† Corresponding author. E-mail:
Project supported by the Science Fund from the Ministry of Science and Technology of China (Grant No. 2015DFR50650), the National Natural Science Foundation of China (Grant Nos. 51521001, 51502220, and 11402183), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. WUT: 2016-ZY-066 and WUT: 2015IA014).
The mechanical properties and deformation mechanisms of boron carbide under a-axis and c-axis uniaxial compression are investigated by ab initio calculations based on the density functional theory. Strong anisotropy is observed. Under a-axis and c-axis compression, the maximum stresses are 89.0 GPa and 172.2 GPa respectively. Under a-axis compression, the destruction of icosahedra results in the unrecoverable deformation, while under c-axis compression, the main deformation mechanism is the formation of new bonds between the boron atoms in the three-atom chains and the equatorial boron atoms in the neighboring icosahedra.
Boron carbide (B4C) has wide industrial and military applications due to its excellent properties, including high hardness, low density and good chemical stability.[1–3] With a low density and high Hugoniot elastic limit (HEL) of about 20 GPa,[4,5] B4C is expected to be a promising material for protective armor. However, when impact pressure is above HEL, an abrupt drop in strength occurs, leading to much poorer dynamics performance than expected.[5]
Since the 1990s, a number of groups have studied the mechanical behavior and related deformation mechanism experimentally.[4–10] Chen et al.[6] studied the formation of nanoscale intragranular amorphous bands in a ballistic experiment, which might be responsible for the lower dynamics response of B4C. Amorphization of B4C was also observed in scratching and indentation experiments.[7–10] By contrast, Zhang et al.[4] performed shock-wave experiments on B4C, and found a sudden drop in the pressure-density plot above 38 GPa. They pointed out that it is related to a phase transition. Similarly, using plate impact experiments including reshock and release configurations, Vogler et al.[5] found that a possible structural change occurs at about 40 GPa. However, it is still difficult to analyze the failure mechanism in B4C experimentally because of its complex crystal structure and the nearly identical scattering cross sections for neutron and electron of B and C.
Over the past few decades, ab initio methods based on the density functional theory have been widely used to study mechanical behaviors, deformation mechanisms and various properties in crystalline materials.[11–14] In particular, several theoretical studies in B4C have been performed.[14–20] An et al.[14,15] considered the structure deformation mechanism under shear stress. They found that the amorphization band formation is associated with the breaking of B–C bond between neighboring icosahedra and the bond formation between the B atoms in the chain center and the C atoms in the nearby icosahedra.[14] They also concluded that the brittle failure of B4C arises from the formation of higher density amorphous bands due to the fracture of the icosahedra through reactive molecular dynamics (RMD) simulations.[15] Besides, Aryal et al.,[16] Yan et al.,[17] and Taylor et al.[18,19] investigated the nature of structural deformation in B4C under c-axis (the direction of three-atom chains) compression. They concluded that the deformation mechanism of B4C is the abrupt bending of three-atom chains. Betranhandy et al.[20] suggested that the formation of C–C bonds in the C–B–C chains results in the dynamic failure of B4C instead of the abrupt bending of C–B–C chains under the c-axis compression. Most of the above studies focused on the deformation mechanism of B4C under the c-axis compression. The deformation behaviors for B4C loading along other directions have not been understood.
Furthermore, Clellan et al.[21] showed experimentally that B4C is more strongly anisotropic in elasticity and interatomic bonding than most solids. Thus, it needs to be considered whether the deformation mechanism for B4C has strong anisotropy. Korotaev et al.[22] studied the structural changes in B4C during compression along different directions (x, y, and z axes). The z axis is the direction of three-atom chains, and the x axis is chosen so that the edge of the unit cell containing the carbon atom lays in the
In order to investigate the anisotropic deformation mechanism in B4C, ab initio methods are used to study the uniaxial compression deformation along a axis and c axis in this work. The rest of this paper is organized as follows. In Section
As illustrated in Fig.
![]() | Fig. 1. (color online) Atomic structure of polar boron carbide B11C ![]() |
In the current study, all periodic calculations were performed with an ab initio method at a local density approximation (LDA) functional level, and Vienna ab initio Simulation Package (VSA)[26–28] was used. To ensure accuracy and efficiency, tests were first made by using experimental unit cell parameters[29] of B11C
![]() | Table 1.
Lattice parameters of B11C |
In order to investigate the deformation mechanism of B4C, the uniaxial compression along different directions were performed. The uniaxial compressive strains were imposed along a axis and c axis respectively. At each strain level, the strain components of the other directions were fully relaxed, and the residual stresses for relaxation of these other strain directions were controlled to be less than 0.1 GPa. To obtain stress–strain curves, a small uniaxial compression strain was applied sequentially to the B4C structure relaxed in the previous step. At each deformation step, we defined a 1% level of strain as a small compression strain increment. The volume of B4C remained unchanged during relaxation. This stress–strain relationship was used to obtain mechanical behaviors and to analyze the related deformation mechanisms for B4C.
Figure
![]() | Fig. 2. (color online) Stress–strain relationships for B4C under uniaxial compressions (a) a axis, (b) c axis. |
In Fig.
When compressive strains are imposed along the c axis (Fig.
The above results show that the maximum stress along a axis (89.0 GPa) is much smaller than that along the c axis (172.2 GPa). Thus the compressive strength along the c axis is higher than that along the a axis in the B4C structure. However, the maximum stress that the B4C can sustain is much larger than the experimental value.[4,5] That is because perfect crystal structure is considered in this work. But it is almost impossible to obtain the ideal compression conditions experimentally.
From the above results, there are some differences between the mechanical behavior of the structure during compression along the a axis and that along the c axis. From
![](cpb_26_4_047101/cpb_26_4_047101_ieqn0033.gif)
![](cpb_26_4_047101/cpb_26_4_047101_ieqn0034.gif)
In other previous research,[16–19] the bending of three-atom chains was considered as the mechanism of B4C under c-axis compression. In order to study whether the deformation mechanism of a axis is also related to the deformation of three-atom chains, the change in the angle of C–B–C chain with a-axis strain is shown in Fig.
Thus, the bending of three-atom chains is not related to the deformation mechanism of a axis. As presented below, the electron localization function (ELF)[31–33] is further studied, which shows that the distortion of B11C
There are some discontinuous points in the stress–strain curve of B4C under the a-axis compression. In order to further investigate the nature of deformation behaviors, we unload at different strain levels (between
![]() | Fig. 4. (color online) Atomic configurations after unloading (a) ![]() ![]() |
Figure
![](cpb_26_4_047101/cpb_26_4_047101_ieqn0079.gif)
Figure
The change in the angle of C–B–C chain during compression along the a axis is quite different from that along the c axis. Under a-axis compression, when the abrupt bending of C–B–C chains occurs, the stress decreases slightly from 68.2 GPa to 60.4 GPa. When the B4C undergoes a stress drop, the fluctuation of angle of C–B–C chains appears. Meanwhile, under the c-axis compression, when the abrupt bending of C–B–C chains occurs, the stress drops suddenly from 172.2 GPa to 14.2 GPa.
Figure
The strong anisotropy of deformation mechanism for B4C is observed. Under the a-axis compression, when the sudden bending of C–B–C chains takes place, the stress drops slightly and the B4C structure is still in the elastic stage. After that, the decrease in stress occurs, which is related to the distortion of B4C structure, and the destruction of B11C
In this work, ab initio methods are used to study the intrinsic mechanical properties and deformation mechanisms of B4C under a-axis and c-axis compression. Strong anisotropy is observed. The maximum stresses are 89.0 GPa and 172.2 GPa along a axis and c axis, respectively. Under the a-axis compression, there is a slight decrease in the stress–strain curve, which is caused by the sudden bending of the C–B–C chains. However, the structure is still in elastic deformation at this time. Then the drop in stress takes place, which is associated with the distortion of B4C structure, while the destruction of icosahedra is the main mechanism for causing the unrecoverable deformation. Under the c-axis compression, the icosahedra remain intact, and the C–B–C chains are almost straight before a drop in stress occurs. The formation of B–B bonds, which leads to the sudden bending of the C–B–C chains, is the main mechanism for causing the stress to abruptly drop.
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