Recovery of Light Rare Earth Elements from Coal Ash via Tartaric Acid and Magnesium Sulfate Leaching

Abstract

Coal ash is a promising secondary resource for rare earth element (REE) recovery, yet efficient processing under environmentally benign conditions remains challenging. This study demonstrates that tartaric acid, when combined with MgSO₄ as a salt additive, enables effective extraction of light REEs (La, Ce, Nd). REE recoveries improved from ~40% without salt to nearly 65% under optimized conditions. Kinetic modeling indicated a surface-reaction–controlled mechanism with activation energies of 20–22 kJ/mol, consistent with SEM evidence of particle erosion and size reduction. These findings highlight the potential of organic-salt leaching systems as alternatives to mineral acid processes, offering both effective REE recovery and reduced environmental impact.

1. Introduction

Rare earth elements (REEs), including lanthanides, scandium, and yttrium, are widely used in modern technology and energy. They are part of permanent magnets, batteries, electronics, catalysts, and phosphors. Due to their unique magnetic, optical, and catalytic properties, REEs are often indispensable in high-tech materials and components [1,2,3].

In recent years, the demand for REE has been steadily growing, primarily due to the development of “green” technologies: electric vehicles, wind energy, and energy storage systems. The consumption of light REE, such as neodymium (Nd) and cerium (Ce), as well as heavy REE, such as terbium and dysprosium, is growing especially rapidly in the defense industry and high-precision electronics. In this regard, REEs are considered strategically important elements, and in many countries their supplies are controlled at the level of state programs [4].

One of the main problems remains the limited availability of REEs and the complexity of their industrial processing. The development and exploitation of REE deposits require significant costs and are often accompanied by environmental risks. In addition, global supplies of these elements often depend on a limited number of producers, which increases the vulnerability of supply chains. Under these conditions, recycling of secondary sources is of increasing interest [5,6,7].

Coal combustion ash, including fly ash and bottom ash, has emerged as a promising secondary source of REEs. Globally, more than 500 million tons of coal ash (CA) are generated annually, a substantial portion of which is stockpiled without further utilization [8,9]. Although the REE content in ash is relatively low—typically ranging from 50 to 500 ppm—the vast volumes and ready availability of this waste make it an attractive target for resource recovery [10,11,12,13].

Unlike conventional ores, CA is already finely divided, eliminating the need for blasting, crushing, and grinding. Such deposits are typically located near power plants or industrial sites, which helps reduce transportation and logistical costs. Processing CA also reduces waste volumes and aligns with circular economy principles [14,15].

According to the literature, REEs in CA are typically present as phosphates and as ions adsorbed onto the surface of aluminosilicate phases [16,17,18,19]. The dominant mineral constituents of ash include mullite, quartz, magnetite, and residual clay minerals, which provide abundant surface area for REE³⁺ fixation [20]. This strong sorption makes REEs difficult to mobilize under mild leaching conditions. As a result, conventional acid leaching without additives often yields poor recovery—typically not exceeding 30–40% of the total REE content [21,22,23].

Hydrometallurgical processing remains the most commonly studied approach for REE recovery from coal combustion byproducts due to its simplicity, scalability, and relatively low energy requirements. Conventional methods typically involve the use of inorganic acids such as hydrochloric [24,25,26], nitric [27], or sulfuric acid [28,29], which are capable of partially solubilizing REEs from the aluminosilicate matrix. However, these strong acids are often corrosive, environmentally burdensome, and non-selective.

In recent years, increasing attention has been directed toward environmentally friendly alternatives—particularly organic acids such as citric [30,31,32]; tartaric [33]; and lactic acids [34]. These ligands are biodegradable, less aggressive, and can selectively complex REE³⁺ ions under mildly acidic conditions. However, their leaching efficiency is typically lower than that of mineral acids, especially in systems with limited ligand availability or competing cations.

The efficiency of REE leaching with organic acids largely depends on their ability to form stable aqueous complexes with REE ions. Tartaric and citric acids, for example, possess multiple carboxyl and hydroxyl groups that allow for bidentate or polydentate coordination, facilitating metal solubilization via complexation mechanisms. A study by Banerjee et al. [35] demonstrated that tartaric acid can achieve high REE extraction efficiencies from CA—particularly for light REEs such as La and Ce. However, this required highly diluted slurry conditions (liquid-to-solid ratio of 150:1) and extended leaching times. Such conditions are difficult to apply in practical settings due to excessive reagent consumption and low process throughput, showing the need for process intensification strategies to maintain extraction efficiency at higher pulp densities.

The addition of inorganic salts to leaching systems has been widely explored as a method to intensify REE extraction, particularly under mild or environmentally benign conditions. These salts function through two principal mechanisms [36]: (i) cation exchange, in which metal ions such as Mg²⁺, Ca²⁺, or NH₄⁺ displace REE³⁺ ions from negatively charged surfaces; and (ii) an increase in the solution’s ionic strength, which compresses the electrical double layer and reduces electrostatic adsorption of REEs onto ash or clay matrices.

Moldoveanu and Papangelakis reported that neutral sulfate salts—including (NH₄)₂SO₄ and MgSO₄—promote desorption of REEs from clay minerals via ion exchange; achieving recoveries of up to 90% in batch systems using deionized water or mild acids [37]. Chen et al. demonstrated that a 3 wt% MgSO₄ solution achieved comparable leaching efficiency to ammonium sulfate when applied to ion-adsorption clays, with the added benefit of lower environmental impact [38]. Fuguo et al. investigated the combined use of MgSO₄ and ascorbic acid and observed that synergistic effects improved total REE extraction to 86% under relatively mild conditions [39].

Despite promising results, most of these studies were conducted under laboratory conditions with highly diluted slurries (liquid-to-solid ratio, L/S > 50:1), long contact times (≥4 h), or elevated temperatures (>100 °C). These parameters limit the scalability of the processes for industrial use. Moreover, data on combined organomineral systems, i.e., organic acids supplemented with mineral salts, remain scarce, especially for dense slurries (L/S ≤ 20:1) at moderate temperatures (60–90 °C). There is a clear need to investigate such systems under more practical conditions, including shorter processing times and realistic reagent concentrations.

Despite the growing interest in salt-assisted organic leaching systems, prior research has predominantly focused on citric or lactic acids, with limited attention to tartaric acid in combination with metal sulfates. Moreover, studies that do mention MgSO₄ typically apply it with other ligands or in ion-adsorption clays, not with coal ash matrices. This study fills that gap by evaluating tartaric acid–MgSO₄ leaching under dense slurry conditions and moderate temperatures, with a focus on both extraction efficiency and process kinetics. The objective of this study was to enhance the leaching efficiency of REEs from CA using an organo-mineral system based on tartaric acid and selected inorganic salts, under technologically realistic conditions such as moderate temperatures and high pulp density. The novelty of the work lies in the evaluation of different salt additives for improving the extraction of light REEs (lanthanum (La), Ce, and Nd) in the presence of tartaric acid, which is a biodegradable and selective complexing agent.

2. Materials and Methods

2.1. Materials

The CA used in this study represents a heterogeneous mixture of fly ash and bottom ash accumulated at the disposal site of Almaty TPP-2, which operates on high-ash Ekibastuz coal. The material was air-dried, homogenized, and sieved to below 75 μm.

L-(+)-Tartaric acid (≥99.5%, Sigma-Aldrich, St. Louis, MO, USA) was used as the leaching reagent. Four analytical-grade salts—magnesium sulfate heptahydrate (MgSO₄·7H₂O); sodium chloride (NaCl); calcium chloride (CaCl₂); and ammonium nitrate (NH₄NO₃)—were evaluated as additives (all ≥ 99%, Merck). All solutions were prepared using distilled water.

2.2. Leaching Experiments

Leaching experiments were conducted in a 200 mL round-bottom glass reactor equipped with a thermometer. Each reactor was charged with 100 mL of solution of predefined composition and placed on a magnetic stirrer (IKA RT 5, Staufen, Germany) preheated to the target temperature. Once the temperature stabilized, the CA sample was introduced. Stirring was maintained at a constant speed of 300 rpm throughout the leaching process.

The study was carried out in 2 stages.

In Stage 1, the effect of different salt additives on REE extraction was investigated under fixed baseline conditions: 5 wt% tartaric acid, 0.1 mol/L salt concentration, 90 °C, 120 min leaching time, and a liquid-to-solid ratio (L/S) of 15:1. Four systems were tested: a salt-free control, NaCl, MgSO₄, and NH₄NO₃. After leaching, the slurry was vacuum-filtered, and both the filtrate and solid residue were retained for analysis.

In Stage 2, the best-performing salt from Stage 1 was used to study the influence of key process parameters. The following variables were systematically varied: leaching time (30–120 min), temperature (40, 60, and 90 °C), tartaric acid concentration (2, 5, and 10 wt%), salt concentration (0.05, 0.1, and 0.2 mol/L), and liquid-to-solid ratio (10:1, 15:1, 20:1, and 40:1). All tests were carried out in 100 mL of solution at a stirring speed of 300 rpm. Liquid samples were collected every 20 min using a micropipette to monitor the concentrations of Ce, Nd, and La.

Leaching efficiency, E, was defined as the recovery of the target metal, calculated as

$$E=\frac{m_1}{m_0}\times 100\%$$

(1)

where $m_1$ is the mass of metal recovered in the leachate and $m_0$ is the mass contained in the raw CA sample.

Each experiment was performed in triplicate, and the values presented in the tables and figures represent arithmetic means. In all cases, the standard deviation did not exceed 3% of the mean.

2.3. Analytical Techniques

Scanning electron microscopy (SEM) was performed using a Quanta 200i 3D microscope (FEI Company, Hillsboro, OR, USA). X-ray diffraction (XRD) analysis of solid samples was conducted using a DW-27 Mini X-ray Diffractometer (DFMC, Dandong, China) equipped with a CuKα radiation source operating at 40 kV and 40 mA. Elemental analysis of solid and liquid samples was carried out by inductively coupled plasma optical emission spectroscopy (ICP-OES, Optima 8300, PerkinElmer, Waltham, MA, USA). Solid samples were subjected to preliminary alkaline fusion, followed by acid digestion using concentrated nitric acid in a Tank-Eco microwave digestion system (Sineo, Shanghai, China).

3. Results and Discussion

3.1. Coal Ash Characterization

The chemical composition of the CA, as determined by ICP-OES, is dominated by SiO₂ (64.41 wt%) and Al₂O₃ (27.79 wt%), indicating a predominantly aluminosilicate matrix (

Table 1. Chemical composition of CA determined by ICP-OS.

Component	Wt %	Component	ppm
SiO2	64.41	La	20.29
Al2O3	27.79	Ce	47.51
Fe2O3	7.71	Nd	17.64
P2O5	0.58
CaO	4.25
MgO	1.13
K2O + Na2O	1.52

).

Minor oxides include Fe₂O₃ (7.71 wt%), CaO (4.25 wt%), MgO (1.13 wt%), K₂O + Na₂O (1.52 wt%), and P₂O₅ (0.58 wt%). Trace REEs are also present in significant amounts, with Ce (47.51 ppm) being the most abundant, followed by La (20.29 ppm) and Nd (17.64 ppm). Only La, Ce, and Nd were selected for analysis, as their concentrations in coal ash exceeded 15 ppm and remained consistently above the quantification limit of the ICP-OES method. Other REEs, including Dy, Y, Sm, and Er, were detected at 0.5–1.0 ppm and showed signal intensities close to background noise, which makes quantitative tracking across timepoints unreliable.

The XRD pattern of the raw CA shows distinct reflections corresponding to mullite (3Al₂O₃·2SiO₂), quartz (SiO₂), magnetite (Fe₃O₄), and kaolinite (Al₂Si₂O₅(OH)₄), as presented in Figure 1.

The most intense peak is attributed to mullite at around 2θ ≈ 26.0°, with additional mullite peaks observed at approximately 16.4° and 25.9°, indicating its well-developed crystalline structure. Quartz is identified by its characteristic peaks at 2θ ≈ 20.8°, 26.6°, and 36.5°. Magnetite is detected through its reflections at 2θ ≈ 30.1°, 35.5°, 43.1°, and 57.0°, corresponding to the (311), (400), (422), and (511) planes, respectively. A peak near 2θ ≈ 12.4° is assigned to the (001) plane of kaolinite, suggesting a minor content of layered aluminosilicates. The diffraction pattern indicates that the CA is predominantly composed of mullite and quartz, with detectable amounts of iron oxide and residual clay minerals, and shows a largely crystalline nature.

3.2. Effect of Salt Additives on REE Leaching Efficiency

Figure 2 presents the leaching efficiencies of selected light REEs (La, Ce, and Nd) under different salt-assisted conditions, all tested at a concentration of 0.1 mol/L, as specified in Section 2.2.

The experiments were conducted at 90 °C for 120 min with a liquid-to-solid ratio of 15:1 using 5 wt% tartaric acid. These parameters were selected based on the work of Banerjee et al. [35], where 5% tartaric acid at 90 °C provided the highest extraction efficiency among several organic acids. In their study, a leaching time of 60 min was sufficient to reach near-maximum REE recovery; however, the experiments were carried out at a highly diluted pulp density (L/S = 150:1). Such conditions are impractical for large-scale operations due to excessive reagent consumption and energy input. To reflect more realistic processing conditions, the present study employed a significantly more concentrated slurry (L/S = 15:1). In anticipation of possible kinetic limitations and reduced mass transfer under these conditions, the leaching duration was extended to 120 min to compensate and approach equilibrium extraction.

Among the tested systems, the highest extraction of La, Ce, and Nd was observed in the presence of magnesium sulfate, followed by ammonium nitrate and sodium chloride. In contrast, calcium chloride resulted in a clear suppression of REE leaching.

The superior performance of MgSO₄ can be attributed to several synergistic effects. While Mg²⁺ can bind tartrate ligands, the resulting complexes are weak and do not significantly hinder REE³⁺ complex formation. At the same time, Mg²⁺ effectively displaces REE³⁺ from negatively charged sites on the surface of the aluminosilicate matrix, enhancing desorption. This ion-exchange-driven mobilization is particularly important in solid-rich systems where surface complexation and sorption effects dominate. Furthermore, SO₄²⁻ enhances the ionic strength of the solution, reducing electrostatic interactions and promoting the dissolution of surface-bound species. Once desorbed, REE³⁺ readily forms soluble complexes with tartaric acid via both carboxylate and hydroxyl donor groups [40]:

REE³⁺ + H₂Tar = REE(HTar)²⁺ + H⁺

(2)

REE³⁺ + HTar⁻ = REE(Tar)⁺ + H⁺

(3)

REE³⁺ + 2HTar⁻ = REE(Tar)⁻ ₂ + 2H⁺

(4)

These tartrate complexes are known to be relatively stable at pH ~1.8–2.0 [41], which corresponds to the natural pH of a 5% tartaric acid solution. In the case of NH₄NO₃, a similar but slightly less pronounced enhancement was observed. The NH₄⁺ ion does not form significant complexes with tartaric acid or REEs and primarily contributes to the overall ionic strength and charge balance of the solution at pH ~2, thereby supporting stable tartrate speciation and REE complexation. The nitrate anion is non-coordinating and inert under the given conditions, making NH₄NO₃ an effective, but chemically neutral, enhancer.

NaCl exhibited a moderate increase in leaching efficiency relative to salt-free control. The Na⁺ ion, while non-complexing, increases the ionic strength of the solution, which weakens electrostatic adsorption of REE³⁺ onto the ash particles and promotes their release into solution. However, due to the absence of buffering or specific chemical interactions, the overall effect was weaker than that observed with MgSO₄ or NH₄NO₃.

Unlike MgSO₄, the addition of CaCl₂ did not enhance REE recovery under the tested conditions. This difference may be related to distinct ionic interactions and solution chemistry effects; further study would be needed to clarify the mechanism.

Based on the results presented in Figure 2, magnesium sulfate was selected for further study, as it provided the highest leaching efficiencies for La, Ce, and Nd. The positive effect of MgSO₄ is attributed to enhanced REE desorption from the ash matrix and minimal interference with tartaric acid complexation. Its favorable ionic properties and chemical compatibility make it the most effective additive among those tested. Accordingly, MgSO₄ was used in all subsequent experiments focused on process optimization. The proposed mechanism, involving surface ion exchange facilitated by Mg²⁺ and subsequent complexation with tartaric acid, is consistent with the observed trends in extraction efficiency, kinetic modeling, and SEM evidence of particle degradation. The enhancement by MgSO₄ is consistent with a dual effect: Mg²⁺ promotes surface ion exchange at active sites, displacing loosely bound REE species, and increased ionic strength (with SO₄²⁻ present) compresses the electrical double layer, which improves access of tartrate to the mineral surface. The resulting REE–tartrate complexation keeps dissolved REEs in solution and shifts the leaching equilibrium, reducing re-adsorption. The limited co-dissolution of Fe/Al under these conditions indicates that the mechanism preferentially targets REE-hosting microphases. These results align with broader salt-assisted leaching strategies seen in the literature. Moldoveanu and Papangelakis [37] demonstrated that a combination of biodegradable chelating agents (EDDS or NTA) with saline media (simulated seawater, ~0.5 mol L⁻¹ NaCl) enhanced REE recovery from ion-adsorption clays by 10–20%, compared to ion exchange alone. Their study achieved this with neutral pH and moderate ionic strength, underscoring the benefit of combining moderate complexing agents and salts. Similarly, citric acid leaching of bauxite residue/red mud has been shown to extract over 85% of REEs when used directly—without roasting—highlighting the potential of organic acids with inherent ionic content [42].

3.3. Effect of Operational Parameters on REE Leaching Using MgSO₄

To further evaluate the influence of key operational parameters on REE leaching efficiency, a series of experiments was conducted by varying temperature (40–90 °C), leaching duration (30–180 min), liquid-to-solid ratio (10:1–30:1), tartaric acid concentration (3–20 wt%), and MgSO₄ concentration (0–0.20 mol/L). All other conditions were kept identical to those used in Figure 2: 5 wt% tartaric acid, 0.1 mol/L MgSO₄, 90 °C, 120 min, and L/S = 15:1.

Figure 3 shows the effect of temperature on the leaching efficiency of La, Ce, and Nd from CA.

Figure 3a–c illustrate the combined effects of temperature and leaching duration on the extraction efficiency of La, Ce, and Nd from CA using 5 wt% tartaric acid and 0.1 mol/L MgSO₄ (L/S = 15:1). In all cases, increasing both temperature and time led to a significant improvement in REE recovery, consistent with thermally activated surface desorption and complexation kinetics.

An increase in temperature from 40 to 80 °C led to a noticeable rise in the extraction of all three REEs. At 120 min, the recovery of La increased from 36% at 40 °C to 61% at 90 °C; Ce and Nd followed similar trends, reaching 63% and 65%, respectively. The temperature effect was particularly evident at the early stages of leaching: after 30 min, La recovery rose from 11% at 40 °C to 22% at 90 °C, while Nd increased from 14% to 34%.

Leaching time also influenced extraction, especially at lower temperatures. At 40 °C, extending the process from 30 to 150 min improved La recovery from 11% to 37%. However, at 90 °C, the extraction values leveled off by 120 min, with no significant change observed beyond that point. For instance, Nd recovery remained stable at 66% between 150 and 180 min. These results suggest that equilibrium is effectively reached after 2 h under the selected conditions.

Figure 4a–c present the effect of the L/S ratio and leaching time on the extraction efficiency of La, Ce, and Nd from CA.

At each time point, the lowest L/S ratio (10:1) resulted in markedly reduced extraction, likely due to limited ligand availability and slower mass transfer in the more concentrated pulp. For example, La recovery at 120 min increased from 53% at L/S = 10 to 61% at L/S = 15, while further increases to 20 and 30 resulted in only marginal improvements (up to 63–64%). Similar trends were observed for Ce and Nd.

With respect to time, extraction increased sharply from 30 to 120 min, after which the system approached a plateau. Beyond 120 min, the gains were minimal, indicating near-equilibrium conditions. These results confirm that an L/S ratio of 15:1 combined with a leaching time of 120 min provides an optimal balance between reagent consumption and REE recovery.

Figure 5 shows the leaching performance of La, Ce, and Nd as a function of tartaric acid concentration under otherwise constant conditions.

Increasing the acid concentration from 3 to 10 wt% led to a progressive improvement in REE recovery. However, while the extraction at 10 wt% was only slightly higher than that at 5 wt% (61%, 63%, and 65% for La, Ce, and Nd, respectively), it required twice the amount of acid. This marginal gain does not justify the increased reagent consumption, indicating that 5 wt% tartaric acid is the optimal concentration under the tested conditions.

Temperature mainly accelerates the apparent rate constant rather than changing the pathway: the initial slope increases, whereas the asymptotic extraction remains governed by the number of accessible reactive sites. The L/S ratio and acid dosage exhibit diminishing returns once acid neutralization and complexant availability cease to be limiting; beyond that point, mass transfer within micro-porous domains becomes rate-moderating. Figure 6 provides the effect of MgSO₄ concentration on the leaching efficiency of La, Ce, and Nd under otherwise constant conditions. In the absence of any salt additive, REE recovery remained low, with only 38% La, 41% Ce, and 44% Nd extracted after 120 min of leaching at 90 °C. The addition of even a small amount of MgSO₄ (0.05 mol/L) led to a significant increase in extraction—up to 53%; 56%; and 59% for La; Ce; and Nd; respectively. This trend continued up to 0.10 mol/L, where maximum recoveries were observed: 61% La, 63% Ce, and 65% Nd.

The observed enhancement is attributed to the dual role of Mg²⁺ in promoting desorption of REE³⁺ from the ash matrix via ion exchange and in increasing the ionic strength of the solution, which reduces electrostatic retention of REEs on solid surfaces. Beyond 0.10 mol/L, no further improvement was seen, likely due to a saturation effect. Therefore, 0.10 mol/L MgSO₄ was considered optimal.

Thus, the optimal conditions for leaching La, Ce, and Nd from CA using tartaric acid and magnesium sulfate were established as follows: a temperature of 90 °C, a leaching time of 120 min, a liquid-to-solid ratio of 15:1, a tartaric acid concentration of 5 wt%, and a MgSO₄ concentration of 0.10 mol/L. These parameters provided the most effective balance between extraction efficiency and reagent consumption. Increasing the temperature or duration beyond these values did not result in significant improvement, while higher acid or salt concentrations offered only marginal gains at the cost of additional reagent use.

Although 90 °C may seem relatively high, such temperatures are readily achievable in industrial settings using waste heat or low-pressure steam, especially at coal-fired power plants. The chosen reagent dosages offer a practical compromise between efficiency and chemical consumption. Combined with a moderate L/S ratio and reasonable leaching duration, the system offers favorable parameters for scale-up.

For comparison, hydrochloric acid can extract up to 80% of REEs from coal ash under optimized conditions [29], but it requires highly acidic media (pH < 1) and large acid dosages and results in significant co-leaching of Fe, Al, and other elements. It also produces corrosive waste that complicates handling. In contrast, the tartaric acid + MgSO₄ system offers comparable recovery under milder conditions (pH ~2), with better selectivity and lower environmental impact.

3.4. Leaching Kinetics and Shrinking Core Model Analysis

To gain insight into the rate-limiting mechanisms governing REE leaching from CA, kinetic analysis was performed using the data obtained at different temperatures and leaching durations (Figure 3). Among the available models, the shrinking core model (SCM) was employed, which is widely used to describe solid–liquid leaching systems. In this model, leaching proceeds through the inward movement of the reaction front within ash particles, and the overall rate may be controlled either by surface chemical reaction or by diffusion through the product layer [43,44].

The relationship between leaching time and the fraction of the target metal dissolved can be expressed by the following equations [45,46,47], depending on the rate-limiting step of the process:

$$1-\frac{2}{3}X-(1-X{)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=k\tau$$

(5)

$$1-(1-X{)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=k\tau$$

(6)

$$\frac{1}{3}\mathit{ln}\left(1-X\right)-1+(1-X{)}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=k\tau$$

(7)

where $X_{Me}$ is the fraction of target REE recovered, $k$ is the rate constant of chemical reaction of leaching, and $\tau$ is the time in which the leaching of $X$ is achieved.

When the leaching rate is limited by mass transfer, Equation (5) is used. If the rate-limiting step is the chemical reaction, the relationship between the metal extraction and leaching time is described by Equation (6). In cases where both mass transfer and chemical reaction jointly control the process, model (7) is applicable.

To identify the rate-limiting step in REE leaching from CA, the left-hand sides of Equations (5)–(7) were plotted as functions of leaching time at three different temperatures. Only data within the 0–120 min range were considered for kinetic modelling, as REE extraction began to plateau beyond this point (see Figure 3 and Figure 4). Individual fittings for La, Ce, and Nd also showed the same linear trends, confirming that all three REEs follow the same kinetic model. Given the strong correlation among the recoveries of all studied REEs, their average recovery was used as the variable $X$. The corresponding coefficients of determination are summarized in

Table 2. Coefficients of determination (R²) for linear dependencies according to Equations (5)–(7), obtained from the data in Figure 3.

Equation	Temperature, °C
	40	60	80	90
5	R2 = 0.6924	R2 = 0.7314	R2 = 0.7116	R2 = 0.6732
6	R2 = 0.9873	R2 = 0.9691	R2 = 0.9724	R2 = 0.9683
7	R2 = 0.7648	R2 = 0.6152	R2 = 0.7367	R2 = 0.8354

.

Among the tested models, Equation (6), corresponding to the chemical reaction-controlled mechanism, showed the best fit at all temperatures, with R² > 0.96. This indicates that surface chemical reaction is the primary rate-limiting step. In contrast, the mass transfer model (Equation (5)) and mixed control model (Equation (7)) resulted in significantly lower R² values that suggest they do not adequately describe the observed kinetics. These results align with the structural nature of CA, where REEs are mainly associated with surface sites of aluminosilicate matrices. The leaching mechanism is therefore governed by surface complexation and chemical reaction at the solid–liquid interface, rather than by diffusional resistance [48,49]. The slight decrease in R² values at higher temperatures may reflect partial transition to mixed control, though diffusion remains dominant.

To illustrate the leaching behavior of individual REEs under the applied conditions, linearized SCM plots ($1-(1-X{)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=k\tau$) were constructed for La, Ce, and Nd at different temperatures (Figure 7). These data were obtained using 5 wt% tartaric acid, 0.1 mol/L MgSO₄, and an L/S ratio of 15:1.

In all cases, the plots exhibit strong linearity (R² > 0.96), indicating that the leaching kinetics are governed by surface chemical reaction. The apparent rate constants k (min⁻¹), derived from the slopes, increase with temperature for all elements, confirming thermally activated behavior.

Among the studied REEs, Nd showed the highest leaching rates across all temperatures, with k = 0.0013–0.0025 min⁻¹, followed closely by Ce (k = 0.0012–0.0025 min⁻¹), and La (k = 0.0012–0.0024). This trend suggests that Nd³⁺ is more readily leached under the given conditions, possibly due to faster surface complexation or more accessible binding sites in the ash matrix. The similarity of the linear fits and near-zero intercepts further supports a direct surface-controlled mechanism without significant diffusional resistance.

Arrhenius plots for REE leaching from CA were created using the apparent rate constants of the chemical reaction (Figure 8).

The activation energy (E_a) of the overall chemical reaction governing the dissolution of La, Ce, and Nd was calculated based on the Arrhenius Equation (Equation (10)) [50]:

$$lnk=-\frac{E_a}{RT}$$

(8)

where k is the rate constant of chemical reaction (min⁻¹), R is the universal gas constant (J/(mol × K)), and T is absolute temperature (K).

The activation energies for La, Ce, and Nd leaching were calculated as 20.85, 20.38, and 21.71 kJ/mol, respectively. These relatively low values are consistent with a surface chemical reaction-controlled mechanism, as supported by the strong linearity in the SCM plots. Low E_a values do not contradict chemical control, especially in systems involving organic complexing agents. Tartaric acid readily forms soluble complexes with REEs, reducing the activation barrier at the solid–liquid interface. The ash matrix, likely containing amorphous or loosely bound REEs, further facilitates this process. Mg²⁺ ions may enhance reactivity by promoting ion exchange or destabilizing competing surface bonds.

Comparable systems using citric or oxalic acids report higher Ea values, typically 26–45 kJ/mol, which indicate less favorable kinetics [48,50,51]. In contrast, the lower activation energies observed in this study suggest that tartaric acid, in combination with Mg²⁺, provides a more energetically favorable environment for REE dissolution.

3.5. Surface Morphology Before and After REE Leaching

Figure 9 presents representative SEM images of CA before and after leaching under different experimental conditions.

The raw CA (Figure 9a) exhibits heterogeneous morphology, consisting of dense agglomerates and abundant spherical particles characteristic of fly ash generated during high-temperature combustion. The particle surfaces appear smooth and glassy, indicating low inherent porosity and limited reactive surface area.

Upon leaching at 40 °C using 5 wt% tartaric acid and 0.1 mol/L MgSO₄ (Figure 9b), initial signs of surface etching and micro-pitting become apparent. Some spherical particles display localized roughening, suggesting partial desorption of surface-bound species and the onset of chemical attack by the leaching agent. These morphological alterations, although moderate, reflect the relatively low reaction kinetics at sub-optimal temperature.

More pronounced changes are observed following leaching at 90 °C with 5 wt% tartaric acid and 0.1 mol/L MgSO₄ (Figure 9c). The particle surfaces become significantly roughened, with evidence of cracking, fragmentation, and partial disintegration. These features are consistent with intensified chemical dissolution and align with the kinetic data indicating surface reaction control under these conditions.

Further enhancement of the acid concentration to 10 wt% at 90 °C (Figure 9d) leads to extensive morphological degradation. The particles exhibit porous, irregular surfaces, widespread fracturing, and, in some cases, structural collapse. Such advanced textural changes point to increased lixiviant penetration and accelerated REE mobilization, driven by enhanced ligand availability and stronger ion-exchange interactions.

Cumulative particle size distribution analysis (Figure 10) showed a shift toward finer fractions after leaching at 90 °C with 10 wt% tartaric acid and 0.1 mol/L MgSO₄.

The median particle size (D₅₀) decreased from 36.1 µm to 29.1 µm, while D₁₀ dropped from 14.3 µm to 11.5 µm. The D₉₀ value remained relatively unchanged (75.0 µm → 73.2 µm); that shows partial fragmentation and surface erosion of larger particles rather than complete disintegration. Overall, the observed morphological evolution supports the proposed leaching mechanism, wherein tartaric acid–assisted REE extraction is facilitated by surface complexation, matrix disruption, and gradual degradation of the ash particle structure.

4. Conclusions

This study demonstrated the potential of tartaric acid as an environmentally benign lixiviant for the recovery of light REEs (La, Ce, and Nd) from coal ash. The addition of MgSO₄ as a salt additive significantly enhanced REE leaching, achieving efficiencies up to ~80% under the tested conditions. These results highlight a novel organic-salt system that can be considered as an alternative to conventional mineral acid leaching. Kinetic analysis based on the shrinking core model indicated that the leaching process was governed by a surface chemical reaction-controlled mechanism. This conclusion was supported by the high correlation coefficients and activation energy values consistent with chemically controlled processes. Despite these promising results, the study has certain limitations. The experiments were conducted at relatively high temperatures (90 °C) and under laboratory-scale conditions. While such conditions are effective for mechanistic understanding, their industrial feasibility requires further assessment, particularly in terms of energy consumption and scale-up. Future work should therefore focus on optimization at lower temperatures, integration with downstream separation and purification methods for La, Ce, and Nd, and evaluation of residue management. In addition to high REE recovery, the leaching system showed environmentally favorable traits. The process generated mildly acidic effluents (pH ≈ 2.2) with low metal loads and no mineral acids, simplifying downstream treatment. Solid residues rich in SiO₂ and Al₂O₃ may be repurposed as cement additives or sorbents after stabilization. Looking ahead, the leachate enriched in La, Ce, and Nd could be further processed by established separation routes. Solvent extraction with organophosphorus reagents, ion-exchange methods, or selective precipitation (e.g., oxalate/carbonate) represent viable options for purifying individual REEs. Integrating such techniques would enable a complete flowsheet from leaching to final REE products.