The shape or morphology of a crystal is extremely important to the energetic materials. It can have enormous impact on the physical and chemical properties, such as fluidity, apparent density, electrostatic accumulation, pressure resistance, stability, and so on1, 2. These properties can directly affect initiating ability, sensitivity and other explosive performance. For example, it is well known that the acicular crystal of lead azide (LA) is poorer for fluidity and stability, but higher sensitivity than the columnar crystal3. The excellent crystal morphology can improve the safety and stability of the energetic materials, which is also helpful to industrial production and safe application4-6. Therefore, the study on the crystal morphology is vital to energetic materials.
Metal carbohydrazide complexes with strong oxidizing acid radical ions, used as initiating explosives, ignition composition, gas generator and burning rate modifier to propellants, have been extensively studied experimentally and theoretically7-15. Structures of metal carbohydrazide derivatives with sulfate, perchlorate, chloride and polymeric nitrogen were successively reported16-18 using infrared spectrum analysis and X-ray single crystal diffraction analysis methods. It is found that metal carbohydrazide derivatives have excellent properties, such as appropriate sensitivity, good safety performance and strong initiating ability. Zhang et al.19-22 carried out an in-depth research on the complexes. They found that cadmium carbohydrazide perchlorate and zinc carbohydrazide perchlorate had excellent properties and they were widely used as green initiating explosives, without using toxic and hazardous raw materials and eliminating waste in the manufacture and application processes.
In this work, we predicted the crystal morphology of manganese carbohydrazide perchlorate ([Mn(CHZ)3](ClO4)2), iron carbohydrazide perchlorate ([Fe(CHZ)3](ClO4)2), cobalt carbohydrazide perchlorate ([Co(CHZ)3](ClO4)2), nickel carbohydrazide perchlorate ([Ni(CHZ)3](ClO4)2) and cadmium carbohydrazide perchlorate ([Cd(CHZ)3](ClO4)2) by Bravais-Freidel-Donnay-Harker (BFDH) and growth morphology method. The crystal-morphologies of them are studied experimentally without crystal-control reagent.
The calculation was performed using the Universal force field (UFF)23, 24, which was successfully applied to model a wide range of complexes metal complexes25-27, DNA28, and other organic systems. It is set based on the element, its hybridization and connectivity29.
The initial configurations of transition-metal carbohydrazide perchlorate complexes were obtained from the experimental data by X-ray single crystal diffraction method. Then the crystal structures were optimized by the density functional theory (DFT) using the CASTEP package30. We found that the GGA (PW91) proposed by Perdew and Wang31, 32 was more reliable to predict the structures. Therefore GGA (PW91) was used in all calculations. For the calculation, the cutoff energy was 300.0 eV on the plane wave. The k-point grid is set as 2 × 2 × 1 in the Brillouin zone by using the Monkhost-Pack scheme. The convergence of total energies is less 0.01% under the selected kinetic energy and the k-point grid. During the self-consistent field (SCF) calculations, the convergence tolerance of energy was set to 2.0 × 10-6 eV, the maximum of residual force was 0.005 eV·nm, the maximum of displacement of atoms was 0.02 nm and the maximum of residual bulk stress was 0.1 GPa. The optimized crystal structures were used as the starting point for the morphology calculations.
The morphology of the crystal structure of these complexes was studied using MORPHOLOGY code. BFDH and growth morphology method were used to predict the crystal growth in vacuum. BFDH method was based on the interplanar spacings of different crystal faces and took into account the crystal symmetry33. The growth morphology (AE model) was based on the intermolecular forces in crystallization by Hartman and Perdok34.
The attachment energy (Eatt) is defined as the energy per molecule released when a new slice of depth dhkl is attached to the crystal face35. It is the sum of the interaction energy per molecule (Ei(hkl)) between a slice of thickness dhkl and the ith underlying slice.
The relationship between the lattice energy of the crystal (Elatt) and the energy of a growth slice of thickness dhkl (Eslice) is given by
The relative growth rate (Rij) of the crystal face is proportional of its attachment energy (Eatt)36. The face with the lowest attachment energies are the slowest growing, and the most important to morphology.
[Mn(CHZ)3](ClO4)2, [Fe(CHZ)3](ClO4)2, [Co(CHZ)3](ClO4)2, [Ni(CHZ)3](ClO4)2 and [Cd(CHZ)3](ClO4)2 used in the experiment were synthesized, purified and dried according to the literature. The purities of products were more than 99.5%. In order to obtain the single crystal, the products of them were dissolved in deionized water (6.25 × 10-8 S·cm-1), and kept the solution in the cups for 15 d. The crystal morphology of them was performed using BX51 microscope (Olympus Corp., Japan). The actual parameters of the equipment are as follow: Built-in kohler illuminator, voltage 12 V, and zoom magnification ×4 to ×100.
The molecular structures of [Mn(CHZ)3](ClO4)2, [Fe(CHZ)3](ClO4)2, [Co(CHZ)3](ClO4)2, [Ni(CHZ)3](ClO4)2 and [Cd(CHZ)3](ClO4)2 are shown in Fig. 1 The crystal structures of them in the solid state are in space group P21/c with Z = 4 in the unit cell. Crystal cell dimensions and cell angles are listed in Table 1.
According to the Arrhenius and Gibbs Thomson equations (equation (4)), the crystal nucleus formation is obtained37.
where r is the nucleation rate, A is the frequency factor, $\sigma $ is the interfacial tension between solid and liquid phases, V is the cell volume, k is Boltzmann′s constant, T is absolute temperature, and S is the degree of the supersaturation of the solution.
It can be seen that the big cell volume can decrease the nucleation rate from the equation (4). That means the order of nucleation rate for the complexes is in the following sequence: [Cd(CHZ)3](ClO4)2 < [Mn(CHZ)3](ClO4)2 < [Co(CHZ)3](ClO4)2 < [Ni(CHZ)3](ClO4)2 < [Fe(CHZ)3](ClO4)2 when A, $ \sigma $, T, and S are certain.
The morphology of transition-metal carbohydrazide perchlorate complexes predicted using the BFDH and AE models in vacuum was shown in Fig. 2-Fig. 6. It can be seen that the morphology of them are close to oblong block shapes. The similar shapes may be attributed to the same the ligand and the outer ion of ClO4-. While the contribution of metal cation contribute to morphology is very little. The regular crystal shapes and the smooth surfaces of them are beneficial to improve the free-running property and safety.
The energy value and the facet area percent for cleaved main growth faces using BDFH and AE models are listed in Table 2. Obviously, the total facet area is mainly contributed by (101), (002), (011) faces and their symmetrical crystal-faces. The percent for the three faces occupied the total crystal-surface area are almost 90%. Hence, we can deduce that the faces of crystal growth for the homologous complexes are similar.
According to the attachment energy, the probable non-bonded energetic interactions during crystal growth can be accounted38. With the more negative the attachment energy in the particular direction, the growth rate of the crystal in the direction is faster, the crystal face bounding the growth direction is less morphologically important39. In Table 2, the minimum attachment energy absolute values of transition-metal carbohydrazide perchlorate complexes are all on (101) or (002) face. There native growth rates (Rij) of different crystal face are also calculated and listed in Table 2. It can be obtained that (101) and (002) faces with the minimum growth rates are the most important growth direction for transition-metal carbohydrazide perchlorate complexes.
Where dm/dt is crystal growth rate, D is diffusion coefficient, d is thickness of liquid film, A is crystal surface area, S is the degree of the supersaturation of the solution.
From the equation (5), the bigger crystal surface area can improve the crystal growth rate. In Table 2, the order of sum facet area is [Fe(CHZ)3](ClO4)2 > [Co(CHZ)3](ClO4)2 > [Ni(CHZ)3](ClO4)2 > [Mn(CHZ)3](ClO4)2 > [Cd(CHZ)3](ClO4)2. Therefore the order of crystal growth rate keeps the same sequence with sum facet area when D, δ and S are same.
Taking BDFH and AE models into consideration, the cleaved main growth face, (101), (002) and (011) faces from the crystal were determined, their structures are shown in Fig. 7-Fig. 11. In those cleaved main growth faces, oxygen atoms from ClO4- and nitrogen atoms from CHZ all existed in or near the crystal surfaces and the intermolecular interactions are strong. Hence, we can choose the surface active agent containing the active hydrogen atoms in the functional groups as the crystal-control reagents. The oxygen atoms on the crystal faces can form hydrogen bond with the hydrogen of the crystal-control reagents, and the relative growth rates can be changed. By this method, the crystal morphology growth was controlled.
In order to detail the growth model on main faces, the bonding network viewed on the top of faces and the schematic images of incorporation of a growth unit for [Cd(CHZ)3](ClO4)2 are shown in Fig. 12-Fig. 14. Where the discrepant color of the balls represents that the four molecular positions are different in the crystal. Along the (002) face, the bonding network appear pleated. The molecules in number 1 and 3 are on the first layer, and those in number 2 and 4 are on the second layer. The molecules alternately grow in rows and lines. Along the (011), the bonding network seems the inclined upward steps. The molecules in identical number grow simultaneously in same floor and the molecular number increase step by step. Along the (101) face, the arrangement in rows is same to that along the (002) face, but the molecules dislocated between adjacent layers.
The crystal-morphology of [Mn(CHZ)3](ClO4)2, [Fe(CHZ)3](ClO4)2, [Co(CHZ)3](ClO4)2 and [Ni(CHZ)3](ClO4)2 without crystal-control reagent was synthesized and observed by BX51 microscope (Olympus Corp., Japan) in Fig. 15.
It can be seen that the crystal morphology of [Mn(CHZ)3](ClO4)2, [Fe(CHZ)3](ClO4)2, [Ni(CHZ)3](ClO4)2 and [Cd(CHZ)3](ClO4)2 are obviously short columnar polyhedrons on the crystal morphology. In literature40, [Co(CHZ)3](ClO4)2 also appear columnar polyhedrons shapes. Through the comparison of BDFH and AE model, it can be concluded that AE model are nearer to experimental morphology, and more better to predict crystal growth morphology. Therefore, we ascertain that the predicted crystal morphologies for carbohydrazide perchlorates by AE model are reliable.
The crystal growth morphologies of manganese carbohydrazide perchlorate, iron carbohydrazide perchlorate, cobalt carbohydrazide perchlorate, nickel carbohydrazide perchlorate and cadmium carbohydrazide perchlorate were predicted by BFDH and AE models. It is found that (101), (002) and (011) faces from the crystal are the main growth faces. The growth on (101) and (002) faces are the most important growth direction because of the minimum relative growth rates. Through the cleaved main growth faces, it can be inferred that crystal-control reagents with the active hydrogen atoms in the functional groups can effectively control the crystal morphology for them. The experimental morphologies of carbohydrazide perchlorates are short columnar polyhedrons using a coldfield-emission scanning electron microscope. By comparing BDFH, AE model with experimental morphology, it is concluded that AE model are more reliable to predict crystal growth morphology for carbohydrazide perchlorates.