Thermodynamic Assessment of chemical and electrochemical stability of iron silicides Текст научной статьи по специальности «Химические науки»

CHEMICAL PROBLEMS 2019 no. 2 (17) ISSN 2221-8688

155

UDC 620.193:669.14

THERMODYNAMIC ASSESSMENT OF CHEMICAL AND ELECTROCHEMICAL

STABILITY OF IRON SILICIDES

P.A. Nikolaychuk

Institut für Biochemie, Universität Greifswald, Felix-Hausdorff-Straße 4, 17487 Greifswald, Germany. E-mail: npa@csu.ru

Recieved 06.02.2019

Abstract: The phase and chemical equilibria in the Fe - Si system at 298 K were considered. The comparison between the available thermodynamic information on the solid solubility of silicon in bcc-iron at low temperatures was performed with and without consideration of the a-phase long distance ordering. The standard Gibbs energy of formation for non-stoichiometric iron silicide was estimated. The possible maximum solid solubility of Si in bcc-Fe at 298 K was estimated. The thermodynamic activities of the components in this saturated solution were calculated. The state diagram of the Fe - Si - O system at 298 K was plotted and the characteristics of their invariant conditions were calculated. The solid solubility of Fe2SiO4 in Fe3O4 and of SiO2 in Fe2O3 at 298 K was estimated. The activity - pH diagrams for the aqueous Fe (II) and Fe (III) species were constructed. The potential - pH diagram of the Fe - Si - H2O system at 298 K, air pressure of 1 bar and activities of ions in solution, equal to 1 mol l-1 was plotted. Basic chemical and electrochemical equilibria in this system were considered. The thermodynamic analysis of chemical and electrochemical stability of the Fe - Si system alloys was performed. Keywords: Fe - Si system, iron silicides, phase equilibria, low temperature oxidation, chemical and electrochemical stability. DOI: 10.32737/2221-8688-2019-2-155-184

1. Introduction

Iron-silicon is a very important binary system. Reliable information on the thermodynamic properties and phase equilibriums in Fe - Si alloys is needed for calculation of the technological quantities for various metallurgical processes. Iron silicides are perspective materials, including metalloid conductors [1], semiconductors [2, 3] and amorphous materials [4], they are well-known for their unusual magnetic, optical and thermodynamic properties [5 - 7]. Iron-silicon alloys can be found in Earth's core [8], they are used in the technology as thin films [9] and nanowires [2, 10]. Moreover, many important ternary and multicomponent systems, including Fe - Si binary system, such as Ni -Fe - Si [11], Al - Fe - Si [12 - 14], Fe - Mn -Si [15, 16], Cu - Fe - Si [17, 18], Cr - Fe - Si [19], Fe - Zn - Si [20 - 22], Fe - Si - C [23 -26], Fe - Si - O [27, 28], Fe - Si - B [29, 30],

Al - Ca - Fe - Si [31] and others, are of great interest for the researchers. The Fe - Si system-based alloys and compounds can be used as corrosion-resistant materials and coatings. The experimental investigations of iron silicides corrosion properties are very intensive; it will be discussed further in the section 5. However, the theoretical research into the issue is also important scientific task. One of the methods to describe the oxidation of silicides both in oxygen-containing gaseous environments (chemical stability) and in water environments (electrochemical stability) is the thermodynamic modelling. The previous investigations of thermodynamic features of Fe - Si system corrosion and oxidation properties [32, 33] do not cover all possible chemical and electrochemical equilibria in the system. The purpose of this study is to revise previous studies and take into account all

uncounted thermodynamic properties. Unlike many other published papers devoted to thermodynamic modeling at higher temperatures, the present paper describes

thermodynamic description of alloy oxidation processes of Fe - Si system at standard temperature only.

2. Phase and chemical equilibria in Fe - Si system at the temperature of 298 K. 2. 1. Comparison of previous thermodynamic descriptions

According to the Fe - Si phase diagram [34 - 35], there are a number of intermetallic phases in the systems Fe3Si7, FeSi2, FeSi, Fe5Si3 and Fe2Si. But only FeSi2 and FeSi are thermodynamically stable at standard conditions. FeSi has a narrow homogeneity range [7, 34], from FeSio,96i to FeSii, o33 which doesn't depend on temperature. Pure silicon is available in diamond modification (Strukturbericht symbol is A4), and the solid solubility of iron inside is negligibly small and can be ignored. Iron exists in face-centered cubic (fcc) and body-centered cubic (bcc) modifications, but only the bcc one is stable at 298 K, and it is called a-Fe. The solid solubility of Si in a-Fe is equal to approx. 25 atomic percent while silicon can form three types of solutions. The first one is the disordered phase where only short range ordering exist (a-phase, the Strukturbericht symbol is A2), two others have long range atomic ordering - a2-phase, the Strukturbericht symbol is B2 and a1-phase, the Strukturbericht symbol is DO3. The crystallographic features and lattice parameters of these phases were described many times [36 - 38]. Additionally, a miscibility gap exists between a2 and a1

phases. The magnetic transformation, which occurs in a-phase, corresponds to elevated temperatures and inflicts no effect on Fe - Si system thermodynamic properties at standard temperature. The Gibbs energy of the magnetic ordering is considered in studies [26, 38] and taken into no account in the present study.

However, there is no single and clear opinion about phase boundaries between a, a2 and ai phases at low temperatures. Experimental data [39 - 41] are available only for high temperatures, all studies, considering Fe - Si phase diagram [34 - 38], provide reliable information about phase boundaries at the temperature diagram exceeding 500° C. Note that attempts of thermodynamic extrapolation of phase diagram below 500°C are often contradictory. Some studies [34, 36] indicate that a - a2 - a1 transformations take place at silicon concentration in solutions slightly above 10 atomic percent. On the other hand, the authors of [38] provide relations between temperatures of phase transition from A2 phase to B2 (TA2-B2) and from B2 phase to DO3 (TB2-DO ) and mole fraction of silicon in solid solution (x) as follows:

TA2-B2 = x • (1 - x) • (-4293,3 • (1 - 2x)3 -112,5 • (1 - 2x)2 + 2515,2 • (1 - 2x) + 9825,6) (1),

TB2-DO = x • (1 - 2x) • (134 • (1 - 4x)3 - 4291,1 • (1 - 4x)2 - 2306,2 • (1 - 4x) +12024) (2),

B2-DO3

where temperatures TA2-B2 and TB2-DO are

given in Kelvins, mole fraction x is dimensionless. These equations are written to fit the experimental data of [39], but they can be solved in relation to x at the transition temperatures set to 298 K, this solution gives x = 0,036 for A2 - B2 transition and x = 0,045 for B2 - DO3 transition. Moreover, there is no information about the exact position of miscibility gap between a2 and a1 phases. And finally, authors of [42] declare that there is no B2 phase either at low temperatures!

As for thermodynamic assessment of ternary and multicomponent systems [12, 13, 15 - 18, 20, 22, 24, 25, 28 - 31], most researchers refer to thermodynamic information about Fe - Si binary system provided in few descriptions [23, 38, 43]. Additionally, the authors of [20] provide their own thermodynamic description of Fe - Si aphase. All of these descriptions do not take into account long range ordering transformations in a-phase completely. The authors of [20, 43] simply ignore it; the authors of [23] consider only a2-phase using

two-sub-lattice model [44] but provide the analytical expression for the excess Gibbs energy Ge [45] without considering a2-phase; the authors of [38] give analytical expressions for the atomic ordering Gibbs energy for both a2 and a1 phases but also offer a single equation for the excess Gibbs energy for all types of solid solutions, without contribution of atomic ordering to it. All of these descriptions estimate FeSi as the stoichiometric phase, without considering its homogeneity range.

Since in all above-mentioned studies [20, 23, 38, 43] the thermodynamic properties of the solid solution are estimated, with due regard for all possible equilibriums with aphase involved, especially in high-temperature region, values of the estimated parameters, provide minimal deviations from the calculated Fe - Si phase diagram from the

experimental one, but these deviations are still significant when only one single equilibrium is taken into account.

However, when considering equilibriums taken separately, these deviations matter. To estimate maximum silicon solid solubility in a-Fe at 298 K, it is important to specify the equilibrium of a-phase with FeSi compound. Therefore the comparison between all available descriptions was performed in order to select one of them and thus ensure the best matching of calculated and experimental data on this single equilibrium. So, at temperatures below 820° C [34, 36] with Fe-rich side on Fe - Si system, the following reaction occurs between a-phase (bcc solid solution) and FeSi compound:

Fe (a) + Si (a) = FeSi (3). It can be described using the following equation:

A GO =-RT • ln K = -RT • ln

1

aFe(a) • aSi(a)

= RT • ln a a + RT • ln a a

(4),

where ArG°T is the Gibbs energy change of reaction (3), J mol-1, Kp is an equilibrium constant of this reaction,

R = 8,3144 Jmol-1K-1is a universal gas constant, T is a temperature in Kelvins, aFe(a) and aSi(a) are, respectively, thermodynamic

activities of iron and silicon in a-phase (reference state - pure component with bcc lattice), which is in equilibrium with FeSi. Here and further in the text, unless otherwise agreed, all compounds, including silicides, oxides and silicates, are treated as pure substances, and their activities are set to unity. The analytical expressions of aFe(a) and aSi(a)

are linked with an expression for the excess Gibbs energy GE of a-phase:

RT • ln a (a) = RT • ln X,a) + /a) (5), where i(a) denotes any a-phase component (Fe or Si), xi(a) is the mole fraction of the

component i and /u^{a) is an excess chemical potential of the component that can be

determined as the partial derivative of excess Gibbs energy GE with respect to the number of moles of this component [45]. Thus, the analytical expression of

GE = f(XFe(a), XSi(a), T) is needed to solve

equation (4).

In the paper [43], the following equations are proposed for the Gibbs energy change of reaction (3) and for the excessive Gibbs energy of a-phase: ArG°T (3) = 27,572T -123010, J mol-1 (6),

GEa = x(1 - x) • ((1 - x) • (7,95T -129704) + x • (136,82T - 297064)), J mol-1

(7).

Here x denotes the silicon mole fraction in the solid solution.

The authors of [20] also use the equation (6) for Gibbs energy change of reaction (3); however, it offers the description of GE according to Redlich-Kister power series [46]:

GEa = x(1 - x) ((34,81T -156900) + (1 - 2x) • (-0,41T - 33470) + + (1 - 2x)2 • (-11,08T + 35780) + (1 - 2x)3 • (-6,92T - 28800)), Jmol-1

Another set of parameters is proposed by the authors of the paper [38]. They consider the reaction of FeSi formation in the following form:

Fe (y) + Si (diamond) = FeSi (9), and provide the value of Gibbs energy change in the reaction (9) by the equation

A G (9) = 10,2906T - 86421,72, J mol-1(10). Additionally, they consider reactions of phase transitions of iron and silicon:

Fe(r) = Fe (a) (11),

Si (diamond) = Si (a) (12), and provide the values of Gibbs energies of these transitions:

ArG° (11) = AtrGT (Fe^J = -6,4-10-4T2 - 8,282T + 1,15T• ln T + 1462,4,J mol-1(13), AG (12) = AG (Sidiamond^) =- 19,54T + 44350, J mol-1 (14).

Obviously, the Gibbs energy of reaction (3) can be calculated according to Hess' law:

ArG°T (3) = ArG°T (9)-ArG°T (11)-ArG°T (12) (15).

The equation for excess Gibbs energy GE is formalism: also written according to Redlich-Kister

GEa = x(1 - x)• ((13,7306T-129038)- 39244• (1 - 2x)), J mol-1 (16).

And, finally, the authors of [23] give another This time, the Gibbs energy of reaction (3) can

set of parameters. They consider formation of be gained in the following way:

FeSi from the elements in their standard ArG° (3) = ArG°T (17)-ArG° (12) (19),

reference states at low temperatures: But instead of using Gibbs energy change of

Fe (a) + Si (diamond) = FeSi (17), reaction (12) offered in [38] and listed in the

providing the value of Gibbs energy of equation (14), the authors of [23] use the

reaction (17) by the equation value, obtained from database [47]: ArG°T (17) = 4,44T - 72761,2, J mol-1(18).

ArG°T (12) = AG (Sid_^J =-22,5T + 47000, J mol-1 (20).

And the excessive Gibbs energy G^ is presented in the following form:

GEa = x(1 - x)• ((46,48T-111236)-92352• (1 - 2x) + 62240• (1 - 2x)2), J mol-1 (21).

After substituting values of these parameters for the equation (4), only two variables remain in it: T and x. The solution of this equation provides the position of line on the Fe - Si phase diagram that corresponds to maximum silicon solid solubility. The solutions obtained with all of above-mentioned parameters sets as compared with values obtained from currently accepted Fe - Si phase diagram [34, 35], are

presented in Fig. 1. As can be seen, the best convergence between the experimental and calculated lines is achieved when using parameters from the paper [43]. This allows to extrapolate this calculated equilibrium line down to the standard temperature. The estimated silicon maximum solid solubility at 298 corresponds to x = 0.262.

T, K

0,20 0,25 0,30 0,35

Figure 1. Maximum solid solubility of Si in a-Fe at various temperatures: 1 - experimental values, obtained from Fe - Si phase diagram [34, 35]; 2 - calculated according to data of [20] using equations (4), (6) and (8); 3 -calculated according to data of [23] using equations (4), (18), (20) and (21); 4 -calculated according to data of [38] using equations (4), (10), (13), (14) and (16); 5 -calculated according to data of [43] using equations (4), (6) and (7); 6 - calculated in present study using equations (7), (20), (25) and (27).

2.2. Considering the non-stoichiometry of FeSi compound

The next step is to extend this thermodynamic description by taking into account the non-stoichiometry of FeSi compound. There are no thermodynamic properties of non-stoichiometric FeSi in literature; therefore it is necessary to predict it. The authors of [48] notice that an approximate functional relationship exist between the reduced chemical potential of oxygen atoms in metal oxide and system oxidation degree:

" A G (Ma A G (MaAbx) = bx (^ i=1 bi

where n is a number of Gibbs energies of formation of binary compounds, accepted as a

reliable initial data; M a Ab - formulae of

i °i

these binary compounds (M - metal atom, A -more electronegative element atom,, ai and bi -indices for M and A atoms in compound, respectively); M a Ab - formula of the

compound, Gibbs energy of formation of which is to be estimated, ax and bx - indices

AfG0 (Me1/xO) = f (x). The assumption is

made by in the paper [49] that similar relationship is valid not only for oxides but also for some other binary compounds with polar covalent bond (sulfides, carbides, nitrides, silicides, etc.). They derived the following interpolation formula for the Gibbs energy of binary compounds formation:

\) n a • (aj • bx- ax • bj) )

j * a* •(a, ■b - a ■b,)

(22),

for the M and A atoms in it.

In spite of the fact that FeSi and FeSi2 solely are stable compounds in the Fe - Si system at standard temperature, the information about the standard Gibbs energies of formation (A fG098) for other iron silicides

is also presented in literature. The data from [23, 38, 43, 50 - 57] are summarized in table 1.

Table 1. Standard Gibbs energies of formation of iron silicides (as referred to bcc Fe and diamond Si).

Compound Reference A/G2O98, J mol 1

FesSi Fe2Si Fe5Si3 FeSi Fe3Siy FeSi2

[23] - -74421 -240500 -71438 -199231 -79038

[38] - -75414 -252822 -83355 - -83764

[43] - - - -76266 -251934 -

[50] -94765 - -233643 -76587 -179307 -78447

[51] -84592 - -197639 -76579 -198495 -73291

[52] -83740 - -244510 -81600 - -80390

[53] -94605 - - -73223 - -78357

[54] - - - -73765 - -79660

[55] - -92064 - -76028 - -92593

[56] -103200 - - -78600 - -91800

[57] -124656 - -306841 -94056 - -97762

* -95850 -90180 -260340 -73180 -194900 -78360

As can be seen from Table 1, there is no convergence between the results given in various papers. The differences are often significant. Only the data for FeSi and FeSi2 agree satisfactorily with one another. The most reliable information on standard Gibbs energies in the formation of these two silicides is obtained from the paper [54], because it was determined within the temperature range of 10 K < T < 400 K by means of adiabatic low-temperature calorimetry, while the data from some other papers involve extrapolations of thermodynamic properties from high-temperature region down to the standard

temperature. From all studies containing dependencies of

AfG° (FeSi, FeSi2) = f (T)[23, 38, 50, 52,

53, 55, 57] only those from the study [53] closely match values from the paper [54]. In this case, the decision is made to use only data for FeSi and FeSi2 from [53] when estimating the non-stoichiometric FeSix with unknown thermodynamic properties. The values in [53] are tabulated in temperature range of 298 K < T < 1200 K, and the approximation of them provides the following equations:

ЛfG° (FeSi) = 0,005172 - 2,84297 - 72785, J mol-

AfG° (FeSi2) = 0,007272 + 4,44657-80321,J mol-

(23),

(24).

Substituting equations (23) and (24) for the equation (22) leads to the following equation

for the Gibbs energy of formation of FeSi* phase:

Л G (FeSi * ) = x2 • (-0,001572 + 5,066157 + 32624,5) + + x • (0,006672 - 7,909057 -105409,5), J mol-1

(25).

Here x is an index in formula FeSix. In order to results

verify formula (25), the values of A fG2o98 for

all iron silicides are estimated in line with the above. They are shown in Table 1 in a column, marked by * and agree more or less satisfactorily with values presented in literature. Thus, this formula can be used for further calculations. It gives the following

Л fG2°98 (FeSi

л c°

^f^7298

at standard temperature: 0961) =-71600J mol-1 and

(FeSi1,033) = -74430J mol-1. Now, the equations (3) and (4) can be

replaced with the following ones:

Fe (a) + 0,961 Si (a) = FeSi0961 (26).

Л GO =-R7 • ln

1

a

,0,961

Fe(a) Si(a)

a

= R7 • ln aFe(„) + 0,961R7 • ln aS^

(27).

The Gibbs energy of formation of FeSi0,961 obtained by setting x = 0,961 in the equation (25), however, refers to standard element reference states: Fe (a) + 0,961 Si (diamond) = FeSi0961 (28),

And have to be combined with the reaction (12) according to Hess' law: ArG°T (26) = ArG°T (28)-0,961 •ArG°T (12)(29)

The expression of silicon Gibbs energy of transition in the reaction (12) is taken from the

equation (20), and previously chosen expression for excess Gibbs energy GE from

[43] (equation (7)) is used. The result of solving equation (27) is also shown in Fig. 1 (line 6) and is very good compatible with values calculated without considering FeSix non-stoichiometry (line 5) and experimental

phase diagram (line 1). The estimated silicon maximum solid solubility at 298 K corresponds to x = 0,264, the activities of this "saturated" solid solution components are

equal to «Fe(«) = 0,114 and «Si(a) = 7,2-!0-20

which means essential negative deviations from ideal behavior.

2.3. Considering sub-silicide

Also, an attempt is made to take into account atomic ordering in a-phase. But, unlike previous descriptions [23, 38], entirely different way is chosen. It is well known [36 -38] that a1-phase where full ordering occurs corresponds to alloy composition of Fe0,75Si0,25. Since the line of maximum silicon solid solubility in a-Fe, depicted in experimental Fe - Si phase diagram [34, 35] stands exactly on this alloy composition at low temperatures, it is possible to treat this fully ordered a1-phase as the independent compound "Fe3Si". There are several evidences in literature [4, 9, 16, 20, 23, 30, 36, 55, 56, 58 - 60] that consider Fe3Si as low-temperature sub-silicide, moreover, even its standard Gibbs energy of formation is estimated in [50 - 53, 56, 57].

Usually, if the temperature is fixed, the next sequence of phase transitions is observed, when moving at the Fe-rich side of Fe - Si phase diagram in the direction of silicon

A rQ°T = -RT • ln ——1-= 3RT

aFe(a) ' aSi(a)

"Fe3Si" and a-phase ordering

concentration increase: a | a2 | a2 + al | al | al + FeSi0,961 and so on. However, if guided by authors' premise [42] that there is no a2-phase at low temperatures, the sequence of phase transitions reduces to a | a1 | a1 + FeSi0,961. When fully ordered a1-phase is treated as the independent compound "Fe3Si", the a1 phase region can be described as the mixture of disordered a-phase and "Fe3Si". Then the sequence of phase transitions becomes as follows: a | a + "Fe3Si" | "Fe3Si" + FeSi0,961. This assumption is certainly a simplification but it allows avoiding addition of special parameters in the equations for the a-phase Gibbs energies to describe its ordering, as it was done in the paper [23, 38].

Instead of equations (3) and (4) describing the line of silicon maximum solid solubility in a-Fe, the next ones can be written now:

3 Fe (a) + Si (a) ="Fe3Si" (30).

ln aFe(a) + RT *ln aSi(a) (31).

Again the comparison between all available thermodynamic data for a-phase [20, 23, 38, 43] is made in order to choose the one that provides better description of this equilibrium. The procedure is similar to the one described in section 2. 1., and thus the calculations are omitted. It reveals that parameters from paper [23] are the best choice at this time. They are

used to extrapolate equilibrium (30) down to the temperature of 298 K. The estimated silicon maximum solid solubility at 298 K corresponds to x = 0,112, the activities of solid solution components are equal to

aFe(a) = 0,473 and aSi(a) = 5,5 ' 10^ , and

deviations of this solution from ideal behavior are negative.

3. The chemical stability of iron silicides

3.1. Phase and chemical equilibriums in Fe - Si - O system at a temperature of 298 K

The chemical stability of an alloy or a influence of natural environment, particularly, compound is the ability to resist the chemical the oxidation by atmospheric oxygen [61, 62].

The thermodynamic features of Fe - Si system chemical stability can be clearly described by plotting Fe - Si - O system' state diagram and considering equilibriums in this system. But prior to plotting a diagram, the primary information about possible oxides in binary Fe - O and Si - O [34] systems, as well as about possible ternary compounds [63], must be taken into consideration.

Note that just one stable oxide - SiO2 -exists in Si - O system. There are also many values of its Gibbs energy of formation available in literature [50 - 53]. However, since electrochemical formation of silicon dioxide is to be considered (see section 4), the value is chosen in line with experimentally determined potential of the silicon electrode [64]:

SiO2 + 4H + + 4e- = Si (diamond) + 2H2O; = -0,857 V (32),

which leads to the following equation:

Si(diamond) + O2 = SiO2; ArG298 = -805067 J mol-

(33).

In the system Fe - O at 25°C two according to [51]), it is thermodynamically

oxides are stable - Fe3O4 and Fe2O3 [34, 35]. unstable at standard a temperature [62, 65]

In spite of the fact that standard Gibbs energy because it is decomposed spontaneously

of formation of the iron monoxide FeO is according to the reaction

negative

( A/G298 (FeO) = -244300

'mol

4 FeO = Fe (a) + Fe3O4; ArG298 =-36960J mol-1

(34).

It is known [65] that some mixed metal oxides exist contain Fe O2 layers. They are, for example, Ba2FeO4 and SrFe2O4 which can be introduced as 2BaO • FeO2 and 2SrO • FeO2 respectively. Moreover, the formation of ferrate-ions is possible in highly oxidized environments [65] and the electrochemical oxidation of Fe+3 state to Fe+6 one cannot proceed it in one step, because iron cannot lose three electrons at once [66]. Therefore, an

intermediate Fe+4 aqueous state species probably exist in the solution. However, in the literature there is no available thermodynamic information about any solid or aqueous iron (IV) species, and at the present time there is no possibility to involve them into the thermodynamic modelling.

Information about thermodynamic functions of the iron oxides [50 - 53, 67, 68] is listed in Table 2.

Table 2. Standard Gibbs energies of formation of iron oxides (as referred to bcc Fe and gaseous O2).

Reference Compound A/G°98, J mol-1

[50] [51] [52] [53] [67] [68]

Fe3O4 -1026182 -1014163 -1019112 -1015391 -1017438 -1007561

Fe2O3 -743800 -740337 -741613 -742413 -743523 -739991

A single ternary compound is available in Fe -Si - O system at a standard temperature and pressure, it is iron orthosilicate (or fayalite) Fe2SiO4 [63]. Another compound, ferrosilite FeSiO3, is formed only at elevated temperatures or very high pressures [28]. Fayalite is available in two forms: a-Fe2SiO4

which has olivine crystal structure and y-Fe2SiO4 with its spinel crystal structure [69, 70]. Note that just a-Fe2SiO4 is thermodynamically stable under standard conditions. The values of standard Gibbs energies of formation of a-Fe2SiO4 [28, 50 -53, 69, 71, 72] are summarized in Table 3.

Table 3. Standard Gibbs energies of formation of iron silicate Fe2SiO4 (referred to bcc Fe, diamond Si and gaseous O2).

Reference [28] [50] [51] [52]

AfG2o98, J mol-1 -1378035 -1375934 -1377004 -1347064

Reference [53] [69] [71] [72]

AfG2o98, J mol-1 -1380890 -1313750 -1379160 -1379188

In addition to iron silicates with well-known composition and structure, there are notifications [73, 74] that some silicates have unknown and complex composition and structure. One of the possible explanations of the fact is related to the ability of Fe3O4 to

form a solid solution with Fe2SiO4, observed by the authors of [75 - 77]. Moreover, they observed a solid solubility of SiO2 in Fe2O3. The information about solid solubility of these compounds at various temperatures [77] is shown in Table 4.

Table 4. The experimentally measured [77] solid solubility of Fe3O4 in Fe2SiO4 and SiO2 in Fe2O3 at various temperatures.

System Fe3O4 - Fe2SiO4 System SiO2 - Fe2O3

Temperature, K Solid solubility in Temperature, K Solid solubility in

mass % atomic % mass % atomic %

1073 20.2 19.9 1073 7.7 18.2

1173 26.2 20.5 1173 9.3 21.4

1273 31.7 24.7 1273 10.9 24.5

The estimation of maximum solid solubility at 298 K is performed using thermodynamic modeling. The equilibrium between pure Fe3O4 (magnetite) and its solid solution in fayalite

Fe3O4 (magnetite) = Fe3O4[in Fe2SiO4](35)

can be characterized with the equality of chemical potentials (p) of Fe3O4 in both phases [45]:

Mf,

^O^in Fe2SiO4]

= Mff

Mf e3O4 (magnetite) = MFe 3O4[in Fe2SiO4] (36).

Since magnetite is treated as pure substance

under standard conditions, its chemical

potential equals to the standard chemical potential

Mf e3O4 (magnetite) = MFe 3O4 (magnetite)

(37).

and chemical potential of Fe3O4 in the solution is presented by the sum of three terms:

^364^ Fe2SiO4]

+ RT ■ ln x

Fe3O4[in Fe2SiO4]

+ Mfe

^364^ Fe2SiO4]

(38),

where ^F°e3O4[inFe2SiO4] is standard chemical

potential of Fe3O4, referred to the lattice of

solvent c°mp°un^ Fe2SiO4; ^FEe3O4[inFe2SiO4] is

its excess chemical potential and -^Fe3o4[in Fe SiO ] is the mole fractions of Fe3O4 corresponding to

maximum solubility at a temperature T. The difference between standard chemical potentials of Fe3O4 in the magnetite lattice and in the lattice of solid solution is equal to molar Gibbs energy of transition of Fe3O4 from pure component to solution:

A .G^O 4 (magnetite) ^ Fe3O4 [in Fe2SiO4]) =MF e3O4 [in Fe2SiO4] e3O4 (magnetite)

(39),

AirGT°(Fe3O4 (magnetite) ^ Fe3O4 [in Fe2SiO4]) = AtrH° -T■ AtrS° (40).

Only the simplest thermodynamic models with employed to describe the excessive chemical minimal number of parameters can be potentials of solution components. This is

explained as being due to the lack of model [78] is used following which: experimental data. The strictly regular solution

^Fe 3O4[in Fe2SiO4] V Fe3O4 [in Fe2SiO4] / Fe3O4, Fe2SiO4 (41).

where LFeO Fe SiO is the energy of mixing the Substituting equations (37) through

compounds in the solution, which isn't depend (41) for the equation (36) gives the following on temperature. expression:

AtrHT - T • AtrST + RT • ln xFe3O4[inFe2SiO4] + (1 - xFe3O4[in Fe2SiO4 ] ) • LFe3O4, Fe2SiO4 = 0 (42).

Substituting data on T and xF^O[inF^SiO] from variables. This system is solved according to

Table 4 for the equation (42) provides the Cramer's method [79]. As a result, values °f system of three linear equations with three the parameters are estimated as follows: AtrGr°(Fe3O4 (magnetite) ^ Fe3O4[in Fe2SiO4]) = 0,235T-1523, J mol-1 (43),

4e3O4,Fe2SiO4 = 25216 J mol-1 (44).

Then, in keeping with calculated values of The equilibrium between pure SiO2

parameters, the equation (42) can be solved (quartz) and its solid solution in hematite according to xF O [inFe SiO ] at a temperature T SiO2 (quartz) = SiO2 [in Fe2O3] (45)

= 298 K. The calculated solid solubility of can be described similarly to the preceeding Fe3O4 in Fe2SiO4 at a standard temperature is one. The parameters are the molar Gibbs xFe3O4[mFe2SiO4] = 6,85 •10-5. Activities of solid energy of phase transition of SiO2 obtained

from the lattice of pure compound (quartz) to the lattice of solution (hematite)

solution components (reference state - pure component with fayalite lattice) are

«Fe3O4 = 0,00233 and aFe2SiO4 « 1 .

AG (SiO2 (quartz) ^ SiO2 [in Fe2O3 ]) = AtrHT - T • AS (46) and the energy of mixing in strictly regular solution of SiO2 and Fe2O3

^SiO2[inFe2O3] = (1 - xSiO2[inFe2O3]) • LSiO2,Fe2O3 (47).

The resulting equation for thermodynamic calculations is similar to equation (42):

A H - T •A S + RT • ln xSiO2[inFe2O3] + (1 - xSiO2[inFe2O3])2 • LSiO2,Fe2O3 = 0 (48). The results of solving equation (48) are the following:

AtrGr°(SiO2 (quartz) ^ SiO2[in Fe2O3]) = 2,621T + 6557,J mol-1 (49),

LSiO2,Fe2O3 = 8740 J mol-1 (50).

The calculated solid solubility of SiO2 in Both solid solutions reveal small

Fe2O3 at a standard temperature positive deviations from ideal behavior.

is xSiO [inFe O ] = 1,54 -10-3. Activities of solid Calculated solid solubility at a standard

2 2 3 temperature in both cases is vanishingly small.

solution components (reference state - pure

It inflicts no effect on crystal structure and

component with hematite lattice) are

a

„ , „ composition of iron silicate.

= 0,0541 and = 0,998. F

3.2. The Fe - Si - O system state diagram

The method of plotting and describing [61, 62]. The Diagram consists of two ordinary three-component state diagrams for metal- orthogonal axes. The abscissa is the mole oxygen-containing systems was developed in fraction of one metal compound in binary

system; in the present study abscissa is presented by silicon mole fraction xSi, assuming xFe = 1 - xSi. The ordinate is presented by system oxidation degree (y) which is the quantity of moles of atomic oxygen in the system, corresponding to the one mole of metallic compounds; in present study it is determined as

y = ■

nr

nFe + nSi

(51).

The Diagram is plotted at fixed temperature and pressure. According to Gibbs' phase rule [45], when these two variables are fixed, maximum of three phases can coexist in three-

component system. Any single compound (one-phase region) is described by any vertex within the diagram, a two-phase region is characterized by any tie-line between two nearest vertices, a three-phase region is depicted by any triangle and it corresponds to invariant system condition. Crossing tie-lines is not allowed because the point of their intersection would correspond to four-phase region which is impossible. Any phase of variable composition is noted by line; any triangle containing this line and filled with dotted lines corresponds to monovariant system condition.

Fe203 Fô.O,

X ...... ^

ix ,,■■''/''/,!

VIII '

7FÎSIO4 S^S //

Vil / VI / /

v / IV J' II / 1 Mw\ /

SiO,

Fe

FeSi

FeSL

Si

Figure 2. The Fe - Si - O state diagram at 298 K without consideration of "Fe3 Si" drawn up according to the reference data

Thus, this kind of state diagram has the same functionality as does the ordinary triangle phase diagrams (which, for example, are plotted for some Metal - Si - O systems by the authors of [80]), but are easier to plot and examine.While any Fe - Si system compound is oxidizing, all equilibriums with oxygen (from thermodynamic point of view) take place in multiple stages, one after another. Since the chemical affinity of silicon to oxygen is much higher than that of iron [61], silicon from iron silicides has to be oxidized in the first order, and the consecutive formation of phases increasingly richer in iron has to be observed.

Along with this, the equilibrium

oxygen pressure rises from the previous stage to the next one. The equilibrium oxygen pressure for each system condition is calculated according to the laws of chemical equilibrium as is shown in [61]. The Fe - Si -O state diagram is plotted in two variants. The first one takes into no account the formation of "Fe3Si" compound and a-phase ordering (as discussed earlier in the section 2. 3.). It is shown in Fig.2.

The second variant of the diagram takes into account formation of "Fe3Si" compound. It is shown in Fig.3. The appropriate characteristics of system conditions for the both diagram variants are represented in table 5.

y----V-

*"s_

XI

IX X

/Fe2Si04

VIII y / Vil

'""V'V / IV II I

/sfcy

Fe a "Fe,Si" FeSi_ FeSi? Si

Figure 3. The Fe - Si - O state diagram at 298 K with consideration of "Fe3Si" drawn up according to the reference data.

Table 5. The characteristics of the Fe - Si - O system conditions at 298 K.

No. of domain at System condition Reaction equation PO2,bar

figure 2 figure 3

I I FeSi2 - Si (diamond) -SiO2 Si (diamond) + O2 = SiO2 7.7 -10-142

II II FeSi1,033 - FeSi2 - SiO2 FeSi2 + 0,967 O2 = = FeSi1,033 + 0,967 SiO2 4.5 -10-141

III III FeSix - SiO2 (0,961 < x < 1,033) FeSin + (n - m) O2 = = FeSim + (n - m) SiO2 (0,961 < m, n < 1,033, m < n ) -

IV - a-phase (Fe) - FeSi0 961 -SiO2 FeSi0,961 + 0,961 O2 = = Fe (a) + 0,961 SiO2 xSi(„) = 0,264; aSi = 7,2 -10-20; aFe = 0,114 1.1 -10-129

- IV "Fe3Si" - FeSi0,961 - SiO2 3FeSi0,961 + 1,883 O2 = = "Fe3Si" + 1,883 SiO2 1.1 -10-130

- V a-phase (Fe) - "Fe3Si" -SiO2 "Fe3Si" + O2 = 3Fe (a) + SiO2 xSi(„) = 0,112; aSi = 5,5 -10-20; aFe = 0,473 6.4 -10-126

V VI a-phase (Fe) - SiO2 Si (a) + O2 = SiO2 -

VI VII a-phase (Fe) - Fe2SiO4 -SiO2 2Fe (a) + Si (a) + 2O2 = Fe2SiO4 Si (a) + O2 = SiO2 xSi(„) = 1,110-27; aSi = 5,3 -10-50; aFe « 1 1.3 -10-99

VII VIII a-phase (Fe) - Fe3O4 -[Fe3O4, Fe2SiO4] 3Fe (a) + 2O2 = Fe3O4 (magnetite) 2Fe (a) + Si (a) + 2O2 = Fe2SiO4 1.3 -10-89

Fe3O4 (magnetite) = = Fe3O4 [in Fe2SiO4]

xSi(«) = 1,02-10-47;

AS = 4,9 -10-70; aFe « 1;

XFe3O4 [in Fe2SiO4 ] = 6,85 '10 ;

AFe3O4 = 0,0°233; «Fe2SiO4 « 1

Fe3O4 [in Fe2SiO4] = Fe3O4

VIII IX Fe3Û4 - Fe2Û3 - [Fe3O4, Fe2SiO4] (magnetite) 4Fe3O4 (magnetite) + O2 = = 6 Fe2O3 2.8 -10 -68

2Fe2SiO4 + O2 = 2Fe2O3 + 2SiO2

IX X [SiO2, Fe2O3] - Fe2SiO4 -S1O2 (quartz) SiO2 (quartz) = SiO2 [in Fe2O3] x = 1 54 -10-3' SiO2[in Fe2O3] 1U ' «Fe3O4 = 0,0541; ^3 = 0,998 1.8 -10-62

X XI "FeO/ - SiO2 - {O2} - -

At domain III, reaction between FeSi^033 phase and oxygen takes place with selective oxidation of silicon. As the result, some silicon oxidizes to SiO2 and x index in FeSix formula decreases, until FeSi0,961 composition is reached. The similar situation occurs at domain V in Fig. 2 and domain VI in Fig.3, where a-phase reacts with oxygen. Silicon from solid solution oxidizes to SiO2 and the new solution composition, more and more rich of iron, forms. Both these system conditions are monovariant, therefore equilibrium oxygen pressure changes during reaction and there is no exact value presented in table 5 for these equilibria.

At domain VII in Fig. 2 and domain VIII in Fig. 3 both components of a-phase are

oxidized, and simultaneous formation of Fe3O4 and Fe2SiO4 takes place. A very small amount of magnetite dissolves in fayalite until the maximum solid solubility is reached. The remaining magnetite forms an independent phase. At the next stage (domains VIII and IX in Fig. 2 and 3, respectively) magnetite phase oxidizes to hematite. This causes the equilibrium (35) to shift in the opposite direction; Fe3O4 from solid solution transforms back to magnetite and then oxidizes. A similar situation occurs with the second solid solution. At domain IX in Fig. 2 and domain X in Fig. 3 the simultaneous formation of Fe2O3 and SiO2 from Fe2SiO4 takes place. A small amount of silicon dioxide dissolves in hematite and the remaining SiO2 forms a separate phase.

4. Chemical and electrochemical equilibria in Fe - Si - H2O system under standard conditions and the electrochemical stability of iron silicides

In order to develop thermodynamic model of Fe - Si alloys oxidation in liquid environments, it is convenient to use the diagrams of electrochemical equilibrium (potential - pH dependencies) [61, 81, 82], that most clearly show the possible chemical and electrochemical equilibria in system.

Method of plotting such diagrams was described in detail several times [81, 82] and the application of potential - pH diagrams to multicomponent and multiphase equilibria was proposed by the author of [83[. Along the above mentioned oxides, the possible ions that can be formed in the solution, have to be considered as the oxidation products. These ions are Fe2+, Fe3+, FeO;;- and SiO;- .

Figure 4. The "activity - pH" diagram for Fe (II) species drawn up according

to the reference data.

The HFeO2 ion mentioned in the paper [84], can be formed only in strongly alkaline environments (pH > 14) and very dilute solutions ( ai < 10-6 mo/ ), therefore they are

taken into no consideration in the present study. The primary information about the Fe -H2O and Si - H2O potential - pH diagrams

and the thermodynamic properties of the ion-involving electrochemical reactions can be obtained from textbooks [64, 85], papers [86 -88] and databases [89 - 97]. The potential -pH diagram for Fe - Si - H2O system was previously plotted in studies [33, 98], but both of these diagrams take into no account all phases in Fe - Si system.

Figure 5. The "activity - pH" diagram for Fe (III) species drawn up according to the reference data.

Any oxides or oxygen-containing ions in the solution can exist in an unhydrated or hydrated form. The transition from the first form to the second one proceeds through the series of intermediate conditions. The thermodynamic stability of various hydrolysis

products of ferric and ferrous cations depends on their thermodynamic activities in the solution. The "activity - pH" diagrams for the Fe+2 and Fe+3 species are presented in figures 4 and 5, respectively.

As can be seen from these diagrams, the hydrolyzed forms of ferrous and ferric species are thermodynamically stable only in much diluted solutions at low activity values. Therefore, in the present study the metal hydroxides and the other particles like FeOH +, FeOOH, FeOH2+, Fe(OH)+ Fe(OH)-, Fe(OH)-, Fe2(OH)4+, Fe3(OH)4

H2SiO;-

H3SiO-:

H4SiO4,

H8SiO6,

H2Si2O5:

)+, )4+,

H6Si2O7,

HSi(OH)-,

H4(H2SiO4)4-, H6(H2SiO4)4-, siO2(OH)2-, SiO(OH)-, Si2O3(OH)2- and others mentioned in [51, 64, 85 - 98], are taken into no consideration, because they are not thermodynamically stable when their activities are equal to 1 mol/l.

Figure 6. The potential - pH diagram of the Fe - Si - H2O system at 298 K, air pressure of 1 bar and activities of ions in solutions, equal to 1 mol/l (unhydrated form of oxides, without consideration of "Fe3Si" compound) drawn up according to the reference data.

The potential - pH diagram of Fe - Si - H2O system at 25°C, air pressure of 1 bar and activities of ions in solutions (standard reference state - hypothetical one molar solution), equal to 1 mol/l without consideration

of "Fe3Si" is shown in Fig. 6. The

characteristics of basic chemical and

electrochemical equilibria in system are summarized in Table 6.

Table 6. Basic chemical and electrochemical equilibriums in the Fe - Si - H2O system at 298 K and air pressure of 1 bar, without consideration of "Fe3Si" compound.

No. of line in Fig. 6 Electrode reaction Equilibrium potential, V (s. h. e.) or solution pH

a 2H++ 2e- = H2 ; PH = 5 -10-7bar 0.186 - 0.0591 • pH

b O2 + 4H + + 4e- = 2H2O;Po = 0,21bar 1.219 - 0.0591 • pH

1 SiO2 + 4H + + 4e- = Si (diamond) + 2H2O - 0.857 - 0.0591 • pH

2 SiO32- + 6H + + 4e- = Si(diamond) + 3H2O - 0.444 - 0.0887 • pH + 0.0148 • lg a^-

3 SiO32-+ 2H + = SiO2 + 2H2O pH = 13,94 + 0,5 • lg aSiO2-

4 FeSi1033 + 0,967 SiO2 + 3,868 H + + 3,868 e- = = FeSi2 +1,934 H2O - 0.845 - 0.0591 • pH

5 FeSi1033 + 0,967 SiO2- + 5,802 H + + 3,868 e-= FeSi2 + 2,901 H2O - 0.433 - 0.0887 • pH + 0.0148 • lgag.o2-

6 Fe (a) + 0,961 SiO2 + 3,844 H + + 3,844 e- = = FeSi0,961 +1,922 ^O; o^«) = 0,114 - 0.677 - 0.0591 • pH

7 Fe (a) + 0,961 SiO2- + 5,766 H + + 3,844 e- = = FeSi0,961 + 2,883 ^O; Of« = 0,114 - 0.264 - 0.0887 • pH + 0.0148 • lg as.Q 2-

8 Fe2SiO4 + 4H + + 4e- = 2Fe(a) + SiO2 + 2H3O OFe(a) = 0,114 - 0.205 - 0.0591 • pH

9 Fe2SiO4 + 2H + + 4e- = 2Fe(a) + SiO2- + H2O OFe(a) = 0,114 - 0.617 - 0.0295 • pH - 0.0148 • lgagio2-

10 Fe2+ + 2e-= Fe(a); a^«) = 0,114 - 0.412 + 0.0295 • lg aFe2+

11 Fe3O4 + 8H + + 8e- = 3Fe(a) + 4H2O; OFe(a) = 0,114 - 0.064 - 0.0591 • pH

12 Fe2SiO4 + 4H + = 2Fe2+ + SiO2 + 2H2O pH = 3.508 - 0.5 • lg aF g2+

13 Fe3O4 + 8H + + 2e- = 3Fe2+ + 4H2O 0.982 - 0,.364 • pH - 0.0887 • lgaFe2+

14 3Fe2O3 + 2H + + 2e- = 2Fe3O4 + H2O 0.231 - 0.0591 • pH

15 Fe2O3 + SiO2 + 2H + + 2e- = Fe2SiO4 + H2O 0.317 - 0.0591 • pH

16 Fe2O3 + SiO2- + 4H + + 2e- = Fe2SiO4 + 2H3O 1.141 - 0.1182 • pH + 0.0295 • lg a 2_

17 Fe2O3 + 6H + + 2e- = 2Fe2+ + 3H2O 0.732 - 0.1773 • pH - 0.0591 • lgaFe2+

18 Fe3+ + e- = Fe2+ a 3+ 0.771 + 0.0591 • lg Fe aFe2+

19 Fe2O3 + 6H + = 2Fe3+ + 3H2O pH =-0.221 - 0.333 • lgaFe3+

20 2FeO2- + 10H + + 6e- = Fe2O3 + 5H2O 2,220 - 0,0985 • pH + 0,0197 • lg a 2 7 o FeO4

17 domains of thermodynamic stability of certain phases are indicated in Diagram

(Fig.6):

I - a-phase (bcc) + FeSix + FeSi2 + Si III - a-phase (bcc) + FeSix + FeSi2 + SiO

(diamond); IV - a-phase (bcc) + FeSix + SiO2;

II - a-phase (bcc) + FeSix + FeSi2 + SiO2; V - a-phase (bcc) + FeSix + SiO^ ;

23

VI - a-phase (bcc) + SiO2;

VII - a-phase (bcc) +SiO32- ;

VIII - a-phase (bcc) + Fe2SiO4;

IX - Fe3+ + SiO2;

X - Fe3+ + Fe2SiO4;

XI - Fe3O4 (magnetite) + [Fe3O4, Fe2SiO4] (fayalite);

Domain I is the one of thermodynamic stability where all components of Fe - Si system remain immune to corrosion. At the domains from II to VII the consecutive decomposition of iron silicides takes place. Domains IX, X and XIII are the ones of active corrosion, where iron dissolves from alloys and passes into solution in the form of cations Fe2+ or Fe3+. Domains II, IV, VI, VIII, XI, XII, XIV and XVI are the ones of passivity where the protective oxide film, consisting of simple oxides of iron or silicon or iron silicate, is formed on the alloy surface to prevent further

171

XII - Fe2O3 + Fe2SiO4;

XIII - Fe3+ + SiO2;

XIV - [SiO2, Fe2O3] (hematite) + SiO2 (quartz);

XV - Fe2O3 +SiO32- ;

XVI -FeO2- + SiO2;

XVII -FeO2-, SiO2-.

Figure 7. The potential - pH diagram of the Fe - Si - H2O system at 298 K, air pressure of 1 bar and activities of ions in solutions, equal to 1 mol/l (unhydrated form of oxides subject to "Fe3Si" compound), designed according to the reference data.

oxidation. Domains III, V, VII, XV and XVII are the ones of transpassivity, where the oxides from passivation layer oxidize further and pass into solution in the form of anions which violates the integrity of the protective film.

The potential - pH diagram of Fe - Si - H2O system at 25°C, air pressure of 1 bar and activities of ions in the solutions equal to 1 mol/l, considering "Fe3Si", is presented in Fig. 7. The characteristics of appropriate chemical and electrochemical equilibria in the system are summarized in Table 7.

No. of line in Fig. 7 Electrode reaction Equilibrium potential, V (s. h. e.) or solution pH

a 2H ++ 2e- = H2;PH = 5 -10-7bar 0,186 - 0,0591-pH

b O2 + 4H ++ 4e- = 2H2O;PO = 0,21bar 1,219 - 0,0591-pH

1 SiO2 + 4H + + 4e- = Si (diamond) + 2H2O - 0,857 - 0,0591-pH

2 SiO2- + 6H + + 4e- = Si(diamond) + 3H2O - 0,444 - 0,0887 - pH + 0,0148 - lga&Q2_

Table 7. Basic chemical and electrochemical equilibria in the Fe - Si - H2O system at 298 K and air pressure of 1 bar allowing for "Fe3Si" compound

3 SlO2- + 2H + = SiO2 + 2H2O pH = 13,94 + 0,5 • lg aSi02-

4 FeSl1033 + 0,967 SiO2 + 3,868 H + + 3,868 e-= FeSi2 +1,934 H2O - 0,845 - 0,0591 • pH

5 FeSl1033 + 0,967 SlO2- + 5,802 H + + 3,868 e = FeSi2 + 2,901 H2O - 0,433 - 0,0887 • pH + 0,0148 • lg a&of

6 "Fe3SlM+1,883 SiO2 + 7,532 H + + 7,532 e-= 3FeSl0 961 + 3,766 H2O - 0,692 - 0,0591 • pH

7 "Fe3Sl"+1,883 SlO2- +11,298 H + + 7,532 e = FeSl0 961 + 5,649 H2O - 0,279 - 0,0887 • pH + 0,0148 • lg a^

B 3Fe (а) + SiO2 + 4H ++ 4e- = ="Fe3Sl"+2H2O; aFe(a) = 0,456 - 0,622 - 0,0591 • pH

9 3Fe (а) + SlO2- + 6H + + 4e- = ="Fe3Si"+3H2O; aFe(а) = 0,456 - 0,210 - 0,0887 • pH + 0,0148 • lg a 2_

10 Fe2SlO4 + 4H + + 4e- = 2Fe(а) + SlO2 + 2H aFeW = 0,456 - 0,222 - 0,0591 • pH

11 Fe2SiO4 + 2H + + 4e- = 2Fe(а) + SlO2- + H2 aFe(а) = 0,456 - 0,635 - 0,0295 • pH - 0,0148 • lg a 2_

12 Fe2+ + 2e- = Fe^); aFe(а) = 0,456 - 0,430 + 0,0295 • lg aFe2+

13 Fe3O4 + 8H + + 8e- = 3Fe(а) + 4H2O; aFe(а) = 0,456 - 0,077 - 0,0591 • pH

14 Fe2SiO4 + 4H + = 2Fe2+ + SlO2 + 2H2O pH = 3,508 - 0,5 • lg aFe 2+

15 Fe3O4 + 8H + + 2e- = 3Fe2+ + 4H2O 0,982 - 0,2364 • pH - 0,0887 • lgaFe2+

16 3Fe2O3 + 2H + + 2e- = 2Fe3O4 + H2O 0,231 - 0,0591 • pH

17 Fe2O3 + SiO2 + 2H + + 2e- = Fe2SlO4 + H2O 0,317 - 0,0591 • pH

18 Fe2O3 + SlO2- + 4H + + 2e- = Fe2SlO4 + 2H. 1,141 - 0,1182 • pH + 0,0295 • lg a^

19 Fe2O3 + 6H + + 2e- = 2Fe2+ + 3H2O 0,732 - 0,1773 • pH - 0,0591 • lgaFe2+

20 Fe3+ + e- = Fe2+ a 3+ 0,771 + 0,0591-lg Fe aFe2+

21 Fe2O3 + 6H + = 2Fe3+ + 3H2O pH =-0,221 - 0,333 • lg aFe3+

22 2FeO2- + 10H+ + 6e- = Fe2O3 + 5H2O 2,220 - 0,0985 • pH + 0,0197 • lg a 2 ' ? f ? ö peOj-

Diagram in Fig. 7 contains 19 domains of thermodynamic stability in certain phases:

I - a-phase (bcc) + "Fe3Si" + FeSix + FeSi2 + Si (diamond);

II - a-phase (bcc) + "Fe3Si" + FeSix + FeSi2 + SiO2;

III - a-phase (bcc) + "Fe3Si" + FeSix + FeSi2

+ SiO32-;

IV - a-phase (bcc) + "Fe3Si" + FeSix + SiO2;

V - a-phase (bcc) + "Fe3Si" + FeSix + SiO2- ;

VI - a-phase (bcc) + "Fe3Si" + SiO2;

VII - a-phase (bcc) + "Fe3Si" + SiO2- ;

VIII - a-phase (bcc) + SiO2;

There are minor differences between Diagrams in Fig. 6 and 7 related to the "Fe3Si" phase. The equilibriums in Fig. involving a-Fe (lines 8 through 11 in Fig. 6 and lines 10 through 13 in Fig. 7) differ by 0,02 V due to different activities of iron in solid solutions. The equilibriums involving oxide phases (lines 12 - 20 and 14 - 22, respectively) are quite the Fig. 7 are identical with the same areas of active corrosion, passivity and trans-passivity.

Along with electrochemical oxidation into oxides or anions, the electrochemical reduction of metal compounds into their hydrides can occur in water environment. Therefore, possible formation of iron and silicon hydrides is taken into consideration. It is well known that iron hydride exists within the Earth's core at high pressures and temperatures [99, 100]. But its synthesis at standard temperature was also studied by the authors of [100, 101]. Iron hydride has hcp structure and the variable composition FeHx {0 < x < 1} [100, 101]. Index "x" strongly depends on the sample synthesis conditions, for example, FeH0,3 - FeH0,4 was reported in [100] and the variety ranging from FeH0,1 to FeH0,8 in [101]. There are a few studies of iron hydride thermodynamic properties [102, 103] since its standard Gibbs energy of formation cannot be determined directly. The authors of [102] performed an estimation of the value with reference to stoichiometric compound

3

IX - a-phase (bcc) + SiO

X - a-phase (bcc) + Fe2SiO4;

XI - Fe2+ + SiO2;

XII - Fe2+ + Fe2SiO4;

XIII - Fe3O4 (magnetite) + [Fe3O4, Fe2SiO4] (fayalite);

XIV - Fe2O3 + Fe2SiO4;

XV - Fe3+ + SiO2;

XVI - [SiO2, Fe2O3] (hematite) + SiO2 (quartz);

XVII - Fe2O3 +SiO2- ;

XVIII -FeO4- + SiO2;

XIX -FeO2-, SiO2-.

same. Consequently, the classification of domains in Fig. 7 is identical to the one shown in Fig. 6. In addition to domains I through V in Fig. 6 there are two extra domains, exactly VI and VII in Fig. 7 that correspond to "Fe3Si" compound stability. Domains VI through XVII in Fig. 6 and domains VIII through XIX in

"FeH". The result of their estimation is as follows:

A/G298 ("FeH") = 23500 J mol-1 (52).

Silicon hydrides SiH2, SiH4 and Si2H6 can be produced only at 120°C, they resist any chemical influence of water environments (unless there are no fluoride ions in solution) and can't be formed electrochemically [65]. Therefore, only equilibria, involving iron hydride are considered in present study.

Calculations show, that "Fe3Si" compound isn't thermodynamically stable in presence of iron hydride. Therefore, it isn't taken into consideration, and the first variant of Fe - Si system potential - pH diagram, presented in Fig. 6, is modified in order to consider possible electrochemical formation of iron hydride. The potential - pH diagram of Fe - Si - H2O system at 25°C, air pressure of 1 bar and activities of ions in the solutions equal to 1 mol l-1, with due regard for "FeH", is presented in Fig. 8. The characteristics of appropriate chemical and electrochemical equilibria in system are summarized in Table 8.

Table 8. Basic chemical and electrochemical equilibriums in the Fe - Si - H2O system at 298 K and air pressure of 1 bar with due regard for "FeH" compound.

No. of line in Fig. 8 Electrode reaction Equilibrium potential, V (s. h. e.) or solution pH

a 2H + + 2e- = H2;PH = 5 -10-7bar 0.186 - 0.0591 • pH

b O2 + 4H + + 4e- = 2H2O; Po = 0,21 bar 1.219 - 0.0591 • pH

1 FeSi2 + H + + e- = "FeH" + 2Si (diamond) -1.064 - 0.0591 • pH

2 2 FeSi1033 + 0,967 H + + 0,967 e- = = 0,967 "FeH" +1,033 FeSi2 - 0.974 - 0.0591 • pH

3 0,961 Fe2SiO4 + 8,61 H + + 8,61 e- = = FeSi0 961 + 0,922 "FeH" + 3,844 H2O - 0.426 - 0.0591 • pH

4 Fe2+ + H + + 3e - = "FeH" - 0.375 - 0.0197 • pH + 0.0197 • lg aFe2+

5 Fe(a) + H + + e- = "FeH" ;aFe(a) = 0,114 - 0.299 - 0.0591 • pH

6 Fe2+ + 2e- = Fe(a); aF<a) = 0,114 - 0.412 + 0.0295 • lg aFe2+

7 Fe3O4 + 8H + + 8e- = 3Fe(a) + 4H2O; aFe(a) = 0,114 - 0.064 - 0.0591 • pH

8 Fe2SiO4 + 4H + = 2Fe2+ + SiO2 + 2H2O pH = 3.508 - 0.5 • lg aFe2+

9 Fe3O4 + 8H + + 2e- = 3Fe2+ + 4H2O 0.982 - 0.2364 • pH - 0.0887 • lgaFe2+

10 3Fe2O3 + 2H + + 2e- = 2Fe3O4 + H2O 0.231 - 0.0591 • pH

11 Fe2O3 + SiO2 + 2H + + 2e- = Fe2SiO4 + H2O 0.317 - 0.0591 • pH

12 Fe2O3 + SiO2- + 4H + + 2e- = Fe2SiO4 + 2H2O 1.141 - 0.1182 • pH + 0.0295 • lg a^

13 SiO2-+ 2H + = SiO2 + 2H2O pH = 13.94 + 0.5 • lg aSiO2_

14 Fe2O3 + 6H + + 2e- = 2Fe2+ + 3H2O 0.732 - 0.1773 • pH - 0.0591 • lgaFe2+

15 Fe3+ + e- = Fe2+ a 3+ 0.771 + 0.0591 • lg Fe aFe2+

16 Fe2O3 + 6H + = 2Fe3+ + 3H2O pH = -0.221 - 0.333 • lg aFe3+

17 2FeO2- + 10H+ + 6e- = Fe2O3 + 5H2O 2,220 - 0,0985 • pH + 0,0197 • lg a 2

The presence of "FeH" changes and simplifies the scheme of iron silicides decomposition; there are only 14 domains of thermodynamic stability of certain phases:

I - "FeH" + FeSix + FeSi2 + Si (diamond);

II - "FeH" + FeSix + FeSi2;

III - "FeH" + FeSix;

IV - "FeH" + Fe2SiO4;

V - a-phase (bcc) + Fe2SiO4;

VI - Fe2+ + SiO2;

VII - Fe2+ + Fe2SiO4;

VIII - Fe3O4 (magnetite) + [Fe3O4, Fe2SiO4] (fayalite);

IX - Fe2O3 + Fe2SiO4;

X - Fe3+ + SiO2;

XI - [SiO2, Fe2O3] (hematite) + SiO2 (quartz);

XII - Fe2O3 +SiO32- ;

XIII -FeO2- + SiO2;

XIV -FeO2-, SiO2-.

According to the calculations, silicon dioxide and iron hydride cannot coexist. Another scheme of iron silicides oxidation is presented (lines 1 - 5 at the diagram), without formation of SiO2 and SiO^. Instead of domains I through VII in Fig. 6 only another domains I through IV are depicted in Fig. 8. These domains can be also classified as domains of passivity of Fe - Si alloy

components where the passivation film consists of iron hydride as opposed to any oxides. The consideration of "FeH" does not affect all equilibriums which take place in Fe -Si - H2O system after Fe2SiO4 was formed. The lines 6 through 17 and the domains V through XIV in Fig. 8 are identical to the lines 10 through 20 and the domains VIII through XVII in Fig. 6.

5. Results and discussion

The partial pressure of oxygen in atmospheric air is equal to 0,21 bar under standard conditions. This means that all equilibria in Fe - Si - O system over which equilibrium oxygen pressure is less than 0,21 bar, take place in air environments. Table 5 shows that oxidation of Fe - Si system alloys ends with the formation of Fe2O3 and SiO2 (domains IX and X in Fig. 2 and 3 respectively) and this agrees with information given in [65]. A smaller part of SiO2 can be dissolved in Fe2O3 while another part forms an independent quartz phase.

The specific composition of oxide layer on Fe - Si alloys depends on their composition. Silicon oxidizes in the first order but if its content in alloy is insufficient to form a continuous passivation layer, Fe2O3 can also be involved in its formation. Even Fe2SiO4 can be presented in protective film in the form of local inclusions due to the kinetic factors and unreachability of the true equilibrium.

The oxidation features of iron-silicon alloys with variable silicon contents therein were studied experimentally several times [104 - 112]; however, these studies deal with high temperatures (800 - 1100°C). It was revealed [109, 111, 112] that due to a very low diffusibility of iron through a silica film, the oxidation rate of Fe - Si alloys is much lower than that of pure iron and typical Cr2O3-forming alloy Fe-26Cr. Oxidation rates become increasingly slower as the silicon content in alloy exceeds ~5 weight percent [111]. It is related to the minimum silicon concentration sufficient to develop and maintain a continuous SiO2 layer on alloy surface [110]. Theoretical studies [32] predict

that this minimum concentration is precisely 5 weight percent at temperatures of 400 - 1000 K. For the alloys composition with lesser silicon content [105 - 108, 112], the presence of Fe2O3, Fe3O4 and Fe2SiO4 is also detected in oxide layer. The primary passivation film made of SiO2, can, however, decompose, if a significant amount of CO2 is presented in atmosphere [106 - 110].

When analyzing Fe - Si alloys electrochemical oxidation, it is important to single out lines a and b in potential - pH Diagrams. They correspond to hydrogen and oxygen electrodes, respectively. An area between these two lines corresponds to water electrochemical stability and matters most in exploring the corrosion processes. In Diagrams presented in Fig. 6 - 8, an area of water electrochemical stability is the same with/without regard to some compounds. In strongly acidic environments (pH < 3) iron oxidizes to Fe2+ or Fe3+ cations, and only in very alkaline environments (pH > 14) silicate ions can be produced. A greater part of this area is occupied by the domain of thermodynamic stability of Fe2O3 + SiO2 which corresponds to rather large passivity region. The author of [33] declares that there are three stages of the oxidation process involving SiO2, Fe2SiO4 and iron oxides. This is a doubtful suggestion, because, in contrast to some other transition metals silicates [113 -117], iron silicate has a very narrow field of thermodynamic stability and plays a minor role in Fe - Si alloys corrosion-electrochemical behavior in the area of water stability. Moreover, Fe2SiO4 is treated as metastable compound in water environments

and excluded from considerations in the study [98]. Conclusions made earlier for chemical stability of iron silicides in regard of Fe2O3 and SiO2-containing passivation film are valid for electrochemical corrosion as well.

However, some aspects of electrochemical behavior of Fe - Si system outside the area of water stability are not so clear. The oxidation of Fe+3 to Fe+6 takes place at the very high potentials greater than 2V that are very hard to achieve experimentally. Therefore, there is no experimental evidences that prove or disprove the possible formation of iron (IV) aqueous species as the intermediates between iron (III) and iron (IV) species.

Note that equilibriums involving iron hydride "FeH" have also predictive nature. There is no data in literature on electrochemical formation of hydride that can verify these calculations which are rather approximate because thermodynamic properties of "FeH" are just estimated rather than directly determined. Consecutive schemes of decomposition of iron silicides with/without iron hydride vary from each other essentially, so an exact mechanism of these processes remains open for discussion.

It has to be kept in mind that corrosion properties of Fe - Si systems were studied thoroughly, including corrosion rate measurements and polarization tests on various iron silicides [118 - 129], particularly in acidic [118 - 122] and alkaline [127 - 129] environments, corrosion studies of Fe - Si solid solutions [130], studies of oxidation

products [131 - 133] and corrosion properties of multicomponent alloys, coatings, films and other complicated wares, including iron-silicon system [134 - 140]. Thermodynamic calculations performed in the present study are not contrary to experimental data presented in the paper. For all iron silicides where the silicon content is high enough, in acidic electrolytes, iron selectively dissolves from the silicide sub-lattice forming cations while silicon remains on the surface and forms a SiO2 film notable for high electrochemical resistance (certainly, if there is no fluorideions in the solution). Later on, the process is limited by the diffusion of metal atoms from the bulk of the silicide toward the surface layer and the diffusion of oxidized metal through the film of hydrated silicon hydroxide. In alkaline electrolytes, the solubility of silicon and silicon dioxide sharply increases, and the mechanism of the anodic process is determined by the formation of protective films composed of Fe3O4 and FeOOH. The films passivate the surface and make the silicides stable against alkalis. The minimal silicon concentration that allows forming protective SiO2 films in acids for Fe - Si containing alloys, is about 5 weight percent.

Despite the lack of reliable information, thermodynamic theory cannot yet give a clear answer to the all aspects of chemical and electrochemical stability of Fe -Si system alloys, just basic regularities are revealed and analyzed. Thermodynamic description can successfully complement and broaden the results of corrosion experiments.

1. Thermodynamic properties of Fe - Si system at 298 K were analyzed, the comparison between available thermodynamic descriptions was made and the thermodynamic estimation of the Gibbs energy of formation of non-stoichiometric iron silicide explored. Also, the thermodynamic analysis of the longdistance ordering in the system at low temperatures was performed and the maximum solid solubility of silicon in bcc-Fe at 298 K estimated. It equals to 26 atomic percent provided that "Fe3Si" is taken into no account

as independent compound together with 11 atomic percent if it is.

2. The Fe - Si - O state diagram at 298 K was plotted and the invariant system conditions calculated. Besides, the maximum solid solubility of Fe2SiO4 in Fe3O4 and of SiO2 in Fe2O3 at 298 K was estimated and the activity of - pH diagrams for the ferrous and ferric aqueous species and the potential - pH diagrams of Fe - Si - H2O system at 298 K, air pressure of 1 bar and activities of ions in solution, equal to 1 mol/l with/without

consideration of "Fe3Si" and "FeH". The characteristics of the basic chemical and electrochemical equilibrium in Fe - Si - H2O system were calculated.

3. Thermodynamic analysis of chemical and electrochemical stability of iron - silicon system alloys was performed and positive influence of silicon on iron corrosion properties revealed.

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ТЕРМОДИНАМИЧЕСКАЯ ОЦЕНКА ХИМИЧЕСКОЙ И ЭЛЕКТРОХИМИЧЕСКОЙ

УСТОЙЧИВОСТИ СИЛИЦИДОВ ЖЕЛЕЗА

П.А. Николайчук

Институт биохимии, Грайфсвальдский университет, Ул. имени ФеликсаХаусдорфа 4, 17487 Грайфсвальд, Германия.

e-mail: npa@csu.ru.

Рассмотрены фазовые и химические равновесия в системе Fe - Si при 298 K. Произведено сравнение имеющейся в наличии термодинамической информации о растворимости кремния в железе с решёткой о. ц. к. при низких температурах с учётом и без учёта дальнего упорядочения в а-фазе. Оценена стандартная энергия Гиббса образования нестехиометричного силицида железа. Оценена возможная максимальная растворимость кремния в железе при 298 K и вычислены термодинамические активности насыщенного раствора. Построена диаграмма состояния системы Fe - Si - O при 298 K и вычислены характеристик инвариантных состояний этой системы. Оценена твёрдая растворимость Fe2SiO4 в Fe3O4 и SiO2 в Fe2O3 при 298 К. Построены диаграммы активность - рН для соединений железа (II) и железа (III) в водных средах. Построена диаграмма потенциал - pH системы Fe - Si - H2O при 298 K, давлении воздуха 1 бар и активностях ионов в растворе, равных 1 моль/л. Рассмотрены основные химические и электрохимические равновесия в системе. Выполнен термодинамический анализ химической и электрохимической устойчивости сплавов системы Fe - Si.

Ключевые слова: система Fe-Si, силициды железа, фазовые равновесия, низкотемпературное окисление, химическая и электрохимическая устойчивость.

DdMiR SÍLÍSÍDLORÍNKiMYdVi Vd ELEKTROKiMYdViDAYANIQLIGININ TERMODÍNAMÍKÍ QiYMdTLdNDiRJLMdSi

P.A. Nikolayquk

Qrayfsvald Universiteti, Biokimya institutu, Almaniya 17487 Qrayfsvald, Almaniya, Feliks Hausdorf küg.,4; e-mail: npa@csu.ru

Fe - Si sisteminda 298K temperaturda faza va kimyavi tarazliqlar nazardan kegirilib. Silisiumun damirda a§agi temperaturda hall olmasi haqqinda adabiyyatda olan informasiya müqayisa edilib va amala galan doymu§ mahlulun termodinamik aktivliyi hesablanib. Fe - Si sistemin kimyavi va elektrokimyavi dayaniqliginin termodinamiki analizi aparilib.

Agar sözbr: Fe - Si sistemi, faza tarazligi, kimyavi va elektrokimyavi dayaniqliq