concentration of 1.07% is the critical concentration at which the potentials align and preferential corrosion behavior is reversed(see Fig.7).Our predictions match closely with experimental observations for SEM images of specimens after immersion in HBSS.For Zn concentrations below 1%,the intermetallic phase gets corroded,whereas for concentrations above 1%,the Mg phase gets corroded.Hence,we have demonstrated a method to predict and control galvanic corrosion behavior in alloys by estimating the concentrations of the alloying elements.This methodology can also be easily extended to any other alloy system.Using formation energy,available from existing materials Big Data repositories such as AFLOWLIB,Materials Project and the Open Quantum Materials Database(OQMD),formation of galvanic couples in alloy systems can be efficiently predicted and our methodology can be used to modify its corrosion properties.

4.2.Experimental verification

Fig.8.(a)Hydrogen evolution rate and(b)Weight Loss rate of Mg-3wt%Sr,Mg-3wt%Sr-0.3wt%Zn and Mg-3wt%Sr-1wt%Zn after immersion in HBSS.

To experimentally verify our predictions,we prepared samples of Mg-3wt%Sr-xwt%Zn(x=0,0.3,1)by casting.The chemical compositions of the alloys were verified by ICP and microstructures were analyzed using FE-SEM and EDS.As shown in Fig.6c.it is observed that the microstructure of Mg-3%Sr consists of 2 phases,mainly the Mg matrix phase(dark)and the Sr2Mg17intermetallic phase(bright)distributed along the grain boundaries.The EDS results of both the Mg and Sr2Mg17phase for different concentrations of Zn is plotted in Fig.6a.A clear agreement can be observed between our theoretical predictions and experimental observations.Zn is more soluble in the intermetallic phase compared to the Mg matrix phase.To verify the corrosion behavior,we immersed the samples in HBSS for 2 days and analyzed the microstructure under FE-SEM(see Fig.6d–f).The bright part is the intermetallic phase,the gray region is the Mg phase and the darkest part is the resin used to load the specimen.The dark region between the sample and resin is the corroded part.For Mg-3%Sr it can be clearly seen that corrosion advances mostly along the grain boundary i.e.,the intermetallic phase.This is due to the lower potential of the intermetallic phase compared to the Mg phase.For the case of Mg-3%Sr-1%Zn,the corrosion behavior is opposite to that of the previous case and corrosion advances mostly in the Mg matrix phase.This is possible only if the potential of Mg phase is lower than that of the intermetallic phase.Such a change in potential is possible only due to the dissolution of Zn into the intermetallic phase and increasing its potential as predicted by our theoretical model.At an intermediate Zn concentration of 0.32%,it can be seen that corrosion advances uniformly along both the phases.This is very close to the 0.42% predicted from our theoretical calculation.We further verified the trend in potential by measuring the OCP of pure Mg and Sr2Mg17(with and without Zn)samples.The OCP of the samples also follow the same qualitative trend as our theoretical predictions(see Fig.2 in supplementary information).The OCP of pure Sr2Mg17samples are lower(more negative)than that of pure Mg and hence get preferentially corroded.Upon alloying with Zn,the OCP of Sr2Mg17is almost the same as that of pure Mg and hence the uniform nature.Finally,we also checked the corrosion behavior by measuring both the hydrogen evolution rate[36]and weight loss[17]in HBSS(see Fig.8).For hydrogen evolution rate,the unalloyed Mg-3wt%Sr sample showed rapid corrosion rate compared to samples containing Zn.It can be clearly seen that the sample with 0.3 wt.% Zn has the lowest corrosion rate among all the samples.Weight loss experiment results showed similar trends to the hydrogen evolution results where the 0.3 wt.% Zn samples showed smallest weight loss followed by 1 wt.% Zn and Mg-3wt% Sr samples.Hence,we have successfully tailored the Zn composition in Mg-Sr-Zn ternary system to prevent the formation of galvanic couples and improve corrosion behavior.

5.Conclusion

(1)We successfully developed a computational methodology based on the thermodynamic Born-Haber cycle to efficiently predict electrochemical potentials of arbitrary phases as a function of compositions and equilibrium compositions of alloying elements in each constituent phase.

(2)We successfully confirmed our methodology by validation from experiments for Mg-Sr-Zn and Mg-Ca-Zn alloy systems.

(3)The methodology presented in this paper has the potential to speed-up materials design process of corrosion resistant alloys,particularly,if it is combined with preexisting materials databases(Materials Project,OQMD,NOMAD)and machine learning.

Acknowledgments

This work was supported by the Technology Innovation Program(20012502)funded by the Ministry of Trade,Industry and Energy and National Research Foundation of Korea(NRF)Grant funded by Ministry of Science and ICT(MSIT)(NRF-2019R1A2C1089593,NRF-2020M3H4A3106736,NRF-2021M3H4A6A01045764).

Supplementary materials

Supplementary material associated with this article can be found,in the online version,at doi:10.1016/j.jma.2021.06.019.