Electrodeposition of Fe-Ni Alloy Films having Invar Compositions with Fe³⁺ as the Sole Iron Source

The fractions of various citric acid species were plotted against pH based on stepwise acid dissociation constants (K_an ), defining citric acid as a tetrabasic acid (H₄Cit). It is known that pK_an varies with the ionic strength of the solution. In the present work, because plating baths typically have very large ionic strengths, pK_an for the three carboxyl groups of H₄Cit was assigned values of pK_a1 = 2.82, pK_a2 = 4.1 and pK_a3 = 5.1. These values represent those reported in the literature for the highest ionic strength of 2 M. ^48,49 However, it should be noted that the ionic strength of all solutions used in the present work was greater than 2 M. In addition, pK_a4 = 14.4 ⁴⁹ was assigned to the hydroxyl group of citric acid. A conditional stability constant—pH diagram for the various ferric-citrate complexes was also generated based on the fraction of Cit⁴⁻ and the stability constants for the main ferric-citrate complexes at different pH values. ⁴⁶ The concentration of the aqua complex formed between Fe³⁺ and water (Fe(H₂O)₆ ³⁺), which does not interact with citrate ions, was calculated from this diagram and an ionic product—pH plot for Fe(OH)₃ was then produced. These data were generated using Fe³⁺ and citrate concentrations of 0.2 and 0.4 M, respectively (that is, with a Fe³⁺:citrate molar ratio of 1:2). The stable pH range for these ferric-citrate complexes was estimated from this plot. Stability tests of 0.2 M FeCl₃·6H₂O + 0.4 M Na₃C₆H₅O₇ solutions at various pH values were conducted at room temperature. The appearance of each solution was observed immediately after preparation and following a one-day interval. The Fe-Ni alloy electrodeposition bath was prepared on the basis of these stability tests and the bath composition used in the present study is summarized in Table I. In this work, H₃BO₃ was used as a buffer and the bath pH was adjusted to 2–4 by the addition of a HCl solution. Pure Cu substrates (C1020) with an exposed surface area of 10 cm² (3 × 3.33 cm) were used as substrates. A Pt-plated Ti plate was used as the anode, and trials were performed in an electrolysis cell of our own design constructed from acrylic plates with internal dimensions of 7 × 3 × 6 cm. The distance between the cathode and anode in this apparatus was approximately 7 cm and electrodeposition was carried out under galvanostatic conditions at 25 °C without stirring, using a total electrical charge of 1000 C. The composition of each electrodeposited film was quantified by X-ray fluorescence spectroscopy (XRF) using a Rigaku, ZSX Primus II wavelength-dispersive spectrometer. The surface morphology and cross-sectional elemental distribution for each film was determined using field-emission scanning electron microscopy (FE-SEM: JEOL, JSM-7000F) together with energy-dispersive X-ray spectroscopy (EDS: JEOL, JED-2300). The crystal structures of the films were evaluated by X-ray diffraction (XRD: Shimadzu, XRD-6100).

The fraction of citric acid species (H₄Cit, H₃Cit⁻, H₂Cit²⁻, HCit³⁻, and Cit⁴⁻) is a function of pH. For example, the fraction of Cit⁴⁻ (α_Cit4−) is given by:

$$\begin{eqnarray}&&{\alpha }_{{\rm{Cit}}4-}=\,\frac{{K}_{a1}{K}_{a2}{K}_{a3}{K}_{a4}}{{\left[{{{\rm{H}}}_{3}{\rm{O}}}^{+}\right]}^{4}+{K}_{a1}{\left[{{{\rm{H}}}_{3}{\rm{O}}}^{+}\right]}^{3}+{K}_{a1}{K}_{a2}{\left[{{{\rm{H}}}_{3}{\rm{O}}}^{+}\right]}^{2}+{K}_{a1}{K}_{a2}{K}_{a3}\left[{{{\rm{H}}}_{3}{\rm{O}}}^{+}\right]+{K}_{a1}{K}_{a2}{K}_{a3}{K}_{a4}}.\end{eqnarray} \tag{ 1 }$$

Figure 1 shows the relationship between the fractions of the various citric acid species and pH. It can be seen that in acidic solutions, no Cit⁴⁻ is present and other species are dominant depending on the pH. In basic solutions, HCit³⁻ is generally dominant, but there is evidence of an increase in the Cit⁴⁻ fraction for pH >12.

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Silva et al. reported that dinuclear (Fe₂(Cit)₂ ²⁻) or trinuclear species (Fe₃(Cit)₃ ³⁻) are more common at lower pH, whereas the mononuclear dicitrate complex (Fe(Cit)₂ ⁵⁻) is predominant at neutral pH, and that the pH range in which these species are the main components depends on both the concentration of the ferric-citrate complex and the Fe³⁺:citrate molar ratio. ⁴⁶ These three complexes consist of Fe³⁺ and Cit⁴⁻, which is a deprotonated species. In this study, for simplicity, it is assumed that Fe³⁺ ions form complexes with only Cit⁴⁻ in acidic and neutral solutions. The stability constant for the ferric- Cit⁴⁻ complex is affected by the acid-dissociation equilibrium for citric acid (H₄Cit). The equilibrium state can be expressed by:

$$\begin{eqnarray*}&&\begin{array}{c}{{\rm{H}}}_{4}{\rm{Cit}}\mathop{\rightleftharpoons }\limits^{{\rm{H}}+}{{\rm{H}}}_{3}{{\rm{Cit}}}^{-}\mathop{\rightleftharpoons }\limits^{{\rm{H}}+}{{\rm{H}}}_{2}{{\rm{Cit}}}^{2-}\mathop{\rightleftharpoons }\limits^{{\rm{H}}+}{{\rm{HCit}}}^{3-}\mathop{\rightleftharpoons }\limits^{{\rm{H}}+}{{\rm{Cit}}}^{4-}\\ +\,{{\rm{Fe}}}^{3+}\rightleftharpoons {\rm{Complexes}}\left({{\rm{Fe}}}^{3+}-{{\rm{Cit}}}^{4-}\right)\end{array}\end{eqnarray*}$$

Therefore, the conditional stability constants that reflect the effect of acid-dissociation equilibrium should be considered. In previous studies, the stability constants for ferric-citrate complexes were determined at very low concentrations (on the order of micromolar to millimolar) and large Fe³⁺:citrate molar ratios (such as 1:10). ^45,46,50 Silva et al. reported that the overall stability constants (β) for the three ferric-citrate complexes were logβ(Fe₂(Cit)₂ ²⁻) = 48.0, logβ(Fe₃(Cit)₃ ³⁻) = 73.8 and logβ(Fe(Cit)₂ ⁵⁻) = 32.73. ⁴⁶ The conditional stability constants (βʹ) for each ferric-citrate complex were determined using Eq. 2 (see Eq. 1)

$$\begin{eqnarray}&&{\beta }^{{\prime} }={\alpha }_{{\rm{Cit}}4-}\,{\rm{\cdot }}\,\beta .\end{eqnarray} \tag{ 2 }$$

In the present work, the pH ranges over which Fe₂(Cit)₂ ²⁻ or Fe₃(Cit)₃ ³⁻ and Fe (Cit)₂ ⁵⁻ were the main species were assumed to be 1–6 and 5–8, respectively.

Figure 2 plots the logβʹ values for the primary ferric-citrate complex species as functions of pH. The βʹ values for the Fe₂(Cit)₂ ²⁻ and Fe₃(Cit)₃ ³⁻ complexes that were predominant at low pH were found to be large, especially for Fe₃(Cit)₃ ³⁻. The concentration of the Fe(H₂O)₆ ³⁺ complex was determined from the βʹ value, and the ionic product [Fe³⁺][OH⁻]³ was then calculated for various pH. During these calculations, the total Fe³⁺ species concentration and the total citric acid species concentration were set to 0.2 and 0.4 M, respectively.

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Figure 3 shows the relationship between log([Fe³⁺][OH⁻]³) and pH for the primary ferric-citrate complexes. The dashed line indicates the log of the solubility product for Fe(OH)₃ (K_sp = 4 × 10⁻³⁸). At lower pH where Fe₂(Cit)₂ ²⁻ or Fe₃(Cit)₃ ³⁻ was predominant, the values of log([Fe³⁺][OH⁻]³) were determined to be much smaller than logK_sp for Fe(OH)₃. In contrast, at neutral pH, where Fe(Cit)₂ ⁵⁻ was the main complex, the values of log([Fe³⁺][OH⁻]³) were similar to logK_sp for Fe(OH)₃. Therefore, we considered that although Fe(OH)₃ is poorly soluble, it does not precipitate in the pH range of 1–6.

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Figure 4 provides photographic images showing the appearance of ferric-citrate solutions having various pH values, produced using Fe³⁺ and citrate concentrations of 0.2 and 0.4 M. The as-prepared solutions in Fig. 4a exhibit greater precipitation of Fe(OH)₃ at a pH of 5 or greater, such that the solutions were transparent at pH values below 4, with a light green coloration within the pH range of 2–4 and a dull green color at a pH of 1. After standing for one day, the pH range over which the solutions were transparent expanded to include a pH of 5, likely because some time was required for the solutions to reach equilibrium. After this point, the appearance of the solutions did not change with further aging. These results roughly agree with the estimated stable pH range in Fig. 3. At a pH of 1, ferric citrate complex ions are not likely to be these oligomeric complexes but other complex ions such as Fe(HCit) ⁴⁶ and/or Fe(H₂O)₆ ³⁺. Thus, these ferric-citrate solutions were stable in the pH range of 2–4.

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The Fe-Ni alloy plating bath used in this work (see Table I) was found to be stable. As noted, H₃BO₃ was added to this bath as a buffer to inhibit the precipitation of Fe(OH)₃ and/or Ni(OH)₂ at the cathode surface during electrodeposition.

Figure 5 shows the appearance of Fe-Ni alloy plating bath specimens having various pH values. Immediately after preparation, the bath solution was transparent and deep green over the pH range of 2–4 (Fig. 5a) and the appearance did not change following one day of standing (Fig. 5b). In this solution, Fe³⁺ was likely present as [Fe₂(Cit)₂]²⁻ or [Fe₃(Cit)₃]³⁻ complexes. In contrast, Ni²⁺ ions are known to combine with citric acid to form mononuclear monocitrate complexes such as NiH₂Cit⁺, NiHCit and NiCit⁻ in the same pH range. ⁵¹ The stability constants for these Ni-citrate complexes for a Ni²⁺:citrate molar ratio of 1:1 are much smaller than those for ferric-citrate complexes (logK(NiH₂Cit)⁺ = 1.5, logK(NiHCit) = 3.35 and logK(NiCit)^—= 5.49). ⁵² Therefore, for the present Fe-Ni alloy plating bath, Ni²⁺ was likely to be present as Ni(H₂O)₆ ²⁺ and as citric complex ions such as Ni(Cit)^–.

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Electrodeposition was carried out at various current densities using plating baths with different pH values. The appearance of the plating bath did not change even after electrodeposition, indicating that Fe(OH)₃ was not precipitated and the solution was stable. The effects of both the current density and bath pH on the Ni content in the electrodeposited Fe-Ni alloy films are shown in Fig. 6. Note that the dashed line in this figure indicates the composition of a Fe-36 mass% Ni specimen corresponding to a perfect Invar alloy. The Ni proportions in the electrodeposited films were in the range of 31–42 mass% and so were close to the desired value of 36 mass%. Note also that an Fe-36 mass% Ni film was formed at 35 mA cm⁻² using a bath having a pH of 4. The Ni concentrations in these films slightly increased with increases in both current density and pH. Because the Fe-Ni alloy electrodeposition mechanism is complicated (involving the well-known anomalous codeposition phenomenon), ^53,54 an explanation for this apparent change in the Ni content is not presented herein.

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The electrodeposition reactions of Fe and Ni are three and two electron processes, respectively. Consequently, the deposition current efficiency (CE) could be calculated as

$$\begin{eqnarray}&&{\rm{CE}}\left( \% \right)=\left\{\frac{F{\,\times \,W}_{{\rm{Fe}}-{\rm{Ni}}}\times \left(\frac{{{WR}}_{{\rm{Fe}}}}{{{\rm{AW}}}_{{\rm{Fe}}}}\times 3+\frac{{{WR}}_{{\rm{Ni}}}}{{{\rm{AW}}}_{{\rm{Ni}}}}\times 2\right)}{{\rm{AE}}}\right\}\times 100,\end{eqnarray} \tag{ 3 }$$

where F is the Faraday constant (96,485 C mol⁻¹), W_Fe-Ni is the mass of the deposited Fe-Ni alloy film, WR_Fe is the mass-based proportion of Fe in the Fe-Ni alloy film, WR_Ni is the mass-based proportion of Ni in the film, AW_Fe is the atomic weight of Fe (55.85 g mol⁻¹), AW_Ni is the atomic weight of Ni (58.69 g mol⁻¹), and AE is the amount of electricity passed through the bath (1000 C). Figure 7 shows the dependence of CE on both the current density and bath pH, and indicates CE values of approximately 70% for each set of conditions. This less than ideal CE can likely be attributed to the reduction of H⁺ ions to H₂ and the reduction of Fe³⁺ ions to Fe²⁺.

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Figure 8 presents an SEM image of the surface of an Fe-36 mass% Ni alloy film electrodeposited at 35 mA cm⁻² using a plating bath with a pH of 4. Although the surface of this sample appears smooth, some cracks can be seen (Fig. 8a). It is also apparent that the film consisted of small grains with diameters in the range of 100–200 nm (Fig. 8b). The other alloy films with different compositions (as shown in Fig. 6) were found to have similar surface morphologies.

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A cross-sectional SEM image and elemental mapping results for the Fe-36 mass% Ni alloy film are shown in Fig. 9. This film was evidently compact and contained no obvious defects such as voids (Fig. 9a). Both Fe and Ni were distributed uniformly throughout the film (Figs. 9b–9d), suggesting that this specimen comprised a solid solution of the two metals.

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XRD patterns for films with different compositions (see Fig. 6) are provided in Fig. 10, in order of increasing Ni content. All the diffraction peaks can be assigned to body-centered cubic (bcc) or face-centered cubic (fcc) structures of Fe-Ni alloy solid solutions (Fig. 10a). Figure 10b shows XRD patterns in the narrow diffraction angle range of 40° to 50°. Here, the peaks at 2θ = 43.6° and 44.7° are assigned to fcc and bcc structures, respectively, and the bcc peak is predominant in the case of the 31 mass% Ni sample, which had the lowest Ni content. Both the bcc and fcc peaks are seen for a Ni content of 33 to 38 mass%. In the case of the sample containing 42 mass% Ni, which was the highest Ni content, the fcc peak is the most intense. Thus, the strongest peak reflected the composition of the Fe-Ni alloy film. The stable phase of an Invar alloy is the fcc phase ⁵⁵ and so the Fe-36mass% Ni alloy film formed in this study was a metastable phase. Previous studies have identified different primary phases in electrodeposited films having the Invar composition. ^4,10,13 Grimmett et al. showed that the phase that was obtained depended on the electrodeposition conditions. Specifically, a mixture of bcc and fcc structures was obtained following direct current deposition, ⁴ similar to the present results. In contrast, Tabakovic and Nagayama reported that a single bcc phase was found in Invar composition Fe-Ni alloy films, but that heat treatment of these specimens transformed the metastable bcc phase to a stable fcc single phase. ^10,13 Although it remains unclear why different primary phases can be formed in this alloy, both the bath composition and the electrodeposition conditions (such as bath temperature and cathode overpotential) are likely to have an effect.

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In future work, we intend to clarify the mechanism by which such films are generated by electrodeposition and evaluate the coefficients of thermal expansion for these films after suppressing the formation of cracks.

In the present study, a novel Fe-Ni alloy plating bath was prepared that contained only Fe³⁺ ions as the iron source together with citrate as a complexing agent. The intent was to mitigate serious problems related to the precipitation of Fe(OH)₃ owing to the oxidation of Fe²⁺ ions to Fe³⁺ ions during electrodeposition in conventional Fe-Ni alloy plating baths. The composition of this bath was established on the basis of equilibrium constants and the solution was shown to be stable over the pH range from 2 to 4. No Fe(OH)₃ precipitation was observed even after electrodeposition and an Fe-Ni alloy film having an Invar composition (that is, Fe-36 mass% Ni) was produced using this bath. Although cracks were seen in the specimen, the film had a compact morphology and uniform composition. The film was determined to possess a metastable bi-phase structure consisting of fcc and bcc phases comprising an Fe-Ni alloy solid solution. The method used to prepare a stable Fe-Ni alloy plating bath incorporating citrate as a complexing agent for Fe³⁺ ions demonstrated in this study could potentially be employed to produce other materials such as permalloy films. In addition, this technique is a promising approach to the formation of other Fe-based alloy plating films.