Temperature-Dependent Crystallization Optimization for Upcycling Purified Ash from the Calcium Carbide Industry: A Sustainable Approach for Mg(OH)₂/Aragonite Coproduction

Abstract

This study employs a wet precipitation–carbonation method to recycle and utilize purification slag from the calcium carbide industry, extracting high-value-added magnesium hydroxide (Mg(OH)₂) and aragonite nanoparticles. Experimental results demonstrate that the reaction temperature significantly influences the yield, morphology, and crystallinity parameters of the products. The optimal preparation temperatures for Mg(OH)₂ and aragonite are 60 °C and 80 °C, respectively. Analysis via X-ray diffraction (XRD) combined with the Williamson–Hall method reveals that within the temperature range of 60–90 °C, the crystallite sizes of Mg(OH)₂ and aragonite are 40.07–59.25 nm and 70.03–109.18 nm, respectively. As the temperature increases, the crystallite size, strain, lattice stress, and energy density of Mg(OH)₂ exhibit a decreasing trend, whereas the corresponding crystallographic parameters of aragonite gradually increase.

1. Introduction

Environmental protection and sustainable development are major global challenges today, which are also two urgent issues to be solved for governments and international organizations. It is reported that over 20 billion tons of solid waste has been generated globally in 2020, which is expected to reach 46 billion tons by 2050 [1,2,3]. Solid waste has caused great harm to the environment. In particular, solid waste generated during industrial processes not only occupies land resources, but also causes pollution to water, soil, and air. Some organic matter, heavy metals, and other pollutants can also enter the human body through the food chain, ultimately threatening human health [4]. Therefore, to reduce the negative impact of industrial solid waste, many policies including reuse, recycling, and recovery of industrial solid waste are often considered for saving resources [5,6,7,8,9,10]. Among various solid waste treatment technologies, green chemical technologies and sustainable utilization technologies exhibit significant application potential [7,8].

During the production process of calcium carbide, a spherical waste residue, usually called purified ash, can be generated, which is mainly composed of CaO, MgO, SiO₂, Al₂O₃, Fe₂O₃, and so on. Among them, the total content of MgO and CaO can reach up to 80%. With an annual production of 28 million tons of calcium carbide during 2023 in China, the total amount of purified ash can reach 1 million tons per year. In general, purified ash is mainly treated by simple landfilling or used as a soil conditioner (adsorbent), which can lead to some serious environmental problems, such as occupying land, causing soil salinization, and polluting groundwater under the long-term infiltration of rainwater or groundwater. Specifically, the direct use of purified ash as an adsorbent may pose potential environmental risks. The presence of heavy metals and impurities in purified ash can lead to secondary pollution during the adsorption process. Moreover, its relatively low chemical stability and mechanical strength may result in particle fragmentation and dispersion, thereby reducing its adsorption efficiency and increasing water turbidity. Accordingly, two basic approaches are proposed for comprehensive utilization of purified ash. The first one is the application for building materials and the other is to extract valuable materials. The application of building materials is low-cost, but the limited operating radius and saturation of the building materials market mean that it is no longer sought [10,11]. Therefore, the extraction of valuable materials such as magnesium hydroxide (Mg(OH)₂) and calcium carbonate nanoparticles with low cost and high accessional value may be a better choice.

Magnesium and its compounds are widely used in modern industry. Due to their elite properties such as excellent fire-retardant quality, great thermal stability, nontoxicity, and low cost, Mg(OH)₂ nanoparticles have received much attention [12]. Lately, Mg(OH)₂ has been widely used as a halogen-free flame retardant, a filler in composite materials, a catalyst, and an additive in refractory materials, paint, and ceramics [13]. According to the literature, Mg(OH)₂ nanostructures have been obtained through several methods including microwave or ultrasonic treatment, precipitation, micro-emulsion methods, the hydrothermal process, and through the use of an ionic exchange membrane crystallizer [14]. It was reported that the morphology of Mg(OH)₂ in the form of platelets or nanosized needles makes it particularly effective as an environmentally friendly, thermally stable flame retardant in polymer composites, mainly because of its low polarity and good compatibility with polymers, thereby reducing the adverse effects on the mechanical properties of materials [8,15]. As for aragonite, its needle-like shape helps improve the mechanical properties and crack resistance of concrete. This reduces the need for concrete repair and replacement during its service life, indirectly lowering resource consumption and environmental burdens. However, numerous studies have indicated that Mg(OH)₂ nanoparticles synthesized at room temperature are prone to aggregate with each other and transfer into complex microstructures, such as a pinecone-like shape or flower-like shape, causing a lack of compatibility and reducing the mechanical properties of the corresponding composite [15]. Consequently, the preparation of Mg(OH)₂ with good dispersibility has always been a focus of attention. The most commonly used approach to improve the dispersion of Mg(OH)₂ is recrystallization of the particles in the hydrothermal process. Ding et al. [16] have successfully produced needle and lamella-structured Mg(OH)₂ nanoparticles by employing the hydrothermal method using various magnesium precursors and reducing agents. Chen et al. [17] prepared dispersive hexagonal-shaped Mg(OH)₂ nanoparticles combined with hydrothermal treatment and organic solvent assistance with magnesium chloride as a raw material. However, the hydrothermal methods greatly hinder the universal preparation of highly dispersed Mg(OH)₂ crystal due to the rigorous, tedious procedure and unacceptable economy. Similarly, several studies have focused on controlling the polymorphs of calcium carbonate (CaCO₃) to synthesis aragonite, a metastable polymorph of CaCO₃. Moreover, aragonite with a needle-like morphology is not only believed to be able to improve the mechanical properties, toughness, and crack resistance of concrete but is also very costly compared to calcite [18].

When preparing inorganic materials with the precipitation method, temperature is a very important parameter for structure control, crystallite size tuning, and surface modifications. Kotresh et al. [19] studied the effect of the reaction temperature on the synthesis of Mg(OH)₂ nanoparticles, and various theoretical methods, such as the Debye–Scherrer method and Williamson–Hall method, have been used to estimate the crystallite size. The results indicated that the synthesized Mg(OH)₂ nanoparticles have shown the shape of flakes and agglomerated particle distribution at temperatures of 50 and 70 °C; meanwhile, the crystal size was smaller at lower temperatures. Kogo et al. [20] synthesized calcium carbonate in the CaCl₂–Na₂CO₃–H₂O reaction system at different reaction temperatures. The results showed that the formation of aragonite was observed at ≥50 °C, and single-phase aragonite was obtained at ≥60 °C according to XRD measurements.

In this work, a wet precipitation carbonization method was used to synthesize dispersed lamellar-like Mg(OH)₂ and aragonite from the impure precursor purified ash, an industrial residue from calcium carbide production, and the temperature-dependent effect on the yields, morphology, and crystallite parameters using theoretical methods were investigated in detail.

2. Experimental

2.1. Materials

The raw, purified ash was collected from Yulin (Shaanxi province). The provided quantity (approximately 500 g) was sampled according to the usual method of sampling. The crystal structure and chemical composition of samples were initially analyzed. All other reagents were of analytical grade.

The chemical composition of the purified ash sample is depicted in

Table 1. Chemical composition of purified ash detected using an X-ray fluorescence spectrometer (wt.%).

Oxide	MgO	CaO	SiO2	K2O	Na2O	Al2O3	SO3	Fe2O3	MnO	ZnO	Cr2O3
Content(%)	49.10	29.50	10.50	4.57	1.92	1.73	1.15	0.65	0.53	0.16	0.04

. It shows that the purified ash consisted mostly of MgO and CaO, which was further confirmed by the XRD pattern and FTIR spectrum, shown in Figure 1 and Figure 2, respectively. MgO came from the enrichment of magnesium in limestone, which was the raw material for calcium oxide.

The FTIR spectrum in Figure 2 shows the strong and narrow absorption band at 3643 cm⁻¹ corresponded to the OH^- stretching mode from water molecules absorbed by CaO or MgO. The peaks at 3420 and 1632 cm⁻¹ were assigned to O-H stretching and C=O stretching modes of hydroxyl and carbonyl groups, respectively. The stronger and broader peaks at 1464 cm⁻¹ corresponded to CO₃^2-, derived from the adsorption of CO₂. The peak at 1426 cm⁻¹ was due to the bending vibration of the O-H bond. The peaks located at 1119 and 993 cm⁻¹ are attributed to SiO₄ group vibrations. The peaks at 918 cm⁻¹ were caused by asymmetrical stretching vibrations of the Si-O-(Si, Al) bonds. The peaks at around 848 and 518 cm⁻¹ are indicative of the vibrational modes corresponding to MgO and CaO structures [21,22].

2.2. Characterization

The microcrystalline structure variations in the samples were investigated using X-ray diffraction (XRD) in a D8 Advance diffractometer (Bruker, Karlsruhe, Germany) with Cu Kɑ radiation (wavelength 1.5406 Å) at a step length of 0.02°/s. The morphologies were obtained with scanning electron microscopy (SEM) using a JSM-6460LV scanning electron microscope (JEOL, Akishima, Tokyo, Japan) at an accelerating voltage of 0.5 kV and 30 kV. To conduct the SEM test, the obtained samples were first deposited on the conductive adhesive and subsequently coated with gold using a gold-sputtering device. The chemical composition was investigated using X-ray fluorescence (XRF) in a S8 TIGER spectrometer (Bruker, Karlsruhe, Germany). The vibrational analysis was conducted using Fourier transform infrared spectrometer (FTIR) in a Nicolet iN10 & iZ10 spectrometer (Thermo Fisher Scientific, Waltham, MA, USA) in the wavenumber region of 4000–400 cm⁻¹.

2.3. Procedure

Figure 3 illustrates the synthesis steps of Mg(OH)₂ and aragonite from purified ash. As depicted, the procedures were as follows: purified ash (10 g) with a particle size of 0~3 mm was dissolved in 6 mol/L hydrochloric acid solution (60 mL) at room temperature for 30 min in a glass reactor. Then, about 4 mL of ammonia was added, and the pH was adjusted to 6~7 at 60 °C to provoke impurity metal ion precipitation based on its solubility product. A special treatment was required for manganese ions because no precipitates can be formed at pH 6~7. And 0.3 g calcium hypochlorite was further added to change manganese ions to MnO₂. Then, the solution was filtered and a (MgCl₂, CaCl₂)-rich filtrate was obtained. The residue mud cake can be landfilled after being washed.

The obtained (MgCl₂, CaCl₂)-rich filtrate was transferred to a glass beaker and an appropriate amount of ammonia was added at different temperatures for 2 h. The suspension was allowed to age at the synthesis temperature for 1 h. Then, the suspension was filtered and Mg(OH)₂ was obtained by washing the cake. Subsequently, proper NH₄HCO₃ was added to the filtrate at different temperatures for 2 h and aging for 1 h. Then, the suspension was filtered; aragonite can also be obtained by washing the cake. The filtrate can be recovered to produce ammonium chloride by evaporation crystallization, and a small number of impurities mainly composed of chloride ions can be specially handled as solid waste through evaporation crystallization. After such processing, the reduction and resource utilization of purified ash can be achieved.

3. Results and Discussion

3.1. Thermogradient-Driven Crystallization Analysis of Mg(OH)₂

Figure 4 shows the X-ray diffractograms of Mg(OH)₂ prepared at different reaction temperatures of 20, 40, 60, and 80 °C. The figures show intense and sharp peaks, indicating the good crystalline characteristics of the samples. The yields and I₀₀₁/I₁₀₁ results of Mg(OH)₂ obtained through the XRD data with different temperatures are shown in Figure 5. In the XRD diffraction peaks of Mg(OH)₂, the higher intensity ratio of the (001) and (101) planes reflects the low surface polarization and good dispersion.

As depicted in Figure 5, the maximum yield and I₀₀₁/I₁₀₁ ratio occur at 60 °C. The changes in yields can be explained by the ionization degree of ammonia being insufficient at lower temperature, while the volatilization degree of ammonia was too high at higher temperature, which resulted in an insufficient concentration of OH^- in the solution and unfavorable conditions for the generation of Mg(OH)₂. The variations in the I₀₀₁/I₁₀₁ ratio can be attributed to the activation energy associated with the growth of different crystal planes. The non-polar (001) crystal surface of Mg(OH)₂ was mainly composed of growth elements formed by Mg-OH ion bonds, with a higher activation energy [23,24]. The (101) crystal surface demonstrated an increase in the number of growth element layers, connected by hydrogen bonds, covalent bonds, etc., with a lower activation energy. Therefore, it was beneficial for the growth of the (101) crystal surface at lower temperatures. With the increase in temperature, higher activation energy can be provided to promote the growth of the (001) crystal surface. When the temperature reached 80 °C, the changes in ionization and volatilization of ammonia caused ion imbalance in the solution, which made the growth of the (101) crystal surface dominant again.

The SEM photographs of Mg(OH)₂ obtained under different reaction temperatures are presented in Figure 6. As depicted in Figure 6, all of the obtained Mg(OH)₂ samples were irregular sheet-like crystals with good dispersibility. It shows that the morphology and size of Mg(OH)₂ crystals are influenced by the preparation temperature. At lower temperatures, the crystals tend to form more regular and smaller particles with a relatively uniform distribution, while at higher temperatures, the crystals become larger and more irregular in shape, with some degree of aggregation observed. This suggests that temperature plays a crucial role in the crystallization process of Mg(OH)₂. Higher temperatures may accelerate the crystallization rate, leading to faster crystal growth and coalescence.

To investigate the effects of temperature on the size of nanocrystals as well as the values of the intrinsic strain, Williamson–Hall method, including the uniform deformation model (UDM), uniform stress deformation model (USDM), and uniform deformation energy density model (UDEDM), was applied for the determination of crystallite size from the XRD peak broadening analysis, mainly because the Williamson–Hall model can provide more effective and precise parameters [25,26]. The 2θ (degree) diffracted positions of synthesized Mg(OH)₂ samples were matched with the standard ICDD database of the card no: 01-084-2164. Lattice parameters such as the lattice constant and unit cell volume were calculated from the Bragg equation and the lattice geometry equation, as presented below [25,26].

$$\lambda =2d_{hkl}\sin \theta$$

(1)

$${\displaystyle \frac{1}{d_{hkl}^2}}={\displaystyle \frac{4}{3}}({\displaystyle \frac{h^2+hk+k^2}{a^2}})+{\displaystyle \frac{l^2}{c^2}}$$

(2)

$$\mathrm{V}={\displaystyle \frac{\sqrt{3}}{2}}{a}^{2}c$$

(3)

where λ is the wavelength of the X-ray (1.5406 Å), d_hkl is interplanar spacing, θ is Bagg’s angle in degree, a,b,c and h,k,l are lattice constants, and V is the unit cell volume. The lattice parameters of Mg(OH)₂ synthesized at different temperatures are summarized in

Table 2. The structure parameters of Mg(OH)₂.

Samples	Lattice Parameters (Å)		V (Å3)
	a = b	c
20 °C	3.1479	4.7796	41.02
40 °C	3.1493	4.7814	41.07
60 °C	3.1496	4.7814	41.08
80 °C	3.1493	4.7801	41.06
Reference data	3.1450	4.7400	40.60

, which were calculated using the crystallographic planes corresponding to the Miller indexes (001) and (100). It can be seen that the lattice constants a and c were found to be in agreement with the standard reference data.

(1)

UDM

The Williamson–Hall method considers that the total broadening of the XRD peak is the result of both the crystallite size and intrinsic strain [27]. Accordingly, the overall broadening owing to the size and intrinsic strain of the crystals can be written as [28] follows:

$${\beta }_{hkl}={\beta }_{size}+{\beta }_{strain}$$

(4)

$${\beta }_{size}={\displaystyle \frac{\mathrm{K}\lambda }{D\cos \theta }}$$

(5)

$${\beta }_{\mathrm{strain}}=4\epsilon \tan \theta$$

(6)

where β_hkl is the FWHM of each XRD peak, β_size is the broadening due to crystallite size, β_strain is the broadening due to intrinsic strain, θ is Bagg’s angle in degree, K is the shape factor (0.9), D is the crystallite size in nm, and ε is the microstrain. Then, the Williamson–Hall equation can be given as follows:

$${\beta }_{hkl}\cos \theta ={\displaystyle \frac{\mathrm{K}\lambda }{d}}+4\epsilon \sin \theta$$

(7)

which is known as the Williamson–Hall equation of UDM. A straight line was found by plotting ${\beta }_{hkl}\cos \theta$ along the y-axis and 4sinθ along the x-axis at different temperatures, as shown in Figure 7. The crystallite size was found from the intercept of the fitted line, and the overall strain was given by the slope. The curves from Figure 7 reveal the existence of intrinsic strain, a phenomenon involving the lattice expansion of nanocrystals [26]. The obtained strains of Mg(OH)₂ were 0.00148 for 80 °C, 0.00146 for 60 °C, 0.00133 for 40 °C, and 0.00135 for 20 °C, and the calculated crystallite sizes were 59.25 nm for 80 °C, 48.65 nm for 60 °C, 51.74 nm for 40 °C, and 40.07 nm for 20 °C.

(2)

USDM

The UDM model is based on the assumption that the sample is homogeneous and isotropic, but real crystal is anisotropic [28]. Accordingly, an anisotropic strain was considered, and lattice deformation stress was regarded as uniform along all the lattice plane directions containing a small microstrain. This modified model was the USDM. According to Hooke’s law, stress and strain have a linear relationship [29]:

$$\sigma ={\mathrm{Y}}_{hkl}\epsilon$$

(8)

where σ is the stress and ${\mathrm{Y}}_{hkl}$ is Young’s modulus or the modulus of elasticity, which has a value of 1.6 GPa for Mg(OH)₂ [30]. Accordingly, the Williamson–Hall equation of USDM can be written as

$${\beta }_{hkl}\cos \theta ={\displaystyle \frac{\mathrm{K}\lambda }{d}}+4\sigma {\displaystyle \frac{\sin \theta }{{\mathrm{Y}}_{\mathrm{hkl}}}}$$

(9)

A linear graph was generated by plotting ${\beta }_{hkl}\cos \theta$ along the y-axis and $4\sin \theta /{\mathrm{Y}}_{hkl}$ along the x-axis at different temperatures, as shown in Figure 8. The calculated crystallite sizes of Mg(OH)₂ were 59.25 nm for 80 °C, 48.65 nm for 60 °C, 51.74 nm for 40 °C, and 40.07 nm for 20 °C, while the stresses calculated were 2.37 MPa for 80 °C, 2.33 MPa for 60 °C, 2.12 MPa for 40 °C, and 2.16 MPa for 20 °C.

(3)

UDEDM

Due to the fact that most of the crystals had defects, Hook’s law’s linear relationship between stress and strain was not valid [25]. So, UDEDM was used to estimate the microstructures and energy density of the crystals. It considered the homogeneous anisotropic nature of the intrinsic strain as the density of dislocation energy was mainly responsible for anisotropic lattice strain. According to Hooke’s law, energy density is related to strain through the following relation [31]:

$$u={\epsilon }^2{\displaystyle \frac{Y_{hkl}}{2}}$$

(10)

where u is the energy density. Combined with Equation (7), the microstrain ε can be written as a function of energy density.

$$\epsilon =\sigma \sqrt{{\displaystyle \frac{2u}{Y_{hkl}}}}$$

(11)

Accordingly, the Williamson–Hall equation of UDEDM can be written as [25]

$${\beta }_{hkl}\cos \theta ={\displaystyle \frac{k\lambda }{d}}+4\sin \theta \sqrt{{\displaystyle \frac{2u}{Y_{hkl}}}}$$

(12)

A linear graph was generated by plotting ${\beta }_{hkl}\cos \theta$ along the y-axis and 4sinθ$\sqrt{2}/\sqrt{Y_{hkl}}$ along the x-axis at different temperatures, as shown in Figure 9. The energy density of Mg(OH)₂ was reported as 1.76 kJ/m³ for 80 °C, 1.70 kJ/m³ for 60 °C, 1.41 kJ/m³ for 40 °C, and 1.45 kJ/m³ for 20 °C; meanwhile, the crystal size was measured as 59.25 nm for 80 °C, 48.65 nm for 60 °C, 51.74 nm for 40 °C, and 40.07 nm for 20 °C, correspondingly.

Table 3. Calculated crystallite parameters of Mg(OH)₂.

Williamson–Hall Model	Crystallite Size, D (nm); Strain, ε (N/m2); Stress, σ (MPa); Energy Density, u (kJ/m3);
	80 °C	60 °C	40 °C	20 °C
UDM	ε = 0.00148	ε = 0.00146	ε = 0.00133	ε = 0.00135
	D = 59.25	D = 48.65	D = 51.74	D = 40.07
USDM	σ = 2.37	σ = 2.33	σ = 2.12	σ = 2.16
	D = 59.25	D = 48.65	D = 51.74	D = 40.07
UDEDM	u = 1.76	u = 1.70	u = 1.41	u = 1.45
	D = 59.25	D = 48.65	D = 51.74	D = 40.07

provides all the calculated crystallite parameters of Mg(OH)₂ using the Williamson–Hall method, including average size, strain, lattice stress, and energy density. From the data comparison in Table 3, it can be observed that with the increase in reaction temperature, the crystallite parameters, including average size, strain, lattice stress, and energy density, showed a gradually increasing trend.

The crystallite size was mainly determined by the relative speed of the nucleation rate and growth rate of crystal. When the nucleation rate was high, more crystal nuclei were formed, resulting in an increase in crystal numbers and a smaller size. If the growth rate is fast, individual crystals may grow rapidly, resulting in a larger crystallite size. As the temperature increased, the solubility of Mg(OH)₂ increased, and the dissolution of small crystals caused the disappearance of crystal nuclei, which was equivalent to reducing the nucleation rate. With the temperature increasing, the diffusion rate of ions in the solution increased, thereby accelerating the growth rate of crystals and increasing their size.

3.2. Temperature-Dependent Synthesis Analysis of Aragonite

Figure 10 shows the X-ray diffractograms of aragonite prepared at different reaction temperatures of 60, 70, 80, and 90 °C. The polymorphic ratio of aragonite and calcite was evaluated using the following equation [32]:

$${\mathrm{F}}_{\mathrm{a}}={\displaystyle \frac{(I_{111}+I_{221})}{(I_{111}+I_{221}+0.5\times I_{104})}}\times 100$$

(13)

where Fa denotes the calculated fractions (wt.%) of aragonite and I₁₁₁ and I₂₂₁ denote the intensities of X-ray diffraction peaks (26.2° and 45.8°) characteristic of the aragonite crystal faces (111) and (221). I₁₀₄ denotes the intensity of the X-ray diffraction peaks (29.4°) characteristic of the calcite crystal face (104).

The yields and aragonite ratios of aragonite obtained through the XRD data with different temperatures are shown in Figure 11. As illustrated in the figure, the yields of aragonite remained basically unchanged with the increase in reaction temperature, while the aragonite ratios increased gradually. The reaction temperature played a decisive role in the nucleation and crystal growth rate of aragonite particles, which was favored at higher temperatures [33]. When aragonite formed, it was necessary to form aragonite crystal nuclei first, which required a higher critical nucleation energy. This critical nucleation energy of the aragonite type is higher than that of the calcite type, so the reaction temperature must be increased in order to obtain more aragonite-type nucleation. Raising the temperature can also accelerate various diffusion processes and increase the crystallization rate. Additionally, an increase in temperature can reduce the viscosity of the system, making the supersaturation of the solution uniform, which is beneficial for obtaining crystals with uniform size.

The SEM photographs of aragonite obtained with different reaction temperatures are presented in Figure 12. As depicted in the figure, it exhibited a mixture of rod-shaped aragonite and some small grains at low temperatures (60 and 70 °C). With the temperature increasing (80 °C), the rod gradually became longer and thinner, while the tiny grains disappeared and needle-shaped crystals with a relatively large aspect ratio were observed. As the temperature continued to increase (90 °C), needle-shaped crystals became thicker and shorter, exhibiting a smaller aspect ratio.

The SEM images reveal that the morphology and size of rod-shaped aragonite are significantly influenced by the preparation temperature. Specifically, at lower temperatures (60 °C), the aragonite crystals appear as short, uniform needles with a relatively narrow size distribution. As the temperature increases to 70 °C and 80 °C, the needles become longer and more developed, with a more pronounced acicular structure. However, at the highest temperature (90 °C), the crystals show signs of aggregation and possibly thicker needles. This suggests that temperature plays a crucial role in the crystallization kinetics of aragonite, affecting both the growth rate and the final crystal habit. Lower temperatures favor the formation of smaller, more uniform crystals, while higher temperatures promote faster growth and potential coalescence.

Similarly, the Williamson–Hall method was applied for the determination of crystallite size of aragonite from the XRD peak broadening analysis. The synthesized aragonite samples have shown an orthorhombic crystalline structure with the values of the lattice constants estimated analogously to the values of ICDD card number (01-071-2392). Lattice parameters such as the lattice constant and unit cell volume were calculated from the Bragg equation and the lattice geometry equations, as presented below.

$${\displaystyle \frac{1}{d_{hkl}^2}}={\displaystyle \frac{h^2}{a^2}}+{\displaystyle \frac{k^2}{b^2}}+{\displaystyle \frac{l^2}{c^2}}$$

(14)

$$\mathrm{V}=abc$$

(15)

The lattice parameters of aragonite synthesized at different temperatures are summarized in

Table 4. The structure parameters of aragonite.

Samples	Lattice Parameters (Å)			V (Å3)
	A	b	c
60 °C	4.9709	7.9905	5.7480	228.31
70 °C	4.9698	7.9840	5.7487	228.10
80 °C	4.9677	7.9817	5.7456	227.82
90 °C	4.9698	7.9887	5.7328	227.61
Reference data	4.9614	7.9671	5.7404	226.91

. From the table, lattice constants a, b, and c were found to be in agreement with the standard reference data.

The crystallite parameters including the crystallite size, strain, stress, and energy density of aragonite synthesized at different temperatures were calculated in the same way as described above. Figure 13, Figure 14 and Figure 15 present the fitting curves of UDM, USDM, and UDEDM, respectively. The Young’s modulus of aragonite was selected as 78.4 GPa [34].

The calculated crystallite parameters including the crystallite size, strain, stress, and energy density of aragonite synthesized at different temperatures are summarized in

Table 5. Calculated crystallite parameters of aragonite.

Williamson–Hall Model	Crystallite Size, D (nm); Strain, ε (N/m2); Stress, σ (MPa); Energy Density, u (kJ/m3);
	90 °C	80 °C	70 °C	60 °C
UDM	ε = 0.00107	ε = 0.00127	ε = 0.00129	ε = 0.00172
	D = 70.03	D = 109.18	D = 83.03	D = 90.04
USDM	σ = 83.88	σ = 99.79	σ = 100.80	σ = 135.00
	D = 70.03	D = 109.18	D = 83.03	D = 90.04
UDEDM	u = 44.88	u = 63.51	u = 64.74	u = 116.28
	D = 70.03	D = 109.18	D = 83.03	D = 90.04

. From the table, it was observed that with the increase in reaction temperature, the crystallite size of aragonite varied from 70.03 to 109.18 nm, and the strain, lattice stress, and energy density showed a gradually decreasing trend. The explanation for this is that the Gibbs free energy required for the nucleation of aragonite crystals was high, and it was more favorable for the formation of aragonite crystals at higher temperatures. Meanwhile, as the temperature increased, the solubility of aragonite decreased, resulting in an increase in aragonite nuclei, which was equivalent to accelerating the nucleation rate, thereby causing a decrease in crystallite size.

The XRD peak broadening analysis using the Williamson–Hall method provided detailed insights and was helpful in determining the strain, stress, and energy density value with a certain approximation. In fact, the use of the full width was limited because it did not account for the whole of a peak profile, which was especially important when broadening was due to dislocations [35]. However, the Williamson–Hall method can provide relatively effective and accurate crystal parameters, as also be proven by several studies [19,36].

3.3. Component and Resource Efficiency Analysis of the Crystallization Product

The synthesized Mg(OH)₂ at 60 °C and aragonite sample in 80 °C were first washed twice with distilled water and calcined at 800 °C and then analyzed using XRF studies to obtain the composition.

Table 6. Chemical composition of the samples studied as oxides (%).

Mg(OH)2		Aragonite
Oxide	Content (%)	Oxide	Content (%)
MgO	99.2826	CaO	98.7940
SiO2	0.2993	SO3	0.4439
CaO	0.1347	Cl	0.3106
SO3	0.1343	SrO	0.1511
MnO2	0.0981	SiO2	0.1461
Fe2O3	0.0252	Cr2O3	0.1250
P2O5	0.0187	K2O	0.0294
MoO3	0.0072

shows the chemical composition of the samples studied as oxides, indicating that samples showed high purity and minute amounts of impurities like SiO₂, Fe₂O₃, and others. The high purity of the samples serves as a prerequisite for their application as high-efficiency additives, while the crystal structure exerts a profound influence on their functional performance. In this study, the synthesized magnesium hydroxide and calcium carbonate samples not only demonstrate exceptional purity levels exceeding 99% and 98.5% respectively, but also exhibit a highly dispersed lamellar configuration and rod-like whisker morphology with significant industrial value. These dual advantages in both purity and crystalline characteristics ensure their superior efficacy as multi-functional additives in flame retardancy, wear resistance, anti-aging, and anti-sedimentation applications. The structural specificity further enhances their economic viability through optimized dispersion efficiency and material durability.

Figure 16 shows the FTIR spectra of Mg(OH)₂ synthesized at 60 °C. The peak at 3699 cm⁻¹ indicated the OH stretching of Mg(OH)₂ crystal structure. A broad peak at around 3420 cm⁻¹ was attributed to asymmetric stretching of O-H. The peaks at around 1488 cm⁻¹ corresponded to CO₃²⁻, which was derived from the adsorption of CO₂. The peak at 1426 cm⁻¹ was due to the bending vibration of the O-H bond and the stretching vibration of Mg-OH. The peaks around 570 cm⁻¹ corresponded to the Mg-O vibrations of Mg(OH)₂ [17,19].

Figure 17 shows the FTIR spectra of aragonite synthesized at 80 °C. The synthesized aragonite nano-whiskers exhibited characteristic peaks at 1789, 1494, 1083, 854, and 713 cm⁻¹, which could be attributed to the functional groups from CaCO₃ [35,37].

This study addresses the critical issue of industrial waste recycling by proposing innovative solutions for the utilization of chemical waste residues. By leveraging purified ash from the calcium carbide industry, it demonstrates a novel approach to converting this industrial waste into highly dispersed magnesium hydroxide and calcium carbonate whiskers, thereby achieving effective resource utilization and advancing sustainable material recovery practices. Furthermore, the manuscript highlights a significant technical challenge: the complex and costly synthesis of highly dispersed magnesium hydroxide particles due to their aggregation tendency. To address this hurdle, the innovative method was introduced to directly synthesize highly dispersed magnesium hydroxide and needle-shaped aragonite crystals from ash, while also providing a foundation for investigating the influence of relevant conditions on crystal formation. This research not only enhances the resource efficiency of industrial waste but also optimizes a promising pathway for overcoming technological limitations in the synthesis of lamellar-like Mg(OH)₂ and calcium carbonate whiskers.

4. Conclusions

This work focused on the preparation of lamellar-like Mg(OH)₂ and aragonite through the wet precipitation carbonization method using purified ash from the calcium carbide industry as a raw material. A detailed investigation of the effects of reaction temperatures on the yields, morphologies, and crystallite parameters (determined using the Williamson–Hall method) was conducted. The results demonstrated that reaction temperature, as a key parameter, significantly influenced the yields, I001/I101 ratio of Mg(OH)₂, aragonite ratio, and morphology of aragonite. Crystallite parameters, including average size, strain, lattice stress, and energy density, were successfully estimated. Importantly, the results demonstrated that the crystallite size of Mg(OH)₂ and aragonite exhibited distinct temperature-dependent variations within ranges of 40.07–59.25 nm and 70.03–109.18 nm, respectively. Intriguingly, the strain, lattice stress, and energy density parameters displayed an inverse correlation with corresponding crystallite dimensions, suggesting a potential relationship between microstructural evolution and thermodynamic conditions during Mg(OH)₂ and calcium carbonate synthesis.