Study On The Evolution And Properties Of Gold Clusters And Possible Defects On The Boron Cage

As it is known, the structure of any material determines its properties. For the difficulty in determining the structures of nanoclusters in experiments, simulation becomes an important method of deciding the structures of nanoclusters. Normally, it is believed that the structure of a nanocluster at zero temperature is its global minima, or to say the lowest point on its potential energy surface (PES). While, the fact is that the number of local minima increases exponentially with the number of atoms within the cluster, it is impossible to find each local minimum and compare them to find the lowest global minimum, so a good global optimizing algorithm is badly needed. Minima hopping is an algorithm to find global minima with high efficiency. It is based on the simple principle to explore the configurational space as fast as possible, and it tries to avoid revisiting known parts of the PES by adjusting some searching optimizing factors. Moreover, it does not base on thermodynamics.The minima hopping method includes two parts, the inner part and the outer part. In the inner part, the system is exited to cross energy barriers to reach the new minimum. And in the outer part, the program compares the new minimum with the history list and decides to accept it or not, and it adjusts the controlling parameters of the inner part to ensure that the system fleets away the visited area and reaches a new minimum as soon as possible. As we have the history list, which records the visited minima, we break the Markov chain, so that we could not get the thermodynamics distribution. However, it is not a defect of the method, as the idea of global optimization is to visit different parts of PES as soon as possible to find the global minimum.The minima hopping algorithm can not only find the global minima, as it could drive the system cross the barriers between different minima, it can also find near global minima isomers, which is also rich of physical importance. This algorithm can be combined with different numerical techniques such as density function theory (DFT), ab initio physical chemistry calculations. So the global hopping method could be applied to many systems.In the thesis, first we study the ground states of small gold clusters, from 13 to 318 atoms, with the minimum hopping method. We use RGL empirical potential, which is less accuracy but high efficiency. We find four types of basic structures, shown in fig.1. And we calculated the excess energy (fig.2), and its relation with different motifs of structures. We can not find clear relation between the clusters. Within the cluster we studied, we can not find certain trend of their evolution.By removing the weakest-bond atom of the global minimum of a cluster with N atoms, we may get the global minimum structure of a cluster withe N-1 atoms. While, it is not always the case. Only 43 cluster of all 213 cluster we studied act that way. There is no tight connection of motifs between neighboring clusters.We find for some clusters, the traditional thought low energy structures Fig. 1: Illustration of our classification of the various cluster structures. One row always shows the different perspectives (along x.y and z) axis of the same cluster. In the case of the 5-fold structure the atoms on the 5-fold axis are shown in grey instead of black. In the case of the t-fcc structure the atoms in the twin plane are shown in grey.Fig. 2: The quantity (?) for all the clusters that were studied. with high symmetry is not as energy favorable as some low symmetry structures. Though the accuracy of RGL potential is not sufficiently support that, it still could give us some idea of clusters structure motifs.Then we carefully study the structures of gold clusters. We find that, the atoms within a cluster local on certain energy stairs according to their energies, as shown in fig. 3:Fig. 3: panel A is Au₇₂ cluster, the color of each atom shows its energy, the darker the lower energy. Panel B is the compare energy of Au₇₂ cluster.The distribution of the atoms is connected with their geometric relation with the lowest energy atom. And between stairs there are some inter-stair atoms, the inter-stair atom number is connected with the symmetry of the cluster, though might be very weak. When a atom is too far away from the stairs, it is a discardable atom, which means that if we remove it we can get a new cluster at its global minimum. We seriously doubt that whether people can find a cluster with a discardable atom experimentally, though it might be the global minimum during simulations. Meanwhile, our analysis shows that, the low symmetric structures sometimes give the cluster better energy stairs, as we can see in fig.4. So we suggest that: when we consider the best structure for a cluster, we must take the energy stairs and inter-stair atoms into account.We study the near global minima isomers. Other low-energy structures for a cluster are so close in energy to the global minima structure that their Boltzman weight is not negligible, which could answer why in experiments we always find different motifs of structures instead of single structure motif.We use minima hopping algorithm with DFT to study B₈₀ system. B₈₀ is a newly theoretical predicted structure and has not be synthesized yet. To study the possible defects may be helpful, if in an initial stage of the syntheses an imperfect structure is generated, and people want to anneal it down to the perfect structure. We explore some 20 configurations with minima hopping algorithm andFig. 4: The energy stairs for several possible structures of Au₅₅ cluster.The blue stars are according the isocahedra; the green squares are according to the truncated octahedra; the red solid squares are according to the simple fcc structure, which is the global minimum structure by minima hopping. summarize some defects. The defects we found is shown in fig.5.Fig. 5: Illustration of the defects we found. Panel A. An illustration of the disturbed B₈₀ and perfect B₈₀ and the grey atoms illustrate the disturbed B₈₀; Panel B. atom c' and d' moves individually alone the vector, we can get hexagon and septagon defect. Panel C. is the hexagon defect, Panel D. is the septagon defect. B, C and D is according defectâ… ,â…¡,â…¢in tableâ… . Panel. E is the crushing defect and Panel. F is the Stone-Wales defect.We calculated the energy of different defects with Local Density Approximation and Generalized Gradient Approximation, and compare them with the energy of the perfect structure, shown in table 1. Once a defect is formed it can drift to any place on the boron cage. Different defects could co-exit, and stabilize each other.The B₈₀ cage like structure is stable against all these pointed defects as well as against strong deformations and changing in the number of atoms. So the B₈₀ Table. 1: The energies of various configurations with respect to the highest symmetry icosahedral fullerene as calculated with the LDA [132] and PBE [131] density functionals. All the energies are the energies of relaxed structures with the exception of perfect icosahedron in PBE and the distorted icosahedron in LDA.could be a kind of super plastic material.Since all boron nanostructures are built up according to the same basic building principle, it is to be expected that the same or very similar defects would be found in other boron nanostructures.