Corrosion of Low-Carbon Steel in a Flow of Phosphoric Acid Solution Containing Iron(III) Phosphate

Abstract

Theoretical aspects of low-carbon steel corrosion in H₃PO₄ solutions containing FePO₄ are considered. In the system under study, reactions of iron with the acid solution and Fe(III) salt are thermodynamically allowed. The oxidizing power of this medium, characterized by the Fe(III)/Fe(II) couple redox potential, is mainly determined by its anionic composition. Phosphate anions of a corrosive medium bind Fe(III) cations into complex compounds, reducing their oxidizing ability. In H₃PO₄ solutions containing FePO₄ and Fe₃(PO₄)₂, the dependence of the system’s redox potential on the Fe(III) and Fe(II) cation relative content is poorly described by the Nernst equation, which is due to the nonequivalent complex formation of these cations with phosphate anions. Analysis of the effect of the studied media convection on the low-carbon steel electrode reactions allowed revealing some of their features. In a FePO₄-containing H₃PO₄ solution, kinetically controlled partial reactions of iron anodic ionization and H⁺ cathodic reduction, as well as diffusion-controlled Fe(III) cation cathodic reduction, occur on the steel. The FePO₄ accelerating effect on the steel corrosion in H₃PO₄ solution is due only to the Fe(III) reduction but does not affect the H⁺ reduction and the iron ionization. The value of the Fe(III)-cation diffusion coefficient in the studied corrosive medium was experimentally determined from the data of cyclic voltammetry of the Pt electrode therein and the results of the studying of the cathodic reaction of a steel disk electrode at different rotation velocities. The data on the low-carbon steel corrosion in the flow of the studied media, obtained from the metal samples mass loss, are in full agreement with the results of the study of the electrode partial reactions. An accelerating effect of FePO₄ on the steel corrosion in H₃PO₄ solutions is observed. In this environment, steel corrosion is determined by the convective factor, which is typical of processes with diffusion control. The empirical dependence of the steel corrosion rate on the medium flow intensity is described by the linear dependence k = k_st + λw^1/2, where k_st is the steel corrosion rate in a static medium, w is the rotation velocity of the propeller stirrer that creates the medium flow, λ is the empirical coefficient.

INTRODUCTION

The phosphoric acid solutions are a perspective alternative to the hydrochloric and sulfuric acid solutions that are used in the iron and steel work and housing and utilities sector for the steel work and production equipment cleaning from heating furnace cinder, the corrosion products, and mineral deposits. An important technological advantage of the H₃PO₄ solutions, as compared with the hydrochloric and sulfuric media, is the high rate of dissolution of the iron oxides (FeO, Fe₃O₄, Fe₂O₃) forming the heating furnace cinder [1]. During operation, the H₃PO₄ solutions accumulate Fe(III) phosphates, mainly due to their interaction with the heating furnace cinder and corrosion products. The latter change significantly the media properties and their aggressiveness toward their contacting steels. The Fe(III) phosphate is water-insoluble. The Fe(III) phosphate solubility in H₃PO₄ solutions is the result of its chemical interaction with the acid, which leads to the formation of a mixture of acid phosphates of complex composition [2]. In this work, we shall formally regard such systems as a FePO₄-containing H₃PO₄ solution.

We see it fit revealing special features of the low-carbon steel corrosion mechanism in the H₃PO₄ solutions containing the Fe(III) phosphate. To better understand the processes occurring in the steel/Fe(III)-phosphate-containing H₃PO₄-solution corrosion systems, one must analyze some thermodynamic and kinetic characteristics of both the corrosive medium per se (the Fe(III)-salt-containing phosphoric acid solution) and the corrosion system. Indispensable is to evaluate the aggressive-medium convection effect on both the steel corrosion integrally and its separate stages. The studying of the effect of the aggressive medium hydrodynamic parameters on the steel corrosion is of importance both in theoretical and in practical respects. Under production-line conditions, the exploiting of acidic solutions often occurs in the liquid streams or is accompanied with a significant natural convection as a result of the hydrogen gas evolution.

To prognose thermodynamic possibility of the metal corrosion in aqueous media and determining the reaction products, the Pourbaix diagrams (E–pH) used to be applied [3–5]. A diagram [6] form has been chosen that described equilibria momentarily occurring in the Fe–H₂O system when iron hydroxides unstable with respect to the oxide phases are formed therein (Fig. 1). This approach reflects more accurately the equilibria that can establish in corrosion media. When the acidity of an aqueous corrosion medium is lowered, the Fe cations in the first instance will form thermodynamically unstable hydroxide phases, rather than the iron oxides. The iron oxide phase formation from hydroxides is a lengthy process.

Fig. 1.

A fragment of E vs. pH diagram of the Fe-metal and Fe(III)-cation stability field in water at 25°С and 101.3 kPa of full pressure [6]: (1) the Fe-metal stability field boundary, (2, 3) the Fe(III)-cation stability field boundaries, (4, 5) the water stability limit lines. The solid phases are only Fe, Fe(OH)₂, and Fe(OH)₃. The stability fields are given only for the cases log a_Fe(III) = log a_Fe(II); they correspond to the values of –6, –4, –2, and 0.

The iron metal and Fe(III) cation stability fields in this system are spaced-apart. This points to the impossibility of coexistence of these components under equilibrium conditions in the corrosion system. In acidic medium, the iron-metal limits of stability in the E–pH diagram are determined by the curve 1 that corresponds to the following equilibrium:

$${\text{Fe}} = {\text{F}}{{{\text{e}}}^{{2 + }}} + 2{{{\text{e}}}^{ - }},\,\,\,E = - 0.440 + 0.0295\log {{a}_{{{\text{Fe(II)}}}}},$$

(1)

whereas the Fe(III) salt solubility, by the curve 2:

$$\begin{gathered} {\text{F}}{{{\text{e}}}^{{3 + }}} + {{{\text{e}}}^{-}} = {\text{F}}{{{\text{e}}}^{{2 + }}},\, \\ E = E_{{{{{\text{Fe(III)}}} \mathord{\left/ {\vphantom {{{\text{Fe(III)}}} {{\text{Fe(II)}}}}} \right. \kern-0em} {{\text{Fe(II)}}}}}}^{^\circ } + 0.059\log \frac{{{{a}_{{{\text{Fe(III)}}}}}}}{{{{a}_{{{\text{Fe(II)}}}}}}}, \\ \end{gathered} $$

(2)

where $E_{{{{{\text{Fe(III)}}} \mathord{\left/ {\vphantom {{{\text{Fe(III)}}} {{\text{Fe(II)}}}}} \right. \kern-0em} {{\text{Fe(II)}}}}}}^{^\circ }$ is the Fe(III)/Fe(II) redox-couple standard electrode potential, whose value is 0.771 V at 25°С, a_Fe(III) and a_Fe(II) is the Fe(III) and Fe(II) active concentrations in the solution. At the equality of a_Fe(III) and a_Fe(II), the value of the Fe(III)/Fe(II) redox-couple potential corresponds to its $E_{{{{{\text{Fe(III)}}} \mathord{\left/ {\vphantom {{{\text{Fe(III)}}} {{\text{Fe(II)}}}}} \right. \kern-0em} {{\text{Fe(II)}}}}}}^{^\circ },$ which is shown in Fig. 1. Under conditions of real corrosion process in discussed aggressive media, the a_Fe(III) and a_Fe(II) ratio can be different, which affects the system’s redox-potential significantly. For example, when the a_Fe(III)-to-a_Fe(II) ratio is 9, the E_{Fe(III)/Fe(II)} value comes to 0.827 V. At a_Fe(III)/a_Fe(II) = 99 we have E_{Fe(III)/Fe(II)} = 0.889 V. By contrast, at the a_Fe(III)/a_Fe(II) = 99^–1 the value E_{Fe(III)/Fe(II)} = 0.653 V. Thus, the oxidizing ability of the discussed system depends significantly on the Fe(III) and Fe(II) soluble salt concentrations ratio therein. The increase in the Fe(III) relative content can lead to a significant increase of the system’s redox-potential.

Also, the stability limits in the discussed system of the Fe(III) salts are determined by the vertical part of line 3, which characterizes the process of the Fe(III) soluble compounds’ transition to insoluble form, thanks to lowering of the medium acidity:

$$\begin{gathered} {\text{F}}{{{\text{e}}}^{{3 + }}} + 3{{{\text{H}}}_{{\text{2}}}}{\text{O}} = {\text{Fe}}{{\left( {{\text{OH}}} \right)}_{{\text{3}}}} + 3{{{\text{H}}}^{ + }},{\text{ }} \\ {\text{log}}a\left( {{\text{F}}{{{\text{e}}}^{{3 + }}}} \right) = 4.84-3{\text{pH}}. \\ \end{gathered} $$

(3)

Thus, in the Fe(III)-salt-containing solutions of acids the iron and steel corrosion occurs in accordance with the following equation:

$$2{\text{F}}{{{\text{e}}}^{{3 + }}} + {\text{Fe}} = 3{\text{F}}{{{\text{e}}}^{{2 + }}}.$$

(4)

Concurrently, the process

$$2{{{\text{H}}}^{ + }} + {\text{Fe}} = {\text{F}}{{{\text{e}}}^{{2 + }}} + {{{\text{H}}}_{2}},$$

(5)

is allowed thermodynamically because the water stability lower limit (curve 4)

$$\begin{gathered} 2{{{\text{H}}}^{ + }} + 2{{{\text{e}}}^{-}} = {{{\text{H}}}_{2}},\,\, \\ E = -0.0295{\text{log}}p({{{\text{H}}}_{2}})-0.059{\text{pH}} \\ \end{gathered} $$

(6)

lies at higher potentials than the equilibrium (1).

The analysis of the Pourbaix diagrams allows predicting the mediated pathway of the Fe(III) salts accumulation in corrosion medium as a result of Fe(II) salts oxidation in the solution with ambient oxygen. The water stability upper limit (curve 5)

$$\begin{gathered} 2{{{\text{H}}}_{{\text{2}}}}{\text{O}} - 4{{{\text{e}}}^{-}} = {{{\text{O}}}_{2}} + 4{{{\text{H}}}^{ + }},\, \\ E = {\text{ }}1.23 - 0.0148{\text{log}}p\left( {{{{\text{O}}}_{2}}} \right)-0.059{\text{pH}}, \\ \end{gathered} $$

(7)

lies at the potentials much more positive than those of the transition (2) even in the case when the oxygen partial pressure р(О₂) = 0.2 atm (which is characteristic of air). This path for the Fe(III) salt accumulate in the acidic solution is discussed in works [7, 8].

The analysis of the Pourbaix diagram of the Fe–H₂O system allowed obtaining important information concerning the studied case of steel corrosion. However, this information is to a great extent formalized because in the discussed system the effect of the anions present in aqueous medium on thermodynamic characteristics is not taken into consideration [9]; the latter fact should be investigated further.

In addition to thermodynamic aspects of the low-carbon steel corrosion in the Fe(III)-salt-containing acidic solutions, it is important to consider specific kinetic features of the process. The low-carbon steel corrosion in inorganic acid can be described in simplified form by the summary reaction (5), which is the result of a predominant passing of the following partial reactions [10]:

the iron anodic dissolution:

$${\text{Fe}} - 2{{{\text{e}}}^{-}} = {\text{F}}{{{\text{e}}}^{{2 + }}}$$

(8)

and the hydrogen cathodic evolution:

$$2{{{\text{H}}}^{ + }} + 2{{{\text{e}}}^{-}} = {{{\text{H}}}_{2}}.$$

(9)

The reaction (9) [10] includes both the H⁺ delivering from the acid bulk to the metal surface

$${{{\text{H}}}^{ + }} \to {{\left( {{{{\text{H}}}^{ + }}} \right)}_{*}},$$

(10)

and the charge transfer stage (the Volmer reaction)

$${{\left( {{{{\text{H}}}^{ + }}} \right)}_{*}} + {\text{ }}{{{\text{e}}}^{-}} \to {{{\text{H}}}_{{{\text{ad}}}}}.$$

(11)

It is followed by the chemical reaction stage (the Tafel process)

$${{{\text{H}}}_{{{\text{ad}}}}} + {{{\text{H}}}_{{{\text{ad}}}}} \to {{\left( {{{{\text{H}}}_{2}}} \right)}_{{{\text{ad}}}}}$$

(12)

or the electrochemical recombination (the Heyrovsky process)

$${{{\text{H}}}_{{{\text{ad}}}}} + {{\left( {{{{\text{H}}}^{ + }}} \right)}_{*}} + {\text{ }}{{{\text{e}}}^{-}} \to {{\left( {{{{\text{H}}}_{2}}} \right)}_{{{\text{ad}}}}}.$$

(13)

The stages (11) and (12) in aggregate is the Volmer–Tafel mechanism; the stages (11) and (13), the Volmer–Heyrovsky mechanism. It is recognized that both mechanisms are realized at the steel surfaces during the hydrogen evolution [11].

The iron anodic ionization mechanism suggested by Heusler [10] believed to have the FeOH_ad compound formation in the course of the Fe crystal lattice atom reaction with the adsorbed OH⁻ anions:

$${\text{Fe}} + {\text{OH}}_{{{\text{ad}}}}^{ - } \to {\text{FeO}}{{{\text{H}}}_{{{\text{ad}}}}} + {{{\text{e}}}^{-}}.$$

(14)

This compound catalyzed the further reaction of the Fe(II) ion transfer through the electrical double layer:

$$\begin{gathered} {\text{Fe}} + {\text{OH}}_{{{\text{ad}}}}^{ - } + {\text{FeO}}{{{\text{H}}}_{{{\text{ad}}}}} \\ \to {{({\text{FeO}}{{{\text{H}}}^{ + }})}_{*}} + {\text{FeO}}{{{\text{H}}}_{{{\text{ad}}}}} + 2{{{\text{e}}}^{-}}. \\ \end{gathered} $$

(15)

In its turn, the FeOH⁺ compound decomposed slowly:

$${{({\text{FeO}}{{{\text{H}}}^{ + }})}_{*}} + {{\left( {{{{\text{H}}}^{ + }}} \right)}_{*}} \to {{({\text{F}}{{{\text{e}}}^{{2 + }}})}_{*}} + {{{\text{H}}}_{{\text{2}}}}{\text{O}}.$$

(16)

By contrast, Bockris [12] regarded FeOH as an intermediate product in the stagewise passing of the reaction:

$${\text{Fe}} + {\text{O}}{{{\text{H}}}^{ - }} \to {\text{FeOH}} + {{{\text{e}}}^{-}},$$

(17)

$${\text{FeOH}} \to {\text{FeO}}{{{\text{H}}}^{ + }} + {{{\text{e}}}^{-}},$$

(18)

$${\text{FeO}}{{{\text{H}}}^{ + }} \to {\text{F}}{{{\text{e}}}^{{2 + }}} + {\text{O}}{{{\text{H}}}^{ - }}.$$

(19)

The iron dissolution in phosphate solutions was shown [13] to involve OH^– and ${{{\text{H}}}_{{\text{2}}}}{\text{PO}}_{4}^{ - },$ at that, the ${{{\text{H}}}_{{\text{2}}}}{\text{PO}}_{4}^{ - }$ ions participated in the anodic process only at рН > 4. Later, in solutions with larger phosphate-anion summary content, their participation in the anodic reaction at the Armco iron was observed at lower pH values [14]:

$${\text{Fe}} + {{{\text{H}}}_{{\text{2}}}}{\text{PO}}_{4}^{ - } \leftrightarrow {{\left[ {{\text{Fe}}{{{\text{H}}}_{2}}{\text{P}}{{{\text{O}}}_{4}}} \right]}_{{{\text{ads}}}}} + {{{\text{e}}}^{-}},$$

(20)

$$\begin{gathered} {{\left[ {{\text{Fe}}{{{\text{H}}}_{{\text{2}}}}{\text{P}}{{{\text{O}}}_{4}}} \right]}_{{{\text{ads}}}}} + {{{\text{H}}}_{{\text{2}}}}{\text{O }} \\ \leftrightarrow {{\left[ {{\text{FeOH}}} \right]}_{{{\text{ads}}}}} + {{{\text{H}}}_{{\text{2}}}}{\text{PO}}_{4}^{ - } + {{{\text{H}}}^{ + }}, \\ \end{gathered} $$

(21)

$${{\left[ {{\text{FeOH}}} \right]}_{{{\text{ads}}}}} \to {\text{F}}{{{\text{e}}}^{{2 + }}} + {\text{O}}{{{\text{H}}}^{ - }} + {{{\text{e}}}^{-}}.$$

(22)

At low-carbon steels, sometimes, another mechanism can be realized:

$${\text{Fe}} + {{{\text{H}}}_{{\text{2}}}}{\text{PO}}_{4}^{ - } \leftrightarrow {{\left[ {{\text{Fe}}{{{\text{H}}}_{{\text{2}}}}{\text{P}}{{{\text{O}}}_{{\text{4}}}}} \right]}_{{{\text{ads}}}}} + {{{\text{e}}}^{-}},$$

(23)

$$\begin{gathered} {{\left[ {{\text{Fe}}{{{\text{H}}}_{{\text{2}}}}{\text{P}}{{{\text{O}}}_{4}}} \right]}_{{{\text{ads}}}}} + {{{\text{H}}}_{{\text{2}}}}{\text{O}} \\ \leftrightarrow \left[ {{\text{Fe}}\left( {{\text{OH}}} \right)\left( {{{{\text{H}}}_{{\text{2}}}}{\text{P}}{{{\text{O}}}_{{\text{4}}}}} \right)} \right]_{{{\text{ads}}}}^{ - } + {{{\text{H}}}^{ + }}, \\ \end{gathered} $$

(24)

$$\begin{gathered} \left[ {{\text{Fe}}\left( {{\text{OH}}} \right)\left( {{{{\text{H}}}_{{\text{2}}}}{\text{P}}{{{\text{O}}}_{{\text{4}}}}} \right)} \right]_{{{\text{ads}}}}^{ - } \\ \to {\text{F}}{{{\text{e}}}^{{2 + }}} + {{{\text{H}}}_{{\text{2}}}}{\text{PO}}_{4}^{ - } + {\text{O}}{{{\text{H}}}^{ - }} + {{{\text{e}}}^{-}}. \\ \end{gathered} $$

(25)

In solutions of acids containing such a strong oxidant as the Fe(III) salt, the process (4) can be realized in parallel; it includes an anodic [equation (8)] and a cathodic

$${\text{F}}{{{\text{e}}}^{{3 + }}} + {{{\text{e}}}^{ - }} = {\text{F}}{{{\text{e}}}^{{2 + }}}$$

(26)

reactions [15, 16]. The cathodic reaction at the low-carbon steel in these media is comprised of the parallel and independent processes of hydrogen evolution under kinetic control and the Fe(III)-cations reduction to Fe(II), passing under diffusion control.

The above-discussed mechanisms of hydrogen cathodic evolution and iron anodic ionization are the common notion, therefore, their refining is out of scope of this work. By contrast, the involvements of the Fe(III) salts dissolved in acids in the low-carbon steel corrosion is disregarded in literature. Because the steel corrosion in these media is controlled by diffusion at one of its stages, of primary importance is the taking into consideration f the convective factor that can contribute markedly to the metal disruption.

EXPERIMENTAL

In the solutions’ preparation, we used H₃PO₄ (reagent grade) and distilled water. The H₃PO₄ solutions containing the Fe(III) phosphate were obtained in the reaction of excess H₃PO₄ with Fe(OH)₃ deposited from FeCl₃ solution under the action of NaOH (reagent grade). To prepare the Fe(III) chloride solution, FeCl₃⋅6H₂O (chemically pure) was used. Because of technical difficulties in the preparation of H₃PO₄ solutions containing the Fe(II) phosphates, which can be used for potentiometric measurements, they were replaced by solutions containing equivalent FeSO₄ concentration. With this approach, sometimes, the ${\text{SO}}_{4}^{{2 - }}$ and ${\text{PO}}_{4}^{{3 - }}$ content unaccounted for was maximally 4.8% each from the summary anion concentration in the solution, which allowed neglecting this factor in further discussion.

The potentiometric measurements in 2 M H₃PO₄ solution containingй 0.1 M Fe(III) + Fe(II) were carried out in thermostatted electrochemical glass cell with reserved zone for saturated silver/silver chloride reference electrode. The working electrode was made of smooth platinum (1.5 сm²); the auxiliary electrode was a saturated silver/silver chloride electrode. The potential difference between the working electrode and reference electrode was controlled using a PI-50 potentiostat.

The platinum electrode cyclic voltammetry in the studied media was applied using an EL-02.061 potentiostat in a thermostatted three-electrode glass cell with separated electrode compartments. The working electrode was platinum wire (S = 15.9 mm²); the reference electrode, silver/silver chloride electrode; the auxiliary electrode, platinum plate (S = 1.5 сm²). The working Pt-electrode potential was scanned from 1.4 to 0.0 V, then, from 0.0 to 1.4 V; the potential scanning rate was 0.05, 0.10, and 0.20 V/s.

The presence of an oxidant, a dissolved ambient oxygen, in the studied aqueous media can affect the results of potentiometric and cyclic-voltammetry studies carried out therein. To remove the dissolved oxygen from the studied aqueous media, they were pre-deaerated for 30 min with argon gas (reagent grade). The mean gas delivery rate was 1 mL/s. The electrochemical measurements were carried out in a static medium upon the stopping of the argon gas bubbling through the studied solution. Prior to the performing of the experiment, the working Pt-electrode was degreased with acetone, then kept in the concentrated HNO₃ for 3 min and washed with distilled water.

Electrochemical measurements at the St3 low-carbon steel (the composition, wt %: С, 0.14–0.22; P, 0.04; Si, 0.15–0.33; Mn, 0.40–0.65; S, 0.05; Cr, 0.3; Ni, 0.3; N, 0.008; Cu, 0.3; As, 0.08; the rest, Fe) were carried out using a rotating disc electrode (n = 460 rpm) in the 2 М H₃PO₄ solution at t = 25°С. The steel potential was measured against silver/silver chloride electrode. The steel electrode was ground with emery paper (М20) and degreased with acetone. Polarization curves were taken using an EL-02.061 potentiostat at a potential scanning rate of 0.0005 V/s. Prior to the applying the polarization, the electrode was kept in the studied solution for 30 min, to set the free corrosion potential E_cor, then the anodic and cathodic polarization curves were taken. Upon their taking, the dependence of cathodic current at Е = ‒0.30 V on the electrode rotation velocity (n = 0, 460, 780, 1090, and 1400 rpm) was studied. In the case of the steel corrosion in the Fe(III)-salt-containing H₃PO₄ solutions, the cathodic process includes the reaction (9). Its character can depend on the hydrogen gas pressure in the system. To obtain stable results of electrochemical measurements, the dissolved oxygen gas was removed from the studied media by their deaeration with gaseous hydrogen, rather than with argon. This allowed performing electrochemical measurements at a constant hydrogen gas pressure in the system. The solutions were deaerated for 30 min prior to the beginning of the studies. The hydrogen was obtained in electrolyzer from NaOH solution. The mean gas flow rate was 1 mL/s. During the performing of electrochemical measurements, no hydrogen bubbling through solution was carried out.

The Fe(III) phosphate effect on the electrode reactions was evaluated by the value of the acceleration coefficient

$${{\gamma }^{{ - 1}}} = {{i}_{{{\text{Fe(III)}}}}}i_{0}^{{ - 1}},$$

(27)

where i₀ and i_Fe(III) is the current densities in the supporting solution and in the solution added with the Fe(III) phosphate.

The lowest of the above-given electrode rotation velocity values (460 rpm) was taken as a basic rotation velocity of the steel disc electrode in the electrochemical studies. At this rotation velocity we obtained the closest values of the kinetic and diffusion current densities characterizing the cathodic reaction realized at the electrode under the experimental conditions. This holds out the promise of the most correct evaluating of the effect of the Fe(III) phosphate additives on the steel partial cathodic reactions.

The electrode potentials are given in the standard hydrogen scale.

The corrosion rate of the 08PS steel (the composition, wt %: С, 0.08; Mn, 0.5; Si, 0.11; P, 0.035; S, 0.04; Cr, 0.1; Ni, 0.25; Cu, 0.25; As, 0.08; the rest, Fe) in 2 М H₃PO₄ solution at a temperature of 20 ± 2°С was determined by the mass loss (≥5 per point) of samples sized 50 mm × 20 mm × 0.5 mm, calculated on the basis of 50 mL of the acid solution per sample:

$$k = \Delta m{{S}^{{ - 1}}}{{\tau }^{{ - 1}}},$$

(28)

here Δm is the change of the sample mass, g; S is the sample surface area, m²; τ is the corrosion test time, h; the test durability is 2 h. The studies were carried out both in static and dynamic corrosion medium at the magnetic stirrer rotation velocity w = 250, 420, 750, and 1080 rpm. Prior to the experiment, the samples were cleaned out at a grinding wheel (ISO 9001, the abrasive grit 60) and degreased by acetone.

The effect of the presence of the Fe(III) phosphate in the acid and the corrosion medium flow mode on the steel corrosion rate were estimated by the corrosion loss increments

$$\Delta k = {{k}_{{{\text{Fe(III)}}}}} - {{k}_{0}},$$

(29)

$$\Delta k = {{k}_{{{\text{dyn}}}}} - {{k}_{{{\text{st}}}}},$$

(30)

And the corrosion acceleration coefficient increments

$${{\gamma }^{{ - 1}}} = {{k}_{{{\text{Fe(III)}}}}}k_{0}^{{ - 1}},$$

(31)

$${{\gamma }^{{ - 1}}} = {{k}_{{{\text{dyn}}}}}k_{{{\text{st}}}}^{{ - 1}},$$

(32)

where k_Fe(III) and k₀ is the rates of the steel corrosion in the acid solution in the presence and in the absence of the Fe(III) salt; k_dyn and k_st is the corrosion rates in the dynamic and static media.

RESULTS AND DISCUSSION

The first step in the understanding of the processes occurring in the aggressive medium/metal system is the study of the aggressive medium thermodynamic and kinetic characteristics. Important information on the effect of the aqueous corrosion medium anionic composition in the presence of oxidative metal cations therein on some its thermodynamic characteristics can be obtained from potentiometric studies [9, 17]. The redox-potential of the discussed system is determined by the equilibrium reaction (2); it can be described by the Nernst equation:

$${{E}_{{{{{\text{Fe(III)}}} \mathord{\left/ {\vphantom {{{\text{Fe(III)}}} {{\text{Fe(II)}}}}} \right. \kern-0em} {{\text{Fe(II)}}}}}}} = E_{{{{{\text{Fe(III)}}} \mathord{\left/ {\vphantom {{{\text{Fe(III)}}} {{\text{Fe(II)}}}}} \right. \kern-0em} {{\text{Fe(II)}}}}}}^{^\circ } + \frac{{RT}}{{zF}}\log \frac{{{{a}_{{{\text{Fe(III)}}}}}}}{{{{a}_{{{\text{Fe(II)}}}}}}},$$

(33)

where R is the universal gas constant; T is the absolute temperature; z is the number of electrons involved in the redox-process [z = 1 for the Fe(III)/Fe(II) couple]; F is the Faraday constant. It is challenging to use the Nernst equation in its present form, the more so, at high electrolyte concentrations, because the activity of any type of potential-determining ions in solutions is by no means connected with their concentration by a simple interrelation. The non-complexed iron cation active concentrations in the solution can be found by using activity coefficients calculated by the Debye–Hueckel equation and the equilibrium constants characterizing the Fe complex compounds. It is highly unlikely that the discussed problem can be solved because it is very complicated and its chemical composition is rather indeterminate.

From a practical standpoint, the real potential is more suitable to describe processes occurring in the Fe-cation-containing acid solutions. It can be interpreted as a potential of redox-system settled in a particular solution under the equality of the initial concentrations of the oxidized and reduced forms of the potential-determining ions uncorrected for the complex-formation, hydrolysis, and like processes [9]. For the studied system, its real potential is most suitable for the qualitative interpreting of experimental data connected with the potential-determining ion complex-formation.

To better understand the processes involving the potential-determining ion in the studied system, we determined its real potential for the 2 M H₃PO₄ + 0.05 M Fe(III) + 0.05 M Fe(II) solution. The similar parameter was determined for 2 M H₃PO₄ solution containing 0.1 М Fe(III) + Fe(II), at С_Fe(III)/С_Fe(II) = 99, 9, 9^–1, and 99^–1 (Fig. 2). When no deviation from the ideal state of the 2 M H₃PO₄ + 0.05 M Fe(III) + 0.05 M Fe(II) solution occurs, the real potential must be equal to $E_{{{{{\text{Fe(III)}}} \mathord{\left/ {\vphantom {{{\text{Fe(III)}}} {{\text{Fe(II)}}}}} \right. \kern-0em} {{\text{Fe(II)}}}}}}^{^\circ }.$ Also, the dependence of the system’s potential on the С_Fe(III)/С_Fe(II) ratio is described by the Nernst equation (Fig. 2, curve 1). The experimentally determined values of the redox-potentials of the Pt-electrode in the Fe(III)- and Fe(II)-salt containing 2 M H₃PO₄ solution (Fig. 2, points) lie much lower than those expected for a system non-deviated from its ideal state. The observed effect is a result of the potential-determining ion interaction with the corrosion medium components. The Fe(III)-cations are bound with the phosphate-anions to complex compounds whose oxidative ability is lower than that of Fe(III) hydrated ions. The formation of the Fe(III) phosphate complexes in the phosphate media is evidenced by their stability constants (Table 1). The Fe(III)-phosphate-complexes’ composition and structure in the H₃PO₄ solutions is discussed in works [19, 20].

Fig. 2.

The Pt-electrode potentials in argon-deaerated 2 М H₃PO₄ solution containing 0.10 М Fe(III) + Fe(II) as a function of the Fe(III)- and Fe(II)-ion concentration ratio. Here (1) the dependence plotted based on the hypothetic suggestion on the absence of the concerned system deviation from ideal state, (2) the experimental dependence. The theoretical dependence is obtained by using the Nernst equation.

Table 1. Cumulative stability constants β of Fe(III) and Fe(II) complexes with phosphate anions at 20–30°С

There is still an open question, whether it is to be expected that the Nernst equation is formally fulfilled in the studied systems when the linear dependence of the system redox-potential on the logarithm of the ratio of the potential-determining particles’ active concentrations has been retained. To solve the problem with due allowances made for the Nernst equation we plotted a model dependence crossing the experimentally determined value of the Pt-electrode potential obtained at С_Fe(III) = С_Fe(II) = 0.05 М (Fig. 2, curve 2). The comparison of experimental data with the model (curve 2) showed the experimental points approaching the theoretical line at С_Fe(III) > С_Fe(II). By contrast, at С_Fe(III) < С_Fe(II) the experimental points lied at larger E_s as compared with the theoretical line, which is most pronounced at С_Fe(III)/С_Fe(II) = 99^–1. The character of this phenomenon, to our view, is mainly based on the non-equivalent complex formation of the Fe(III-) and Fe(II)-cations with phosphate-anions. In spite of the lesser stability of the Fe(II) complexes with phosphate-anions (Table 1), at larger С_Fe(II) in H₃PO₄ solutions the Fe(II)-cations are mainly bound into the complexes, which is beneficial in the increase of the potential.

The cyclic voltammetry is a more informative method for the studying of the properties of the discussed corrosion medium. Voltammograms of a Pt-electrode in FePO₄-containing 2 М H₃PO₄ solution have two peaks (Fig. 3, Table 2). The first (cathodic) peak observed at more negative potentials corresponds to the Fe(III)-cation reduction at the Pt-electrodeе:

$${\text{F}}{{{\text{e}}}^{{3 + }}} + {{{\text{e}}}^{ - }} = {\text{F}}{{{\text{e}}}^{{2 + }}},$$

(34)

whereas the second (anodic) one, to the oxidation of the formed Fe(II)-cations:

$${\text{F}}{{{\text{e}}}^{{2 + }}}-{{{\text{e}}}^{-}} = {\text{F}}{{{\text{e}}}^{{3 + }}}.$$

(35)

Fig. 3.

Cyclic voltammogram of Pt-electrode taken at 25°C in argon-deaerated 2 M H₃PO₄ solution containing 0.1 М FePO₄ at the potential scanning rate, V/s: (1) 0.05; (2) 0.10; (3) 0.20.

Table 2. The cathodic and anodic peak (E_pc and E_pa) potentials, their difference (E_pa – E_pc), the half-wave potentials (E_1/2), the cathodic peak currents (I_pc) at Pt-electrode in the 2 М H₃PO₄ deaerated solution containing 0.1 М FePO₄, and the Fe(III)-cation diffusion coefficients obtained at 25°C at different electrode potential scanning rates. The dimensionality of Е is V; of I, mА; of D, μm² s^–1

The oxidative ability of the Fe(III)-cations in phosphoric-acid medium is determined by the half-wave potential:

$${{E}_{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}} = \frac{{{{E}_{{{\text{pc}}}}} + {{E}_{{{\text{pa}}}}}}}{{\text{2}}},$$

(36)

which is widely judged as the system’s redox-potential [21]. Here E_pc, E_pa is the cathodic and anodic peak potential, respectively. At that, in the studied system the E_1/2 values approach the E_{Fe(III)/Fe(II)} value determined by the potentiometric method at С_Fe(III) = С_Fe(II), which also points to the presence of the Fe(III)-cations in the H₃PO₄ solution as their complex compounds with the phosphate-anions.

The maximal cathodic current in the current–voltage curves is given by the Randles–Ševčik equation [21]:

$${{I}_{{\text{p}}}} = PzFSC{{\left( {{{zFvD} \mathord{\left/ {\vphantom {{zFvD} {RT}}} \right. \kern-0em} {RT}}} \right)}^{{{\text{0}}{\text{.5}}}}},$$

(37)

where S is the electrode surface area (m²); С is the electroactive substance concentration (mol/m³); D is the electroactive particle diffusion coefficient (m²/s); v is the potential scanning rate (V/s); P is the parameter, a function of zFvτ/RT, where τ is the time. Based on equation (37) and using the experimentally determined values of the maximal cathodic currents, we found the Fe(III)-cation diffusion coefficient in 2 М H₃PO₄ (Table 2). The obtained D_Fe(III) mean value in 2 M H₃PO₄ is 110 ± 10 μm² s^–1, which is close to D_Fe(III) = 120 μm² s^–1 in 1 M H₃PO₄ at 20°С [22].

The visions of the corrosion medium properties are necessary for the understanding of processes occurring in the corrosion medium at the aggressive medium/metal interface. The most relevant information on the steel corrosion mechanism in acidic solutions is obtained in the course of the revelation of specific features of electrode reactions occurring thereat. In 2 M H₃PO₄ the form of the low-carbon steel polarization curves is characteristic of the corrosion occurring in the area of the steel active dissolution (Fig. 4, Table 3). In this medium, the slope of the steel cathodic polarization (b_с) approached that theoretically predicted for iron (0.120 V). However, the metal anodic polarization (b_a) appeared being higher than the theoretical value (0.035 V) [14]. The increase in the steel slope b_a resulted from the formation of a visually observed mud layer at its surface. The presence of the FePO₄ acid in the solution shifted the steel free corrosion potential (E_cor) toward more positive values, which is a result of the cathodic reaction counterinhibition by this additive. The Fe(III)-cations practically do not affect the anodic process; however, the cathodic reaction order with respect to their concentration is positive. As the FePO₄ content in the corrosion medium increased, the cathodic reaction acceleration coefficient also grows. The initial section of the cathodic polarization curves is characterized by a limiting current (i_lim). By contrast, the slope of the anodic polarization curves corresponds to the background dependence.

Fig. 4.

Polarization curves of the St3 steel in FePO₄-containing 2 M H₃PO₄ solution, М: (1) 0; (2) 0.01; (3) 0.02; (4) 0.05; (5) 0.10. n = 460 rpm; t = 25°C.

Table 3. Corrosion potentials (E_cr) of the St3 steel, Tafel slopes of polarization curves (b_c and b_а), the cathodic and anodic current densities (i_c and i_а), acceleration coefficients for the cathodic and anodic reactions (${{\gamma }}_{{\text{c}}}^{{ - 1}}$ and ${{\gamma }}_{{\text{a}}}^{{ - 1}}$) obtained at Е = –0.30 and –0.10 V, respectively. The Е dimensionality is V; i, А/m^2.; n = 460 rpm, t = 25°C

The presence of FePO₄ additives in the H₃PO₄ solution practically does not affect the character of the anodic reaction which passed in accordance with equation (8) both in the absence and in the presence of the Fe(III) phosphate. The form of cathodic polarization curves points to the Fe(III) involvement in the cathodic reaction. In concentrated solutions of acids (рН < 2) the cathodic reaction corresponding to equation (9) passed under kinetic control [23], which is confirmed by the character of cathodic polarization curves. In the presence of Fe(III) phosphate they are complicated by a limiting current, which points to the change of the cathodic reaction mechanism. The observed limiting current can be caused by diffusion limitations in the delivery of oxidants present in the acid solution—H⁺ and Fe³⁺—to the steel surface. Because the H⁺ concentration is larger by more than one order of magnitude than С_Fe(III), the limiting current is rather the result of the diffusion limitations in the delivery of Fe(III)-cations to the steel surface. To confirm this suggestion, it is necessary to study the effect of the electrolyte solution flow on the steel cathodic reaction rate. Such studies used to be carried out with the rotating disc electrode. By varying its rotation velocity, the regime of the liquid flow near the metal surface can be controlled [24, 25].

The cathodic process at steel including the reaction (9) passing under the kinetic control and the reaction (26) controlled by diffusion can be characterized by the following expression:

$${{i}_{{\text{c}}}} = {{i}_{{\text{k}}}} + {{i}_{{\text{d}}}},$$

(38)

where i_k and i_d is the kinetic and diffusion current densities. In the case of laminar liquid flow near the rotating metal disc electrode surface, the i_d value is proportional to the square root from the disc electrode rotation velocity (n). Therefore, expression (38) can be rewritten as:

$${{i}_{{\text{c}}}} = {{i}_{{\text{k}}}} + f{{n}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}}.$$

(39)

In the 2 M H₃PO₄ + FePO₄ solution, the i_c vs. n^1/2 experimental dependence is linear (Fig. 5). However, in 2 M H₃PO₄ there is no cathodic current response to the change in the steel disc rotation velocity, which points to the kinetic nature of the reaction (9). In the presence of FePO₄ the cathodic current kinetics component is the same as in the absence thereof, which points to the mutual independence of the reactions (9) and (26). Moreover, it is clear that the reaction (9) is under kinetic control; the reaction (26), under diffusion control.

Fig. 5.

Dependence of the cathodic current density on the steel disc rotation velocity in FePO₄-containing 2 M H₃PO₄ solution, М: (1) 0; (2) 0.01; (3) 0.02; (4) 0.05; (5) 0.10. Е = –0.30 V, t = 25°C.

The diffusion current of the Fe(III) reduction at a steel cathode at the laminar liquid flow is described by the following formula [23]:

$${{i}_{{\text{d}}}} = 0.62zFC{\text{*}}{{D}^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0em} 3}}}}{{\eta }^{{ - {1 \mathord{\left/ {\vphantom {1 6}} \right. \kern-0em} 6}}}}{{n}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}}.$$

(40)

Here C* is the Fe(III) concentration in the solution bulk, η is the kinematic viscosity of the liquid (0.011 сm²/s [26]), n is the in the steel disc angular rotation velocity. By using equation (40), it is possible to calculate D_Fe(III) in 2 M H₃PO₄ (Table 4). The obtained D_Fe(III) values are in good agreement with the data, found by the cyclic voltammetry method (Table 2). The difference between the D_Fe(III) value obtained by cyclic voltammetry at Pt-electrode and the mean value of the same quantity calculated from the measurements at the rotating disc electrode does not exceed 18%. To our view, the cyclic voltammetry method produced more correct values of D_Fe(III). The D_Fe(III) value determined from the measurements in real corrosion medium is less accurate because several parallel processes occur therein. The larger D_Fe(III) values obtained from the measurements at the rotating steel disc electrode are mainly due to the hydrogen bubbles formed at the metal surface, as the hydrogen is evolved at cathodic potentials. These bubbles adhered to the electrode are likely to facilitate turbulent flows near the electrode surface during its rotation, which violates the laminar regime of the corrosion-medium motion.

Table 4. Values of the i_k and f constants in the equation i_c = i_k + fn^1/2 at Е = –0.30 V for cathodic reaction at the steel rotating disc electrode in the FePO₄-containing 2 M H₃PO₄ solution. Values of i_k are given in А/m²; f, in А/(m² rpm^1/2), t = 25°C

The revelation of some thermodynamic and kinetic parameters of the studied corrosion medium allowed predicting the low-carbon steel corrosion character. The results of potentiometry showed that the presence of the Fe(III) phosphate in the corrosion medium increased its redox-potential and, as a consequence, its aggressivity toward the steel. In spite of the decrease in the Fe(III) cation oxidative ability because of its binding to the complexes with the phosphate-anions, it remained well perceptible. The E_{Fe(III)/Fe(II)} value is 0.323 V even at low Fe(III)-cation concentration (0.001 M). The presence of the Fe(III) salt in H₃PO₄ solution increased the systems oxidative ability. The higher the Fe(III) content, the more noticeable is the effect. It is logical to assume that the increase of the Fe(III) phosphate content in the studied aggressive medium will have a detrimental effect on low-carbon steel corrosion stability. In addition, the steel corrosion in the FePO₄-containing 2 M H₃PO₄ passed through the stages characterized by both kinetic control and diffusion limitations. Correspondingly, the steel corrosion in such systems must depend on the aggressive medium convection type significantly.

The postulated suggestions were confirmed in the studies of the low-carbon steel corrosion in the FePO₄-containing 2 M H₃PO₄ flow, with regard to the metal samples’ mass loss (Fig. 6).

Fig. 6.

Dependence of the 08PS steel corrosion rate on the propeller mixer rotation velocity in corrosion medium at 20 ± 2°C in FePO₄-containing 2 M H₃PO₄ solution, M: (1) 0; (2) 0.005; (3) 0.01; (4) 0.02; (5) 0.05; (6) 0.10. The results are given both noncorrected (а) and corrected for the natural convection (b). The experiment duration is 2 h.

In particular, the low-carbon steel corrosion in the FePO₄-containing 2 M H₃PO₄ is intensified upon the increasing of the salt content. In all studied media, we observed a clear response of the corrosion process to the corrosion medium agitating intensity. The experimental dependence of the low-carbon steel corrosion rate on the propeller mixer rotation velocity used in the medium forced convection can be described by the following formula:

$$k = {{k}_{{{\text{st}}}}} + \lambda {{w}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}},$$

(41)

where k_st is the low-carbon steel corrosion rate in the static medium, w is the mixer rotation velocity, λ is the empirical coefficient (Table 5). Equation (41) formally corresponds to expression (39) that characterized electrode reactions passed under diffusion control.

Table 5. The constants k_st (g/(m² h)) and λ (g/(m² h rpm^1/2)) in equation (41) for the 08PS low-carbon steel corrosion at T = 20 ± 2°C in the FePO₄-containing 2 M H₃PO₄ solution

When analyzing experimental dependences, it should be borne in mind that according to the diffusion kinetics laws, only kinetic component of the corrosion process must occur in the static medium, whereas the diffusion component cannot be realized because of the absence of the liquid motion. Correspondingly, the k_st values obtained in the FePO₄-containing media must equal the k_st value in 2 M H₃PO₄ where the process occurs strictly in the kinetic regime. However, the k_st actual values observed in the FePO₄-containing media are significantly larger than the value in 2 M H₃PO₄. This effect results from the natural convection occurring in the static medium. The effect is still more intensified as a result of the hydrogen gas bubbles plentiful evolution in the course of the corrosion process at a rather large steel surface area because the pop up hydrogen bubbles agitate the aggressive medium. Nonetheless, when passing from static medium to dynamic one, this effect is leveled out as the propeller mixer rotation velocity increased. With reference to the above mentioned, the obtained experimental results are presented in two extreme dependences, both without taking into account and with consideration to the natural convection processes. It is to be noted that in the FePO₄-free 2 M H₃PO₄ we observed but quite insignificant response from the corrosion process to the increase of the medium flow rate, which resulted from the presence of air oxygen therein. The effect is negligibly small, however.

The analysis of experimental data showed that the increase of FePO₄ content in aggressive medium accelerated the low-carbon steel corrosion (Table 6). Also, in the presence of FePO₄ in the phosphoric acid solution the intensity of the steel corrosion increased when passing from the static medium to dynamic one. For example, at С_Fe(III) = 0.1 М in 2 M H₃PO₄ solution the passing from the static medium to dynamic one (w = 1080 rpm) was accompanied by the increment of the corrosion loss Δk = 36.6 g/(m² h). At that, the steel corrosion rate in the static medium is k_st = 9.2 g/(m² h), which is much lower than the increment of the corrosion loss observed in dynamic medium.

Table 6. The corrosion rate (k), corrosion loss increment (Δk), and corrosion acceleration coefficient (γ^–1) for the 08PS steel corrosion in the FePO₄-containing 2 M H₃PO₄ solution. k and Δk are given in g/(m² h). The experiment duration is 2 h. t = 20 ± 2°C

CONCLUSIONS

(1) The low-carbon steel corrosion in FePO₄-containing H₃PO₄ solutions can be realized through the iron reactions with the acid and the Fe(III) salt. The oxidative ability of the FePO₄-containing H₃PO₄ solutions is lower than that predicted theoretically because of the Fe(III) binding into complexes with phosphate-anions.

(2) In the FePO₄- and Fe₃(PO₄)₂-containing H₃PO₄ solutions the dependence of the system’s redox-potential on the Fe(III)- and Fe(II)-cation relative content is unsatisfactorily described by the Nernst equation which is due to non-equilibrium complex-formation of these cations with phosphate-anions.

(3) In the FePO₄-containing 2 M H₃PO₄ solution, three partial reactions are realized at the steel: the iron anodic ionization, H⁺ and Fe(III) cathodic reduction. The first two reactions occurred under kinetic control; the last one, under diffusion control. The increase in the FePO₄ concentration in the corrosion medium accelerated the cathodic reduction reaction.

(4) In the FePO₄-containing H₃PO₄ solutions, the Fe(III) diffusion coefficient (D_Fe(III)) can be determined experimentally by the Pt-electrode cyclic voltammetry or by the measurements of the dependence of Fe(III)-cation reduction current on the steel disc electrode rotating velocity; both methods provided close results.

(5) The data on the low-carbon steel corrosion in the H₃PO₄ solution flow obtained from the metal sample mass loss is in good agreement with the results of electrochemical studies. A FePO₄ accelerating effect on the steel corrosion in 2 M H₃PO₄ solutions is found. The empirical dependence of the steel corrosion rate on the medium flow intensity (under agitation with a propeller mixer agitation) can be presented as a linear dependence:

$$k = {{k}_{{{\text{st}}}}} + \lambda {{w}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}},$$

where k_st is the steel corrosion rate in static medium; w is the propeller mixer rotation velocity; λ is the empirical coefficient.