Research on the Mechanical and Photoelectric Properties Regulation of the New-Type Ceramic Material Ta₂AlC

Abstract

Ta₂AlC is an emerging ceramic material characterized by its high melting point, high hardness, excellent thermal stability, and superior mechanical properties, which allow for broad application prospects in aerospace and defense fields. This paper investigates the physical mechanisms underlying the modulation of the mechanical and photoelectric properties of Ta₂AlC through doping using the first-principles pseudopotential plane-wave method. We specifically calculated the geometric structure, mechanical properties, electronic structure, Mulliken population analysis, and optical properties of Ta₂AlC doped with V, Ga, or Si. The results indicate that doping induces significant changes in the structural parameters of Ta₂AlC. By applying the Born’s criterion as the standard for mechanical stability, we have calculated that the structures of Ta₂AlC, both before and after doping, are stable. The mechanical property calculations revealed that V and Si doping weaken the material’s resistance to deformation while enhancing its plasticity. In contrast, Ga doping increases the material’s resistance to lateral deformation and brittleness. Doping also increases the anisotropy of Ta₂AlC. Electronic structure calculations confirmed that Ta₂AlC is a conductor with excellent electrical conductivity, which is not diminished by doping. The symmetric distribution of spin-up and spin-down electronic state densities indicates that the Ta₂AlC system remains non-magnetic after doping. The partial density of states diagrams successfully elucidated the influence of dopant atoms on the band structure and electronic state density. Mulliken population analysis revealed that V and Ga doping enhance the covalent interactions between C-Ta and Al-Ta atoms, whereas Si doping weakens these interactions. Optical property calculations showed that V and Si doping significantly enhance the electromagnetic energy storage capacity and dielectric loss of Ta₂AlC, while Ga doping has minimal effect. The reflectivity of doped and undoped Ta₂AlC reaches over 90% in the ultraviolet region, indicating its potential as an anti-ultraviolet coating material. In the visible light region, both doped and undoped Ta₂AlC exhibit a similar metallic gray appearance, suggesting its potential as a temperature control coating material. The light loss of Ta₂AlC is limited to a narrow energy range, indicating that doping does not affect its use as a light storage material. These results demonstrate that different dopants can effectively modulate the mechanical and photoelectric properties of Ta₂AlC.

1. Introduction

With the continuous advancement of technology, the requirements for material properties have become increasingly stringent. Traditional ceramic materials, due to their relatively low strength and toughness, face certain limitations regarding their areas of application. To overcome these shortcomings, a new type of ternary layered ceramic material has emerged, with the general formula Mn+1AXn (where n = 1, 2, 3), commonly referred to as MAX phase ceramic materials [1,2]. In these materials, M represents transition metal elements, including titanium (Ti), vanadium (V), tantalum (Ta), and zirconium (Zr), among others; A denotes elements from group IIIA or ⅣA, such as aluminum (Al), silicon (Si), gallium (Ga), or germanium (Ge); and X is typically the element carbon (C) or nitrogen (N). MAX phase ceramic materials integrate the excellent properties of both metals and ceramics. At room temperature, they exhibit not only the superior electrical and thermal conductivity of metals but also relatively low Vickers microhardness and high values of elastic and shear moduli [3,4,5,6]. These materials can be mechanically processed like metals and maintain good plasticity at elevated temperatures. Moreover, they possess the high yield strength, high melting point, high thermal stability, and good oxidation resistance characteristics of ceramic materials [7,8,9,10,11,12,13,14,15,16,17]. Notably, this new type of ceramic demonstrates excellent strength and a very low friction coefficient at high temperatures, and like graphite, it also has good self-lubricating properties. These attributes render MAX phase ceramic materials a new type of structural and functional integrated ceramic material with broad potential for application.

The properties of MAX phase ceramic materials are highly dependent on their constituent elements. As a typical representative of novel ternary layered MAX phase ceramic materials, Ta₂AlC has attracted considerable attention from researchers due to its unique elemental composition, its potential performance advantages, and the current insufficient understanding of its synthesis–property correlation mechanisms and associated research demands. Therefore, extensive explorations and studies have been conducted on its synthesis techniques and performance characterization, with the aim of further uncovering and optimizing its potential applications. For instance, Jeitschko [18] was the first to discover the ternary layered ceramic Ta₂AlC. To date, the experimental preparation methods for Ta₂AlC materials include hot pressing (HP) and self-propagating high-temperature synthesis (SHS). Each of these methods possesses distinct advantages that render the fabrication of Ta₂AlC materials feasible. Yeh et al. [19] and Tian et al. [20] employed SHS to investigate the influence of Al content on the synthesis of Ta₂AlC. Manoun et al. [21] and Hu et al. [22] synthesized Ta₂AlC via static pressing and analyzed the synthesis and decomposition mechanisms of Ta₂AlC through reaction pathway analysis. Following the successful synthesis of Ta₂AlC, Hu et al. [22] conducted characterization tests on its fundamental physical properties. The test results revealed that the compressive strength of Ta₂AlC reached 804 MPa, a figure that underscores its remarkable performance as a damage-resistant material. Regarding electrical conductivity, as the temperature increased from 10 K to 300 K, the electrical conductivity of Ta₂AlC correspondingly decreased from 37.8 × 10⁶ W⁻¹m⁻¹ to 3.89 × 10⁶ W⁻¹m⁻¹. Notably, when the temperature exceeded 70 K, the resistivity exhibited linear growth, indicating that Ta₂AlC displayed typical metallic behavior. Additionally, within the temperature range from room temperature to 1100 °C, the thermal expansion coefficient of the material was 8.0 × 10⁻⁶ K⁻¹, and from room temperature to 1227 °C, the thermal conductivity gradually decreased from 28.4 Wm⁻¹K⁻¹ to 25.5 Wm⁻¹K⁻¹. These data collectively confirm that Ta₂AlC is an excellent conductor of heat and electricity and possesses superior mechanical properties.

Moreover, theoretical calculations have also played a significant role in the study of the ternary layered ceramic material Ta₂AlC. For instance, Lin et al. [23] used density functional theory (DFT) to calculate the lattice parameters of Ta₂AlC, which were in agreement with those measured by Jeitschko [13]. Qian et al. [24] employed first-principles calculations based on DFT to investigate the microscopic structure and electronic properties of Ta₂AlC. Sun et al. [25] calculated the theoretical density of Ta₂AlC to be 11.52 g/cm³ and its elastic modulus to be 318.6 GPa using first-principles methods. Music et al. [26] used ab initio calculations to study the shear behavior of Ta₂AlC, and the results indicated that the C₄₄ value is independent of the corresponding TaC, with the shear-resistant bands being filled by Ta atoms. Guo et al. [27] utilized DFT to explore the effects of vacancy defects on the structural, electronic, elastic, thermal conductivity, and optical properties of Ta₂AlC. Lv et al. [28] conducted first-principles calculations on the electronic structure and optical properties of Ta₂AlC, and the results suggested that Ta₂AlC can be used as a temperature control coating material and an anti-ultraviolet coating material, with potential applications in the fields of aerospace and defense technologies.

In summary, research on Ta₂AlC has primarily focused on its experimental synthesis and physical property testing, as well as theoretical calculations of its bulk microscopic structure, electronic properties, and optical characteristics. Doping is a crucial method for modulating the electronic structure and optical properties of materials. Therefore, theoretical studies on doping as a means of modifying the ternary layered ceramic material Ta₂AlC hold noteworthy scientific guiding significance. However, studies on the doping modification of Ta₂AlC are relatively rare. Thus, this paper takes Ta₂AlC as the matrix and selects the elements V, Ga, and Si as dopants. Utilizing the first-principles pseudopotential plane-wave method, the study investigates the mechanical properties, electronic structure, and optical properties of doped Ta₂AlC. It preliminarily reveals the physical mechanisms by which doping modulates the mechanical and photoelectric properties of Ta₂AlC, providing a theoretical reference for experimental research on Ta₂AlC materials.

2. Model and Method

The crystal structure of Ta₂AlC belongs to the hexagonal crystal system with the space group P63/mmc (#194), and the lattice constants are a = b = 0.3079 nm and c = 1.3854 nm [29]. The coordinates of the non-equivalent atoms are as follows: Ta (1/3, 2/3, 1/12), Al (1/3, 2/3, 3/4), and C (0.0, 0.0, 0.0). The unit cell contains a total of 8 atoms, comprising 4 Ta atoms, 2 Al atoms, and 2 C atoms. In this study, a 2 × 2 × 2 supercell of Ta₂AlC was selected for calculations, consisting of 64 atoms in total. Based on the 2 × 2 × 2 Ta₂AlC supercell, substitutional doping was performed using two neighboring atoms from the same group as Ta-Al-C (such as V, Ga, and Si). The specific substitution methods were as follows: V replaced Ta, Ga replaced Al, and Si replaced C. The substitutional doping models of Ta₂AlC selected for the calculations are shown in Figure 1.

The computational method employed in this study was the first-principles pseudopotential plane-wave method, with the primary calculations carried out using the Castep 8.0 software package [30]. The interaction between the ionic cores and electrons was treated using the ultrasoft pseudopotential (USPP) [31], while the exchange-correlation energy among electrons was handled using the Perdew–Burke–Ernzerhof (PBE) functional [32] within the generalized gradient approximation (GGA). The plane-wave cutoff energy was set at 300 eV, and the energy convergence criterion was 1.0 × 10⁻⁵ eV/atom. The valence electron configurations selected for the calculations were Ta 5d³6s², Al 3s²3p¹, C 2s²2p², V 3s²3p⁶3d³4s², Ga 3d¹⁰4s²4p¹, and Si 3s²3p², with the remaining electrons treated as core electrons. The Brillouin zone integration adopted the symmetrical special k-point method in the form of a 5 × 5 × 1 Monkhorst-Pack [33] and set 32 × 32 × 144 FFT grid parameters.

The binding energy (E_b) is given by the expression [34]:

E_b = [E_tot (Ta_xA1yCzM_m) − xE(Ta) − yE(Al) − zE(C) − mE(M)]/(x + y + z + m)

(1)

where E_tot (Ta_xA1_yC_zM_m) is the total energy of the doped system, x is the number of Ta atoms in the system, y is the number of Al atoms in the system, z is the number of C atoms in the system, m is the number of dopant atoms M (such as V, Ga, or Si), E(Ta) is the total energy of an isolated Ta atom, E(Al) is the total energy of an isolated Al atom, E(C) is the total energy of an isolated C atom, and E(M) is the total energy of an isolated dopant atom M.

3. Results and Discussion

3.1. Geometric Structure

Changes in the elements and their positions at specific lattice sites within a crystal structure inevitably lead to systematic variations in interatomic bonding patterns. These changes can provide valuable guidance for the optimization and design of material properties. Therefore, the phonon spectrum, structural parameters, and binding energy of Ta₂A1C before and after V, Ga, and Si doping are calculated in this paper, as shown in Figure 2 and

Table 1. Structural parameters and binding energies of doped Ta₂AlC.

Sample	a (nm)	b (nm)	c (nm)	V (nm3)	E (eV)	Eb (eV)
Ta2A1C	0.6309	0.6309	2.7941	0.9633	−7797.3365	−8.3016
V doped Ta2A1C	0.6287	0.6287	2.7849	0.9534	−11,475.9034	−8.2683
Ga doped Ta2A1C	0.6315	0.6315	2.7883	0.9631	−11,789.8840	−8.2742
Si doped Ta2A1C	0.6377	0.6377	2.8050	0.9858	−7696.9951	−8.1058

.

We performed phonon spectrum calculations to evaluate the thermal stability of doped Ta₂AlC. As shown in Figure 2, the phonon spectrum analysis reveals no imaginary frequencies, indicating that both undoped and doped Ta₂AlC are thermally stable.

From Table 1, it can be seen that the lattice constants a and b of the 2 × 2 × 2 Ta₂AlC supercell, after structural optimization, are within a 0.2% error margin of the results reported in the literature [27] (0.6320 nm), and the c/a ratio is within a 1.6% error margin of that reported in the literature [29]. These results indicate that the computational model used in this study can accurately describe the bonding state of Ta₂AlC. Upon doping with V, Ga, and Si, the structural parameters of Ta₂AlC undergo significant changes. The changes in lattice parameters are attributed to the differences in covalent radii of the substituted atoms. For instance, V (0.122 nm) replaces Ta (0.134 nm), Ga (0.126 nm) replaces Al (0.118 nm), and Si (0.111 nm) replaces C (0.077 nm). The data in Table 1 show that the trends in structural parameters of Ta₂AlC after V and Si doping are consistent with the order of atomic sizes. However, after Ga doping, while the trends in lattice constants a and b are consistent with the order of their atomic sizes, the trends in lattice constant c and volume V do not match the order of their atomic sizes. This discrepancy may be due to the fact that along the c-axis direction, whether Ga and Ta can form bonds has a greater impact on the volume than the influence of atomic radii. Lattice defects or structural irregularities due to doping may result in significant changes in the mechanical and optical properties studied below.

The binding energies (E_b) listed in Table 1 for the doped Ta₂AlC systems are all negative, indicating that the structures of all three doped systems are stable. The trend in formation energies is E_b(Ga) < E_b(V) < E_b(Si). From a thermodynamic perspective, the negative values of E_b suggest that the doped systems can be formed, and the Ga-doped system is more likely to form compared to the V- and Si doped systems.

3.2. Mechanical Properties

In this study, the elastic constants of Ta₂AlC were calculated both before and after doping, and the effects of V, Ga, and Si doping on the mechanical properties of Ta₂AlC were investigated.

Table 2. Elastic constants of doped Ta₂AlC.

Sample	C11	C12	C13	C33	C44	C66
Ta2A1C	348.7114	114.0028	128.6486	312.5064	164.5408	118.6462
V doped Ta2A1C	341.0590	114.4546	126.3630	299.7501	163.4924	115.7912
Ga doped Ta2A1C	335.5614	94.7569	118.5429	281.2559	164.4988	121.4161
Si doped Ta2A1C	299.7089	90.5178	121.9969	263.7427	152.3105	102.3365

lists the elastic constants of doped Ta₂AlC.

For the Ta₂AlC crystal with a hexagonal structure, according to the mechanical stability criterion, Born’s criterion [35], the following four conditions (2)–(5) must be simultaneously satisfied.

C₁₁ > C₁₂

(2)

(C₁₁ + 2C₁₂)C₃₃ > 2C₁₃²

(3)

C₄₄ > 0

(4)

C₆₆ > 0

(5)

By processing the elastic constants listed in Table 2, it can be determined that the elastic constants of Ta₂AlC before and after doping with V, Ga, and Si meet the aforementioned four conditions. This indicates that the systems studied in this paper possess mechanical stability. Additionally, it can be observed from Table 2 that, apart from a slight increase in C₁₂ after V doping and a significant increase in C₆₆ after Ga doping, the remaining elastic constants have decreased.

Based on the Voigt–Reuss–Hill method (VRH) [36,37,38], the elastic constants C_ij listed in Table 2 can be used to derive the bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio υ using the following Formulas (6)–(15). The results are presented in

Table 3. Mechanical properties parameters of doped Ta₂AlC.

Sample	B	G	E	υ	B/G
Ta2A1C	194.6353	129.2186	317.4124	0.2282	1.5062
V doped Ta2A1C	190.5174	126.2935	310.3121	0.2285	1.5085
Ga doped Ta2A1C	179.3631	127.7701	309.7579	0.2122	1.4038
Si doped Ta2A1C	170.2374	112.1657	275.9019	0.2299	1.5177

.

B_V = (1/9)[2(C₁₁ + C₁₂) + C₃₃ + 4C₁₃]

(6)

G_V = (1/30)(M + 3C₁₁ − 3C₁₂ + 12C₄₄ + 6C₆₆)

(7)

M = C₁₁ + C₁₂ + 2C₃₃ − 4C₁₃

(8)

C² = (C₁₁ + C₁₂)C₃₃ − 2C₁₃²

(9)

B_R = C²/M

(10)

G_R = 15{(18B_V/C²) + [6/(C₁₁ − C₁₂)] + (6/C₄₄) + (3/C₆₆)}⁻¹

(11)

B = (B_V + B_R)/2

(12)

G = (G_V + G_R)/2

(13)

E = 9BG/(3B + G)

(14)

υ = (3B − 2G)/[2(3B + G)]

(15)

Table 3 lists the mechanical properties parameters of doped Ta₂AlC. As can be seen from Table 3, the Young’s modulus of Ta₂AlC is approximately 317 GPa, which deviates by no more than 2.5% from the result reported by Guo [27] (325 GPa) is larger than that of Ti₂A1C (305 GPa) of the same material type. Due to its high Young’s modulus and shear modulus, Ta₂AlC exhibits exceptional rigidity and resistance to deformation, making it a promising candidate material for manufacturing aerospace engine components and aircraft structural parts. After doping with V and Si, the bulk modulus B, shear modulus G, and Young’s modulus E of Ta₂AlC all decrease, while the Poisson’s ratio υ and the B/G ratio increase. This indicates that the material’s ability to resist deformation is weakened while its plasticity is enhanced after doping with V and Si. In contrast to the situation after doping with V and Si, the Poisson’s ratio υ and the B/G ratio of Ta₂AlC doped with Ga decrease, indicating that the introduction of Ga strengthens the material’s ability to resist lateral deformation and increases its brittleness.

The bond energy plays a regulatory role in lattice distortion, and this in turn significantly affects the plasticity and brittleness of materials. Due to differences in bond energy between the substituted atoms and the original atoms—for instance, V (514 kJ/mol) replacing Ta (782 kJ/mol), Ga (271 kJ/mol) replacing Al (330 kJ/mol), and Si (326 kJ/mol) replacing C (346 kJ/mol)—the plasticity or brittleness of the doped material undergoes changes. When V and Si are introduced as dopants, the lower bond energy of the substituting atoms weakens their ability to suppress lattice distortion caused by atomic size mismatch. This facilitates dislocation motion within the lattice, thereby enhancing the plasticity of Ta₂AlC. Conversely, Ga doping hinders the generation of dislocations in the lattice, leading to the increased brittleness of Ta₂AlC. This is also consistent with the significant increase in C₆₆ after Ga doping shown in Table 2. The main reason for brittleness is the introduction of Ga; whether Ga and Ta can form bonds along the c-axis becomes the main consideration in exploring brittleness. This is the same reason for the change in lattice parameters analyzed earlier.

The arrangement of atoms in a crystal and the different environments in various directions lead to different physical properties in different directions, thus giving rise to anisotropy. Elastic anisotropy is represented by the elastic anisotropy index, which is specifically characterized by the general elastic anisotropy index A^U, the compressional anisotropy percentage A_comp, and the shear anisotropy percentage A_shear. In addition, the shear anisotropy factors (A₁, A₂, and A₃) can be used to indicate the degree of anisotropy of the material on the (001), (010), and (100) planes, respectively. Therefore, based on the data in Table 2 and Table 3, the elastic anisotropy indices and shear anisotropy factors of Ta₂AlC before and after doping were calculated. The specific calculation formulas [39,40,41,42] are shown in Equations (16)–(21). The results of the elastic anisotropy calculations are presented in

Table 4. Elastic anisotropy indices of doped Ta₂AlC.

Sample	AU	Acomp	Ashear	A1	A2	A3
Ta2A1C	0.2307	0.07%	2.25%	1.6294	1.6294	1.1749
V doped Ta2A1C	0.2652	0.14%	2.57%	1.6851	1.6851	1.1935
Ga doped Ta2A1C	0.2989	0.16%	2.88%	1.7328	1.7328	1.2790
Si doped Ta2A1C	0.4150	0.00%	3.98%	1.9071	1.9071	1.2814

.

A^U = 5G_V/G_R + B_V/B_R − 6

(16)

A_comp = (B_V − B_R)/(G_V + G_R) × 100%

(17)

A_shear = (G_V − G_R)/(G_V + G_R) × 100%

(18)

A₁ = 4C₄₄/(C₁₁ − 2C₁₃ + C₃₃)

(19)

A₂ = 4C₄₄/(C₁₁ − 2C₁₃ + C₃₃)

(20)

A₃ = 4C₆₆/(C₁₁ − 2C₁₃ + C₃₃)

(21)

A^U can evaluate the anisotropy of material. If the material is isotropic, A^U = 0. The deviation of A^U from zero indicates the degree of anisotropy of the material. As can be seen from Table 4, before doping, A^U = 0.2307, indicating that Ta₂A1C is anisotropic, which is very consistent with the result (0.237) in reference [27]. When doped with V, Ga, or Si, the A^U, A_shear, A₁, A₂, and A₃ values of the Ta₂A1C material increase, indicating that the degree of anisotropy of the material increases. The increase in anisotropy is due to lattice distortion caused by doping. According to anisotropy, the cause is that the directional difference of the atomic ar-rangement causes the physical properties to change with the direction. Due to the incorporation of V, Ga, or Si dopants, the position of each atom in the cell is shifted, which leads to changes in the lattice parameters of Ta₂AlC, so that the lattice is distorted, and these changes directly affect the change in the anisotropy index, manifesting in the enhanced anisotropy of the Ta₂AlC material. However, it is worth noting that after Si doping, A_comp = 0, indicating that the compression anisotropy of Ta₂A1C can be effectively eliminated after Si replaces the C atom through doping. However, the fact that A_shear = 3.98% indicates that shear anisotropy still exists and trends upward, so the material is still anisotropic on the whole.

3.3. Electronic Structure

Figure 3 shows the band structure of Ta₂A1C before and after V, Ga, and Si doping at energies ranging from −14 eV to 2 eV. Figure 3 shows the band structure in the Brillouin region along the direction of highly symmetric points, and it can be seen that Ta₂A1C does not have a band gap. It is shown that the valence band and conduction band near the Fermi level (E_F = 0 eV) overlap each other; that is, the Fermi level passes through multiple energy bands of A-H, K-Γ, Γ-F, and Q-H. It can be seen that Ta₂AlC is a conductor with excellent conductivity, and its conductive characteristics are not weakened after doping with V, Ga, or Si. After doping, the energy band increases significantly, which indicates that the introduction of impurity atoms changes the interaction between different atoms.

Figure 4 shows the total electronic density of states of Ta₂AlC before and after doping. As can be seen from Figure 4, the electronic density of states is non-zero near the Fermi level, indicating that Ta₂AlC is a conductor, which is consistent with the previous analysis of the band structure. In the density of states diagrams, the electronic density of states for spin-up and spin-down electrons is symmetrically distributed, indicating that the Ta₂AlC system is non-magnetic both before and after doping.

To elucidate the mechanisms by which dopant atoms influence the band structure and electronic density of states, partial density of states diagrams for each atom in Ta₂AlC before and after doping are specifically plotted, as shown in Figure 5, Figure 6, Figure 7 and Figure 8. As can be seen from Figure 5, the electronic density of states between −14 eV and −10 eV is primarily contributed by the 2s states of C and the 5d and 6s states of Ta, with an electronic transition peak existing between Ta-5d and C-2s at the valence band −11.71 eV. The electrons between −10 eV and −3.41 eV are mainly contributed to by the 2p states of C and the 5d states of Ta, with an electronic transition peak existing between Ta-5d and C-2p at the valence band −4.82 eV. The electrons between −3.41 eV and 2.50 eV are predominantly contributed to by the 5d states of Ta and the 3p states of Al, with electronic transition peaks existing between Ta-5d and Al-3p at the valence band −1.87 eV and the conduction band 1.06 eV.

As can be seen from Figure 6, after V doping, two new peaks appear in the electronic density of states between −64.54 eV and −38.29 eV, which are attributed to the contributions of the V-3p and V-4s states. The emergence of these new peaks is consistent with the changes in the band structure shown in Figure 3 (the two new bands are not depicted in the figure). The introduction of a very small number of V-3d states weakens the C-2s states between −14 eV and −10 eV, resulting in a decrease in the electronic transition peak between Ta-5d and C-2s. This corresponds to the sparser bands in Figure 3 and the reduced density of states peak in Figure 4. Additionally, near the Fermi level, the introduction of V-3d states increases the number and density of bands in this region, leading to a slight increase in the total electronic density of states, which is consistent with the results shown in Figure 3 and Figure 4.

As depicted in Figure 7, after Ga doping, a new peak in the electronic density of states emerges near −14.67 eV, attributed to the contribution of Ga-4d states. The appearance of this new peak aligns with the changes in the band structure illustrated in Figure 3 (the new band is not depicted in the figure). Near −2.57 eV, the introduction of Ga-4p states leads to electronic transitions between Ga-4p and Ta-5d, resulting in an increase in the number and density of bands in this region, as well as an enhancement in the density of states peak. This indicates that the introduction of Ga strengthens the covalent interaction between Ta and Al, which is consistent with the analysis of lattice parameters and mechanical properties parameters presented in Table 1, Table 2 and Table 3.

As depicted in Figure 8, after Si doping, near −12.07 eV, the introduction of Si-3s states weakens the C-2s states, resulting in a reduction in the electronic transition peak between Ta-5d and C-2s. This corresponds to the sparser bands in Figure 3 and the reduced density of states peak in Figure 4. Near −9.60 eV and −8.62 eV, the introduction of Si-3s states results in the non-zero total electronic density of states in Figure 4, corresponding to the appearance of two new bands in Figure 3. Additionally, near the Fermi level, the introduction of Si-3p states leads to electronic transitions between Si-3p and Ta-5d, resulting in an increase in the number and density of bands in this region, as well as an enhancement in the density of states peak. This indicates a strong covalent interaction between Si and Ta. In conjunction with the supercell model of Si doped Ta₂AlC shown in Figure 2, the replacement of C atoms with Si atoms at the four crystal edges and the center of the unit cell effectively eliminates the compressive anisotropy of Ta₂AlC.

3.4. Mulliken Population Analysis

Table 5. Mulliken population analysis of doped Ta₂AlC.

Sample	Bond	Population	Length (nm)
Ta2A1C	C-Ta	0.44	0.22
	Al-Ta	0.36	0.29
V doped Ta2A1C	C-Ta	0.52	0.22
	Al-Ta	0.39	0.28
	V-C	0.23	0.21
	V-Al	0.22	0.29
Ga doped Ta2A1C	C-Ta	0.46	0.22
	Al-Ta	0.39	0.29
	Ga-Ta	−0.64	0.27
Si doped Ta2A1C	C-Ta	0.43	0.23
	Al-Ta	0.33	0.28
	Si-Ta	0.50	0.24
	Ta-Ta	0.12	0.30

presents the Mulliken population analysis of adjacent bonds between atoms in doped Ta₂AlC. As indicated in Table 5, in undoped Ta₂AlC, the population value of the C-Ta bond is 0.44, while that of the Al-Ta bond is 0.36, indicating that the covalent bond between C and Ta is stronger than that between Al and Ta.

After the V doping of Ta₂AlC, the population value of the C-Ta bond increases to 0.52, and that of the Al-Ta bond increases to 0.39, suggesting that the introduction of V enhances the covalent interactions between C-Ta and Al-Ta atoms. Additionally, V atoms form chemical bonds with neighboring C and Al atoms, with population values of 0.23 and 0.22, respectively. The above results indicate that the introduction of V enhances the covalent interaction between atoms, which clearly explains the reason for the enhanced plasticity of the Ta₂A1C material after doping with V reported in Section 3.2.

Following Ga doping in Ta₂AlC, the population value of the C-Ta bond rises to 0.46, and that of the Al-Ta bond rises to 0.39, indicating that Ga doping strengthens the covalent interactions between C-Ta and Al-Ta atoms. However, the population value of the Ga-Ta bond between Ga atoms and neighboring Ta atoms is −0.64, suggesting that no chemical bond is formed between Ga and Ta. Combined with V doped Ta₂AlC models, as shown in Figure 2c, along the c-axis direction, the interaction between the two layers of Ta atoms is significantly weakened because Ga-Ta does not form a chemical bond, which clearly explains the reason why the Ta₂A1C material becomes brittle after Ga doping, as reported in Section 3.2.

After the Si doping of Ta₂AlC, the population value of the C-Ta bond decreases to 0.43, and that of the Al-Ta bond decreases to 0.33, indicating that Si doping weakens the covalent interactions between C-Ta and Al-Ta atoms. Meanwhile, Si atoms form chemical bonds with neighboring Ta atoms, attaining a population value of 0.50, indicating a strong covalent interaction between Si and Ta. Unlike V and Ga doping, Ta-Ta bonds are formed after Si doping, with a population value of 0.12. Due to the strong covalent interaction between Si and Ta atoms and the bonding between Ta atoms, the plasticity of Ta₂A1C doped with Si becomes stronger.

3.5. Optical Properties

To investigate the impact of doping on the optical properties of Ta₂AlC, this study calculated the optical properties of this material, including the complex dielectric function, absorption coefficient, reflectivity, refractive index, and loss function.

The complex dielectric function is of paramount importance for studying the optical properties of metallic materials. Within the linear response regime, the complex dielectric function ε(ω) can be expressed as:

ε(ω) = ε₁(ω) + ε₂(ω)

(22)

Here, ε₁(ω) represents the real part of the dielectric function, while ε₂(ω) represents the imaginary part.

Figure 9 depicts the variation in the real and imaginary parts of the dielectric function of doped Ta₂AlC with energy.

As can be seen from Figure 9a, the static dielectric constant of Ta₂AlC, ε₁(0), is 79.63. After doping with V and Si, the static dielectric constant increases significantly to 124.18 (V) and 128.32 (Si), respectively, while doping with Ga results in a decrease to 76.14. These changes in the static dielectric constant suggest potential applications for optical components where specific dielectric constants are required. Furthermore, it can be observed that within the energy range of E < 0.55 eV (in the infrared region), the real part of the dielectric function ε₁(ω) is much larger for Ta₂AlC doped with V and Si than that of the undoped material. This indicates a significant enhancement in the ability of V- and Si doped Ta₂AlC to store electromagnetic energy. In contrast, Ga doping results in almost no change in ε₁(ω).

The imaginary part of the dielectric function ε₂(ω) serves as a bridge between the microscopic physical processes of interband transitions and the electronic structure of solids, reflecting the electronic structure of solids and various spectral information. As can be seen from Figure 9b, Ta₂AlC has a single dielectric peak in ε₂(ω) with a value of 24.55, located near E = 0.38 eV. After V doping, the dielectric peak significantly increases to 41.88 and exhibits a slight red shift towards lower energies. Following Ga doping, the dielectric peak slightly decreases to 24.18 and shows a noticeable blue shift towards higher energies. After Si doping, the position of the dielectric peak remains almost unchanged, but the peak value significantly increases to 42.26. Within the energy range of E < 1.58 eV (in the infrared region), the imaginary part of the dielectric function ε₂(ω) is much larger for Ta₂AlC doped with V and Si than that of the undoped material, indicating a significant enhancement in dielectric loss after V and Si doping. In conjunction with the partial density of states diagrams, the changes in the dielectric peaks can be attributed to the hybridization of V-3d, Ga-4p, and Si-3p states with Ta-5d and Al-3p states near the Fermi level, which alters the electronic transitions within and between bands, thereby affecting the dielectric function and other optical properties of Ta₂AlC.

Figure 10 depicts the optical properties of doped Ta₂AlC. From Figure 10a, it can be observed that when E = 0 eV, the absorption coefficients of doped Ta₂AlC materials are all non-zero. As the energy E increases, the absorption coefficient rises sharply, reaching a peak near E = 5.01 eV (ultraviolet region). This indicates that the doped Ta₂AlC can absorb photons ranging from low-frequency electromagnetic waves to those in the ultraviolet region, implying the absence of an optical band gap. These results are consistent with those reported in refs. [27,28]. Notably, after V doping, a new absorption peak appears near E = 39.29 eV, attributed to electronic transitions from the V-3p state to the Fermi level. As can be seen from Figure 10b, the reflectivity of Ta₂AlC achieves its maximum value of 95% near E = 9.53 eV (in the ultraviolet region). The exceptionally high reflectivity of Ta₂AlC (up to 95%) primarily stems from free electron effects, driven by its high carrier concentration, which induces a metal-like plasmonic response [43]. Specifically, the metallic bonding (Ta-Al bonds) in Ta₂AlC provides a substantial number of free electrons, forming a metal-like electron gas. Under the oscillating electric field of incident light, these free electrons undergo plasmon oscillations, resulting in high reflectivity for photons with energies below the plasma frequency. After doping with V, Ga, and Si, the reflectivity peak slightly decreases to 94%, 94%, and 92%, respectively. These results indicate that both doped and undoped Ta₂AlC can serve as potential anti-ultraviolet coating materials. Moreover, within the energy range of E < 8.66 eV, Si doping significantly enhances the reflectivity of Ta₂AlC. It can also be observed that in the visible light region between 1.58 eV and 3.18 eV, the photon frequency has minimal impact on the reflectivity, which remains around 50% for both doped and undoped Ta₂AlC. This suggests that Ta₂AlC, before and after doping, exhibits a similar metallic gray appearance, indicating its potential as a temperature control coating material in the visible light region. As can be seen from Figure 10c, the refractive index of Ta₂AlC is n₀ = 8.99, which changes to n₀(V) = 11.28, n₀(Ga) = 8.79, and n₀(Si) = 11.43 after doping with V, Ga, and Si, respectively. For optical devices made from Ta₂AlC material, where specific refractive index values are required, these results can be used as a reference. As can be seen from Figure 10d, the loss function of Ta₂AlC reaches its peak value of 247.82 near E = 9.75eV (in the ultraviolet region). After doping with V, Ga, and Si, the peak of the loss function is significantly reduced. However, the light loss of Ta₂AlC is confined to this energy range, indicating that both doped and undoped Ta₂AlC materials can be used as light storage materials.

4. Conclusions

In this study, the geometric structure, mechanical properties, electronic structure, Mulliken population analysis, and optical properties of Ta₂AlC doped with V, Ga, and Si were investigated using the first-principles pseudopotential plane-wave method. The results show the following:

(1)

The structural parameters of Ta₂AlC undergo significant changes after doping with V, Ga, and Si. The variations in lattice parameters are attributed to the differences in covalent radii of the substituted atoms. The mechanical stability of bulk Ta₂AlC and Ta₂AlC doped with V, Ga, and Si were confirmed using Born’s criterion.

(2)

The mechanical properties analysis of doped Ta₂AlC reveal that V and Si doping weaken the material’s resistance to deformation while enhancing its plasticity. In contrast, Ga doping increases the material’s resistance to lateral deformation and brittleness. The elastic anisotropy indices (A^U, A_shear, A₁, A₂, and A₃) of Ta₂AlC increase after V, Ga, and Si doping, indicating an enhanced degree of anisotropy.

(3)

The electronic structure calculations demonstrate that Ta₂AlC is a conductor with excellent electrical conductivity, which is not diminished by V, Ga, or Si doping. The symmetric distribution of spin-up and spin-down electronic states density confirms that the Ta₂AlC system remains non-magnetic after doping. The partial density of states diagrams successfully elucidate the mechanisms by which dopant atoms influence the band structure and electronic states density, providing results consistent with the analysis of the material’s lattice parameters and mechanical properties.

(4)

The Mulliken population analysis indicates that V and Ga doping enhance the covalent interactions between C-Ta and Al-Ta atoms, while Si doping weakens these interactions.

(5)

The optical properties calculations reveal that V and Si doping significantly enhance the electromagnetic energy storage capacity and dielectric loss of Ta₂AlC, whereas Ga doping has almost no effect. The reflectivity of Ta₂AlC in the ultraviolet region peaks at 95% for the undoped material and decreases to 94%, 94%, and 92% after V, Ga, and Si doping, respectively, indicating that both doped and undoped Ta₂AlC can serve as potential anti-ultraviolet coating materials. In the visible light region, doped and undoped Ta₂AlC exhibit a similar metallic gray appearance, suggesting their potential as temperature control coating materials in the visible light region. The light loss of Ta₂AlC is confined to a narrow energy range, unaffected by doping, indicating its suitability as a light storage material.

The above results demonstrate that different dopants can effectively modulate the mechanical and photoelectric properties of Ta₂AlC.