On the Tensile Strength of Spark Plasma Sintered AlMgB14 Ceramics

In this work, the structure, phase composition, hardness and tensile strength of the AlMgB14-based material obtained by spark plasma sintering (SPS) were investigated. According to the XRD results, the spark plasma sintered material contains 94 wt% AlMgB14 phase and 6 wt% spinel MgAl2O4. Analysis of the SEM images showed that the obtained AlMgB14 sample has a dense structure; the relative density of the sample is 98.6%. The average microhardness of the spark plasma sintered (SPSed) sample is 29 ± 0.88 GPa. According to the results of the Brazilian test, the tensile strength of AlMgB14 is 56 MPa. The fracture is characterized by a single straight tensile crack that divides the sample along the compression line into two halves. The type of fracture in the AlMgB14 sample can be characterized as a cleavage fracture due to crack growth occurring in accordance with the transcrystalline fracture. The tensile strength of the obtained material is in good agreement with the tensile strength of boride and oxide ceramics studied in other works.


Introduction
Superhard materials are characterized by a hardness of over 40 GPa [1]. Traditionally, diamond (HV = 80-100 GPa) and cubic boron nitride (HV = 60-80 GPa) are considered to be superhard materials [2]. It is known that solid materials have a high symmetry of the crystal lattice, the atoms of which have a strong interatomic bond. Thus, diamond has a strong sp 3 covalent bond in the tetrahedral lattice configuration, while cubic BN has the cF8 diamond structure and belongs to the class of superhard materials due to the strong covalent bond of BN [2]. However, obtaining boron nitride in a cubic configuration is extremely expensive due to the need for high temperature and pressure in the synthesis process [1]. In this regard, the search for hard materials with excellent mechanical properties is an urgent scientific problem. To date, the attention of researchers is attracted by boron carbide (B 4 C), titanium diboride (TiB 2 ) [3][4][5][6][7], cubic silicon carbide (β-SiC) [8], titanium carbide (TiC) [9,10], etc. Despite the fact that these materials cannot formally be classified as superhard, in the form of thin-film coatings, they demonstrate hardness values above 40 GPa [11].
It is important to note that all of the above materials have a simple symmetrical structure that satisfies the traditional paradigm of superhard materials [2,12,13]. However, since 2000, AlMgB 14 -based materials, which have a complex low-symmetric orthorhombic structure and, at the same time, high properties, have been actively studied. Aluminum magnesium boride (AlMgB 14 ) has many excellent physical properties, such as high hardness (up to 32 GPa), relatively low density (2.59 g/cm 3 ), oxidation resistance, excellent wear resistance and a very low coefficient of friction (up to 0.02) [2,[14][15][16]. In combination with titanium diboride, materials based on AlMgB 14 demonstrate hardness reaching 46 GPa [2], which classifies AlMgB 14 -TiB 2 composite materials as superhard. As of yet, the main efforts of scientists have been directed at studying the influence of production methods (one-stage or two-stage sintering) and the composition of the initial mixture (ratio of initial elements, pre-reacted powders or mechanical mixture) on the structure, phase formation processes and properties of AlMgB 14 -based materials [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Today, it is traditionally considered that the best sintering methods for obtaining AlMgB 14 are spark plasma sintering and hot pressing of AlMgB 14 powder mixtures [2,[14][15][16][17][21][22][23]. At the same time, the properties of the obtained materials are mainly influenced by the purity of the material (the presence of MgAl 2 O 4 spinel in the samples leads to a significant decrease in the properties of AlMgB 14 [27]). Nevertheless, despite the comprehensive number of publications devoted to the study of hardness, density, oxidation resistance, friction coefficients, coefficients of thermal expansion (CTE), and other properties of AlMgB 14 -based materials [2,[14][15][16][17][18][19]28], there are no publications on their strength characteristics, in particular, on the tensile strength/flexural strength/compressive strength. At the same time, the tensile strength plays an important role in the analysis of the failure mechanism of structural ceramics and in the design of various structural ceramic parts; therefore, obtaining data on the strength characteristics of AlMgB 14 is an important research task.
Tensile strength can be determined mainly by the direct tensile test and the Brazilian test. Conducting tensile experiments on ceramics is too difficult due to their low fracture strain. In turn, the Brazilian test, an indirect tensile method, is a popular choice for testing ceramic materials [29,30] due to the ease of material preparation and testing. Thus, the purpose of this work is to study the tensile strength using the Brazilian test, as well as the structure and the phase composition of AlMgB 14 ceramics obtained by spark plasma sintering. The working chamber was evacuated to a vacuum level of 6 Pa. Mechanical pressure was applied to the graphite die in the first minute of the sintering process and kept constant throughout the process. The sample was heated from room temperature to 1400 • C at a heating rate of 50 • C min −1 . The diameter and thickness of the obtained samples were~12.5 mm and 3 mm, respectively. The sintered sample was polished for further research. The characteristics of the raw powders are given in Table 1. To obtain a mixture of Al 12 Mg 17 -B, the powders of Al 12 Mg 17 and amorphous black boron were mixed in an atomic ratio of 2:14 and mechanically activated (MA) in a planetary mill (Activator 4M, Engineering Plant "Activator", Ltd., Dorogino, Russia) for 3 h in an argon atmosphere with a rotational frequency of 14 Hz. The mass ratio of grinding bodies to the powder mixture was 3:1. The average size of the resulting Al 12 Mg 17 -B powder mixture was 400 nm.

Brazilian Test
Tests at 24 • C and a loading rate of 0.75 mm/min were performed on an Instron 3369 double column testing machine. The specimens were placed in the testing machine between flat plates such that the loading force was applied along the center line of the specimen base. The ASTM D3967 (Brazilian test for brittle materials) recommended formula for calculating the tensile strength of a test material is given below: where σ t is the splitting stress (MPa), which is the value of the indirect tensile strength; P-the maximum applied force (N), is selected from the maximum value of the experimental curve "force-displacement"; L is the sample thickness (mm); D is the sample diameter (mm).

Characterization
X-ray diffraction analysis of the obtained sample was performed using a Shimadzu 6000 diffractometer with CuKα radiation and using the PDF-4 (Powder Diffraction File) database. The phase composition was refined using the Rietveld method. For this work, the CASTEP program code [31] was used to calculate the energies of the referenced and refined crystal lattices within the framework of the density functional theory (DFT). The exchange-correlation potential was treated within the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE-GGA) scheme [32]. A plane-wave cutoff energy of 500 eV was used. The microstructure of the obtained sample was determined using a QUANTA 3D microscope with energy dispersive spectroscopy (EDX). The density of the sintered sample was calculated using the Archimedes method. The Vickers hardness (HV) was determined using a Metolab-502 microhardness tester at a load of 1 kg (9.8 N). The loading time was 10 s. Ten indentations were made from different places of the sample.

Microstructure and Phase Composition of the Obtained AlMgB 14 Ceramics
The results of the XRD analysis of the spark plasma sintered AlMgB 14 sample are shown in Figure 1  Using the Rietveld method, the quantitative content of the phases was determined. It was found that the weight content of the AlMgB 14 phase is dominant and amounts to 94 wt%, while the content of spinel MgAl 2 O 4 in the obtained samples is no higher than 6 wt%. Structural parameters (a, b, c, α, β, γ) and the free energy (E) of the crystal lattices of AlMgB 14 and MgAl 2 O 4 in both the reference and the refined states are given in Table 2. As can be seen from Table 2, the structural parameters of the AlMgB 14 lattice do not change. At the same time, the lattice volume V of the MgAl 2 O 4 spinel changes significantly from 528.101 (reference state) to 520.688 (refined state) Å 3 . The lattice energy of MgAl 2 O 4 in the refined state is higher than in the reference state, which indicates a lower lattice stability. The microstructure of the sintered sample is shown in Figure 2. As can be seen from Figure 2, spark plasma sintering of the Al12Mg17-B powder mixture leads to the formation of a dense homogeneous structure with inclusions of the oxide phase. According to the EDX results of the orange area in Figure 2, O, Al and Mg elements were found in the light areas (MgAl2O4 phase). In the dark areas, B, Al and Mg elements were found in the ratio corresponding to the AlMgB14 phase. EDX spectra are given in the Supplementary Materials. In the structure of the obtained sample, single pores with an average size of 3 μm were observed. The average grain size in the sintered samples is 3-5 μm. Based on the calculations using the Archimedes method, the relative density of the AlMgB14-based sample is 98.6% (if we take into account the 6% content of MgAl2O4 spinel, the theoretical density of the sample is 2.63 g/cm 3 ). The microstructure of the sintered sample is shown in Figure 2. As can be seen from Figure 2, spark plasma sintering of the Al 12 Mg 17 -B powder mixture leads to the formation of a dense homogeneous structure with inclusions of the oxide phase. According to the EDX results of the orange area in Figure 2, O, Al and Mg elements were found in the light areas (MgAl 2 O 4 phase). In the dark areas, B, Al and Mg elements were found in the ratio corresponding to the AlMgB 14 phase. EDX spectra are given in the Supplementary Materials. In the structure of the obtained sample, single pores with an average size of 3 µm were observed. The average grain size in the sintered samples is 3-5 µm. Based on the calculations using the Archimedes method, the relative density of the AlMgB 14 -based sample is 98.6% (if we take into account the 6% content of MgAl 2 O 4 spinel, the theoretical density of the sample is 2.63 g/cm 3 ).

Mechanical Properties of the Sintered Sample
The results of the hardness measurements of the obtained materials based on AlMgB14 are shown in Table 3. The average hardness of the obtained sample is 29 ± 0.88 GPa. The reported values of microhardness of the AlMgB14-based materials are 27.87 ± 0.97 [14], 26.7 ± 2.2 [15] and 26.1 [16] GPa, respectively. Thus, the value obtained in this work is in good agreement with the reported data [2,[14][15][16][17]21,22].  Figure 3a shows the dependence of the change in the loading force applied to the AlMgB14 sample on the displacement during the experiment for the Brazilian test at a temperature of 24 °C and a loading rate of 0.75 mm/min (10 −3 s −1 ). According to the obtained results, the tensile strength of AlMgB14 is 56 MPa.

Mechanical Properties of the Sintered Sample
The results of the hardness measurements of the obtained materials based on AlMgB 14 are shown in Table 3. The average hardness of the obtained sample is 29 ± 0.88 GPa. The reported values of microhardness of the AlMgB 14 -based materials are 27.87 ± 0.97 [14], 26.7 ± 2.2 [15] and 26.1 [16] GPa, respectively. Thus, the value obtained in this work is in good agreement with the reported data [2,[14][15][16][17]21,22].  Figure 3a shows the dependence of the change in the loading force applied to the AlMgB 14 sample on the displacement during the experiment for the Brazilian test at a temperature of 24 • C and a loading rate of 0.75 mm/min (10 −3 s −1 ). According to the obtained results, the tensile strength of AlMgB 14 is 56 MPa.

Discussion
The appearance of the AlMgB14 sample, fractured after the Brazilian test, is shown in Figure 3b. Analyzing the image of a fractured AlMgB14 sample after the Brazilian test, we observe that the fracture is characterized by a single straight tensile crack that splits the specimen along the compression line into two halves. This failure is considered typical for loading conditions in the Brazilian test in terms of analytical strength theory assumptions [33][34][35]. At the same time, in [36,37], the fracture of ceramic materials after the Brazilian test was accompanied by a ternary fracture and multiple branching cracks. Such a fracture pattern can be explained by the inhomogeneous phase composition, which leads to dispersion strengthening due to inclusions with mechanical characteristics that differ from the base material. Thus, the AlMgB14-based material obtained in this study has a homogeneous phase composition, and therefore the fracture is characterized by a single straight crack.
The SEM image of the fracture surface of the AlMgB14 sample and the integrated elemental analysis of a typical microsection on the fracture surface are shown in Figure 3c,d.

Discussion
The appearance of the AlMgB 14 sample, fractured after the Brazilian test, is shown in Figure 3b. Analyzing the image of a fractured AlMgB 14 sample after the Brazilian test, we observe that the fracture is characterized by a single straight tensile crack that splits the specimen along the compression line into two halves. This failure is considered typical for loading conditions in the Brazilian test in terms of analytical strength theory assumptions [33][34][35]. At the same time, in [36,37], the fracture of ceramic materials after the Brazilian test was accompanied by a ternary fracture and multiple branching cracks. Such a fracture pattern can be explained by the inhomogeneous phase composition, which leads to dispersion strengthening due to inclusions with mechanical characteristics that differ from the base material. Thus, the AlMgB 14 -based material obtained in this study has a homogeneous phase composition, and therefore the fracture is characterized by a single straight crack.
The SEM image of the fracture surface of the AlMgB 14 sample and the integrated elemental analysis of a typical microsection on the fracture surface are shown in Figure 3c,d. The crack initiation region is marked with a white arrow in Figure 3c. The initiation of a crack in the sample occurred not far from the central region of the sample, closer to the loading point. Most of the fracture surface, except for the crack initiation area, is relatively smooth without sharp drops and relief changes. Obviously, when under tension, the crack grew without resistance in local centers, which indicates the homogeneity of the composition and internal structure. The type of fracture can be characterized as a cleavage fracture due to crack growth occurring in accordance with the transcrystalline scenario. Multiple small fragments of the same elemental composition (Figure 3d) as the integral composition of the material were found on the fracture surface, with a predominance of Al, Mg and B chemical elements. The presence of other elements across the entire fracture surface is determined at the level of error (Table 4). A small number of micropores were also found, distributed evenly across the entire destruction surface with sizes not exceeding 20 µm. The tensile strength of the obtained AlMgB 14 -based material is in good agreement with the tensile strength of the various ceramics studied in other works (Table 5). Apparently, the lower tensile strength of AlMgB 14 compared to other ceramics can be associated with its complex low-symmetry orthorhombic crystal lattice and the presence of pores and microdefects in its structure. At the same time, as can be seen from Table 5, the composite material based on Al 2 O 3 -ZrO 2 eutectic has the highest tensile strength. Due to the presence of the second phase in the structure of the material and due to phase transformations in the ZrO 2 during destruction, the propagating cracks can branch and stop. In [2], a significant increase in the hardness of AlMgB 14 -based materials was reported due to the introduction of additives. With the addition of silicon, the hardness of AlMgB 14 increased to 35 GPa; with the addition of titanium diboride, it increased to 46 GPa. In [38], the authors reported that AlMgB 14 and TiB 2 have an exceptionally strong bond due to very close values of their surface energies. In AlMgB 14 -TiB 2 composite materials, AlMgB 14 provides both good wetting and internal strength of the composite. In combination, these two borides can provide a high degree of mutual enhancement [38]. Based on the above, in the future, it will be of great interest to study the tensile strength of AlMgB 14 -TiB 2 composite materials.

Conclusions
In this work, the AlMgB 14 -based ceramic material was obtained by spark plasma sintering. The mechanical properties, structure and phase composition were studied. The AlMgB 14 phase content in the obtained sample was 94 wt% with a spinel MgAl 2 O 4 content no higher than 6 wt%. According to the results of density and hardness measurements, the relative density of the sintered AlMgB 14 -based material was 98.6% with an average microhardness of 29 GPa. According to the results of the Brazilian test, the tensile strength of AlMgB 14 was 56 MPa. The fracture is characterized by a single straight tensile crack that divides the sample along the compression line into two halves. The type of fracture of the AlMgB 14 sample can be characterized as a cleavage fracture due to its crack growth appearing in accordance with the transcrystalline fracture. The tensile strength of the obtained material is in good agreement with the tensile strength of boride and oxide ceramics studied in other works.

Data Availability Statement:
The data presented in this study are available in the article.