Abstract
Aluminum and magnesium are the lightest structural metals, and therefore, various alloys based on them are widely used in both, automotive and aerospace industries. However, aluminum and magnesium are very easily affected by atmospheric and aqueous corrosion, and, therefore, the alloying elements should enhance their corrosion stability. In this work, the thermodynamic analysis of phase and chemical equilibria involving aluminum and magnesium alloys doped with silicon in oxygen–containing air environments, as well as the analysis of chemical and electrochemical equilibria involving these alloys in aqueous environments is conducted. The phase and chemical equiliibria in the Al–Mg, Al–Si, Mg–Si, and Al–Mg–Si systems at 298 K are considered, and the thermodynamic activities of the components of common Al–Mg–Si system alloys are calculated. The invariant chemical equilibria in the systems Al–Mg–O, Al–Si–O, Mg–Si–O at 298 K are considered, the isothermal section of the state diagrams of these systems are plotted, and the oxidation scheme of the Al–Mg–Si system alloys in excess oxygen is proposed. The chemical and electrochemical equilibria in the Al–Mg–Si–H2O system at 298 K are considered and presented in form of the activity – pH and the potential – pH diagrams, and the oxidation of the Al–Mg–Si system alloys in aqueous environments is discussed.
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Introduction
The alloys of aluminum1,2,3,4,5,6,7 and magnesium8,9,10,11,12 are widely used in the automotive3,4,5,10,11,12 and aerospace industry1,2,8,9 from the second half of the 20th century. Applications of such alloys were analysed in detail in multiple review articles1,2,3,4,5,6,7,8,9,10,11,12. Different alloy groups used in various environments were distinguished depending on the alloying additives. The main alloying elements for aluminum are chromium, copper, magnesium, silicon, titanium, zinc, zirconium, scandium, tin, lithium and iron1,5,13,14, and for magnesium they are aluminum, bismuth, copper, cadmium, iron, thorium, lithium, manganese, nickel, lead, silver, silicon, chromium, zinc, strontium and rare–earth elements10,11,12.
Corrosion of metals and alloys is a complex problem, and the research methods of the corrosion studies are very diverse. They include the thermodynamic analysis of the oxidation processes and the formed products, the kinetic studies of chemical and electrochemical processes on the phase boundaries, the surface investigation, and the studies of the physical, chemical and mechanical properties of formed corrosion products. There were several experimental studies devoted to the various aspects of corrosion of different aluminum15,16,17 and magnesium17,18 alloys, these studies were reviewed in the papers15,16,17,18. However, the thermodynamic description of the oxidation of a particular alloy is always the first step toward understanding the corrosion mechanism and products, which forms a basis for the subsequent studies of reaction kinetics and product properties. Silicon is one of the major alloying elements for both aluminum and magnesium. Aluminum alloys doped by magnesium and silicon are characterised by moderate strength, good ductility1, good formability, weldability and machinability5, and excellent corrosion resistance1,5. However, the thermodynamic estimations of the corrosion behaviour of these alloys are low–numbered, scattered, and limited by the small number of alloys, systems, and corrosive environments19,20,21,22,23,24,25. This paper therefore aims to systematically describe the corrosion and electrochemical properties of the Al – Mg – Si system alloys from a thermodynamic viewpoint both in aerial and aqueous environments in excess of oxidant.
Results and discussion
Thermodynamic description of the metallic systems at 298 K
The thermodynamic modeling of the equilibrium composition and properties of the alloys mentioned in this section at 298 K was performed using the MatCalc software26 using the mc_al.tdb database, version 2.035. The solid solutions were modeled in terms of the substitution solution model27 using the Redlich–Kister polynomial expressions28 for the excess Gibbs energies of the solutions.
The system Al–Mg
The aluminum alloys containing magnesium belong to the 5000 series of wrought aluminum alloys and to the 5xx.x series of the cast aluminum alloys29. The composition of some Al–Mg alloys is presented in Table 1. The phase diagram of the system Al–Mg was modeled several times30,31,32,33. The system contains two solid solutions of Mg in (Al) with the fcc crystal structure and of Al in (Mg) with the hcp crystal structure, and three intermetallic phases. However, the ε-phase (Al30Mg23) is not thermodynamically stable at 298 K. The β-phase (Al140Mg89) is a stoichiometric compound, whereas the γ-phase has a noticeable homogeneity range. The expressions for the parameters of the model were taken from work30. According to the thermodynamic prediction, the maximum solid solubility of Mg in fcc-Al at 298 K equals 0.621 weight percent (xAl (fcc) = 0.9931, xMg (fcc) = 0.0069, aAl (fcc) = 0.9933, aMg (fcc) = 0.0519, where x is the mole fraction, and a is the thermodynamic activity), and that of Al in hcp-Mg at 298 K equals 0.231 weight percent (xAl (hcp) = 0.0021, xMg (hcp) = 0.9979, aA (hcp) = 0.0067, aMg (hcp) = 0.9990). The equilibrium phases of the alloys at 298 K and the thermodynamic activities of the components of the corresponding solid solutions are presented in Table 1.
The system Al–Si
The aluminum alloys containing silicon belong to the 4000 series of wrought aluminum alloys and to the 4xx.x series of the cast aluminum alloys29. Wrought Al–Si alloys contain usually no more than 5 weight percent Si, whereas cast alloys may contain up to 20 wt.% Si, and the alloys produced by powder metallurgy may contain up to 50 wt.% Si. The composition of some Al–Si alloys is presented in Table 2. The phase diagram of the system Al–Si was modeled several times34,35,36,37. The system contains a solid solution of Si in (Al) with the fcc crystal structure, and Al is practically insoluble in (Si) with the diamond crystal structure at any temperature. Although the formation of aluminum silicides in thin layers38, at high pressures39, and as the metastable compounds during alloy crystallisation40 was reported, no thermodynamically stable aluminum silicides exist as bulk phases. The expressions for the parameters of the model were taken from work34. According to the thermodynamic prediction, the maximum solid solubility of Si in fcc-Al at 298 K equals 6.7·10−6 weight percent (aAl (fcc) = 1, aSi (fcc) = 1.6·10−8). The equilibrium phases of the alloys at 298 K are presented in Table 2.
The system Mg–Si
Although there exist no commercially available binary alloys containing only magnesium and silicon, there were some studies, where such alloys were prepared and their mechanical properties were studied41,42,43. The phase diagram of the system Mg–Si44 shows that a solid solution of Si in (Mg) with the hcp crystal structure exists, but magnesium is practically insoluble in (Si) with the diamond crystal structure. The expressions for the parameters of the model were taken from work44. The calculations show that at 298 K both, magnesium and silicon, are practically insoluble in each other. A stoichiometric magnesium silicide Mg2Si also exists in this system.
The system Al–Mg–Si
The aluminum alloys containing both magnesium and silicon belong to the 6000 series of wrought aluminum alloys26. The composition of some Al–Mg–Si alloys is presented in Table 3. The thermodynamic properties of the system Al–Mg–Si were modeled several times45,46,47,48. The expressions for the parameters of the model were taken from works45,48. The equilibrium phases of the alloys at 298 K and the thermodynamic activities of the components of the corresponding solid solutions are presented in Table 3.
Thermodynamic properties of the intermetallic compounds
The estimated standard Gibbs energies of formation of the intermetallic compounds Al12Mg17, Al140Mg89 and Mg2Si are collected in Table 4.
Apparently, there is a considerable difference between the value of the standard Gibbs energies of formation of Mg2Si predicted by the authors of the work44 and those presented in the reference book49. In this case, the latter value is chosen for further calculations.
The γ-phase in the Al–Mg system was modeled by the authors of the work30 as the solid solution in terms of the sublattice model50,51. However, for the thermodynamic calculations at the room temperature, such comprehensive model is not needed, and the thermodynamic description of the phase can be simplified. The range of non-stoichiometry of the γ-phase at 298 K from the data from30 was estimated using the MatCalc software26. It was found that the γ-phase exists at room temperature in the interval of \(0.5764 \, \leqslant \, {x}_{{\rm{Mg}}(\gamma )}\, \leqslant \, 0.5860\). In the paper30 the γ-phase was modeled using three sublattices as (Mg)5(Al,Mg)12(Al,Mg)12. The Mg-rich phase boundary corresponds to the stoichiometric compound (Mg)5(Al)12(Mg)12 (or Al12Mg17). When the aluminum mole fraction in the γ-phase grows, it partially displaces magnesium from the third sublattice, and, in this case, the γ-phase might be described by the formula Al12+kMg17–k. The Al-rich phase boundary corresponds to the value k = 0.284, and to the compound Al12.284Mg16.716. Using the data from paper30, the standard Gibbs energies of formation of two end-members of the γ-phase, namely (Mg)5(Al)12(Mg)12 and (Mg)5(Al)12(Al)12 were estimated. The estimated values are \({\Delta }_{{\rm{f}}}{G}_{298}^{{\rm{o}}}\left({{\rm{Al}}}_{12}{{\rm{Mg}}}_{17}\right)=-67900\,{\rm{J}}\cdot {{\rm{mol}}}^{-1}\) and \({\Delta }_{{\rm{f}}}{G}_{298}^{{\rm{o}}}\left({{\rm{Al}}}_{24}{{\rm{Mg}}}_{5}\right)=67600\,{\rm{J}}\cdot {{\rm{mol}}}^{-1}\). From these values, the following expression was derived using the Waring–Lagrange interpolation formula52,53: \({\Delta }_{{\rm{f}}}{G}_{298}^{{\rm{o}}}\left({{\rm{Al}}}_{12+{\rm{k}}}{{\rm{Mg}}}_{17-{\rm{k}}}\right)=11290\cdot {\rm{k}}-67900\,{\rm{J}}\cdot {{\rm{mol}}}^{-1}\), from which it follows that \({\Delta }_{{\rm{f}}}{G}_{298}^{{\rm{o}}}\left({{\rm{Al}}}_{12.284}{{\rm{Mg}}}_{16.716}\right)=-64700\,{\rm{J}}\cdot {{\rm{mol}}}^{-1}\). These estimated values of the standard Gibbs energies of formation of Al12Mg17 and Al12.284Mg16.716 were used in further calculations.
Thermodynamic description of the oxide systems at 298 K
The oxides of aluminum, magnesium, and silicon
A single oxide exists in the Al–O system54, and it is corundum (Al2O3). In the Mg–O system55,56, only a magnesium monoxide (periclase, MgO) is thermodynamically stable at room temperature and normal pressure, other oxides exist only at elevated pressures57. In the Si–O system58 a single oxide SiO2 is present, which exists at room temperature in the form of quartz.
The system Al2O3–MgO
Thermodynamic modeling of the system Al2O3–MgO was performed several times59,60,61,62,63. There is a considerable solid solubility of corundum in periclase at high temperatures (up to 9.6 mol. % Al2O3 at 2270 °C), but it rapidly lowers with the temperature decrease64, and at temperatures lower than 1000 °C, this solid solubility can be neglected. On the other hand, periclase is practically insoluble in (α-Al2O3) at any temperature. In addition, Al2O3 and MgO form a spinel-type solid solution, which has a wide homogeneity range at high temperatures, but below 1000 °C, it reduces to the stoichiometric compound Al2MgO4.
The system Al2O3–SiO2
Thermodynamic modeling of the system Al2O3–SiO2 was performed several times63,65,66,67,68. According to these studies, there is no solid solubility of either corundum in quartz, or quartz in corundum at any temperature. Two stable aluminum silicates are present in the system, namely, Al2SiO5 and Al6Si2O13. The former exists in three polymorphic modifications, namely, kyanite, andalusite, and sillimanite, and the latter forms the mineral mullite. However, there are considerable contradictions between these studies concerning the thermodynamic stability of these silicates at low temperatures. The phase diagrams of the system Al2O3–SiO2 proposed by the authors of the works65,66,68,69 show mullite as the only thermodynamically stable aluminum silicate in the system at ambient pressure and any temperature. The authors of the work66 indicate that mullite decomposes to the single oxides of aluminum and silicon at 460 K, and that there are no stable intermediate phases in the system at 298 K. However, in the book devoted to the mullite70, it is stated that it is formed from the Al2SiO5-family minerals on heating and decomposes to sillimanite and alumina on cooling or pressure increase, and therefore, is thermodynamically unstable at lower temperatures. The recent thermodynamic modeling of Al2O3–SiO2 system63 also shows the thermodynamic stability of andalusite and kyanite at lower temperatures. The T–p phase diagram of Al2SiO5 polymorphs is also still controversial71,72,73,74,75,76,77,78. It was well-studied in the vicinity of the triple point, but different authors still debate on whether andalusite or kyanite are thermodynamically stable at low temperatures and low pressures. In the most recent thermodynamic modeling of the system63, kyanite was defined as the thermodynamically stable aluminum silicate at 298 K and 1 bar.
The system MgO–SiO2
Thermodynamic modeling of the system MgO–SiO2 was performed several times63,79,80,81,82,83. There are contradictory data on the solid solubility of quartz in periclase. Whereas in the paper80, a considerable solid solubility was observed, other authors64,79,82,83 report the absence of solid solubility. In any case, even if this solid solubility exists, it might be neglected at the temperature of 298 K. On the other hand, periclase is practically insoluble in quartz at any temperature. Two stable magnesium silicates are formed in the system, namely Mg2SiO4 and MgSiO3. Both are the stoichiometric compounds but exist in a variety of polymorphic modifications. The former forms a variety of phases at elevated pressures and temperatures84, but, at ambient pressure and temperature, only the mineral forsterite is thermodynamically stable80. The latter also forms several phases at elevated pressures and temperatures85, but at the lower pressures exists in three polymorphic modifications, namely, protoenstatite, orthoenstatite and clinoenstatite86,87. According to the data from the work80, clinoenstatite is thermodynamically stable at 298 K and 1 bar.
The system Al2O3–MgO–SiO2
Thermodynamic modeling of the ternary system Al2O3–MgO–SiO2 was performed several times62,63,88,89. In addition to the compounds mentioned in the previous sections, two mixed silicates are present in this system, namely, cordierite (Mg2Al4Si5O18) and sapphirine (Mg7Al18Si3O40).
Thermodynamic properties of the simple and mixed oxides
The estimated standard Gibbs energies of formation of the simple and mixed oxides are collected in Table 5. As could be seen, the values of the standard Gibbs energies of formation estimated by the thermodynamic modeling of the phase diagrams59,62,67,80 agree well with those ones from the reference books49,90. Consequently, the values from the reference book49 were chosen for further calculations. No value of the standard Gibbs energy of formation for pyrope Mg3Al2(SiO4)3 was found in the literature, and this compound was not considered further.
In order to double-check the selected data, the Gibbs energy changes and the equilibrium constants for the reactions of formation of the aforementioned mixed oxides from the corresponding simple oxides were calculated and presented in Table 6. The calculations prove that all the complex oxides except mullite are thermodynamically stable relative to the simple oxides at 298 K and 1 bar. Therefore, mullite was excluded from further consideration.
Thermodynamic description of the aerial oxidation of alloys at 298 K
Using the data on the metallic systems and on the oxide systems from previous sections, the oxidation reactions of aluminum–magnesium–silicon alloys at 298 K were considered from the thermodynamic viewpoint. The results are presented in form of the isothermal sections91,92 of the Al–Mg–O, Al–Si–O and Mg–Si–O phase diagrams, and the oxygen partial pressures for the invariant equilibria.
The system Al–Mg–O
An isothermal section of the phase diagram of the Al–Mg–O system is presented in Fig. 1, and the equilibria in the system are listed in Table 7.
The description of corresponding phase equilibria is presented in Table 7.
The system Al–Si–O
An isothermal section of the phase diagram of the Al–Si–O system is presented in Fig. 2, and the equilibria in the system are listed in Table 8.
The description of corresponding phase equilibria is presented in Table 8.
The system Mg–Si–O
An isothermal section of the phase diagram of the Mg–Si–O system is presented in Fig. 3, and the equilibria in the system are listed in Table 9.
The description of corresponding phase equilibria is presented in Table 9.
The system Al–Mg–Si–O
The equilibria in the quaternary system Al–Mg–Si–O consist of the equilibria in the boundary ternary systems and the equilibria concerning the formation of cordierite and sapphirine, which are listed in Table 10. It was found that only the formation of cordierite and sapphirine from corundum, periclase and quartz is thermodynamically favoured.
Thermodynamic description of the aqueous species of aluminum, magnesium and silicon at 298 K
The system Al–H2O
Aluminum exists in an aqueous medium primarily in the +3 oxidation state. In the acidic environments, it forms a cation Al3+ (aq), which, upon alteration of the pH value, exhibits a series of consecutive hydrolysis reactions and forms several cationic and anionic species. In concentrated solutions, various polynuclear aluminum species might be formed93. Corundum in the aqueous media undergoes hydration and forms either an oxyhydroxide AlOOH (s), or a hydroxide Al(OH)3 (s). Aluminum oxyhydroxide exists in two polymorphic modifications, namely, diaspore and böhmite94,95,96,97, and aluminum hydroxide has four polymorphs, namely, gibbsite, bayerite, doyleite and nordstrandite94,98,99,100,101. The system Al2O3–H2O is very complex, its phase diagram is still discussable, and the stability of certain phases strongly depends on temperature, pressure, pH of the environment, and the presence of other ions94,95,96,97,98,99. At ambient temperature and pressure, gibbsite is a thermodynamically stable phase94,95,96,98. In addition, aluminum might be reduced to the solid hydride AlH3102 or to the aqueous ion \({{\rm{AlH}}}_{4}^{-}\) 103.
Thermodynamic properties of aluminum aqueous species are summarised in Tables 11–13. Table 11 presents the standard Gibbs energies of formation93,104,105,106,107, Table 12 presents the standard electrode potentials of different half–cell reactions106,108,109, and Table 13 presents the equilibrium constants for various acid–base equilibria110,111. In order to double-check the data, the electrode potentials from Table 12 and the equilibrium constants from Table 13 were calculated from the Gibbs energies of formation from Table 11 and vice versa. Good agreement between the literature data of the various kinds is observed. The values of the standard Gibbs energies of formation of AlH3 (s) and \({{\rm{AlH}}}_{4}^{-}\) (aq) were estimated from the standard electrode potentials. No thermodynamic data on the polymeric species \({{\rm{Al}}}_{30}{{\rm{O}}}_{8}{({\rm{OH}})}_{56}{({{\rm{H}}}_{2}{\rm{O}})}_{26}^{18+}\) 112,113 was found in the literature, and consequently, this cation was excluded from further consideration.
Figure 4 presents the calculated speciation diagram of monomeric aluminum species. It reveals that the cation \({\rm{Al}}{({\rm{OH}})}_{2}^{+}\) (aq) does not predominate in a solution at ambient temperature at any pH level, and is thermodynamically stable only at elevated temperatures. The calculated diagram coincides well with several experimental studies of aluminum speciation112,114,115,116,117,118,119,120,121.
Dashed lines correspond to the equilibrium constants of the hydrolysis reactions of aluminum aqueous species.
Figure 5 presents the activity – pH diagram for Al (III) species. The calculations show that gibbsite precipitates from the aqueous solutions if the thermodynamic activities of aluminum species exceed 1.2·10−8 M. The dashed lines in the diagram represent the formation of polynuclear aluminum species, which is possible only in a hypothetical oversaturated solution, when the precipitation of gibbsite is hindered.
Dashed lines represent hypothetical equilibria in an oversaturated solution.
Figures 6, 7 present the potential – pH diagrams of aluminum at 298 K, 1 bar, and the thermodynamic activities of aluminum species equal to 1 M (Fig. 6) and 10−8 M (Fig. 7). In very diluted solutions, no solid phases are thermodynamically stable (Fig. 7), and aluminum tends to dissolve at any values of potentials and pH. When the concentration of aluminum in the solution rises, the solid gibbsite becomes a thermodynamically stable phase in neutral and alkaline media. As the calculations show, elemental aluminum in an aqueous solution is thermodynamically unstable, because both, aluminum aqueous ions and gibbsite, are reduced directly to alanate-ion \({{\rm{AlH}}}_{4}^{-}\). Solid aluminum in an aqueous media spontaneously disproportionates, however, this reaction is kinetically hindered, so aluminum is not dissolved instantly.
Dashed lines represent hypothetical equilibria with solid aluminum, a short-dashed line corresponds to the standard hydrogen electrode.
Dashed lines represent hypothetical equilibria with solid aluminum, a short-dashed line corresponds to the standard hydrogen electrode.
The thermodynamic expressions for the chemical and electrochemical equilibria in the Al–H2O system are collected in Table 14.
The system Mg–H2O
Magnesium exists in an aqueous medium primarily in the +2 oxidation state. In acidic environments, it forms a cation Mg2+ (aq), and at higher pH values it undergoes hydrolysis first to the cation MgOH+ (aq), and then to the solid magnesium hydroxide (brucite). In concentrated solutions, the polynuclear species \({{\rm{Mg}}}_{4}{({\rm{OH}})}_{4}^{4+}\) (aq) might be formed93. Periclase in an aqueous solution also undergoes hydration to brucite122. In addition, magnesium might be reduced to the solid hydride MgH2123.
Thermodynamic properties of magnesium aqueous species are summarised in Tables 11–13. The values of the standard Gibbs energies of formation of Mg+ (aq) and \({{\rm{Mg}}}_{4}{({\rm{OH}})}_{4}^{4+}\) (aq) were estimated from the standard electrode potentials.
Figure 8 presents the activity – pH diagram for Mg (II) species. The calculations show that brucite precipitates from the aqueous solutions if the thermodynamic activities of magnesium species exceed 3.4·10−7 M. The dashed lines in the diagram represent the formation of polynuclear magnesium species, which is possible only in a hypothetical oversaturated solution when the precipitation of brucite is hindered.
Dashed lines represent hypothetical equilibria in an oversaturated solution.
The thermodynamic expressions for the chemical and electrochemical equilibria in the Mg – H2O system are collected in Table 15.
Figures 9, 10 present the potential – pH diagrams of magnesium at 298 K, 1 bar and the thermodynamic activities of magnesium species equal to 1 M (Fig. 9) and 10−8 M (Fig. 10). The solid brucite becomes the thermodynamically stable phase in neutral and alkaline media. As the calculations show, elemental magnesium in an aqueous solution is thermodynamically unstable, because both, magnesium cations and brucite, are reduced directly to magnesium hydride MgH2. Solid magnesium in an aqueous media spontaneously disproportionates. The aqueous cation Mg+ has no domain of thermodynamic stability.
Dashed lines represent hypothetical equilibria with solid magnesium, a short-dashed line corresponds to the standard hydrogen electrode.
Dashed lines represent hypothetical equilibria with solid magnesium, a short-dashed line corresponds to the standard hydrogen electrode.
The system Si–H2O
In aqueous media, silicon dioxide hydrates to orthosilicic acid H4SiO4 that may form orthosilicates (\({{\rm{H}}}_{3}{{\rm{SiO}}}_{4}^{-}\) and \({{\rm{H}}}_{2}{{\rm{SiO}}}_{4}^{2-}\)) in very alkaline solutions. Other silicates, including polynuclear silicon species, are not thermodynamically stable. Thermodynamic data on various silicon species were summarised and analysed, the activity – pH and potential – pH diagram of the Si–H2O system were plotted, and the thermodynamic expressions for the chemical and electrochemical equilibria were calculated previously124.
Thermodynamic properties of the mixed hydroxides
Just like the simple oxides of aluminum, magnesium and silicon in aqueous media undergo hydration and form the corresponding hydroxides, the mixed oxides do the same. A variety of different clay minerals precipitate from the aqueous solution125. The compound Al2Si2O5(OH)4 forms different polymorphs, namely, kaolinite, dickite, nacrite, and halloysite95,126,127, but kaolinite is thermodynamically stable at the ambient temperature and pressure127,128. The system MgO–SiO2–H2O is also very complex129. The compound Mg3Si2O5(OH)4 forms two polymorphs, namely, chrysolite and lizardite, and there are still different opinions regarding the question of which one is thermodynamically stable at 298 K and 1 bar130,131,132. Other complex hydroxides that might be formed in the system Al2O3–MgO–SiO2–H2O include pyrophillite, talc, anthophyllite, antigorite, sepiolite, chlorite, saponite, palygorskite and montmorillonite. The standard Gibbs energies of formation of these mixed hydroxides are collected in Table 16. In order to double-check the selected data, the Gibbs energy changes and the equilibrium constants for the reactions of formation of the mixed oxides from Table 5 and the mixed hydroxides from the corresponding simple hydroxides are calculated and presented in Table 17. The calculations show that all the complex oxides except mullite, sapphirine and stoichiometric spinel Al2MgO4, and all the complex hydroxides are thermodynamically stable relative to the simple hydroxides and water at 298 K and 1 bar. Therefore, mullite, sapphirine and spinel are excluded from the further consideration.
Thermodynamic description of the aqueous oxidation of alloys at 298 K
Using the data on the metallic systems and on the aqueous systems from previous sections, the equilibria describing the chemical and electrochemical oxidation of aluminum–magnesium–silicon alloys in aqueous environments at 298 K are considered from the thermodynamic viewpoint. The results are presented in form of the potential – pH diagrams133,134 of the systems Al–Mg–H2O, Al–Si–H2O, Mg–Si–H2O and Al–Mg–Si–H2O. The diagrams are plotted at the thermodynamic activities of the aqueous species equal to 10−6 M, because this value is the most representative for the corrosion processes of metals and alloys133. The thermodynamic activities of the components of specific alloys might be taken from Tables 1–3.
The system Al–Mg–H2O
The potential – pH diagram of the Al–Mg–H2O system without consideration of aluminum and magnesium hydrides is presented in Fig. 11, and the equilibria in the system are listed in Table 18.
A short-dashed line corresponds to the standard hydrogen electrode.
The system Al–Si–H2O
The potential – pH diagram of the Al–Si–H2O system without consideration of aluminum hydride is presented in Fig. 12, and that with consideration of alanate-ions – in Fig. 13. The equilibria in the system are listed in Table 19.
A short-dashed line corresponds to the standard hydrogen electrode.
A short-dashed line corresponds to the standard hydrogen electrode.
The system Mg–Si–H2O
The potential – pH diagram of the Mg–Si–H2O system without consideration of magnesium hydride is presented in Fig. 14, and that with consideration of hydride – in Fig. 15. The equilibria in the system are listed in Table 20.
A short-dashed line corresponds to the standard hydrogen electrode.
A short-dashed line corresponds to the standard hydrogen electrode.
The system Al–Mg–Si–H2O
The potential – pH diagram of the Al–Mg–Si–H2O system obviously includes the equilibria from the subsystems Al–Mg–H2O, Al–Si–H2O, and Mg–Si–H2O, and those with the complex silicates of aluminum and magnesium. However, such a complex diagram would be overloaded by the lines and hard to interpret. In order to simplify the diagrams, the aforementioned equilibria from Tables 18–20 are omitted, and only those with quaternary compounds are present. The diagram without consideration of aluminum and magnesium hydrides is presented in Fig. 16, and that with consideration of hydrides – in Fig. 17. The equilibria in the system are listed in Table 21.
A short-dashed line corresponds to the standard hydrogen electrode.
A short-dashed line corresponds to the standard hydrogen electrode.
Concluding remarks
Although the specially designed amorphous-Al2O3 film provides better protection of aluminum surfaces135, and the deposition of the atomic layer of Al2O3 was even used to protect the surface of steel136 and copper137 from aqueous corrosion, the general opinion17,18 is that the native oxides of aluminum and magnesium cannot form a stable protective film on the metal surface and provide a sufficient protection. The chemical affinity of magnesium and aluminum to oxygen largely exceeds that of silicon. This implies that, from the thermodynamic viewpoint, alloying of aluminum and magnesium with silicon improves their oxidation resistance through the formation of different mixed oxides. There are numerous experimental evidences of formation of Al2MgO4138,139, Al2SiO5140,141,142, Mg2SiO4143, MgSiO3144,145, cordierite146,147, sapphirine148 and halloysite149 during the corrosion of different alloys.
The complexity of the corrosion behaviour of the systems Al–Mg–Si–O and Al–Mg–Si–H2O resembles the complexity of the equilibria describing the formation of clay minerals in the Earth’s crust. In air environments, different simple and mixed oxides are thermodynamically stable depending on the alloy composition and the partial pressure of oxygen. In aqueous environments, different mixed hydroxides become thermodynamically stable at different pH values. Moreover, the presence of aluminum and magnesium hydrides drastically changes the oxidation mechanism and the corrosion properties of Al–Mg–Si alloys.
The extreme complexity of the system and the similarity of the thermodynamic properties of different mixed oxides and hydroxides lead to the fact that thermodynamics alone does not provide an exhaustive answer to the question of the mechanism and the products of the Al–Mg–Si alloys corrosion. To a greater extent, the corrosion properties of the specific alloys in a specific environment are determined by the precipitation kinetics and the mechanical properties of the formed oxides. The knowledge of the chemical and electrochemical equilibria in the system and of the possible formed oxidation products opens the way to the study of the physical, chemical and mechanical properties of the passivation films formed on the alloy surface. The thermodynamic expressions of electrochemical reactions listed in Tables 18–21 may help to interpret the experimental electrochemical data and lead to a deeper understanding of the kinetics of the formation of the oxide films. Because the crystal structure of the various simple and mixed oxides and hydroxides in the Al–Mg–Si system is already known, the knowledge of the oxidation products formed in any specific environment is helpful in interpreting the results of the surface investigations using X-ray diffraction or X-ray photoelectron spectroscopy. The study of the physical and mechanical properties of the films formed on the alloy surface including density or porosity, hydrophilicity, thermal and electric conductivity, hardness and adhesion to the metal surface is also not possible without the prediction of the formed products. Therefore, the present thermodynamic calculations might be a useful starting point for the subsequent complex evaluation of the corrosion behaviour of aluminum–magnesium–silicon alloys.
Methods
Thermodynamic description of the metallic and oxide systems at 298 K
The method of calculation of the phase and chemical equilibria by minimisation of the Gibbs energy was proposed by van Laar150,151,152, further developed by Kaufman153, and later by several other researchers154,155,156,157,158. According to it, the molar Gibbs energy of the solid solution with the crystal structure α in the ternary system Al–Mg–Si (Gα) can be expressed as154,155:
where xi is the mole fraction of the i-th component (i = Al, Mg, or Si), \({G}_{i}^{o,\,\alpha }\) is the molar Gibbs energy of the pure i-th component with the crystal structure α, the expressions for molar Gibbs energies for aluminum, manganese and silicon were taken from the work159, GE, α is the molar excess Gibbs energy of the phase α160,161,162,163,164, T is the absolute temperature165,166 in Kelvins, and R is the universal gas constant167,168. For the thermodynamic description of the solid metallic solutions the substitution solution model27,169 can be employed. In this case, the molar excess Gibbs energy of the solution can be expressed as154,155:
Here, each of the parameters LAl, Mg, LAl, Si, LMg, Si and LAl, Mg, Si could be a function of the solution composition (xi) and temperature (T), and the for the binary parameters this dependency could be expressed using a Redlich–Kister power series28. The expressions for the parameters for the Al–Mg binary system were taken from work30, for the Al–Si binary system – from work34, for the Mg–Si binary system – from work44, and for the Al–Mg–Si ternary system – from works45,48. The thermodynamic activities170,171,172 of the components of solid solutions can be calculated as follows:
where \({\mu }_{i}^{{\rm{E}}}\) is an excess chemical potential of the i-th component of the solution160,161,162,163,164. The equations that link the excess chemical potentials of the solution components with the excess Gibbs energy of the solution are detailed in papers28,50,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193.
For intermetallic compounds and oxides, the expression of the Gibbs energy becomes154,155:
where \({\Delta }_{{\rm{f}}}{G}_{298}^{{\rm{o}}}\) is the standard Gibbs energy of formation of the compound. Their values were collected from various papers and textbooks.
The values of the standard Gibbs energies of formation of non-stoichiometric compounds might be predicted using a Waring–Lagrange interpolation formula52,53 according to a method that was first proposed by Gorichev for non-stoichiometric oxides194, and later generalised195.
The thermodynamic modeling of the equilibrium composition and properties of the alloys at 298 K with the described method was performed using the MatCalc software26 using the mc_al.tdb database, version 2.035.
Thermodynamic description of the aerial oxidation of alloys at 298 K
When de Donder developed the free energy definition of chemical affinity196,197,198, the Gibbs energy of reaction became the measure of the ability to different substances react with each other. However, the Gibbs energies of different reactions are usually not directly comparable with each other due to the different stoichiometries. This problem is usually overcome by converting the different equations to the same stoichiometry, or by using the related properties independent of stoichiometry. Particularly, for the reaction of metal Me with oxygen, which results in the formation of the oxide MeaOb, normalised to the single oxygen atom199:
the chemical affinity M of the metal to oxygen is determined as the quantity:
where ΔrG is the Gibbs energy change of the reaction (5), and ΔfG is the Gibbs energy of formation of the oxide MeaOb. The same equations may be written for the formation of mixed oxides, and for the further oxidation of one oxide to another with the higher oxidation degree.
If the reaction participants are pure bulk phases, and their thermodynamic activities are assumed equal to unity, then the expression of the equilibrium constant becomes:
from which follows the relation between the chemical affinity of the metal to oxygen and the equilibrium partial pressure of oxygen:
but if the oxidation of alloy components is considered, the thermodynamic activities of the alloy components should be taken into consideration in these thermodynamic expressions.
Both, the affinity to oxygen and the equilibrium oxygen partial pressure might be used to compare the tendency metals to oxidise199. The greater is the affinity of the compound to oxygen, and the lesser is the corresponding oxygen partial pressure, the more thermodynamically favourable is the oxidation reaction.
According to the Gibbs’ phase rule200, when both temperature and pressure are fixed, maximum of three phases can coexist in three-component system. From the all possible phase and chemical equilibria with the alloy components involving no more than three phases in the presence of the excess oxygen, those with the least equilibrium oxygen partial pressure determine the oxidation behaviour of the alloy. These equilibria are usually visualised using the ternary state diagrams, proposed by Gibbs200,201, Roozeboom202,203 and de Finetti204. In such diagram, a single compound is depicted by any vertex within the diagram, a two-phase region is depicted by any tie-line between two nearest vertices, and a three-phase region is depicted by any triangle91. More detailed description of the presentation of ternary state diagrams in barycentric coordinates is presented in works91,92,155.
Thermodynamic description of the aqueous oxidation of alloys at 298 K
In an aqueous solution both chemical and electrochemical reactions are possible. In a general case, the reaction could be described by the following equation:
Here A and B are the reactants, C and D are the products, a, b, c, d, m are the stoichiometric coefficients, n is the number of electrochemical equivalents205 in the reaction.
The Gibbs energy change of the reaction (9) is as follows:
where \({\Delta }_{{\rm{r}}}{G}_{T}^{{\rm{o}}}\) is the standard Gibbs energy of reaction, ai are the thermodynamic activities170,171,172 of the reaction participants.
For chemical equilibria (where n = 0), after substitution of the thermodynamic definition of \({\rm{pH}}=-\mathrm{lg}\,{a}_{{{\rm{H}}}^{+}}\) 206,207,208,209 into Eq. (10), changing the base of the natural logarithm to the decimal, and applying the condition \({\Delta }_{{\rm{r}}}{G}_{T}=0\), the generalised form of the Hendersson–Hasselbalch equation209,210,211,212 yields:
In an aqueous solution, upon alteration of concentrations and the pH value, ionic species may undergo hydrolysis, polymerisation, and precipitation of the solid oxides and hydroxides93,110. These equilibria could be visualised in form of speciation diagrams proposed by Bjerrum213, or as the activity – pH diagrams93,110. Several textbooks93,110,214,215 explain the mathematical background, and the procedure of construction of speciation diagrams and activity – pH diagrams.
For electrochemical equilibria, the relationship between the Gibbs energy of half-reaction (9) and its electrode potential is determined by the basic equation of electrochemical thermodynamics216,217,218:
After substitution of Eq. (12) into (10), and some rearrangements, the generalised form of the Nernst219,220,221 and Peters222 equations yields:
The Eqs. (11) and (13) are the master equations for thermodynamic calculations of chemical and electrochemical equilibria in aqueous environments.
The method of visualisation of the electrochemical equilibria in form of the potential – pH diagrams was proposed by Clark223,224,225, and further developed by Michaelis226 and Pourbaix133. The mathematical background and procedure for plotting the complex potential – pH diagrams for multielement systems was described several times133,134,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247.
The thermodynamic modeling of both the aerial and aqueous oxidation of the alloys at 298 K with the described method was performed using the EpHDiagrPlot software.
The more detailed description of the methods of thermodynamic calculations used in this paper is provided in the dissertation work248.
Data availability
All the reference data on the standard Gibbs energies of formation of the compounds, the standard electrode potentials of half-cell couples, and the equilibrium constants of the reactions were obtained from published papers and reference books. All the calculated data on the chemical and electrochemical equilibria in the Al–Mg–Si–O and Al–Mg–Si–H2O systems at 298 K are present in the article.
Code availability
MatCalc is a proprietary software26. Its description and files for download are available at https://www.matcalc.at/index.php/download/matcalc. The open databases including mc_al.tdb are available at https://www.matcalc.at/index.php/databases/open-databases. EpHDiagrPlot is a non-commercial software. Its description and the source code are freely available in the dissertation work248.
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The work was supported by Federal Ministry of Education, Science and Research of Republic of Austria, OeAD – Austria´s Agency for Education and Internationalisation, grant No ICM–2020–00118. Open Access funding was provided by the Library of Technische Universität Wien.
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P.A.N. acquired the reference data, performed the thermodynamic calculations of the aerial and aqueous oxidation of alloys, and wrote the manuscript draft. E. K. performed the thermodynamic calculations of phase and chemical equilibria in the metallic systems, provided the funding and supervised the research. Both authors read and agreed the manuscript before submission.
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Nikolaychuk, P.A., Kozeschnik, E. Thermodynamic evaluation of the aerial and aqueous oxidation of Al – Mg, Al – Si and Al – Mg – Si system alloys at 298 K. npj Mater Degrad 8, 94 (2024). https://doi.org/10.1038/s41529-024-00446-w
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DOI: https://doi.org/10.1038/s41529-024-00446-w
