Molecular Dynamics Study of Cubic Boron Nitride Nanoparticles: Decomposition with Phase Segregation during Melting Hsiao-Fang Lee, Keivan Esfarjani, Zhizhong Dong, Gang Xiong, Assimina A. Pelegri, and Stephen D. Tse* Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, New Jersey 08854, United States S Supporting Information *
ABSTRACT: The relative stability and melting of cubic boron nitride (c-BN) nanoparticles of varying shapes and sizes are studied using classical molecular dynamics (MD) simulation. Focusing on the melting of octahedral c-BN nanoparticles, which consist solely of the most stable {111} facets, decomposition is observed to occur during melting, along with the formation of phase segregated boron clusters inside the c-BN nanoparticles, concurrent with vaporization of surface nitrogen atoms. To assess this MD prediction, a laser-heating experiment of c-BN powders is conducted, manifesting boron clusters for the post-treated powders. A general analysis of the geometrical and surface dependence of the nanoparticle ground-state energy using a Stillinger−Weber potential determines the relative stability of cube-shaped, octahedral, cuboctahedral, and truncated-octahedral c-BN nanoparticles. This stability is further examined using transient MD simulations of the melting behavior of the differently shaped nanoparticles, providing insights and revealing the key roles played by corner and edge initiated disorder as well as surface reconstruction from {100} to the more stable {111} facets in the melting process. Finally, the size dependence of the melting point of octahedral c-BN nanoparticles is investigated, showing the well-known qualitative trend of depression of melting temperature with decreasing size, albeit with different quantitative behavior from that predicted by existing analytical models. KEYWORDS: cubic boron nitride, nanoclusters, melting, phase segregation, faceting, surface reconstruction, geometric stability, size effect was the first naturally occurring boron-nitride mineral found, being affirmed as an analog of c-BN in 2013.5 The first artificial synthesis of c-BN was achieved under high-pressure and hightemperature (HP-HT) conditions by Wentorf6 in 1957; following which, the physical properties of c-BN were intensively studied experimentally by many groups.1,7−10 The electronic properties and band structure of c-BN were first studied by Kleinman and Phillips in 1960,11 finding the energy gap of c-BN (∼10 eV) to be about twice that of diamond. Since then, there have been strong efforts in the community to study c-BN via first-principles calculations, with a diverse array of approaches employed, including density functional theory (DFT),12−15 molecular dynamics (MD) simulations,16−20 and analytical methods.21 The structural, mechanical, and thermodynamic properties were reported in these studies, but none of them discussed the melting of c-BN crystals, with only a few
C
ubic boron nitride (c-BN) is a ceramic material wellknown for its outstanding mechanical and thermal properties, along with wide band gap structure.1 The crystalline structure of c-BN is similar to that of diamond, with sp3 bonding and zincblende/sphalerite structure; and its hardness is second only to diamond, with a Mohs scale hardness of 9.5−10. Its superior hardness makes c-BN a great substitute for diamond in various mechanical and thermal applications. For example, c-BN is commonly used in industrial cutting, machining, drilling, polishing, and grinding tools as replacement for synthetic carbon diamond. Especially at high temperatures, diamond tends to react with some metals to form metal carbides, while c-BN is much less reactive. In addition, cBN possesses a large band gap energy of approximately 6.3 eV, with various potential electronic and electrical applications.2,3 Cubic-BN can also be utilized as a heat sink substrate for Sibased electronic devices because of its high thermal conductivity and similar thermal expansion coefficient as that of Si near room temperature.4 Boron nitride (group III−V) compounds have been historically produced synthetically. Only recently, in 2009, © 2016 American Chemical Society
Received: September 29, 2016 Accepted: October 31, 2016 Published: October 31, 2016 10563
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{111} facets. From this energy analysis, the octahedron is the most stable shape as a result of its lowest surface energy, and this type of c-BN particle has been observed in experiments. Wentorf6 found octahedral c-BN crystal fragments of up to 300 μm in HP-HT synthesis of c-BN, and Lian et al.24 obtained octahedral c-BN particles of around 1 μm in hydrothermal solutions. Tian et al.25 have successfully synthesized nanostructured c-BN samples having average size of nanograins around 3.8 nm, and the grains contained spaced lamellar {111} twins. As such, in this work, we focus on the melting mechanism and properties of c-BN nanoparticles of octahedral shape in our MD investigations. Melting and Decomposition with Phase Segregation in c-BN Nanoparticles. A 2.04 nm octahedral c-BN nanoparticle containing 969 atoms is heated up to 3340 K in MD simulation using the canonical ensemble (NVT). This temperature is about 100 K higher than the reported melting point of c-BN crystals.26 Here, melting starts from the vertices, then propagates to edges and surfaces, and finally proceeds inward toward the core. Hexagonal rings along the {111} direction of c-BN can be seen in Figure 2a, with boron and nitrogen represented by red and yellow, respectively. This octahedron has eight {111} facets, with half of the surface terminations being boron and the other half nitrogen, as shown in the inset of Figure 2a. The six vertices have the same coordination number of 2. At the 500 ps mark of the NVT simulation, seven nitrogen atoms have vaporized from the nanoparticle, and quite a few nitrogen atoms have diffused around the surface to form small clusters on the boronterminated surface, as displayed in the inset of Figure 2b. In addition, half of the octahedron’s corners have melted, and some boron−boron bonds have formed in the corners, resulting in mini-boron clusters, as revealed in Figure 2b. At the 1 ns mark, melting has spread to the edges and surfaces; see Figure 2c. The mini-boron clusters have gradually grown larger; and at the 2 ns mark, they have clumped together to form one large boron cluster inside the nanoparticle, as shown in Figure 2d. At the 3 ns mark, only half of the nanoparticle remains crystalline, as shown in Figure 2e. At the 3.5 ns simulation mark, there are 130 vaporized nitrogen atoms; and a boron-rich nanoparticle is formed. The formation of phase-segregated boron cluster covered by nitrogen atoms on the surface occurs unexpectedly, and the c-BN crystalline structure is no longer visible at this moment, as presented in Figure 2f. Melting seems to occur through phase segregation since it is concurrent with the latter. Melting of octahedral c-BN nanoparticles has been evinced. Here, owing to the lower coordination number, melting starts from the corners and then spreads to edges and surface. This process contrasts the well-known surface melting mechanism of spherical nanoclusters where melting starts from the surface, resulting in an amorphous/liquid shell that propagates inward and forms a liquid-shell/solid-core coexisting structure.27,28 Although this corner-initiated melting mechanism of octahedral c-BN nanoparticles is different from traditional surface melting behavior, it can still be quantitatively monitored by calculating the Lindemann indexes of different shells that comprise the nanoparticle. For spatial analysis of the phenomenon, each cBN nanoparticle is divided into four regions or concentric shells, i.e., a surface shell, a next outer shell, an inner shell, and a core, for assessment. The Lindemann index is defined by
studies mentioning the sublimation and decomposition aspects of BN.6,22 A study23 on the formation of BN nanotubes mentioned that laser heated c-BN could melt at high pressure (above the h-BN−c-BN−liquid triple point at P = 9 GPa and T = 3500K), but there exists no study discussing the possible melting of c-BN near atmospheric pressures. To the best of our knowledge, MD has not been previously applied to study c-BN nanoparticles. In this work, the special focus is on their melting behavior. The Stillinger−Weber (SW) potential based on previous studies of bulk c-BN20 is employed here for MD simulations; and the surface energies of {100} and {111} facets are extracted based on this empirical potential. The SW potential reproduces the cohesive energy of −6.717 eV and the lattice constant of 3.6076 eV to within 2% of the experimental values. The stability of c-BN nanoparticles of various shapes is analyzed, and the faceting of c-BN nanoparticles is observed in the MD simulations. Concentrating on the stable octahedral-shaped c-BN nanoparticle, we investigate in detail the melting behavior. Surprisingly, the phenomenon of boron and nitrogen atoms phase segregating with rising temperature is observed, and this simulation result is seemingly corroborated by experiments of laser-heated c-BN particles. Finally, the size dependence of the melting temperature of octahedral c-BN nanoparticles is studied through MD simulations, and the results are compared with analytical models of melting-point depression with size.
RESULTS AND DISCUSSION Stability of Nanoparticle Shapes Based on General Energy Analysis. First, the modified SW potential20 is utilized to carry out an energy analysis of c-BN and to extract the bulk and surface energies from the calculation of c-BN crystals and slabs of varying sizes. The energy per unit volume of c-BN is ebulk = −1.1572 eV/Å3, and the stabilities of different crystallographic terminations of c-BN are also obtained. The energy per unit surface area of c-BN {100} facet, Υ100, and {111} facet, Υ111, are Υ100 = −1.0438 eV/Å2 and Υ111 = −2.1240 eV/Å2, respectively, as shown in Table 1, for both Table 1. Summary of Surface Energies of Different Facets of c-BN facet
energy per unit surface area (eV/Å2)
average coordination number
{100} {111}
γ100 = −1.0438 γ111 = −2.1240
2 3
boron and nitrogen terminations. From the results, the {111} facet is found to be more stable than the {100} facet because of its larger average coordination number (i.e., a value of 3 for the {111} facet and a value of 2 for the {100} facet versus the value of 4 for fully coordinated c-BN). Comparing the potential energy of a pure {111}-faceted c-BN nanoparticle (i.e., octahedron) with one having {100} facets (e.g., cube) and a mixture of {100} and {111} facets (e.g., cuboctahedron and truncated octahedron) by simply calculating the bulk and surface energies (E = ebulk × C1L3 + Υ × C2L2), Figure 1 charts the energy per atom versus the cube root of number of atoms comprising the nanoparticle. The cube has the steepest slope because of the highest surface energy of pure {100} facets, followed by the cuboctahedron with six square {100} facets and eight triangular {111} facets, and then the truncatedoctahedron with six square {100} facets and eight hexagonal 10564
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Figure 1. Surface energy of various shapes of c-BN nanoclusters. L refers to the side length, and the circled symbols are those investigated in the detailed MD simulations.
Figure 2. Phase segregation occurs during melting of a 2.04 nm octahedral c-BN nanoparticle in NVT simulation with T = 3340K. Bond structure view on main graphics and surface atom view on insets (where red and yellow denote boron and nitrogen respectively): (a) the initial configuration (inset shows the half-boron half-nitrogen terminations); (b) 500 ps simulation time: melting starts from corners and small phase-segregated boron clusters form (the nitrogen atoms diffuse around surface as shown in inset); (c) 1 ns simulation time: melting proceeds to edges; (d) 2 ns simulation time: melting propagates to surfaces, and the boron clusters tend to aggregate; (e) 3 ns simulation time: more than half of the nanoparticle is melted; (f) 3.5 ns simulation time: no crystalline c-BN is visible, and phase-segregated boron clusters have formed in the interior of the nanoparticle.
δi =
1 Nb
∑ j ϵNb
other three shells increase steadily. At 3.5 ns, the Lindemann index values of every shell exceed 0.1, viz. there is 10% bond fluctuation, implying that the whole nanoparticle is melted or phase separated and no longer crystalline. This threshold is in agreement with the generic Lindemann index value of 0.08− 0.15 used to determine melting for simple solids.28,29 The total number of B−N, B−B, and N−N bonds are tracked, as given in the lower plot of Figure 3. The number of B−N bonds continuously decreases because of bond breaking, while the numbers of B−B and N−N bonds steadily increase, validating the simultaneous occurrence of decomposition with phase segregation during the melting of the c-BN nanoparticle. The
(rij − aB̅ − N)2 aB̅ − N 2
where aB̅ −N is the average of the boron−nitrogen bond length, and Nb denotes the total number of atoms within the neighbor list. Then, the neighbor list of each atom is constructed at every picosecond, and the average Lindemann index of each shell is determined for qualitative monitoring of the corner-initiated melting. The upper plot of Figure 3 shows the Lindemann index values of this c-BN nanoparticle, and the values of the core do not increase much until 1 ns, while the values of the 10565
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Figure 4. Lindemann index versus temperature of the 2.55 nm octahedral c-BN nanoparticle, with the red solid line indicating linear behavior of the Lindemann index below 2950 K. The fluctuations in this line are due to faceting and surface reconstruction events.
index is from nitrogen atoms diffusing around on the surface of the nanoparticle as well as from the interior to the surface driven by vaporization of surface nitrogen atoms. The Lindemann index value starts to upturn and deviate from linear behavior when the temperature goes beyond 2950 K, and the deviation exceeds 5% at 3000 K, which is then estimated as the onset of melting. Since the value of the Lindemann index for the entire nanoparticle at 3000 K is 0.11, this value for melting is consistent with the general rule-of-thumb for Lindemann index values of 0.08−0.15 that are used to demarcate melting for simple solids.28,29 To test our estimate of the melting temperature, a series of computationally intensive NVT simulations are carried out in the temperature range of 2618−3218 K, in increments of 100 K, from which the specific heat behavior is determined. The NVT simulation at each temperature is stopped when the core of the octahedral nanoparticle starts melting or is terminated at 50 ns of simulation time with a time step of 0.1 fs if the core remains crystalline at lower temperatures. The total energy versus temperature data from the simulation results are plotted in the upper chart of Figure 5. A discontinuity of the caloric curve is found to occur between 2918 and 2968 K, indicating a phase transition. Traditionally, this manifestation would indicate a solid-to-liquid phase transition; however, in c-BN nanoparticles, the upturn estimates the onset of a melting instability that occurs in tandem with phase segregation. To assess the behavior of the heat capacity as a function of temperature, it is calculated in two different ways to validate the phase transition. First, the derivative from the total energy as a function of temperature, i.e., C(T) = dU/dT, is taken, which is shown as the green curve in the lower chart of Figure 5. Second, using the fluctuation−dissipation theorem, the specific heat is calculated from the fluctuation of the total energy, i.e., C(T) = (U − ⟨U⟩)2/kBT2, which is shown in the red curve in the lower chart of Figure 5. Both curves have spikes indicating the occurrence of a phase transition, and the peaks of the curves evince that the melting instability happens at about 2950 K, which is close to where the Lindemann index curve starts to upturn. Therefore, we are confident that the estimated melting point from the Lindemann index calculation of the computationally economical NVE simulation provides a lower bound for the onset of a melting instability of the 2.55 nm octahedral cBN nanoparticle.
Figure 3. Lindemann index of each investigated shell of the 2.04 nm octahedral c-BN nanoparticle as a function of time. The lower graph plots the total number of B−N, B−B, and N−N bonds during NVT simulation at T = 3340 K, which is higher than previously reported melting temperature of c-BN.
rapid increase in the total number of B−B bonds and the final number of B−B bonds at 3.5 ns provides quantitative support for the formation of a boron cluster. An experimental study of laser heating of c-BN powders is also conducted, and phase segregation of boron from the laser-treated c-BN powders is discovered under transmission electron microscope (TEM) scans. The details are discussed toward the end of this paper. Definition of Melting Point of Nanoparticle. In order to define the melting temperature of the c-BN nanoparticle, a computationally economical NVE simulation is carried out for a 2.55 nm octahedral c-BN nanoparticle with initial temperatures ranging from 2200 to 3500 K, in increments of 100 K. The octahedral nanoparticle is relaxed in NVE for 3 ns at each initial temperature, then the Lindemann index of the entire nanoparticle is calculated, and the curve with respect to the average temperature of the nanoparticle over the last 150 ps of simulation duration is plotted, as given in Figure 4. The melting temperature is then defined as the point at which the Lindemann index upturns, with a noticeable change in the first derivative. Figure 4 shows the overall cluster Lindemann index of a 2.55 nm octahedral c-BN nanoparticle, where the Lindemann index is observed to increase linearly initially from 2150 to 2950 K, as the vibrational motion of the atoms increases with kinetic energy. At the onset of melting, the Lindemann index exhibits nonlinear behavior because the boron−nitrogen bonds start to break, and boron clusters begin to form. In addition, part of the contribution to the Lindemann 10566
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Figure 6. Surface reconstruction on c-BN {100} facets. Relaxation of the cube-shaped nanoparticle in microcanonical ensemble with an initial temperature of 2400 K: (a) the initial configuration shown as bond structure seen from {100} direction; (b) 0 ps: red and yellow spheres denote boron and nitrogen, respectively; (c) 10 ps: dimerized boron pairs on {100} facet; (d) 10 ps: dimerized nitrogen pairs on {001} facet; (e) 2700 ps: reconstructed {111) facet and dimerized {100} facets on the surface of cube-shaped nanoparticle; (f) 2700 ps: the same orientation as (e) but shown as bond structure.
Figure 5. Caloric curve of the 2.55 nm octahedral c-BN nanoparticle, showing a jump at 2950 indicating melting. The plots below of the specific heat also show melting occurring around 2950 K. The disagreement at higher temperatures above Tm is due to nonequilibration of the phase-segregated clusters.
Surface Reconstruction of {100} Facet of c-BN Nanoparticles. A cube-shaped c-BN nanoparticle with six {100} facets (half-boron and half-nitrogen terminations), a side length equal to 2.08 nm, and containing 1728 atoms is relaxed in MD under the microcanonical ensemble (NVE) with an initial temperature around 2400 K for 3 ns. Significant reconstruction of the {100} surfaces with formation of dimer pairs is found, similar to the well-known reconstruction of Si {100} surfaces.30 The original configuration of the cube-shaped nanoparticle is shown in Figure 6a,b. In Figure 6c,d, the atoms on both the boron and the nitrogen terminated {100} surfaces of the cube-shaped nanoparticle tend to dimerize and form pairs of boron and nitrogen. This reconstruction is due to pairing of the dangling bonds of the surface atoms, resulting in formation of dimers with lower energies. The dimerization on bulk c-BN {100} facets has been studied by quantum chemical31 and DFT32 calculations. After 50 ps relaxation, the {100} facets further reconstruct to form {111} facets on the surface, in addition to the steps of dimerized nitrogen pairs, as displayed in Figure 6e. The transformation from {100} into {111} upholds the result from our surface energy analysis that the {111} facet is more stable than the {100} facet. In Figure 6f, the nanoparticle is seen to be partially melted, and the 90° angled edges from the original cube no longer exist, having reconstructed into {111} facets (Figure 6e). The final temperature of this reconstructed nanoparticle rises to about 3070 K in the 3 ns NVE simulation from an initial temperature of 2400 K, indicating a large gain in potential energy because of dimerization and surface reconstruction. Since reconstruction into the {111} facet increases potential energy, the reconstructed surface should stabilize the cube-shaped nanoparticle, which is corroborated by the Lindemann index of the cube-shaped nanoparticle. The 3 ns NVE simulations are carried out for the 2.08 nm cube-shaped c-BN nanoparticle in the temperature range of 1000−2400 K, at 200 K intervals. Dimerization is observed to occur at all temperatures. The Lindemann index of the
nanoparticle at the end of NVE simulations is recorded and plotted versus the final temperatures of the nanoparticle, as shown in Figure 7. At 2900 K, a distinct inflection point is seen with a depressed Lindemann index, indicating that there are reduced fluctuations at that temperature. The mechanism for this stabilization is the formation of {111} facets because of surface reconstruction at around 2900 K, which is verified by visualizing the nanoparticle at 2902 K and slightly below at 2665 K, as shown in the insets in Figure 7. The left inset in
Figure 7. Lindemann index of cube-shaped c-BN nanoparticle, showing the Lindemann index value of both the entire nanoparticle in purple squares, and of the surface shell in blue diamonds. The inset figures show the melted nanoparticles at 2665 and 2902 K, with significant {111} reconstruction at 2902 K. 10567
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Figure 8. Lindemann index values of various shapes of c-BN nanoparticles show that the cube shape melts at the lowest temperature and that the truncated octahedron melts at the highest temperature.
This phenomenon can be explained by the melting mechanism of the c-BN nanoparticles, where melting begins from the corners and then propagates to the edges. The corner and edge atoms have higher mobility because of lower average coordination number than that for surface atoms. The specific truncated octahedron used in this study is formed by removing the six corners of a regular octahedron with the removal length equal to 1/3 of the side length of octahedron, forming six {100} square facets. After taking away the six sharp tips of the octahedron, the surface to volume ratio drops from 0.288 (for octahedron with L = 2.55 nm) to 0.266 (for truncatedoctahedron with L = 0.89 nm). In addition, the energy difference between octahedron and truncated octahedron is quite small, and the dimerization of boron and nitrogen atoms on {100} facets helps in stabilizing the truncated-octahedral nanoparticle. Therefore, it is reasonable that the truncated octahedron has a slightly higher melting temperature than the octahedron, even though the octahedron has a slightly lower cohesive energy per atom from our energy analysis of the SW potential. Although dimerization also occurs in the cuboctahedron, its cohesive energy is at least 150 meV/atom smaller than those of the octahedron and the truncated octahedron; hence, dimerization is not expected to affect the relative stability significantly. The effects of corners and edges on melting33 as well as shape effects34,35 in other nanoparticles have been previously addressed. Next, we will discuss the effects of c-BN nanoparticle size on melting behavior, focusing on only {111} faceted octahedral nanoparticles, as this will allow us to avoid the complicating effects of {100} surface reconstruction during melting. Size Dependence of Melting Point of Octahedral c-BN Nanoparticles. The computationally economical method of 3 ns NVE simulations and calculation of the Lindemann indexes of the entire octahedral c-BN nanoparticles are employed to study the size dependence of the melting point. There are four different-sized octahedral c-BN nanoparticles discussed in this section, namely, 2.04 nm (969 atoms), 2.55 nm (1771 atoms), 3.57 nm (4495 atoms), and 4.59 nm (9139 atoms). All of them are cut to have half boron−half nitrogen terminations, with the same configuration of edges and corners. Figure 9 shows the overall cluster Lindemann indexes of the four nanoparticles with respect to temperature. The curve of the 2.04 nm
Table 2. Summary of Dimensions of Various Shapes of c-BN Nanoparticles Studied geometry
total number of atoms
length (nm)
cube cuboctahedron truncated octahedron octahedron
1728 1846 1592 1771
2.08 1.53 0.89 2.55
data points represent the ones chosen for MD study. The order of stability of these four different-shaped nanoparticles remains as what is expected, even though the total number of atoms of each nanoparticle is not exactly the same. All of them are cut to terminations at the surfaces that are half boron and half nitrogen. Each nanoparticle is relaxed in a microcanonical ensemble with varied initial temperatures for a computationally economical MD simulation (3 ns). As discussed earlier, an estimate of the onset of melting for each nanoparticle is obtained by determining the point at which the Lindemann index curve deviates from its low-temperature linear behavior; therefore, Figure 8 displays the Lindemann index values of the entire clusters with respect to temperature for all four shapes. The Lindemann index for the cube-shaped nanoparticle starts to turn up at around 2300 K, followed by cuboctahedron at around 2700 K, and then octahedron at 2950 K. The truncated octahedron has the highest estimated melting temperature at around 3100 K. In general, the melting temperatures of the nanoparticles, as estimated from the energy analysis, follow the same trend, with the exception of the truncated octahedron having a slightly higher melting temperature than that for the octahedron, even though it has a slightly smaller cohesive energy, i.e., a difference of 73.9 meV/atom. 10568
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Figure 9. Lindemann index values versus temperature of differentsized octahedral c-BN nanoparticles. The melting points are determined by the upturning points of the Lindemann index curves.
nanoparticle starts to upturn at the lowest temperature, followed by the 2.55 nm nanoparticle. The difference between the 3.57 nm and the 4.59 nm nanoparticle is not significant. Since the 4.59 nm nanoparticle contains about 10,000 atoms, the 3 ns simulation time is not long enough to observe complete melting. However, the nanoparticle exhibits melting of the corners, thereby providing a lower bound on the estimated melting temperature at about 3090 K. Using the 5% deviation point from linear behavior of the Lindemann index curve, the upper limits of the melting points for 2.04, 2.55, and 3.57 nm octahedral nanoparticles are determined to be 2890, 3000, and 3090 K, respectively. Our results are also compared with several models of melting point depression. From our study, the nanoparticle shape affects the melting point, so the traditional spherical liquid-drop or liquid-shell models are not suitable. Other models considering coordination number,36 cohesive energy,37 and geometric factors38 also seem to differ from our MD results. The average coordination number of the nanoparticles is measured and used as the reference for comparison between different models (as presented in the xaxis in Figure 10). First, the melting temperatures are calculated by using the ratio of octahedral nanoparticle to bulk cohesive energy at 0 K (ground state). The melting temperatures (displayed as blue diamonds in Figure 10) are identical to the average coordination number model (ZNP/ZBULK). These ratios are compared to the NP to bulk melting temperatures for subtracting the effect due to the difference of the reference bulk melting temperature. In addition, the Wautelet model38 is compared, which considers different geometries, including spherical, cube-shaped, and octahedral among others; and the calculated melting points, shown as green triangles in Figure 10, are slightly lower than those for the cohesive energy model. The estimate of melting points of c-BN nanoparticles (TmNP) from our MD results (shown as red squares in Figure 10), using the reference bulk melting point (TmBULK) of 4150 K from our MD computation, gives the lowest value of the ratio of TmNP and TmBULK. This phase transition temperature of 4150K is obtained in our MD simulation for bulk c-BN crystal (10 × 10 × 10 unit cells) by introducing two plane dislocations as nucleation sites, producing an imperfect c-BN crystal consisting of 7620 atoms, since there are no external surfaces for melting to initiate. Given that the melting mechanism of c-BN nanoparticles is corner-initiated and phase-segregation-driven,
Figure 10. Predictions from several melting point depression models, compared to our MD results for melting points of c-BN octahedral nanoparticles. The results show that standard melting theories may not apply to cases where melting occurs with decomposition and phase segregation.
it is not surprising that the other analytical models do not predict the melting temperature similar to our simulations. Laser Heating of c-BN Powders for Validation of Decomposition and Phase Segregation during Melting. To verify the possibility of concurrent phase segregation during melting of c-BN, a laser is used to heat up c-BN powders, and the post-treated samples are characterized with TEM. The second harmonic (532 nm) of an Nd:YAG laser operating at 10 Hz at 20 mJ/pulse is employed to irradiate the c-BN powders in an argon atmosphere. In situ spectroscopic analysis of the thermal emission, similar to the work done by Xu et al.,39 indicates that the maximum heating temperature is in the range of 3050−3350 K. For the detailed information about the specifics of the setup for the laser treatment and the spectroscopy measurements, please refer to our previous works.40−42 The TEM image, Figure 11a, shows some of the initial c-BN particles, having a size of approximately ∼100 nm; and the inset shows the selected area electron diffraction (SAED) pattern of c-BN particles before laser heating, confirming the single crystalline structure. After laser treatment, decomposition and phase segregation of boron particles (∼50− 100 nm diameters) can be observed from the TEM images, as seen in Figure 11b. From the SAED pattern of the boron particles, inset of Figure 11b, the indexed spots with d-spacings of 4.40, 3.75, and 2.47 Å match very well with the reflections from the {200}, {111}, and {311} planes of tetragonal boron, respectively. In addition, some c-BN particles with nonmonocrystalline nanostructured features can be seen from the postheating results, which may be caused by the high intensity laser heating, as revealed in Figure 11c. The SAED pattern (inset of Figure 11c) confirms these features as polycrystalline cubic boron nitride. These results seem to indicate that the original c-BN particles have been reconstructed, rather than having been vaporized and condensed back onto the powder, which would likely take on discrete nanoparticle form. Further parametric investigation of varying laser fluences, along with in 10569
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octahedron is the most stable, followed by the truncatedoctahedron, then the cuboctahedron, and finally the cube. However, the transient MD simulations divulge that the specific truncated octahedron used here has a slightly higher melting point than the octahedron because of the decrease in surface to volume ratio after the removal of six tips of the octahedron and the dimerization on the {100} facets. The melting mechanism is further studied by investigating octahedral c-BN nanoparticles. The results reveal that melting starts from the corners and edges because the atoms with lower coordination number act as imperfection sites for initiating the melting process. Melting then propagates across the surface and proceeds to the interior, resulting in gradual increase in potential energy and Lindemann index of the nanoparticlea universal feature of melting of clusters. The size dependence of the melting point of octahedral nanoparticles is also reported here, and we conclude from the MD simulations that the size effect on melting is significant for small c-BN nanoparticles with a total number of atoms
