Effect of Fe₂O₃@SiO₂ Core–Shell Nanoparticle Doping Ratio on Color Appearance of Synthetic Opal Films Inspired by Natural Fire Opal

Abstract

Synthetic opal-based photonic materials with tunable optical properties not only exhibit significant application potential but also provide valuable models in terms of understanding color formation mechanisms in natural gemstones. Inspired by natural fire opals containing small amounts of Fe₂O₃ nanoparticle inclusions (0 wt%~0.23 wt%), we fabricated short-range ordered opal films doped with low concentrations (0 wt%~2.00 wt%) of Fe₂O₃@SiO₂ core–shell nanoparticles using a modified vertical deposition method. The Fe₂O₃@SiO₂ nanoparticles were synthesized via a sol–gel process to encapsulate the Fe₂O₃ core with a 10-nm-thick SiO₂ shell, preventing agglomeration and enhancing the chemical stability. Experimental results show that even small amounts of doping significantly affect the reflection peak intensity of the films, leading to notable color appearance changes. Combined with numerical simulations, we attribute this modulation to both light absorption and backward scattering effects introduced by the doped nanoparticles. Moreover, the numerical simulation results for Fe₂O₃ nanoparticles and Fe₂O₃@SiO₂ nanoparticles (with a 10 nm silica shell and similar particle size) show comparable optical properties, suggesting that such inclusions may contribute similarly to the color formation mechanisms in natural fire opals. This work demonstrates that low-concentration Fe₂O₃@SiO₂ NP doping provides an effective strategy to tune the color appearance of opal films, with implications for both structural color material development and gemological research.

1. Introduction

Structural color materials based on opal structures have attracted significant research interest due to their tunable optical properties and broad application potential [1]. These synthetic opal-based materials are currently utilized in ceramic glazes [2,3], wood coatings [4,5], 3D printing [6,7], sensors [8,9], and anti-counterfeiting technologies [10,11]. As research progresses, attention has shifted beyond perfectly periodic structures to amorphous photonic structures with short-range order, valued for their low angular dependence in structural coloration [12,13]. While non-iridescent structural colors offer desirable angle independence, they typically suffer from low saturation and brightness due to incoherent scattering [14]. Incorporating nanoparticle pigments into these assembled structures is an effective approach to address the low saturation and brightness issues inherent in non-iridescent structural color materials [15]. Current research primarily focuses on black pigments (carbon black, iron oxide, melanin, and polydopamine), which absorb scattered light across the visible spectrum, enhancing the color purity and visibility [16,17,18,19]. Beyond the use of black pigments, an alternative doping strategy involves the incorporation of colored nanoparticle pigments [12,20,21]. Unlike black additives that uniformly absorb across the visible spectrum, colored nanoparticle pigments exhibit dual functionality: within their absorption ranges, they act like black additives by suppressing incoherent scattering to enhance structural color saturation, while, in non-absorption wavelengths, they contribute their inherent hues, creating a synergistic effect between structural and chemical coloration [22]. However, this saturation enhancement is not without limitations. Previous studies have shown that pigment doping must be carefully optimized to avoid excessive absorption, which compromises the structural brightness. For example, Lee et al. demonstrated that, while low concentrations of graphene oxide effectively enhanced the color purity, higher loadings led to diminished reflectance and broadened spectral features due to scattering disruption and over-absorption [23]. Similarly, Sai et al. reported that increasing the pigment content in multilayered Bragg reflectors improved the reflectance only up to a threshold (~40 wt%), beyond which the enhancement plateaued or even reversed due to the reduced absorption length and interference breakdown [13]. These findings indicate that structural color saturation can be effectively tuned via the pigment concentration, but within a defined range, limited by optical and material constraints. Despite these constraints, when properly optimized, such pigment-doped structural color systems can achieve optical effects that are difficult to achieve through a single mechanism alone. Such material systems not only exhibit tunable optical properties and broad application potential but are also particularly relevant to gemological research, serving as experimental models enabling an understanding of the color formation mechanisms in natural precious opals.

Precious fire opal, a highly valued gemstone with significant commercial importance, is a typical natural material that exhibits the combined effects of structural coloration and nanoparticle-induced coloration, providing an example for the study of this hybrid color generation mechanism. Fire opal is a distinctive variety of gem-quality opal characterized by its red–orange–yellow intrinsic color (body color). The most valuable subtype of fire opals, known as precious fire opal, exhibits a combination of body color and structural color (play of color). This feature results in distinctive esthetic value and sets it apart from other opals [24]. Previous studies have identified the presence of Fe₂O₃ nanoparticle inclusions in the fire opal structure [25]. These inclusions are suggested to play an important role in influencing the body colors of fire opals, with the iron content in natural fire opals reported to range from 2 ppm to 1648 ppm, corresponding to approximately 0 wt% to 0.23 wt% Fe₂O₃ [26,27]. However, the effect of Fe₂O₃ nanoparticles (Fe₂O₃ NPs) on the final color appearance of fire opals in the presence of structural color remains to be further explored. Studies on other material systems have demonstrated that nanoparticles can affect both the structural color and the overall color appearance of materials [28,29]. Previous work has investigated opal films fully infiltrated with Fe₂O₃ NPs in all porous spaces, achieving high filling fractions and significant shifts in reflection peak positions [30]. However, how variations in the concentration of small amounts of Fe₂O₃ NPs, as observed in natural fire opals, influence the resulting color expression remains to be further investigated. Addressing this question would not only deepen our understanding of the color formation mechanisms in natural fire opals but also provide valuable insights for the design of structural color materials that reflect the unique esthetic characteristics of fire opal. A promising approach to investigate this effect is to synthesize a series of opal-like materials with varying Fe₂O₃ NP doping ratios.

For the synthesis of opals, self-assembly is one of the most recognized methods developed by researchers [31]. The self-assembly process refers to the behavior of nanoparticles achieving an equilibrium-ordered structure governed by the principles of statistical physics, through driving forces such as van der Waals interactions, capillary forces, electrostatic forces, and gravity [32,33,34]. Depending on the dominant driving force in the assembly process, methods for the synthesis of opals can be classified into sedimentation, electrodeposition, horizontal deposition, vertical deposition, physical confinement, and sonication-assisted drying [35]. Among the various self-assembly methods, the vertical deposition method is the most suitable for investigating the factors influencing the color changes of opals under controlled variable conditions, as it can generate highly ordered structures or amorphous photonic structures, with precise control over the thickness (number of deposition layers) [36]. In the vertical deposition method, where a hydrophilic substrate is vertically dipped into a colloidal suspension, a meniscus forms near the contact interface, where a solvent evaporation-induced convective fluid flow draws closely packed microspheres into its top region, resulting in a thin film of ordered stacked spheres [37]. This method not only offers a simple and environmentally friendly preparation process but also allows precise control over the coverage rate and particle ordering of films in a single deposition by adjusting parameters such as the angle of inclination, pressure, temperature, suspension concentration, and solvent volatility [36,38].

Fe₂O₃ NPs have long been recognized as effective inorganic pigments, and their use dates back centuries [39,40]. However, introducing Fe₂O₃ NPs into synthetic opal systems would face several challenges. Firstly, Fe₂O₃ NPs exhibit significant agglomeration tendencies in dispersion systems, which would affect their uniform dispersion during the fabrication process [41,42]. In addition, under high-temperature reduction conditions, Fe₂O₃ NPs transform into Fe₃O₄, causing undesirable dark red chromatic shifts [43]. Furthermore, due to the voids within the opal structure, Fe₂O₃ NPs are prone to reaction and color fading under chemical pollution effects. To address these limitations, surface modification through SiO₂ shell encapsulation is effective in preventing particle aggregation, optimizing the interparticle spacing in the assembled structures, enhancing the chemical stability of the Fe₂O₃ core, and maintaining chromatic integrity in synthetic fire opal systems [40,44]. Therefore, Fe₂O₃ core–SiO₂ shell structure nanoparticles (Fe₂O₃@SiO₂ NPs) are highly suitable as doping pigments for the synthesis of fire opals.

In this study, inspired by Fe₂O₃ NP inclusions in natural fire opals, we synthesized and investigated the influence of the Fe₂O₃@SiO₂ NP doping ratio (0 wt%~2.00 wt%) on the color appearance of short-range ordered opal films. Unlike previous research that focused on the reflection properties of synthetic opals with Fe₂O₃ NPs completely infiltrated throughout all porous spaces, our work examined the color effects under low doping ratios with varying concentrations. Monodisperse SiO₂ nanoparticles (SiO₂ NPs) and Fe₂O₃@SiO₂ NPs with uniform dimensions were synthesized via a sol–gel method based on silane hydrolysis [45]. Using a modified vertical deposition self-assembly technique, short-range ordered opal films were fabricated under controlled conditions. We studied the correlations and underlying mechanisms between the doping ratios and color appearance by integrating experimental characterization, theoretical calculations, and numerical simulations. The theoretical calculations established the correlation between the reflection peak positions and close-packed crystal planes. The numerical simulations determined the optical properties of the Fe₂O₃ NPs and Fe₂O₃@SiO₂ NPs and the multiple scattering characteristics of the SiO₂ NPs. Our findings reveal that both the absorption and backscattering capabilities of Fe₂O₃@SiO₂ NPs affect the opal film’s color performance. In addition, the numerical simulation results indicate that a 10-nm-thick SiO₂ shell coating slightly enhances the light-modulating properties of Fe₂O₃ NPs while preserving their intrinsic optical characteristics [12], allowing the doping effects of Fe₂O₃@SiO₂ NPs to approximate those of Fe₂O₃ NPs. This work not only provides insights into the design of nanoparticle-doped structural color materials with natural opal-like optical properties but also contributes to the theoretical understanding of the optical mechanisms in natural fire opals through controlled synthesis approaches.

2. Materials and Methods

2.1. Materials

All chemicals for our synthesis experiments were analytical-grade reagents and used as received, without further purification. Tetraethyl orthosilicate (TEOS) was purchased from Anhui Senrise Technology Co., Ltd. (Anqing, China). Ammonia hydroxide (NH₄OH, 35%), ethyl alcohol (EtOH, 99%), and polyvinylpyrrolidone (PVP) were purchased from Xilong Scientific Co., Ltd. (Chengdu, China). Fe₂O₃ NPs were purchased from Shanghai Macklin Biochemical Co., Ltd. (Shanghai, China). Hydrophilic glass slides were purchased from Haimen Changlong Instrument Co., Ltd. (Nantong, China).

2.2. Synthesis Process of Samples

2.2.1. Synthesis of Fe₂O₃@SiO₂ NPs

The core–shell structure Fe₂O₃@SiO₂ NPs were obtained by coating the SiO₂ shell on surface-modified Fe₂O₃ NPs based on the sol–gel method, referring to previous studies [40,43]. Firstly, Fe₂O₃ NPs were functionalized with PVP and stirred for 12 h at 25 °C in water before being collected (Figure 1a—①, ②). Then, 2.5 mL of NH₄OH was added to the EtOH dispersion of PVP-modified Fe₂O₃ NPs (100 mL). Subsequently, TEOS (2.5 mL) was injected into the mixture at a rate of 25 µL/min (Figure 1a—③). The reaction mixture was stirred for 3 h at 25 °C. Fe₂O₃@SiO₂ NPs were then collected by a centrifuge at 6000 rpm for 1 h, washed repeatedly with EtOH, and redispersed in EtOH.

2.2.2. Synthesis of SiO₂ NPs

SiO₂ NPs were also synthesized based on a sol–gel method [46]. For this experiment, we kept the volume ratio of NH₄OH, TEOS, and water at 8:6:3, while the size of the SiO₂ NPs was controlled by the volume of EtOH (Figure 1a—④). Firstly, anhydrous ethanol, aqueous ammonia, and DI water were mixed with vigorous stirring in a flat-bottomed flask at 60 °C in a water bath. TEOS was then added to the solution under continuous stirring for 3 h, with the volume of TEOS to EtOH at a ratio of 1:12 (i.e., V_TEOS:V_EtOH = 1:12). The SiO₂ NPs were then collected through centrifugation and rinsed with anhydrous ethanol. Finally, the resulting products were dispersed in EtOH at 5.00 wt% and prepared for the fabrication of opal films.

2.2.3. Fabrication of Opal Films

Opal films with or without Fe₂O₃@SiO₂ NPs were fabricated using a modified vertical deposition method, following previous studies [35,37]. Compared with other commonly used self-assembly techniques for the fabrication of long-range ordered structures and amorphous photonic structures—such as drop casting [47], spray coating [48], electrophoretic deposition [49], spin coating [50], and microfluidic fabrication [51]—vertical deposition offers several key advantages. These include a controllable film thickness, high reproducibility due to a steady solvent evaporation rate, and good compatibility with a wide range of nanoparticle systems. These features make it especially advantageous for experiments requiring systematic control of the doping variables while maintaining consistent structural parameters. A suspension with different weight percentages of SiO₂ NPs and Fe₂O₃@SiO₂ NPs was introduced into a glass container equipped with a conduit at the bottom, which was linked to a peristaltic pump through rubber tubing to control the dropping velocity of the liquid surface (Figure 1b—⑤). The flow rate of the pump was set to 3.5 mL/min, resulting in a liquid drawing rate of 16 μm/s on the glass slide substrate. The bottom of the container was heated by a heating platform, maintaining a constant temperature of 50 °C. A clean glass microslide was used as a deposit substrate. The glass substrates were immersed over inclined surfaces at a 75° angle in the colloidal suspension using an adjustable fixture (Figure 1b—⑥). These assembly parameters (75° angle and 50 °C temperature) were selected based on the ranges explored in previous studies [36] and experimentally validated to achieve an optimal balance between film coverage and flatness, ensuring high-quality opal films for our investigation. The opal film thickness was controlled by performing 5 deposition cycles in this experiment. After the deposition, the samples were dried at 80 °C in an oven for 12 h. This moderate-temperature treatment ensured complete solvent removal and improved both the substrate–film attachment and mechanical stability through enhanced van der Waals interactions between nanoparticles, while avoiding higher-temperature structural modifications that could alter the original colloidal arrangement and optical properties under investigation.

2.3. Characterization Method

The morphologies of the SiO₂ NPs and Fe₂O₃@SiO₂ NPs were characterized by scanning electron microscopy (SEM, ZEISS GeminiSEM 300, Zeiss GmbH, Oberkochen, Germany). The size distribution of the nanoparticles was measured and analyzed using the ImageJ software (version 1.54f). The core–shell structure of the Fe₂O₃@SiO₂ NPs was confirmed by high-resolution transmission electron microscopy (TEM, FEI Talos F200S, Thermo Fisher Scientific, Hillsboro, OR, USA), which was integrated with energy-dispersive X-ray spectroscopy (EDS). The samples for TEM analysis were prepared by drop-casting a dilute solution of the Fe₂O₃@SiO₂ NPs onto ultrathin, C-coated copper grids. The crystal structure of the nanoparticles was analyzed using X-ray diffraction (XRD, Rigaku SmartLab SE, Tokyo, Japan) with a Cu target at a generator voltage of 40 kV, a generator current of 30 mA, and a scanning rate of 0.1 °/min. The surface composition of the Fe₂O₃@SiO₂ NPs was characterized by X-ray photoelectron spectroscopy (XPS, Thermo Scientific K-Alpha, Waltham, MA, USA). The reflectance spectra were measured by ultraviolet–visible spectroscopy (UV–Vis, Skyray Gem UV-100, Skyray Instrument Co., Ltd., Kunshan, China) from 300 to 800 nm. The incident light was perpendicular to the opal film surface, and the diameter of the light spot was 5 mm.

2.4. Numerical Simulation

In this work, the optical properties of a single Fe₂O₃ nanoparticle and a single Fe₂O₃@SiO₂ nanoparticle were numerically simulated using PyMieLab v1.0 (https://gitlab.com/Climb12/pymielab, accessed on 24 March 2025), an open-source software program based on Mie theory, used for the calculation of the light scattering and absorption of spherical particles [52]. This software provides a comprehensive database of particle refractive indices and a reliable platform for optical property calculations, enabling accurate simulations of light–matter interactions in single-nanoparticle systems. The refractive indices of the SiO₂ NPs and Fe₂O₃ NPs used in the simulation were obtained from Gao et al. [53] and Querry [54], respectively. Additionally, the multiple scattering of SiO₂ NPs was simulated using the polydisperse distributions mode of the open-source software Mie Simulator GUI v1.3 (https://github.com/VirtualPhotonics/MieSimulatorGUI, accessed on 24 November 2024), another open-source tool based on the Lorentz–Mie solution with the BHMIE code. The simulation was performed for 100 spherical SiO₂ NPs with a packing fraction of 74%, which represents the typical face-centered cubic (FCC) packing structure of opal films.

3. Results and Discussion

3.1. Characterization of Nanoparticles for Opal Film Fabrication

As expected, the sol–gel method produced well-dispersed SiO₂ and Fe₂O₃@SiO₂ NPs, demonstrating the positive effects of silica coating in terms of uniform doping. This effect was attributed to the surface chemistry properties of the SiO₂ shells and SiO₂ NPs [55]. Visual observation confirmed that the colloidal dispersions of Fe₂O₃@SiO₂ NPs, SiO₂ NPs, and their mixtures remained sufficiently stable without visible precipitation for 3 h (longer than the duration of the self-assembly experiments) at room temperature (Figure 2a—①, 2b—①; Figure 2c). The SEM analysis showed SiO₂ NPs with a uniform spherical morphology, with an average diameter of 273 ± 26 nm (Figure 2a—②, ③). After the coating process, the Fe₂O₃@SiO₂ NPs showed good monodispersity and a slight increase in particle size compared to the Fe₂O₃ NPs, with a mean diameter of 225 ± 55 nm (Figure 2b—②, ③). While the majority of the coated particles were monodispersed and spherical with similar dimensions, a minor fraction (2.5%) presented as near-spherical structures with larger diameters of approximately 500 nm. This size variation and large standard deviation likely resulted from the aggregation of the Fe₂O₃ NPs during the coating process, leading to the formation of larger particles and a broader size distribution.

To verify the successful formation of the core–shell structure, we characterized the detailed structure of the Fe₂O₃@SiO₂ NPs using TEM. Before the SiO₂ shell coating experiment, SEM images revealed that the Fe₂O₃ core exhibited a near-spherical particle shape, as shown in Figure 3a. The TEM images clearly showed a distinct core–shell structure (Figure 3b–d), where the crystalline Fe₂O₃ core with well-ordered lattice fringes was encapsulated in a 10-nm-thick amorphous silica shell. The high-resolution TEM image of the core–shell interface region (Figure 3d) reveals clear lattice fringes in the core, with a measured d-spacing of 0.13 nm, corresponding to the (1,0,10) lattice plane of α-Fe₂O₃. The two-dimensional Fast Fourier Transform patterns (2D-FFT) obtained from the Fe₂O₃ core (Region ③ marked by red dashed line in Figure 3d, shown in Figure 3e) and from the SiO₂ shell (Region ④ marked by yellow dashed line in Figure 3d, shown in Figure 3f) further confirmed the crystalline characteristics of the Fe₂O₃ core and the amorphous phase of the SiO₂ shell, respectively.

To further confirm the core–shell structure, EDS elemental mapping was performed (Figure 4). The elemental mapping clearly visualized the spatial distribution of constituent elements, with Fe signals (Figure 4b) precisely confined to the core region, exhibiting a well-defined spherical distribution that corresponded to the Fe₂O₃ core. In contrast, both Si (Figure 4c) and O (Figure 4d) signals extended uniformly throughout the entire particle, with a noticeable enhancement in the signal intensity in the shell region. This distribution pattern provides conclusive evidence of the successful formation of the Fe₂O₃@SiO₂ core–shell structure, with the complete encapsulation of the Fe₂O₃ core by the SiO₂ shell, consistent with the TEM observations.

The crystal structure and phase composition of the samples were investigated by XRD analysis (Figure 5a). The sharp diffraction peaks of the Fe₂O₃ NPs (Figure 5a—①) matched well with the standard α-Fe₂O₃ phase (PDF#98-000-0240), which belongs to the hexagonal crystal system with space group R-3c (167). This good agreement indicates the high phase purity of the sample. The broad peak centered at around 2θ = 15°~25° in Figure 5a—② corresponded to amorphous SiO₂. After core–shell formation, the Fe₂O₃@SiO₂ NPs exhibited the characteristic peaks of both the α-Fe₂O₃ and SiO₂ phases (Figure 5a—③), showing the superposition of the sharp diffraction peaks from crystalline α-Fe₂O₃ and the broad peak from amorphous SiO₂. The presence of only these two phases indicates that the SiO₂ was merely coated on the surfaces of the α-Fe₂O₃ NPs, without forming any new phases. This confirms the successful synthesis of the intended core–shell structure. The XPS spectrum analysis (Figure 5b) revealed no Fe₂O₃-related peaks on the surface, confirming the complete encapsulation of the nanoparticles and validating the successful formation of the core–shell structure through surface chemical composition analysis.

These results demonstrate that the Fe₂O₃ NPs were completely encapsulated in the SiO₂ shell through the sol–gel method, forming a dense and non-porous coating with a uniform thickness. The SiO₂ shell in this structure effectively protects the Fe₂O₃ core and enables the uniform dispersion of the nanoparticles by preventing agglomeration and providing compatible surface chemistry with the opal matrix.

3.2. Characterization of Opal Films

Figure 6 shows the structural features of the opal films assembled with pure SiO₂ NPs (Figure 6a–c) and the mixture of SiO₂ NPs and Fe₂O₃@SiO₂ NPs (Figure 6d–f). The self-assembly process resulted in opal films with a uniform thickness, exhibiting distinct structural colors under normal-incidence sunlight illumination (Figure 6a,d). The undoped opal film exhibited a yellow–orange structural color in the central region and a pink–red body color in the edge region (Figure 6a). As shown in Figure 6b,e, the SiO₂ NPs exhibited a hexagonal close-packed arrangement in localized areas, revealing their dense packing behavior in the face-centered cubic (FCC) structure or hexagonal closed packed (HCP) structure. The corresponding 2D-FFT images (Figure 6c) present discrete concentric circle patterns, providing firm evidence of the isotropic and short-range order of the opal films [56]. After mixing with Fe₂O₃@SiO₂ NPs (1.00 wt%), the doped film maintained its structural integrity while exhibiting a modified color appearance (Figure 6d,e). The 2D-FFT pattern (Figure 6f) remained unchanged, demonstrating that the opal film maintained the periodic structure of the colloidal crystal at the low doping ratio of Fe₂O₃@SiO₂ NPs.

3.3. Color Effects of Fe₂O₃@SiO₂ NP Doping Ratio

The variation in the Fe₂O₃@SiO₂ NP doping concentration led to clear color evolution in the visual appearance of the opal films (Figure 7a). As the doping ratio increased from 0 wt% to 2.00 wt%, the films exhibited a gradual structural color transition. This color evolution was quantitatively analyzed through reflection spectroscopy (Figure 7b). The reflection spectrum of the undoped film showed dual peaks, with a dominant peak at 390.5 nm and a secondary peak at 651.4 nm. Previous studies have reported similar double reflection peaks in opals as exhibited by our samples, attributing them to distinct Bragg reflections originating from different crystallographic planes within the close-packed structure [3]. With increasing Fe₂O₃@SiO₂ NP content up to 2.00 wt%, the reflectance intensity at 390.5 nm decreased consistently from 17.6% to 8.0%. At 651.4 nm, the reflectance intensity exhibited a more complex trend: it first decreased from 13.6% to 11.5% as the doping ratio increased from 0% to 0.5% and then returned to the same reflectance intensity of 11.5% at a 1% doping concentration, and it finally increased to 12.8% at a 2% doping concentration. The overall downward trend in the reflectance intensity from a 0% to 0.5% doping ratio, followed by an identical reflectance value at a 1% concentration, suggests that the minimum reflectance intensity likely occurred at an approximately 0.75% doping ratio.

The color coordinates derived from the reflection spectra provided a visual representation of the color evolution in the CIE 1931 chromaticity space (Figure 7c). The significant shift in the chromaticity coordinates with increasing doping concentrations demonstrates that the precise control of the Fe₂O₃@SiO₂ NP concentration could effectively modulate the optical reflection properties of opal films. To quantitatively assess the significance of these color shifts, we calculated the total color difference (ΔE*) in the CIELAB color space (see Supplementary Information for calculation details).

The ΔE* calculations reveal substantial color shifts with Fe₂O₃@SiO₂ NP doping ratio variation: from undoped 0 wt% to 0.35 wt%, ΔE* = 19.47; from 0.35 wt% to 0.50 wt%, ΔE* = 6.67; from 0.50 wt% to 1.00 wt%, ΔE* = 3.85; from 1.00 wt% to 1.40 wt%, ΔE* = 3.81; and from 1.40 wt% to 2.00 wt%, ΔE* = 27.10. According to established color difference interpretation standards [57], ΔE* values between 3.5 and 5 represent noticeable color differences, while values above 5.0 indicate that observers perceive two distinctly different colors. The cumulative color shift from undoped to 2.00 wt% Fe₂O₃@SiO₂ NPs is remarkably large (ΔE* = 52.79), demonstrating the significant range of color tunability achievable through precise control of the Fe₂O₃@SiO₂ NP concentration. This significant chromaticity shift demonstrates that Fe₂O₃@SiO₂ NPs can effectively modulate the optical reflection properties of opal films. The color shifts could be further enhanced by optimizing the size distribution of SiO₂ nanoparticles to better align with the Fe₂O₃@SiO₂ NPs’ optical properties, exploring core–shell nanoparticles with higher refractive index contrast, or investigating core materials with stronger selective absorption characteristics.

The Bragg–Snell equation is an effective formula for the prediction of the reflection peak positions of opals (Equation (1)). This theoretical framework provides reliable predictions that show excellent agreement with experimental measurements [58]. While traditionally applied to perfectly periodic structures, research has demonstrated that the Bragg–Snell equation maintains validity for systems with short-range order but limited long-range periodicity, like our Fe₂O₃@SiO₂ NP-doped opal structures. As Ono’s work showed [3], even in quasi-ordered silica arrays with significant aperiodicity, the values calculated using this approach can correlate strongly with experimental measurements (R² ≈ 0.99). This applicability stems from the coherent scattering within local ordered domains, primarily from planes with the highest packing density, albeit with characteristic effects like peak broadening and reduced angular dependence compared to perfect crystals.

To comprehend the underlying mechanism, we applied the Bragg–Snell equation to calculate the theoretical positions of the reflection peaks in the opal films and determine the optical characteristics of the nanoparticles embedded within these opal films. Within this theoretical framework, we utilized the Bragg–Snell law to determine the corresponding crystal planes responsible for each reflection peak. This approach enabled us to establish a direct correlation between the structural parameters and optical properties.

The position of the reflection peak (λ) for a close-packed plane with Miller indices (hkl) can be determined using the Bragg–Snell law [59]:

$${\mathrm{m}\mathrm{\lambda }}_{\mathrm{peak}}=2{\mathrm{d}}_{\left(\mathrm{hkl}\right)}\sqrt{{\mathrm{n}}_{\mathrm{ave}}^2-{\sin }^2\mathrm{\theta }}$$

(1)

where d_(h,k,l) is the interplanar distance of the close-packing plane (hkl), m is the order of the Bragg reflection, n_ave denotes the average refractive index of the opal film, and θ is the angle of observation measured relative to the normal of the reflecting surface, which is 0° in this research.

n_ave is determined using the following equation:

$${\mathrm{n}}_{\mathrm{ave}=}=\sqrt{{\mathrm{f}}_{{\mathrm{SiO}}_2}{\mathrm{n}}_{{\mathrm{SiO}}_2}^2+{\mathrm{f}}_{\mathrm{air}}{\mathrm{n}}_{\mathrm{air}}^2}$$

(2)

where ${\mathrm{f}}_{{\mathrm{SiO}}_2}$ is the volume fraction of SiO₂, ${\mathrm{f}}_{\mathrm{air}}$ is the volume fraction of air, ${\mathrm{n}}_{{\mathrm{SiO}}_2}$ is the refractive index of SiO₂, and ${\mathrm{n}}_{\mathrm{air}}$ is the refractive index of air.

The interplanar distance d_(hkl) of the FCC close-packing structure can be calculated by the following equation:

$${\mathrm{d}}_{\left(\mathrm{hkl}\right)}={\displaystyle \frac{\mathrm{D}\sqrt{2}}{\sqrt{{\mathrm{h}}^2+{\mathrm{k}}^2+{\mathrm{l}}^2}}}$$

(3)

where D is the diameter of the SiO₂ nanoparticle.

The interplanar distance d_(hkl) of the HCP close-packing structure can be calculated by the following equation:

$${\mathrm{d}}_{\left(\mathrm{hkl}\right)}={\displaystyle \frac{1}{\sqrt{\frac{4}{3}\frac{{\mathrm{h}}^2+\mathrm{hk}+{\mathrm{k}}^2}{{\mathrm{a}}^2}+{\left(\frac{\mathrm{l}}{\mathrm{c}}\right)}^2}}}$$

(4)

where a and c are the lattice parameters, with a = D and c = $2\sqrt{2/3}$D for ideal HCP-packed SiO₂ NPs of diameter D.

Based on the Bragg–Snell law calculations for SiO₂ spheres (273 ± 26 nm) in close-packing opal films in

Table 1. Theoretical ranges and main positions of reflection peaks of SiO₂ opal films.

Close-Packing Plane (hkl)	1st-Order Diffraction Peak Range (nm)	Main 1st-Order Diffraction Peak Position (nm)	2nd-Order Diffraction Peak Range (nm)	Main 2nd-Order Diffraction Peak Position (nm)
FCC (111)	588.9~712.9	650.9	294.4~356.4	325.4
FCC (100)	1020.0~1234.7	1127.4	509.9~617.4	563.7
FCC (110)	721.2~873.1	797.2	360.6~436.5	398.6
HCP (001)	1177.8~1452.7	1301.8	588.9~712.9	650.9
HCP (100)	624.6~756.1	690.4	312.3~378.1	345.2
HCP (101)	551.8~668.0	609.9	275.9~334.0	305.0
HCP (110)	360.6~436.5	398.6	180.3~218.3	199.3
HCP (111)	344.8~417.4	381.1	172.4~208.7	190.6

SiO₂ sphere diameter D = 273 ± 26 nm; volume fraction of SiO₂ ${\mathrm{f}}_{{\mathrm{SiO}}_2}$ = 74%.

, the reflection peaks at 390.5 nm can be attributed to the second-order Bragg diffractions from the (110) close-packing planes in the FCC structure (2nd-(110)-FCC) or the first-order Bragg diffractions from the (110) close-packing planes in the HCP structure (1st-(110)-HCP). Moreover the reflection peak at 651.4 nm can be attributed to the first-order Bragg diffractions from the (111) close-packing planes in the FCC structure (1st-(111)-FCC) or the second-order Bragg diffractions from the (001) close-packing planes in the HCP structure (2nd-(001)-HCP). At first, the 2nd-(110)-FCC (or 1st-(110)-HCP) exhibits a higher intensity than the 1st-(111)-FCC (or 2nd-(001)-HCP). With increasing Fe₂O₃@SiO₂ NP doping ratios, the 2nd-(110)-FCC (or 1st-(110)-HCP) decreases continuously, while the reflection intensity of the 1st-(111)-FCC (or 2nd-(001)-HCP) shows minimal variation, with an initial decrease followed by an increase. Figure 6c,f demonstrate that the opal film maintains its short-range order structure under low doping concentrations of similarly sized Fe₂O₃@SiO₂ NPs; these intensity variations likely originate from the optical properties of the incorporated Fe₂O₃@SiO₂ NPs, rather than structural changes.

While Table 1 presents theoretical estimates based on Bragg diffraction theory, it is important to acknowledge that the Fe₂O₃@SiO₂-doped silica opal films exhibit significant aperiodicity, as is evident in the SEM images. In such quasi-ordered structures, Bragg diffraction theory remains applicable primarily to local domains with preserved short-range order. The SEM images reveal hexagonal close-packed arrangements within these local domains, which correspond to planes with the highest packing density. These domains support coherent scattering despite the absence of long-range periodicity. The experimental full width at half-maximum values, exceeding the theoretical predictions for perfectly crystalline structures, provide direct evidence of this structural aperiodicity. Nevertheless, the good agreement between the measured peak positions and theoretical calculations confirms that the short-range periodicity within local domains remains sufficient to generate the observed structural colors. The broader peaks and reduced angle dependence in our samples compared to long-range ordered structures are characteristic features of such quasi-ordered systems, where local domains rather than long-range order dominate the optical response.

Previous studies have demonstrated that both Bragg diffraction and the absorption/scattering properties of nanoparticles influence the optical behavior of doped opal systems [8]. Given the critical role of scattering in light–matter interactions, which has been widely investigated in core–shell systems across different spectral regions—including the visible to near-infrared (NIR) range [60], the mid-infrared to terahertz (THz) range [61], the broadband optical range for localized plasmons [62], and microwave to infrared [63]—it is important to further examine how scattering contributes to the optical response in our core–shell nanoparticle-doped opal system. Therefore, we compared the optical properties of 225 nm Fe₂O₃ nanoparticles and Fe₂O₃@SiO₂ nanoparticles (with a 10 nm shell thickness) by simulating their absorption, scattering, and extinction spectra (Figure 8a). The spectral features remained unchanged after SiO₂ coating, with only enhanced intensities observed. The SiO₂ shell enhanced the absorption and scattering properties of Fe₂O₃ nanoparticles, leading to an increase of up to 13% in the absorption cross-section and a 15% enhancement in the scattering cross-section. The electric field distributions revealed an enhanced light–matter interaction around the core–shell-structured nanoparticle at 650 nm (Figure 8b,c), especially in the negative direction of incident light (backscattering), as demonstrated by a 15% increase in the scattering cross-section. In the wavelength range of 300 nm~500 nm, the scattering and absorption cross-sections were comparable. However, in the range of 500 nm~800 nm, the scattering effect of Fe₂O₃@SiO₂ nanoparticles became dominant, with the scattering cross-section being up to seven times greater than the absorption cross-section at its maximum difference. This indicates that the SiO₂ shell shows a stronger effect on the scattering properties of the nanoparticles. These results suggest that Fe₂O₃@SiO₂ NPs can effectively replace Fe₂O₃ NPs in practical applications, offering improved processability while maintaining comparable optical performance. The changes in the optical properties of opal thin films caused by the doping of Fe₂O₃@SiO₂ NPs can be considered equivalent to those induced by Fe₂O₃ NPs under the same doping conditions. While our simulations show comparable optical effects between Fe₂O₃ nanoparticles and Fe₂O₃@SiO₂ nanoparticles (with a 10 nm shell thickness), it is important to determine which functionalities can be achieved with core-only particles versus those that require the core–shell structure. The Fe₂O₃ core alone contributes the primary light absorption properties (particularly in the 300 nm~550 nm range), the fundamental color contribution, and the basic modulation of the reflection peak intensities. However, the SiO₂ shell provides several critical advantages: improved colloidal stability, preventing agglomeration during assembly; enhanced chemical stability, protecting against environmental factors and undesired transformations under reducing conditions; and optical property enhancement, with an up to 15% increased scattering cross-section while maintaining the characteristic absorption profile of the Fe₂O₃ nanoparticles. These benefits of the core–shell design offer both practical fabrication advantages and optimized optical performance that would be difficult to achieve with bare Fe₂O₃ NPs.

Combining the above findings, we compared the optical properties (i.e., absorption and backscattering) of the nanoparticles with the reflection peak regions of opal films to gain insights into the color effect mechanism (Figure 9). The key feature of Fe₂O₃@SiO₂ NPs is their strong absorption in the short-wavelength range (300 nm~550 nm), as well as their significant backscattering abilities, with the backscattering cross-section being nearly four times than that of the absorption at 630 nm. The backscattering peak of Fe₂O₃@SiO₂ NPs falls within the reflection peak range of the 1st-(111)-FCC or the 2nd-(001)-HCP of the opal film, although it is slightly offset from the center position at 651.4 nm. While the Fe₂O₃@SiO₂ NPs exhibited absorption and backscattering contributions, the pure SiO₂ NPs showed predominantly scattering behavior. In the reflection peak region of the 2nd-(110)-FCC or the 1st-(110)-HCP, multiple scattering simulations for SiO₂ NPs indicate that the scattering cross-section exceeds the absorption cross-section and decreases with the wavelength. However, the backscattering cross-section constitutes only a small fraction of the total scattering cross-section, indicating the presence of incoherent scattering driven by complex multiple scattering interactions. These findings suggest that the relatively higher reflection peak intensity at 390.5 nm compared to 651.4 nm in undoped opal films may be attributed to multiple contributing factors. These include the 2nd-(110)-FCC or 1st-(110)-HCP, the multiple backscattering of SiO₂ NPs, and the incoherent scattering of SiO₂ NPs. In contrast, the 651.4 nm reflection peak appears to primarily arise from the 1st-(111)-FCC or 2nd-(001)-HCP. As the doping concentration increases, both peaks decrease, with the 390.5 nm peak showing a more significant reduction. This is likely due to the strong absorption of incoherent scattering by Fe₂O₃@SiO₂ NPs [64], which dominates the reflection at this wavelength. The 651.4 nm reflection peak exhibits an initial decrease followed by an increase with higher Fe₂O₃@SiO₂ NP doping concentrations, potentially due to the contribution of Fe₂O₃@SiO₂ nanoparticle backscattering to the peak intensity.

The experimental and simulation results demonstrate how Fe₂O₃@SiO₂ NPs influence the optical properties of synthetic opal films. These core–shell nanoparticles function through dual optical mechanisms, i.e., wavelength-selective absorption and enhanced backscattering, which modify the reflection spectra in a concentration-dependent manner. The reflection peak width characteristics observed in our samples result primarily from the SiO₂ nanoparticle size distribution (273 ± 26 nm), consistent with predictions from the Bragg–Snell equation. The inherent polydispersity creates slight variations in the reflection wavelengths, leading to peak broadening, which corresponds with our structural characterization showing multi-scale ordering. Importantly, our simulation results indicate that Fe₂O₃@SiO₂ NPs exhibit optical properties similar to those of Fe₂O₃ NPs, suggesting that the color mechanisms identified may parallel those in natural fire opals containing Fe₂O₃ nanoparticle inclusions. The Fe₂O₃@SiO₂ NPs provide a tunable parameter for the control of the reflection peak intensities across the visible spectrum, with distinctive effects at different wavelengths, determined by the balance between absorption and backscattering contributions. The interplay between Bragg diffraction from the SiO₂ NP assembly and the localized optical responses (absorption and backscattering) of Fe₂O₃@SiO₂ NP dopants demonstrates that the structural colors of synthetic opal films can be systematically tuned through controlled doping concentrations.

In relation to earlier investigations on doped opal films, our results offer additional insights into how low-concentration Fe₂O₃@SiO₂ NP doping (0~2.00 wt%) modulates the color appearance of opal structures. Unlike previous studies that focused on opal films fully infiltrated with Fe₂O₃ NPs in all porous spaces [30], achieving high filling fractions and significant shifts in the reflection peak positions, our work specifically investigated the effects of small amounts of Fe₂O₃@SiO₂ NP doping on the color appearance of opal films. This concentration range is particularly relevant as it more closely aligns with the iron content reported in natural fire opals (0 wt%~0.23 wt%) [26,27]. Furthermore, while previous research on doped opals has primarily focused on either structural or pigmentary effects separately, our work uniquely combined experimental characterization with theoretical calculations and numerical simulations to elucidate the dual mechanisms (both absorption and backscattering) through which Fe₂O₃@SiO₂ NPs modulate the structural color. By demonstrating that the 10 nm SiO₂ shell coating enhances the optical properties of Fe₂O₃ NPs while maintaining their core characteristics, we provide new insights into how such core–shell structures contribute to color formation in both synthetic systems and potentially in natural gemstones. The similarity in the simulated optical properties of 225 nm Fe₂O₃ NPs and Fe₂O₃@SiO₂ NPs (with a 10 nm shell thickness) suggests that Fe₂O₃ nanoparticle inclusions may contribute similarly to the color formation mechanisms in natural fire opals. This approach bridges the gap between synthetic material design and natural gemology, with implications for both photonic material development and our understanding of the color mechanisms in natural fire opals.

4. Conclusions

In this study, we successfully synthesized Fe₂O₃@SiO₂ NPs by coating a SiO₂ shell on Fe₂O₃ NPs through the sol–gel method. The Fe₂O₃@SiO₂ NPs were applied as pigments to fabricate fire opal films with SiO₂ NPs. A series of opal films with short-range ordered and long-range disordered structures were fabricated with controlled doping ratios to investigate the influence of Fe₂O₃@SiO₂ NPs on color appearance. We observed that the Fe₂O₃@SiO₂ NPs could affect the color appearance by changing the reflection peak intensity within our investigated doping range (0 wt%~2.00 wt%). Specifically, for our synthetic opal films (273 ± 26 nm SiO₂ NPs, short-range ordered), the short-wavelength reflection peak (390.5 nm) decreased continuously with increased doping. Meanwhile, the long-wavelength peak (651.4 nm) followed a non-monotonic trend, decreasing to the minimum intensity at around 0.75% before increasing. This wavelength-selective modulation produced the distinctive color transitions observed in our samples. A comparison with numerical simulation results revealed that the Fe₂O₃@SiO₂ NPs influenced the color appearance through the combined effects of absorption and backscattering. The similarity in the simulated optical properties of Fe₂O₃ NPs and Fe₂O₃@SiO₂ NPs (with a 10 nm silica shell and similar particle sizes) suggests that the same mechanisms and trends may operate in natural fire opals containing Fe₂O₃ NPs. This work demonstrates the potential applications of Fe₂O₃@SiO₂ NPs in the design of synthetic fire opals and other related structural color materials. Additionally, it advances our theoretical understanding of the color formation mechanisms in natural fire opals through a controlled synthesis and characterization approach.

Based on the findings of this study, our future research will focus on several aspects. First, opal films with different SiO₂ particle sizes should be synthesized to investigate how Fe₂O₃@SiO₂ NP doping affects the color properties of opals with varying reflection characteristics, especially when the main reflection peaks do not align with the backscattering peak range of Fe₂O₃@SiO₂ NPs. Additionally, exploring the development of Fe₂O₃@SiO₂ NPs with different core sizes and shell thicknesses could provide more opportunities to tune the optical properties. The influence of the Fe₂O₃@SiO₂ NPs’ morphology on their absorption and scattering properties, and how these factors affect the overall color appearance of synthetic opals, warrants further investigation. Moreover, advanced assembly conditions that offer better control over the opal structure and spatial distribution of Fe₂O₃@SiO₂ NPs could lead to more precise color control. Finally, incorporating other types of core–shell nanoparticles with distinct optical properties may expand the range of achievable colors and functionalities in synthetic opals.