Cr₂Se₃, a transition metal chalcogenide, has attracted attention for its diverse magnetic, electronic, and structural properties [1–3]. For instance, Cr₂Se₃ was previously recognized as a metal with negligible magnetization, that is, an antiferromagnet (AFM). However, recent studies have suggested that it can be a half-metal with fully compensated magnetization [2,3]. Half-metals with AFM characteristics are exceedingly rare, making them highly intriguing for researchers. This aligns with the increasing interest in a new class of AFMs, known as altermagnets [4]. Cr₂Se₃ is a promising candidate for various technological applications, including spintronics, catalysis, and thermoelectrics [2–11].

As the crystal structure directly determines a material’s properties, understanding the impact of the synthesis conditions, defects, and dopants on its crystalline structure is crucial for optimizing its performance and enabling targeted property tuning [12]. The crystal structure is characterized by the lattice symmetry, lattice parameters, atomic types and positions, and site occupancies. Powder X-ray diffraction (XRD) is an indispensable tool that provides precise and detailed information on these attributes [13].

In this study, we investigated the crystalline structure of Cr₂Se₃ using both experimental and simulated XRD patterns. The experimental samples include chemical vapor deposition (CVD)-grown Cr₂Se₃ on SiO₂ and highly oriented pyrolytic graphite (HOPG) substrates, as well as bulk Cr₂Se₃ grown via chemical vapor transport (CVT). We investigated the influence of the substrate-induced strain, growth temperature, and epitaxial alignment on the observed diffraction peaks. Additionally, we simulated the effects of Cr vacancies, Ti doping at distinct Wyckoff sites, and random defect incorporation to understand their impact on lattice contraction or expansion and the corresponding peak shifts. This comprehensive analysis highlights the interplay between synthesis conditions, defects, and doping on the structural stability and tunability of Cr₂Se₃, providing a foundation for optimizing its properties for diverse applications.

At room temperature, XRD patterns were obtained on the CVD/C VT-grown Cr₂Se₃ samples using a Rigaku SmartLab X-ray diffractometer with Cu Kα radiation (λ = 0.15418 nm). Detailed information on the synthesis conditions of the samples can be found in the literature [3].

Structural relaxation was performed using density functional theory (DFT) as implemented in the Vienna Ab initio Simulation Package to ensure that the structure was fully relaxed with high precision [14]. Valence electrons were treated by the Perdew−Burke−Ernzerhof version of the projector augmented wave with a plane-wave basis, setting a cutoff energy of 500 eV [15]. The electronic self-consistent calculations were converged to an energy criterion of 10⁻⁸ eV, and atomic positions were optimized until the forces on all atoms were less than 0.001 eV/Å. The Brillouin zone was sampled using a finely spaced Monkhorst-Pack grid, generated with a k-spacing of 0.030 Å⁻¹, resulting in a 9 × 9 × 2 k-point mesh [16]. All DFT calculations were performed using spin polarization.

Ab initio molecular dynamics simulations were conducted to determine the effect of temperature variations on the structure. Defected Cr₂Se₃ supercells were used with an electronic energy convergence of 10⁻⁴ eV, a 1-fs time step, and a Γ-centered 1 × 1 × 1 k-point mesh. The measured structures were obtained after equilibration for 5 ps in a canonical ensemble with a Nosé-Hoover thermostat [17,18]. The simulated XRD patterns were generated using Pyxtal [19].

3.1. Experimental XRD patterns

XRD analysis was conducted to characterize the Cr₂Se₃ crystals grown under various conditions, including CVD-grown Cr₂Se₃ on SiO₂ and HOPG substrates and CVT-grown bulk Cr₂Se₃, as shown in Fig. 1. Compared with the reference bulk powder diffraction pattern, the primary peak near 2θ = 32.5°, corresponding to the (113) plane, is absent in the CVT-grown sample (synthesized at 950 °C). Instead, a prominent peak near 2θ = 31°, associated with the (006) plane, is observed, indicating preferential growth or alignment along the (001) epitaxial direction due to the thin-film nature of the sample. The CVD-grown sample on SiO₂ (synthesized at 830 °C) exhibits both a minor (006) peak and a prominent (113) peak, consistent with the reference powder pattern [3,5,7,8,10]. However, the (113) peak notably broadened and split, likely reflecting the high density of defects in the material. Interestingly, the (113) peak varied depending on the growth method, appearing distinctly only in CVD-grown Cr₂Se₃. For Cr₂Se₃ grown on the HOPG substrate, the XRD pattern exhibits a leftward shift, which may indicate tensile strain in the material. This shift suggests that the lattice mismatch between Cr₂Se₃ and the HOPG substrate induced strain during growth [20].

Figure 1. XRD profile of Cr₂Se₃ flakes grown under different conditions and diffraction planes. (a) XRD patterns of Cr₂Se₃ grown via CVD on SiO2/Si (black) and HOPG (red), CVT-grown bulk Cr₂Se₃ (blue), along with the reference powder diffraction pattern of bulk Cr₂Se₃ (gray). (b) Crystal structure of rhombohedral Cr₂Se₃ with the (003) and (113) diffraction planes highlighted. Cr and Se atoms are color-coded in blue and green, respectively.

3.2. Vacancy effect

Figure 2 shows the simulated powder XRD patterns used to explore the influence of Cr vacancies on the Cr₂Se₃ crystalline structure. The primary and distinct XRD peaks could be indexed to the pristine rhombohedral structure of Cr₂Se₃. The sharp peaks at specific angles denote high crystallinity. Note that the powder diffraction is one-dimensional; therefore, the index has multiplicity and is not determined as one. For instance, the (113) plane has the same spacing d with (2-13), as highlighted in the rhombohedral Cr₂Se₃ crystal structure in Fig. 1. Thus, (2-13) can be indexed to the primary peak of Cr₂Se₃. This peak satisfies Bragg’s rule, and 2dsinθ is an integer multiple (also known as the diffraction series) of the incident wavelength, where 2θ = 32.464°, d_[113] = 2.758 Å; thus, 2dsinθ = 1.54 Å, which corresponds to the wavelength of an X-ray (corresponding to emission from Copper Kα).

Figure 2. Simulated and indexed powder XRD pattern for bulk Cr₂Se₃. The Cr vacancies at three Wyckoff sites are denoted as v-Cr(I), v-Cr(II), and v-Cr(III), respectively. The VESTA data comes from the VESTA powder diffraction module.

The first five peaks in the Cr₂Se₃ XRD pattern correspond to the (006), (113), (116), (300), and (119) planes of Cr₂Se₃. As vacancies were introduced in the Cr(I), Cr(II), and Cr(III) sites in Cr₂Se₃ [corresponding to v-Cr(I), v-Cr(II), and v-Cr(III), respectively], a right shift is observed for all Cr vacancy cases. In this case, the vacancy level was 3.33 % (one Cr vacancy out of 30 total atoms in the pristine unit cell). A rightward peak shift (to a higher angle) with the same index indicates that the system contracts or the lattice constant shrinks, as presented in Table I. This tendency is clearly displayed in the order of Cr(I), Cr(II), and Cr(III). The magnitude of the right shift becomes more pronounced as the angle increases. For instance, for the peak corresponding to (119) [or (2-19), which has the same interplanar distance in Cr₂Se₃] near 55°, the peaks for v-Cr(I), v-Cr(II), and v-Cr(III) are well split and easy to distinguish, providing helpful information for the XRD analysis of the experimental results. The interplanar spacing d_[119] for the pristine structure is 1.645 Å. However, when a Cr vacancy is introduced, d_[119] decreases to 1.609, 1.623, and 1.635 Å for v-Cr(I), v-Cr(II), and v-Cr(III), respectively. The pristine sample (VESTA) in Fig. 2 shows the pattern obtained by the VESTA XRD module (which utilizes RIETAN-FP) [21].

Table I. Lattice constant (a = b, c), magnetization (M), and space group of vacant Cr₂Se₃ and its pristine condition..

	v-Cr(I)	v-Cr(II)	v-Cr(III)	2 × 2 Supercell	Pristine bulk
a = b (Å)	6.224	6.243	6.228	6.230	6.272
c (Å)	16.920	17.103	17.293	17.204	17.384
M(µB/f.u.)	0.11	0.30	1.17	1.25	0
Space group	143	147	147	1	148

3.3. Temperature effect

Crystals produced via CVD or CVT exhibit distinct crystallinities, grain sizes, and defect densities, which are highly dependent on the synthesis temperature and operational conditions. Temperature variations during synthesis influence the growth kinetics, phase formation, and overall structural quality of the crystals. We investigated temperature-dependent changes in the XRD patterns to understand these effects. This analysis revealed how the synthesis temperature affects the lattice parameters, peak intensities, and emergence of secondary phases, providing insights into optimizing the growth conditions for high-quality crystal production.

The simulated XRD pattern at T = 300 K was similar to that of pristine Cr₂Se₃, as shown in Fig. 3. At T = 1,600 K, while the primary peak indexed as (113) remained unchanged, new peaks emerged in the previously almost zero-intensity regions, indicating the formation of a different structural phase. At T = 1,000 and 1,400 K, the primary peaks exhibited a noticeable rightward shift. However, the relative ordering of the primary, secondary, and other peaks was preserved, and no further peak shifts were observed between T = 1,000 and 1,400 K, suggesting stability in the structural phase within this temperature range.

Figure 3. Simulated and indexed powder XRD pattern for bulk Cr₂Se₃ at different temperatures.

Compared to the experimental XRD patterns shown in Fig. 1(a), the change in the primary peaks in the experiment−(113) at T ≈ 1,100 K and (006) at T ≈ 1,200 K−may not result from the temperature but rather from the fundamental differences between the CVT and CVD methods. As mentioned earlier, the CVT-grown sample exhibited a preferential growth direction along (001), which made the (006) peak more prominent than the (113) peak. Interestingly, the material experiences contraction rather than the common thermal expansion, implying an unusual structural response that is potentially driven by phase transitions, internal stresses, or anharmonic lattice dynamics. This atypical behavior highlights the complex interplay between thermal effects and structural stability, warranting further investigation of the underlying mechanisms.

3.4. Doping effect

Doping affects the structure of materials, and its impact can be observed in the XRD patterns. It can change the lattice size, shift or broaden the peaks, and even alter the phase stability. These changes reveal how the dopant influences the material’s structure and properties.

We conducted substitutional Ti doping for Cr at three distinct Wyckoff sites in the structure. Remarkably, the XRD patterns shown in Fig. 4 reveal that the peaks and relative intensities of the prominent peaks remain nearly identical regardless of the specific Wyckoff site for Ti substitution. The primary noticeable effect of doping is a leftward shift of the peaks compared to those of the pristine material, indicative of lattice expansion, as presented in Table II. This shift is particularly prominent near 2θ = 55°, corresponding to the (119) plane, where the interplanar spacing d_[119] increases by approximately 0.01 Å.

Figure 4. Simulated and indexed powder XRD pattern for Ti-doped bulk Cr₂Se₃. The Ti substitutional doping at three Wyckoff sites are denoted as Ti(I):Cr₂Se₃, Ti(II):Cr₂Se₃, and Ti(III):Cr₂Se₃, respectively.

Table II. Lattice constant (a = b, c), magnetization (M), and space group of Ti-doped Cr₂Se₃ and its pristine condition..

	v-Cr(I): Cr2Se3	v-Cr(II): Cr2Se3	v-Cr(III): Cr2Se3	2 × 2 Supercell	Pristine bulk
a = b (Å)	6.286	6.286	6.286	6.274	6.272
c (Å)	17.523	17.526	17.526	17.494	17.384
M(µB/f.u.)	0.32	0.32	0.32	0.41	0
Space group	147	143	143	1	148

This increase in d arises from the Ti doping, likely owing to the larger ionic radius of Ti compared to that of Cr, which introduces subtle changes in the lattice geometry. The consistency in the peak intensities across all Wyckoff sites indicates that the substitution does not disrupt the crystal symmetry or phase stability, preserving the overall structural integrity. These observations suggest that Ti doping effectively modifies the lattice parameters without causing significant distortions, making it a promising method for tuning the material’s properties.

3.5. Random defect effect

Using the supercell approach, we investigated two scenarios: (i) randomly incorporated Cr vacancies and (ii) random Ti substitution. For the supercell cases, the vacancy (Ti doping) level was 3.33 % (4 Cr vacancies or Ti dopants out of 120 total atoms in the pristine supercell), similar to the unit cell case. Introducing random Cr vacancies results in a rightward shift of the XRD peaks, most prominently observed in the peak corresponding to the (119) plane, as shown in Fig. 5. This shift indicates crystal lattice contraction owing to the missing Cr atoms, which causes it to shrink. By contrast, random Ti substitution induces a leftward shift in the peaks, indicating lattice expansion. The interplanar spacing d_[119] decreases by 0.016 Å for the random-Crvacancy case, whereas it increases by 0.007 Å for the Ti-doping case compared to the pristine structure.

Figure 5. Setup for the noise figure measurement of the X-band GaN LNA, including test instruments and the X-band GaN LNA MMIC chip.

The magnitude of these shifts correlates with the vacancy or doping level, offering a quantitative measure of the structural impact. Here, we aimed to confirm the general trends associated with random vacancies and doping. Overall, introducing Cr vacancies caused the crystal structure to shrink, resulting in a rightward peak shift, whereas Ti doping led to lattice expansion, as reflected in a leftward shift of the peaks. These opposing effects underscore the distinct influence of Cr vacancies and Ti substitution on the lattice, highlighting the tunability of the material’s structural properties through controlled defect engineering.

In this study, the impact of Cr vacancies, Ti substitution, and temperature on the crystalline structure of Cr₂Se₃ was explored. Cr vacancies caused lattice contraction, producing right shifts, whereas Ti substitution induced lattice expansion, which was observed as left shifts. Additionally, elevated temperatures result in unusual lattice contraction, suggesting complex structural dynamics. These findings highlight the potential of fine-tune Cr₂Se₃ properties through defect engineering, doping, and thermal control, offering key insights for experimental optimization and material design.

This research was supported by Sungkyunkwan University and the BK21 FOUR (Graduate School Innovation), funded by the Ministry of Education (MOE, Korea), the Samsung Science and Technology Foundation (project no. SRFC-MA2102-02), and the National Research Foundation of Korea (NRF, 2023R1A2C2005383). M. Joe was supported by the Basic Science Research Program through the NRF, funded by the MOE (RS-2023-00248011) and the KISTI supercomputing center (Grant KSC-2024-CRE-0312).

The authors declare no conflicts of interest.