Synthesis, crystal structure and properties of YB₂C₂

ABSTRACT

YB₂C₂ is a novel ultra-high temperature ceramic material with high damage tolerance. In this work, the synthesis mechanism, crystal structure, electronic structure, elastic properties and thermal shock resistance of YB₂C₂ were systematically investigated through experiments and calculations. It was determined by differential scanning calorimetry with the heating rate of 10°C/min that YB₂C₂ was formed by the reaction of YB₂C and C at about 1202°C, and became the main phase at 1450°C. The space group of YB₂C₂ was determined to be P4/mbm by X-ray diffraction, transmission electron microscopy, Rietveld refinement and first-principles calculations for the first time. The lattice constants are a = b = 0.5351 nm and c = 0.3561 nm. The atom positions are as follows: Y is located at 2a (0, 0, 0), B is located 4 h (0.133, 0.633, 0.5) and C is located at 4 h (0.662, 0.162, 0.5). The chemical bonding of YB₂C₂ displayed sharp anisotropy, with strong B-C bond within the B₂C₂ nets, and weak Y-B/Y-C bond between Y atom layers and B₂C₂ nets. Additionally, YB₂C₂ exhibited abnormal thermal shock resistance when the thermal shock temperature exceeded 800°C, with the residual flexural strength at 1300°C being more than 70% of the strength at room temperature.

KEYWORDS:

• YB₂C₂
• synthesis mechanism
• crystal structure
• properties

1. Introduction

Ultra-high temperature ceramics (UHTC) based on transition metal borides or carbides are important candidate materials for nose and leading edges of hypersonic vehicles [1,2]. However, the intrinsic brittleness, poor machinability and thermal shock resistance due to strong covalent bonding limit their application in the field of hypersonic aircraft [2]. Therefore, it is urgent to explore novel ultra-high temperature ceramics with high damage tolerance and thermal shock resistance.

In recent years, rare earth diborodicarbides (REB₂C₂, RE = Sc, Y and lanthanides), a new class of ternary layered ceramics, have attracted increasing interest [3–9]. YB₂C₂ is a member of the REB₂C₂ family. In 2016, our previous work [3] proved for the first time that it is an ultra-high temperature ceramic with excellent damage tolerance and good machinability. Since then, these materials have been attracting the attention of researchers. Very recently, our research further proved that YB₂C₂ has excellent ultra-high temperature thermal stability and is the first high damage tolerance ceramic with a melting point exceeding 2500°C, further confirming its application prospects in the field of hypersonic aircraft [4]. However, due to the narrow composition range of YB₂C₂ in phase diagram, the fabrication of single-phase YB₂C₂ has proved to be quite difficult, and early studies mainly focused on the calculation of its phase diagram, crystal structure and electronic structure [5,6]. It is worth noting that there are still disputes about the crystal structure of YB₂C₂. The two “competing” crystal structures of YB₂C₂ are tetragonal with P2c symmetry or P4/mbm symmetry. Both structures have a tetragonal symmetry with planar BC nets held together by Y atoms. The positions of the Y atoms are the same and the difference is only related to the distribution of the B and C atoms within the planes, which are built of distorted fourfold cyclobutadiene-like and eight-membered B-C rings. For the P_42c YB₂C₂, each B atom is coordinated by two C atoms and one B atom, and each C atom is coordinated by two B atoms and one C atom. For the P4/mbm YB₂C₂, each B is coordinated by three C atoms and vice versa. The problem of the preferable distribution of B and C atoms with respect to each other is often called a “coloring” problem. Khmelevskyi [5] confirmed that the crystal structure with P4/mbm symmetry is more stable than the originally claimed P_42c structure by ab initio calculation. Reckeweg [6] used five different tetragonal unit cell settings for the integration and refinement of the intensity data, and the only refinement without obvious inconsistencies was obtained in the “standard model” with the space group P4/mbm. Zhou [7] calculated the differences in electronic structure, chemical bonding, mechanical properties and lattice dynamics of the two structures. They found that both structures are stable under mechanical perturbations, while the P4/mbm YB₂C₂ is more stable from the calculated total energy. Due to the small differences in their X-ray scattering power, the distribution of B and C atoms with respect to each other – the so-called “coloring problem” – is hard to settle conclusively with X-ray methods only. Therefore, the crystal structure of YB₂C₂ needs to be more accurately resolved from the atomic scale by transmission electron microscopy (TEM).

In the last 5 years, various methods for synthesizing YB₂C₂ have been investigated. We have prepared YB₂C₂ bulk with high purity and density using YH₂ B₄C and C as raw materials at 1900°C for 30 min by in-situ reactive hot pressing method [4]. Nguyen [8] synthesized YB₂C₂ via modified spark plasma sintering (SPS) using high energy ball milled Y₂O₃, B₄C and carbon as starting materials. Although some progress has been made in the synthesis of YB₂C₂, however, many fundamental scientific questions related to this material remain unresolved, such as the formation mechanism and properties of YB₂C₂, which still need to be investigated.

In the present work, the reaction path of YB2C2 with YH₂/B₄C/C was systematically studied with DSC (Differential scanning calorimetry) and XRD (X-ray diffraction analysis) to reveal its formation mechanism. Considering the current controversy about the crystal structure of YB₂C₂, the crystal structure and electronic structure of YB2C2 were analyzed by TEM characterization, theoretical structure optimizations and first-principles calculations. The mechanical properties and thermal shock resistance of YB2C2 were also investigated.

2. Experiment and calculation

YB₂C₂ powder was prepared by in-situ hot pressing commercially available YH₂ powder (purity 99%, particle size 200 mesh, TITD, China), B₄C powder (purity 99%, particle size 200 mesh, Jingangzhuan, China) and graphite powder (purity 99%, particle size 200 mesh, Tianyuan, China) in a 1.95:0.9:2.95 molar ratio. The starting powders were ball milled for 12 h in a Si₃N₄ jar, in which Si₃N₄ balls were used as mixing balls with ball to power ratio of 3:1 and alcohol was added as the mixing media. The mixed powders were subsequently dried, and placed in a graphite crucible. Then they were heated to the target temperatures at a rate of 10°C/min and holding for 1 h in a graphite heating furnace under flowing argon atmosphere. For the synthesis of bulk YB₂C₂, the mixed powers of YH₂:B₄C:C with the molar ratio of 1.95:0.9:2.95 were placed in a graphite die after ball milling. After cold-pressed under a pressure of 5 MPa, the green compact was heated to 1900°C at a rate of 10°C/min and held for 1 h under a pressure of 30 MPa before cooling to room temperature.

DSC experiment was performed on a Setsys 16/18 thermal analyzer (SETARAM, Caluire, France) to understand the reaction paths for YB₂C₂ formation. The raw powder mixture was placed in an Al₂O₃ crucible and heated up to 1450°C at a heating rate of 10°C/min in a flowing Ar atmosphere. The sample mass was about 20 mg.

The phase compositions of the samples were determined by XRD (Rigaku D/max-2400, Tokyo, Japan), using Cu Kα (λ = 1.54178 Å) radiation with a scanning step of 0.02°/min. The X-ray diffraction pattern of YB₂C₂ was refined using GSAS-II software according to the Rietveld method-fitting the lattice constant, crystal plane spacing, 2Ɵ angle, and intensity of the diffraction peak of YB₂C₂. The intensity of the diffraction peak can be expressed as:

$I_{\mathit{Rietveld}\mathit{\hspace{0.17em}}}\left(2\mathit{\theta }\right)=\mathit{b}\left(2\mathit{\theta }\right)+\mathit{s}\sum _k{L}_K{\left|F_K\right|}^2\mathrm{\varnothing }\left(2{\theta }_i-2{\theta }_k\right)P_K{A}_K$

The base strength is represented by b(2θ), with a scale coefficient denoted as s. The polarization factor, Lorentz factor, and multiplicity factor Sub are included in L_K, while the shape function is expressed as$\mathrm{\varnothing }$. The preferred orientation function is referred to as P_K, with the absorption factor labeled as A_K and the structural factor described as F_K. Here, K represents the Miller index of Bragg diffraction. The reliability factor is defined as:

$\mathit{R}-\mathit{P}=100\frac{{\sum }_i\left|y_i^{obs}-y_i^{cal}\right|}{{\sum }_i{y}_i^{obs}}$

$\mathit{R}-\mathit{wP}=100{\left[\frac{{\sum }_i\mathit{wi}{\left(y_i^{obs}-y_i^{cal}\right)}^2}{{\sum }_i{w}_i{\left(y_i^{obs}\right)}^2}\right]}^2$

Where $y_i^{obs}$ and $y_i^{cal}$ are the experimental intensity and theoretical calculation intensity of the ith step of the X-ray, respectively, and w_i is the weight factor, defined as:

$\mathit{wi}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}\frac{1}{y_i^{obs}}$

The morphology of the samples was analyzed with a scanning electron microscope (SEM, LEO Supra35, Ammerbuch, Germany) equipped with an energy dispersed spectroscopy (EDS) system. Further analysis of the microstructure was conducted on a Tecnai G² F20 transmission electron microscope (TEM, FEI, Eindhoven, the Netherlands).

To obtain the crystal structure and electronic structure of YB₂C₂, first-principles calculations based on density-functional theory (DFT) were performed [10]. The Vanderbilt type ultrasoft pseudopotential [11] and generalized gradient approximation [12] (GGA-PBE) were used in the Vienna Ab-initio Simulation Package. The plane-wave basis set cutoff was 600 eV for the calculation. The Broyden-Fletcher-Goldfarb-Shanno [13] (BFGS) minimization scheme was used for geometric optimization. The tolerances are differences in total energy of within 5 × 10⁻⁶ eV/atom, maximum ionic Hellmann-Feynman force of within 0.01 eV/Å, maximum ionic displacement of within 5 × 10⁻⁴ Å and maximum stress of within 0.02 GPa.

The elastic coefficients were determined by applying a set of given homogeneous deformations with a finite value and calculating the resulting stress with respect to optimizing the internal degrees of freedoms, as implemented by Milman [14]. The criteria for convergences in optimizing atomic internal freedoms was selected as follows: difference on total energy within 1 × 10⁻⁶ eV/atom, ionic Hellmann-Feynman force within 0.002 eV/Å, and maximum ionic displacement with 1 × 10⁻⁴ Å.

Elastic properties are very important in understanding of physical, chemical, and mechanical properties of solid-state materials. Elastic constants of YB₂C₂ are defined by six independent components of the elastic tensor (c₁₁, c₁₂, c₁₃, c₃₃, c₄₄ and c₆₆). Their values can be determined by using the stress-strain approach [15], starting from the optimized geometry of unit cell at given pressure. From the calculated elastic constants, the bulk modulus (B), shear modulus (G) and Young’s modulus (E) of orthorhombic crystal can be obtained using the Reuss approximations [16]:

$\begin{array}{rl}& B_R=\mathit{\hspace{0.17em}}1/\left[\left(s_{11}+s_{33}\right)\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}2\left(s_{12}+s_{13}\right)\right]\\ & G_R=\mathit{\hspace{0.17em}}15{\left[4\left({\mathit{s}}_{11}+s_{33}\right)\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}4\left(s_{12}+s_{13}\right)\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}3\left(s_{44}+s_{66}\right)\right]}^{-1}\\ & c_{\mathit{ij}}=1/s_{\mathit{ij}}\end{array}$

The polycrystalline Young’s moduli, and Poisson’s ratio were calculated using the following equation [17]:

$\mathit{E}=\frac{9\mathit{BG}}{3\mathit{B}+\mathit{G}}$

$\mathit{v}=\frac{3\mathit{B}-2\mathit{G}}{2\left(3\mathit{B}+\mathit{G}\right)}$

The oxidation behavior of YB₂C₂ was characterized using a thermogravimetry (TG, HENVEN, China) in air at 1300°C. The heating rate was 10°C/min. Thermal shock resistance of YB₂C₂ was tested by annealing the samples (3 mm × 4 mm × 36 mm) at the testing temperature for 20 min in a vertical furnace in air, and then immediately quenching in the ambient water. The testing temperatures were 600, 800, 1000, 1200, and 1300°C, respectively. The retained flexural strength was measured by a three-point bending method in a universal testing machine. Four bars were performed to the thermal shock resistance test. The surface and cross-section morphologies of quenched samples were investigated by SEM. The surface compositions of quenched samples were determined by XRD.

3. Results and discussion

Figure 1 is the DSC curve of the YH₂/B₄C/C mixed powders with the molar ratio of 1.95:0.9:2.95. The powder mixture was heated from room temperature to 1450°C at a heating rate of 10°C/min under a flowing Ar atmosphere. As shown in Figure 1, there is a strong endothermic peak at 969°C. In addition, there are several weak exothermic peaks at about 1105°C, 1202°C, and 1347°C. In order to study the phase evolution process during the synthesis of YB₂C₂, the powder mixtures were heated to the temperatures near the endothermic and exothermic peaks (1000°C, 1150°C, 1250°C and 1400°C), respectively. The powder mixtures were holding for 20 min at these temperatures and then cooling down to room temperature. X-ray diffraction analysis was performed on these heated powder samples and the results are shown in Figure 2.

Figure 1. DSC curve obtained with YH₂, B₄C and C mixture at a heating rate of 10 °C/min up to 1450°C under a flowing Ar atmosphere.

Figure 2. XRD patterns of mixed powders at (a) RT, and after sintering at (b) 1000 °C, (c) 1150 °C, (d) 1250 °C, (e) 1450°C.

Figure 2 presents the XRD patterns of the YH₂/B₄C/C powder mixtures sintering at different temperatures. The XRD pattern of the raw powder mixture is also listed for comparison. After heated at 1000°C for 20 min, the diffraction patterns change obviously. As shown in Figure 2(b), the intensities of the diffraction peaks of YH₂ (PDF # 12–0388) and B₄C (PDF # 35–0798) reduce significantly, but the diffraction peaks of graphite (PDF # 41–1487) are still very strong. At the same time, there appears diffraction peaks of YB₂ (PDF # 25–1032) and some diffraction peaks that cannot be calibrated. When sintering at 1150°C (Figure 2(c)), strong diffraction peaks of Y₂C₃ (PDF # 22–0988), YB₄ (PDF # 07–0057) and YB₂C (PDF # 27–0970) appear, while the diffraction peaks of YH₂, B₄C and YB₂ disappear, and the diffraction peaks of graphite decrease significantly. Interestingly, compared with Figure 2(b), it can be found that some of the unlabeled diffraction peaks reduce significantly (e.g. at 31.3°), while some increase significantly (e.g. at 26.7°). This means that there are at least two new phases. As the temperature increases to 1250°C (Figure 2(d)), a large amount of YB₂C₂ (PDF # 27–0970) is formed, and the intensity of the diffraction peaks of YB₂C, YB₄, Y₂C₃, graphite and unknown phases reduce significantly. When the temperature is up to 1450°C (Figure 2(e)), the diffraction peaks of YB₂C, Y₂C₃ and graphite disappear. Meanwhile, YB₂C₂ becomes the predominant phase and there exists minor YB₄ and unknown phases.

For the unknown phases, they are supposed to be some ternary compounds in the Y-B-C system. As all the binary compounds in the Y-B-C system have been reported, and none of the available PDF cards is consistent with those peaks in Figure 2(b). As to ternary compounds, the currently discovered ternary phases in the Y-B-C system are YB₂C₂, YB₂C and YBC [18], while more compounds are reported for other ternary rare earth boron-carbon compounds. For example, 8 ternary phases are reported in the La-B-C system [19], and 11 ternary phases are reported in the Pr-B-C system [20]. It is quite possible that there are many unreported ternary phases in the Y-B-C system, which needs to be further studied. It is reasonable to believe that the unlabeled peaks come from some unreported ternary compounds in the Y-B-C system.

Based on the experimental results of DSC and XRD, it is concluded that the strong endothermic peak at 969°C in the DSC curve is mainly caused by the reaction of YH₂ with B₄C, in other words, the dehydrogenation reaction of YH₂. Figure 3 shows the change of Gibbs free energy (ΔG) and enthalpy (ΔH) as a function of temperature for the dehydrogenation reaction of YH₂ (YH₂ = Y + H₂ (g)). It can be seen that the dehydrogenation reaction of YH₂ occurs only at above 1220°C, and it is a strong endothermic reaction in the entire temperature range. Thanks to the existence of substances such as B₄C in the present system, the dehydrogenation reaction of YH₂ can be promoted and occur at a relative lower temperature. Therefore, we believe that the endothermic peak at about 969°C corresponds to the dehydrogenation reaction of YH₂. The exothermic peak at 1105°C is from the reaction of YH₂ with B₄C and graphite. Wang et al. found that there is no chemical reaction between YH₂ and SiO₂ at 1000°C, and YH₂ disappears at 1200°C [21]. Yan et al. also found that YH₂ still did not decompose at 1100°C when YH₂ powder and Ti-6Al-4 V powder coexisted [22]. For the exothermic peak at 1202°C, it is related to the formation of YB₂C₂, as the XRD results show that a large quantity of YB₂C₂ was formed in the sample heat treated at 1250°C. The exothermic peak at 1347°C is derived from the reaction of YB₄ with graphite and the unknown phases.

Figure 3. ΔG and ΔH curves of dehydrogenation reaction of YH₂.

In summary, the reaction pathway of YB₂C₂ can be summarized as follows:

YH₂ + B₄C → YB₂ + Y_x1B_y1C_z1 + Y_x2B_y2C_z2+ H₂(g) (969°C)

YH₂ + C = Y₂C₃ + H₂(g) (1105°C)

YH₂ + YB₂ + B₄C = YB₄ + YB₂C + H₂(g) (1105°C)

YB₂C + C = YB₂C₂ (1202°C)

YB₄ + Y₂C₃ + Y_x2B_y2C_z2 → YB₂C₂ (1347°C)

In order to further improve the purity of the sample, the raw powder was heat-treated at 1600°C for 1 h, and the XRD patterns are shown in Figure 4. It can be seen that all of diffraction peaks are from YB₂C₂, which proves the high purity of the synthesized samples.

Figure 4. XRD patterns of mixed powders with a molar ratio of YH₂:B₄C:C = 1.95:0.9:2.95 after sintering at 1600°C.

In order to resolve the controversy about the crystal structure of YB₂C₂, the crystal structure of YB₂C₂ was systematically investigated using TEM. According to previous studies, YB₂C₂ is built from square Y-atom and B/C-atom layers, which are alternatively stacked in a manner that the Y atoms are located at the center the 8-member-ring formed by B and C atoms in the projection along the stacking direction [5]. Two crystal structures have been reported for YB₂C₂, i.e. P_42c and P4/mbm. The Y-layers in the two structures are the same. But in P_42c, B and C atoms form B-B and C-C pairs, and the pairs take the edge positions of the 8-member-ring alternatively. While in P4/mbm, B and C atoms occupy the apex sites of the 8-member-ring alternatively. As the structural difference only exists in the B-C layers with weak scattering ability, the main peaks in X-ray diffraction patterns of the two structures are nearly identical and it is almost impossible to determine the crystal structure by normal X-ray diffraction. However, the electron diffraction patterns of the two structures are totally different, as shown in Figure 5(a–d). The experimental diffraction patterns in Figure 5(e,g) perfectly match the simulated diffraction patterns in Figure 5(c,d) except that the diffraction spots highlighted with white circles appear in Figure 5(g). Because of the screw axes along [100] and [010], the diffraction spots of (h00) with h = 2n and (0k0) with k = 2n (n is an integer) at the positions marked by the red dots in Figure 5(d) should have no intensity. But double diffraction in the experiment breaks the extinction rule and makes them appear in the diffraction patterns in Figure 5(g). In addition, the [1_10] diffraction pattern in Figure 5(f) is also consistent with the structure. In Figure 5(h), the convergent beam electron diffraction pattern shows a 4-fold rotation axis (perpendicular to the screen) and two mirrors (green and pink lines) in P4/mbm. Thus, it is confirmed that the as-synthesized YB₂C₂ has the P4/mbm symmetry.

Figure 5. Simulated electron diffraction patterns of the P_42c (a, b) and P4/mbm (c, d) structure along the [010] (a,c) and [001] (b,d) zone axes. Red dots in (d) show the positions of extinction diffraction spots. For the two structures, the diffraction patterns along [100] are identical to those along [010] and not provided here for brevity. Experimental selected area electron diffraction patterns along [010] (e), [1_10] (f) and [001] (g). Convergent beam electron diffraction pattern along [001]. The green and pink lines denote the mirror planes.

Rietveld refinement was conducted to validate the XRD data for the YB₂C₂ powder. In the process of refinement, the tetragonal unit cell setting in the space group of P4/mbm was used as the crystal structure of YB₂C₂. Figure 6 shows the observed, simulated and differential patterns for YB₂C₂. The lower line corresponds to the differential profile between the observed and the simulated profiles. Clearly, the simulation data fits well with the experiment results. The weighted-profile and expected reliability factors converged to R_wp = 13.5% and x² = 1.77, respectively, suggesting the higher reliability of the results. The lattice constants obtained by Rietveld refinement are a = b = 0.5351 nm and c = 0.3561 nm. Correspondingly, the atom occupations are as follows: Y is located at 2a (0, 0, 0), B is located 4 h (0.133, 0.633, 0.5) and C is located 4 h (0.662, 0.162, 0.5) Wyckoff positions, respectively. The calculated and experimental data of reflections, 2θ positions and intensities of YB₂C₂ are listed in Table 1. For YB₂C₂ powders, d and 2θ are well consistent with the calculated data, with a deviation of ˂0.2%.

Figure 6. Powder XRD spectra of YB₂C₂: observed spectrum (the × black dotted line), Rietveld generated spectrum (the red upper solid line) and difference between the two (the bottom purple solid line). The blue vertical ticks below the pattern represent possible bragg reflections of YB₂C₂.

Table 1. Calculated (cal.) and experimental (Obs.) data of reflections, 2θ positions and intensity for YB₂C_2.

Reflection(hkl)	2θObs.(^o)	2θCal.(^o)	d Obs.(Å)	d Cal.(Å)	I/I0Obs.(%)	I/I0 Cal. (%)
1 1 0	23.59	23.53	3.77	3.77	63.5	54.5
0 0 1	25.08	25.01	3.55	3.56	17.7	14.2
2 0 0	33.56	25.98	2.69	3.426	21.5	24.1
1 1 1	34.66	34.60	2.59	2.59	100	100
2 1 0	37.90	37.61	2.37	2.38	0.3	0.2
2 0 1	42.31	42.26	2.13	2.13	46.1	49.5
2 2 0	48.15	48.13	1.89	1.88	12.5	12.9
0 0 2	51.37	51.32	1.78	1.78	13.7	14.1
3 1 0	54.26	54.24	1.69	1.68	17.9	23.01
2 2 1	55.01	54.98	1.67	1.67	12.2	18.3
1 1 2	57.23	57.2	1.61	1.61	13.1	13.9
3 1 1	60.64	60.58	1.53	1.52	12.0	16.5
3 2 0	62.73	62.67	1.48	1.48	8.6	10.7
4 0 0	70.43	70.42	1.34	1.33	1.5	2.7
2 2 2	73.00	72.94	1.30	1.29	5.8	9.2
3 3 0	75.41	75.35	1.26	1.29	1.2	1.7
4 0 1	76.04	75.98	1.25	1.30	5.6	7.6
3 1 2	77.93	77.89	1.23	1.22	10.6	12.3
4 1 1	78.16	78.41	1.22	1.21	4.7	2.1

First-principles calculations were also conducted to investigate the crystal structure of YB₂C₂. YB₂C₂ crystallizes in the tetragonal structure with P4/mbm symmetry. The theoretical density of YB₂C₂ is 4.35 g/cm³. The lattice constants were calculated to be a = b = 0.5353 nm and c = 0.3593 nm. In this structure, Y is located at 2a (0, 0, 0), B is located 4 h (0.1379, 06379, 0.5) and C is located 4 h (0.6606, 0.1606, 0.5) Wyckoff positions, respectively.

Table 2 presents the comparison of lattice constants derived from first-principles calculations, Rietveld refinement, electron diffraction and from literature. These results agree well with each other, with the deviation of lattice constants less than 0.5%. Therefore, all the above results confirm the crystal structure YB₂C₂ to be of tetragonal P4/mbm symmetry.

Table 2. Comparison of lattice constants of YB₂C₂ derived from first-principles calculation, Rietveld refinement, electron diffraction, and from literature.

Lattice parameters (nm)	a	b	c
First-principles calculation	0.5353	0.5353	0.3593
Rietveld refinement	0.5351	0.5351	0.3561
Electron diffraction	0.531	0.531	0.354
Reckeweg′s result [6]	0.5333	0.5333	0.3546

To identify the characteristics of chemical bonds, the electronic structure is analyzed. Figure 7(a) shows the total and projected electronic density (TDOS and PDOS) of states of YB₂C₂. The TDOS of YB₂C₂ has finite value of 1.87 states·(eV·unit·cell)⁻¹ at the Fermi level, indicating the metallic characteristics of YB₂C₂. Contribution to this finite value comes from Y, B and C atoms with finite peaks in the corresponding PDOS, indicating that the Y 4d, B 2p and C 2p electrons all contribute to the electrical conductivity of YB₂C₂.The lowest lying states from −16.2 to −11.8 eV originate mainly from the B 2s-C 2s and B 2p-C 2s covalent bonding. The B 2p-C 2p and B 2s-C 2p covalent bonding dominates the states ranging from −10 to −5 eV. At higher energy range from −5 eV to the Fermi level, the states are mainly from Y 4d-B 2p and Y 4d-C 2p interatomic bonds. Clearly, the B and C atoms contribute to the most of the TDOS of valence states, while the contribution of Y to the TDOS are mainly in high energy range below the Fermi level. The higher energy range of Y-B and Y-C pd hybridization indicates that the Y-B and Y-C bond is much weaker than the B-C coherent bond, which means that the intraplanar bonding along the basal B2C2 plane is much stronger than interplanar bonding between adjacent layers of Y-B or Y-C in YB₂C₂.

Figure 7. (a) Total and projected electronic density of states (DOS) of YB₂C₂; (b) Mulliken population and bond length of chemical bonds in YB₂C₂; (c) pressure dependence of lattice constants a and c; (d) relative bond-length contractions for YB₂C₂ at various pressures.

Figure 7(b) shows the Mulliken population and bond length of chemical bonds in YB₂C₂. It is apparent that the bond length of B-C is shorter than that of Y-B and Y-C. The Mulliken population for the two types of B-C is 1.19 and 0.85, while it is −0.13 and −0.05 for Y-B and Y-C, respectively. This suggests that the intraplanar bonding of B-C along the basal plane is much stronger than interplanar bonding of Y-B and Y-C. That is to say, the atoms of B with C in B₂C₂ plane form strong chemical bond, while the atoms of Y with B or C between adjacent layers forms relative weaker chemical bond. Therefore, YB₂C₂ exhibits obvious anisotropy of chemical bonding, which could result in the elastic anisotropy and the formation of weak bond plane, making high damage tolerance possible.

In Figure 7(c), we present the pressure dependence of lattice constants a and c. With increasing hydrostatic pressure continuously to 50 GPa, the lattice constants decrease continuously without sudden change, proving the maintenance of phase stability. Besides, the lattice constant c contracts more dramatically than a in the pressure range examined. Therefore, the material is stiffer in the basal plane than in c when YB₂C₂ is under isotropic pressure. This elastic anisotropy suggests that interplanar bonding along c is weaker than intraplanar bonding along the basal plane in YB₂C₂.

The strength of the interatomic bond can be characterized by its resistance against external pressures by first-principles calculations. This method has been widely used in the evaluation of the bond strength for MAX phases [23,24]. Following the same method, we examine the degree of bond length contraction for YB₂C₂ under various pressures, and illustrate the results in Figure 7(d). The lower two lying curves is seen to be associated with the Y-B and Y-C bond, which are more compressible. Above them are the curves for B-C1 and B-C2 covalent bonds, which are less compressible. Figure 7(d), illustrates that the interatomic bonding of Y-C and Y-B is softer than the B-C bonding. These results are consistent with the above results of electronic structure, bond-length and Mulliken population, confirming the typical layer structure of YB₂C₂ with strong intraplanar bond and weak interplanar bond.

The elastic constants of a material describe its response to applied stress and provide useful information about its bonding character. Young’s modulus E measures the resistance against uniaxial tensions. Bulk modulus B describes the resistance of a material to volume change and provides an estimate of its response to a hydrostatic pressure. Shear modulus G measures the resistance to shape change. These are important parameters for defining the mechanical properties of a material. Table 3 lists the full set of second-order elastic coefficients, as well as the B, G, E and Pisson’s ratio v of YB₂C₂. The c₁₁ and c₃₃ represents the resistance against the principal strains of ε₁₁ and ε₃₃, and E_x and E_z is the corresponding elastic moduli. It can be seen that c₁₁ > c₃₃, and E_x > E_z, with the values of c₁₁/c₃₃ and E_x/E_z up to 2.42 and 2.03. This means that the c-axis is the more compressible crystallographic direction than that of a-axis. The c₄₄ and c₆₆ are related to the resistances to the basal and prismatic shear deformations. The relative low value of c₄₄ and G indicates that shear deformations occur easily.

Table 3. Second order elastic constants c_ij, anisotropic Young’s modulus ex and E_z, bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio of YB₂C_2.

Second order elastic constants (cij) and anisotropic Young’s modulus of single crystal
c11	c12	c13	c33	c44	c66	Ex	Ez
494	204	24	204	72	176	410	202
Elastic moduli of polycrystalline YB2C2
B		G		E		ν
140		103		249		0.20

For a tetragonal crystal [25], the mechanical stability conditions under pressure are as follows:

$c_{11}>0,c_{33}>0,c_{44}>0,c_{66}>0,\mathit{\hspace{0.17em}}(c_{11}-c_{12})>0,\mathit{\hspace{0.17em}}(c_{11}+c_{33}-2c_{13})>0,\mathit{\hspace{0.17em}}\left(2\left(c_{11}+c_{12}\right)+c_{33}+4c_{13}\right)>0$

From Table 3, it can be seen that the calculated elastic constants obey the above criteria well, suggesting that YB₂C₂ is mechanically stable under elastic strain perturbation.

From the second order elastic constants and anisotropic Young’s modulus in Table 3, anisotropy in elastic properties of YB₂C₂ is obvious.

From the above analysis, YB₂C₂ is one typical ternary rare earth boride carbides, with alternating Y and B₂C₂ slices stacking along the c axis. It exhibits anisotropic chemical bonding, with strong bonding within the B2C2 layers and weak bonding between Y and B2C2 nets. The anisotropic structure endorses YB₂C₂ with high damage tolerance and good machinability, which has been proved in our previous literature [4].

The thermal shock resistance was also investigated by measuring the residual strength after quenching. Figure 8 shows the relative residual strength of YB₂C₂ and several other structural ceramics as a function of quenching temperature [26–30]. When quenching at 800°C, the retained flexural strength is about 11% of unquenched ones (52MPa). When increasing the quenching temperature, the abnormal thermal shock behavior of YB₂C₂ appears. Up to 1300°C, the residual flexural strength increases to 350MPa, which is more than 70% of the strength at room temperature. To understand this abnormal thermal shock behavior, the XRD patterns, SEM surface and cross-sectional morphologies of the sample quenched at 800 and 1300°C, as well as the TG curve from RT to 1300°C of the YB₂C₂ sample were observed and the results are shown in Figure 9. From the TG curve for the oxidation of YB₂C₂ at a heating rate of 10°C/min in air from RT to 1300°C (Figure 9(a)), it can be seen that the weight of YB₂C₂ begins to increase above 800°C, indicating that the oxidation takes place above 800°C. Moreover, for the YB₂C₂ sample after quenched at 800°C, no oxides are detected in the surface XRD (Figure 9(b)), and no visible morphologies of oxides are observed on the surface of the quenched sample by SEM (Figure 9(c)), which further proves that no oxides existed on sample quenched at 800°C. Furthermore, it can be seen that large cracks appeared on the surface of YB₂C₂ after quenching at 800°C, and the cracks in different directions interconnected, forming penetrating cracks, which results in the remarkable decrease of the flexural strength. For the YB₂C₂ sample quenched at 1300°C, the oxidation weight gain is obvious (Figure 9(a)). It can be seen from XRD that the surface of the sample is completely composed of YBO₃, and no diffraction peaks of YB₂C₂ are observed (Figure 9(b)). YBO₃ is obtained by the reaction of Y₂O₃ and B₂O₃. The oxidation reaction equation of YB₂C₂ is:

Figure 8. Dependence of the retained flexural strength of YB₂C₂ and several other structural ceramics on the quenching temperature.

Figure 9. (a) TG curve of YB₂C₂ at 100–1300 °C; (b) XRD patterns of the YB₂C₂ sample surface after quenching at 800°C and 1300 °C; (c) SEM morphology of the YB₂C₂ sample surface after quenching at 800 °C; (d) SEM morphology of the YB₂C₂ sample surface after quenching at 1300 °C; (e) is a partial enlargement of (d); (f) SEM morphology of the cross-section of the YB₂C₂ sample after quenching at 1300°C.

$2\mathit{Y}{B}_2{C}_2+6.5O_2=2\mathit{YB}{O}_3+B_2{O}_3+4\mathit{CO}$

However, no diffraction peaks of B₂O₃ were observed in the sample after quenching at 1300°C. This is because 1300°C has exceeded the boiling point of B₂O₃ and it volatilized in large quantities [31]. For the YB₂C₂ sample after quenched at 1300°C, the surface, cross-section and matrix of the sample are continuous and complete, and there are no radioactive cracks. Combined with XRD, it can be seen that the surface is composed of submicron YBO₃ equiaxed grains. Apparently, the surface oxide layer is favorable for inhibiting crack initiation and propagation, thereby preventing damage to the YB₂C₂ matrix. This abnormal thermal shock behavior has also been reported for MAX phases [26–28]. It is believed that the surface oxide layers essentially formed on the MAX phases’ surface essentially acted as thermal barriers that reduced the surface heat transfer coefficient so that the transient tensile stresses in the substrate was decreased. In addition, the oxide layers formed on the surface can heal surface defects and reduce thermal stress. Therefore, in this work, it is reasonable to believe that the YBO₃ layer formed on the surface of YB₂C₂ plays an important part in decreasing the residual strength for the samples quenched from above 800°C and results in the good thermal shock resistance of YB₂C₂.

4. Conclusions

In this work, high purity YB₂C₂ was synthesized by the in-situ hot pressing method with initial powders of YH₂, B₄C and graphite. The reaction route and the microstructure were analyzed by DSC, XRD and TEM. The crystal structure, electronic structure, chemical bonding and elastic properties of YB₂C₂ were investigated by first-principles calculations. The main conclusions are as follow:

1. During synthesis of YB₂C₂, the dehydration reaction of YH₂ firstly occurred at 969–1105°C, with the formation of YB₂, YB₄ or YB₂C. Then YB₂C₂ was formed by consuming YB₂C and C earliest at about 1202°C. YB₂C₂ was also formed at 1347°C with the reaction of YB₄ and some unknown Y-B-C compound.

2. It is confirmed by TEM that YB₂C₂ has the tetragonal structure with P4/mbm symmetry. The lattice constants are a = b = 0.5351 nm and c = 0.3561 nm. The atom positions are as follows: Y is located at 2a (0, 0, 0), B is located 4 h (0.133, 0.633, 0.5) and C is located at 4 h (0.662, 0.162, 0.5).

3. Electronic structure investigations reveal that YB₂C₂ is electrically conductive and the contribution to the electrical conductivity are from Y as well as B and C electrons.The chemical bonding of YB₂C₂ displays sharp anisotropy, with strong B-C bond within the B₂C₂ nets, and weak Y-B/Y-C bond between Y atom layers and B₂C₂ nets. The second-order elastic coefficients, bulk modulus, shear modulus and Young’s moduli show the elasticity anisotropy of YB₂C₂.

4. YB₂C₂ exhibits abnormal thermal shock resistance when the thermal shock temperature exceeds 800°C, with the residual flexural strength at 1300°C being more than 70% of the strength at room temperature.

Disclosure statement

The author(s) declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This work was supported by the Guangdong Major Project of Basic and Applied Basic Research (2021B0301030002), the National Natural Science Foundation of China (Nos. 52101091 and 52032011), the Guangdong Basic and Applied Basic Research Foundation (Nos. 2021B1515140061), Dongguan Sci-tech Commissioner Program (20221800500592), SSL Sci-tech Commissioner Program (20234374-01KCJ-G), the Start-up Funding support from Songshan Lake Materials Laboratory (Y2D1041C711) and the National Key Research and Development Program of China (2022YFA1403500 and 2022YFC2403702).