If one considers the mass-balance of the previously described coprecipitation experiments, the nature and the relative abundances of the iron containing compounds that form are governed by two parameters: (i) the ferric molar fraction of the initial mixed Fe^II–Fe^III solution, i.e. the ratio x=n(FeIII)/[n(FeII)+n(FeIII)]; (ii) the hydroxylation rate that corresponds to the molar ratio R=n(OH−)/[n(FeII)+n(FeIII)] where n(OH⁻) represents the number of moles of hydroxyl species added in solution, n(Fe^III) and n(Fe^II) are the numbers of Fe^III and Fe^II ions introduced into the initial solution. The value of the ratio R is well defined when the basic solution used in the experiment is a strong base such as NaOH.

It is convenient to represent in a mass-balance diagram [14] the ratio R=n(OH−)/[n(FeII)+n(FeIII)] as a function of the ferric molar fraction x=n(FeIII)/[n(FeII)+n(FeIII)] of the various iron species that may form (Fig. 1), where n(OH⁻), n(Fe^III) and n(Fe^II) represent here the number moles of OH⁻, Fe^III and Fe^II consumed during the precipitation of 1 mol of iron of a given compound. As an example, the ferric oxyhydroxides of chemical formula FeOOH (or the ferric oxides Fe₂O₃) are represented by point (1,3) in the diagram presented in Fig. 1, because the precipitation of 1 mol of Fe^III into these compounds is described by the following chemical reactions:

In a same manner, the position of the different solid compounds can easily be determined: ferrous hydroxide Fe(OH)₂, green rust (GR) of general chemical formula [FeII(1−x)FeIIIx(OH)2]x+⋅[(x/n)An−⋅mH2O]x−, magnetite Fe₃O₄ and ferric oxide Fe₂O₃ correspond respectively to points (0,2), (x,2), (2/3,8/3) and (1,3) (Fig. 1). Non-stoichiometric magnetite Fe_(3−x)O₄ is situated on the tie-line that links point (2/3,8/3) to point (1,3). The aqueous species FeIIaq and FeIIIaq are represented by points (0,0) and (0,1), respectively.

A coprecipitation experiment that is realised at a constant ferric molar fraction ratio x0 corresponds to the vertical line x=x0 shown in Fig. 1. At each instant of the experiment, i.e. for each point P(x0,R) situated on the vertical line, the nature and the relative abundance of the different compounds that may precipitate can be determined graphically. Therefore, the following cases will be considered:

• – (a) a single compound forms if P is situated at a point (x,R) that corresponds to a given compound, e.g., point (0.33,2) that corresponds to GR in Fig. 1;
• – (b) a two-compound system forms if point P is situated on a tie-line that joins two compounds, e.g., the tie-line that joins Fe(OH)₂ to GR in Fig. 1. In a general case, let us consider the formation of a mixture of two compounds α and β that correspond to the two points P[α](x[α],R[α]) and P[β](x[β],R[β]) presented in Fig. 2. The conservation of matter leads to:

  n(OH−)=n(OH−)[α]+n(OH−)[β]

  (2)

  n(FeIII)=n(FeIII)[α]+n(FeIII)[β]

  (3)

  where n(OH⁻), n(Fe^III), n(OH⁻)^[α], n(Fe^III)^[α], n(OH⁻)^[β] and n(Fe^III)^[β] are the respective mole numbers of OH⁻ and Fe^III consumed during the formation of the whole mixture and their repartition in the α and β compounds. It can be demonstrated that Eqs. (2) and (3) are equivalent to the following equations:

  R=n(OH−)/n=(X[α]⋅R[α])+(X[β]⋅R[β])

  (4)

  x=n(FeIII)/n=(X[α]⋅x[α])+(X[β]⋅x[β])with X[α]=(n[α]/n) and X[β]=(n[β]/n)

  (5)

  It should be noted that if Mössbauer spectroscopy is performed for analysing the {α+β} mixture, X[α] and X[β] occur to be the relative areas of the subspectra of phases α and β, respectively. The quantitative predictions made with the mass-balance diagram can be directly compared to quantitative analyses made with Mössbauer spectroscopy as already done in a previous work [16];

• – (c) a three-compound mixture forms if point P is situated inside a triangle of three compounds, e.g., Fe(OH)₂, GR and Fe₃O₄ in Fig. 1. Let us again consider the general case of three compounds represented by the three points P[α](x[α],R[α]), P[β](x[β],R[β]) and P[γ](x[γ],R[γ]) in Fig. 2. A similar demonstration to that followed for the two-compounds mixture will lead to the vectorial relation:

  OP2=X[α]OP[α]+X[β]OP[β]+X[γ]OP[γ]

  (9)

  The Fe molar fractions X[α],X[β] and X[γ] can be determined graphically by using the parallel to the sides of triangle (P[α], P[β], P[γ]) as shown in Fig. 2 and the following equations are verified:

  X[α]=|M1[α]P[β]|/|P[α]P[β]|=|M2[α]P[γ]|/|P[α]P[γ]|

  (12)

  X[β]=|M1[β]P[γ]|/|P[β]P[γ]|=|M2[β]P[α]|/|P[β]P[α]|

  (13)

  X[γ]=|M1[γ]P[α]|/|P[γ]P[α]|=|M2[γ]P[β]|/|P[γ]P[β]|

  (14)

For 10 different values of the ferric molar fraction x, titration curves were presented in a previous work [14] and three typical curves are shown in Fig. 3. The curves are characterised by three plateaus separated by two equivalent points E₁ and E₂. For x⩽0.2, a slow down of the pH curves is observed around a critical point called E^* and the jump of pH is always preceded by a small peak between R∼1.7 and 1.95. A direct visualisation of the compounds that form during the titration is presented in Fig. 4 where the R values that correspond to equivalent points E₁, E₂ and E^* are indicated in the mass-balance diagram. One observes that the (x,R1) values of points E₁ are situated on a line R=∼2.75x. This indicates that the compound that forms during the first plateau is a sulphated ferric basic salt, i.e. a ferric oxyhydroxide where some of the OH⁻ anions are substituted by SO42− anions. Schwertmanite of general chemical formula Fe₁₆O₁₆(OH)_y(SO₄)_z⋅n H₂O (16−y=2z and 2⩽z⩽3.5) [4], which is also presented in the mass-balance diagram, is an example of such a ferric basic salt. When x⩽0.2, the (x,R2) values of points E₂ follow the line R=2 of the binary system {Fe(OH)₂, GR(SO₄)}. For 0.25⩽x⩽0.67, the points are situated in the triangle of the three-compound system {Fe(OH)₂, GR(SO42−), Fe₃O₄}. The formation of these compounds was confirmed by using Mössbauer spectroscopy and the TMS spectra of two samples taken at points E₂ of the titration curves are given in Fig. 5a and b. Hyperfine parameters and quantitative predictions made with the mass-balance diagram are given in Table 2. At T=12K, the Mössbauer spectrum of GR(SO42−) is easily distinguished from the spectrum of Fe(OH)₂, which is characterised by an octet, as already discussed [14]. There is a relative good agreement between the predicted and measured quantities for the mixture {GR(SO42−), Fe(OH)₂}. It is not the case for the three-compound mixture and this may be attributed to the existence of non-stoichiometric magnetite.

The most interesting part of this analysis is the position of points E^* observed on the pH curves when x⩽0.2 (Fig. 3). The pH values of the flat part of the second pH plateau, i.e. when R∗<R<2, is very close to those measured during the titration of a standard Fe^II solution (not shown). It is therefore natural to propose that the first step of the second pH plateau, i.e. when R<R∗, corresponds to the full transformation of the initially formed ferric oxyhydroxide into GR(SO42−). In the second step, i.e. when R∗<R<2, the precipitation of the excess of FeIIaq present in solution leads to the formation of Fe(OH)₂. The (x,R∗) of points E^* presented in the mass-balance diagram in Fig. 4 increases roughly linearly according to R∗=αx where α=7±∼0.5. This last linear relation is equivalent to a molar ratio n(OH⁻)/n(Fe^III)=7±∼0.5. In a previous work [16], it was demonstrated with Mössbauer spectroscopy that GR(SO42−) forms in the absence of any others solid compounds when exactly 7 moles of OH⁻ per mole of Fe^III were added. When x=0.14, the Mössbauer spectrum of the sample obtained in these conditions contains only one ferrous doublet D₁ and one ferric doublet D₂ (Fig. 5c). The measured ratio RA(D1)/RA(D2)=1.94 is in good agreement with the chemical formula FeII4FeIII2(OH)12SO4⋅∼8H2O. The fact that GR(SO42−) forms when an excess of OH⁻ species is added is in apparent contradiction with what is expected if one considers the previous chemical formula where the ratio n(OH⁻)/n(Fe^III) is equal to 6. This means that a certain amount OH⁻ species are consumed by another process that is concomitant to the formation of GR(SO42−). Another important experimental evidence that such a process occurs is the fact that the value R2=2.16 observed for the second equivalent point of the pH titration curves of the ‘stoichiometric’ solution, i.e. when x=0.33, overshoots clearly the expected value R=2 (Fig. 3). It can be seen on the same figure that such a phenomenon does not occur when x=0.67 and the measured value R2=2.67 is in very good agreement with the value expected for the formation of stoichiometric magnetite.

The different steps of the coprecipitation experiments were analysed by measuring the concentrations of Fe, Fe^II and SO42− that remain in the aqueous medium during the titration of the x=0.33 solution (Fig. 6). The grey dilution curve presented in Fig. 6a corresponds to the expected SO42− concentration assuming that these anions are not incorporated in any precipitates. In this case, the variation of concentration is only due to the increase of volume corresponding to the addition of the NaOH solution. Calculated concentration curves were done by using the following hypotheses: (i) a ferric oxyhydroxide FeOOH precipitates during the first pH plateau by consuming 3 mol of OH⁻ per mole of Fe^III and the reaction is therefore finished at point B of abscissa R=1; (ii) FeOOH reacts with FeIIaq to form GR(SO42−) by consuming 2 mol of OH⁻ per mole of iron and the reaction is accomplished at point C of abscissa R=2; (iii) GR(SO42−), which is unstable at pH ∼ 12 [16], is fully transformed into a mixture {Fe₃O₄, Fe(OH)₂} at the end of the titration curve (R=3).

The concentration of SO42− anions measured in solution ([SO42−]exp) is clearly situated under the calculated curve between points A and B of Fig. 6a. This represents an experimental proof of the formation of a ferric sulphated basic salt, which begins when the flat part of the first pH plateau is reached. The decrease of the [SO42−]exp values is followed by an increase at R∼0.8 and the experimental values reach again the calculated values around point B. This means that the initially formed ferric basic salt transforms into a ferric oxyhydroxide by releasing SO42− anions in solution around equivalent point E₁. As expected, the [SO42−]exp values decrease during the formation of GR(SO42−) between points E₁ and E₂ and then increase when GR(SO42−) transforms into the mixture {Fe₃O₄, Fe(OH)₂}.

The Fe concentrations measured in solution ([Fe]_exp) are also situated slightly above the calculated values between points A and B confirming the formation of the ferric basic salt (Fig. 6b). By using both values [SO42−]exp and [Fe]_exp measured during the titration of the reference Fe^III solution (x=1), the molar ratio n(SO42−)/n(FeIII) of the ferric basic salt was calculated and it decreases between ∼0.6 to 0.3 for increasing values of R (1.25⩽R⩽2.27). The evolution of the [Fe]_exp values between points E₁ and E₂ is very interesting because the breakdown of the curves occurs at point B^*, situated at R∼1.15 (Fig. 6b). Then, the experimental curve decreases at a similar rate than the calculated curves, but stays always shifted to the right. As presented in Fig. 6b, this means that it is necessary to introduce an excess of OH⁻ in solution in order to precipitate a given amount of Fe^II into GR(SO42−). This experimental result was confirmed by measuring the concentrations of Fe^II in solution. Between points E₁ and E₂, the curves corresponding to both [Fe]_exp and [Fe^II]_exp follow the same trends and are more or less superposed. Therefore, the concentration of Fe^III cations present in the aqueous solution when GR(SO42−) forms is negligible.

Analyses of the pH titration curves performed with the mass-balance diagram, Mössbauer spectroscopy and measurements of Fe and SO42− concentrations in solution show that an excess of OH⁻ species is consumed while GR(SO42−), i.e. [FeII4FeIII2(OH)12]2+⋅[SO42−⋅∼8H2O], is forming. This excess corresponds to an n(OH⁻)/n(Fe^III) ratio of 7 instead of 6. It can be noticed that this amount corresponds also to the formation of the hypothetical mixture [FeOOH + 2 Fe(OH)₂], which would contain no sulphate. In fact, once point E₁ of the titration curves is reached, Fe(OH)₂ does not form but the surface of the initially formed FeOOH solid acts as a hydroxylating ligand towards Fe^II ions in solution. Therefore, the mechanism of formation of GR(SO42−) more likely involves a surface reaction between the ferric oxyhydroxide and octahedrally co-ordinated Fe^II cations. At pH ∼ 5 (point E₁), partially hydroxylated ferrous species adsorbs on the FeOOH surface. At pH > 6–7, hydroxylation proceeds further and the formation of brucite like clusters by olation of [Fe(OH)₂(OH₂)₄]⁰ complexes occurs [10,11]. As presented in Fig. 7, previously adsorbed SO42− (or SO42− anions coming from the solution) can get into the gap between the brucite like cluster and the FeOOH surface (Fig. 7b). This helps electrons to transfer from the ferrous cluster to the ferric interface through the interlayer. The hydroxylated solid-solution interface of bulk FeOOH can be consider as an Fe^III(OH)₃ layer and therefore the chemical reaction can be written as follows:

The interlayer of SO42− anions between two brucite-like Fe^II–III(OH)₂ layers is electrostatically balanced and an excess of OH⁻ ion is released; a Fe^II–III(OH)₂ cluster is now separated from the bulk substrate (Fig. 7c). Lateral growth of the clusters in the [100] direction proceeds much faster than in the [001] direction in order to obtain the flat hexagonal plates observed with TEM (Fig. 12). The process can be repeated if a new Fe^II(OH)₂ cluster forms on the top of this first GR₂(SO42−) nucleus (Fig. 7d). Two SO42− interlayers may form simultaneously and the electron transfer is again accomplished from the Fe^II donor within the brucite-like cluster towards the Fe^III acceptor of the oxyhydroxide interface (Fig. 7e). Therefore, it seems inappropriate to qualify the process as dissolution–reprecipitation. The GR₂(SO42−) crystal grows in situ at the expense of the FeOOH substrate by electron transfer.

Fe^II–Fe^III solutions were precipitated by a NaOH solution at a constant ratio R=n(OH−)/n(Fe)=2, as presented in Table 1. The Mössbauer spectra and hyperfine parameters obtained for three different values of the ferric molar fraction x are presented in Fig. 8 and Table 3, respectively. It appears that GR(SO42−) precipitates in the quasi-absence of any other compound only when x=0.33 (Fig. 8b). Nevertheless, traces of Fe₃O₄ and/or FeOOH that correspond to a very low intensity sextet are present. When x=0.28, the sample is a mixture of two compounds, i.e. {GR(SO42−), Fe(OH)₂}, and a mixture of three compound when x=0.46, i.e. {GR(SO42−), Fe₃O₄, FeOOH}. Whatever the sample is, a Fe^II:Fe^III ratio of ∼1:2 is measured by using the relative areas of doublets D₁ and D₂ of GR(SO42−). Therefore, GR(SO42−) has a well-defined stoichiometry that corresponds to the normalised chemical formula [FeII0.67FeIII0.33(OH)2]0.33+⋅[(0.165)SO4⋅∼(1.33)H2O]0.33−.

Fe^II–Fe^III solutions were precipitated by a Na₂CO₃ solution at a constant molar ratio R=n(CO32−)/n(Fe)=2.5, as presented in Table 1. The samples were filtered and analysed immediately after the synthesis in order to avoid the transformation of GR(CO32−) in a mixture of magnetite and siderite. On the contrary to what was observed for GR(SO42−), typical spectra of GR(CO32−) that contain three doublets were obtained for both values x=0.25 and x=0.33 (Fig. 9a and b and Table 4). As predicted by using structural models [7], the area ratio between doublets D₁:D₂:D₃ is close to 1/2:1/3:1/6 for the sample prepared at x=0.33. Doublet D₃ was attributed to Fe^II species that has CO32− anions in their neighbourhood and a decrease of the relative area of doublet D₃ is effectively observed for the green rust sample that contains less carbonate anions, i.e. when x=0.25 (Fig. 8a).When x=0.4, the Mössbauer spectrum corresponds to a mixture of green rust and magnetite {GR(CO32−), Fe₃O₄} and the Fe^II:Fe^III ratio of GR(CO32−) is close to 2:1. The relative abundance of Fe₃O₄ that is given in Table 4, i.e. 23%, is in good agreement with the quantity predicted by using the lever rule in the mass-balance diagram, i.e. 21%. Finally, GR(CO32−) has a variable chemical composition that corresponds to the normalised chemical formula [FeII(1−x)FeIIIx(OH)2]x+⋅[(x/n)CO32−⋅mH2O]x− where ∼0.25<x<0.33.

It has been often reported that most of the members of the M^II–M^III layered double hydroxides (LDH) family of general chemical composition [MII(1−x)MIIIx(OH)2]x+⋅[(x/n)An−⋅mH2O]x+ [13] have an upper limit of composition x=0.33. This limit is generally attributed to the fact that if x>0.33, M^III cations become nearest neighbours in the brucite-like layer and this is hardly possible due to electrostatic repulsion. If this last rule is respected for x=0.33, the cation layer is characterised by an ordered array, where all M^III cations are surrounded by six M^II cations. It appears that green rusts obey the same rule than the other LDHs.