An Investigation of the Mechanism on Interfacial Charge Transformation of the TiB2/Cu Composites Studied by the First Principles

Yao Shu (  shuyao_jack@2008.sina.com ) Guangdong Academy of Sciences https://orcid.org/0000-0001-8847-0549 Juan Wang Guangdong Academy of Sciences Yongnan Xiong Guangdong Academy of Sciences Xing Luo Guangdong Academy of Sciences Jiazhen He Guangdong Academy of Sciences Cuicui Yin Guangdong Academy of Sciences Fei Gao Nanchang University Shaowen Zhang Beijing Institute of Technology Kaihong Zheng Guangdong Academy of Sciences Fuxing Yin Guangdong Academy of Sciences Fusheng Pan Guangdong Academy of Sciences


Introduction
Copper metals have been widely applied into the electronic technology, transportation and aerospace fields due to its high electrical conductivity and premium ductility [1][2][3] . However, owing to the lower hardness and strength of the pure copper metals, the further applications of the copper metals are limited. Therefore, the copper alloy and copper matrix composites (CMCs) were designed to enhance the hardness and strength properties of the copper metals. Though, the copper alloy owns the better properties, the hardness while the ductility are still the conflict of not settled [4][5][6][7] . However, due to the reinforcements introduced into the copper metals, the hardness and strength of the copper matrix have been apparently enhanced. Therefore, CMCs have been widely utilized into the electronic technology, transportation and aerospace fields [8][9][10][11] .
Due to the wildly application of the CMCs, the reinforcements have been verified to be the key factors for enhancing the hardness and strength of the CMCs. The reinforcements, however, are mainly classified as the carbide (B4C, TiC, and WC) [12][13][14] , the oxide (Al2O3, ZrO2) [15,16] and the ceramic (Si3N4, AlN) [17,18] and which had been already applied into CMCs for years. Nevertheless, many theoretical studies have been investigated in interfacial electronic properties of the CMCs via the first principles studies, such as Al2O3/Cu [19 ] , TiC/Cu [20 ] , WC/Cu [21 ] ,ZrC [22 ] and TiB2/Cu [23 ] composites. Although, these investigations are mainly focused on interfacial stabilities, electronic properties and interfacial ultimate tensile stresses, the quantum interfacial charge transformations of the CMCs were less to be considered. Therefore, the influence of interfacial stabilities specifically with the charge transformation of the interfacial atoms were not further discussed.
As is known to all, the charge communications have widely existed in biomolecules [24] , organic electronic devices [25] , semiconductors [26] , super-molecules [27] , catalysts [28] , ceramics [29] , metals [30] , polymers [31] and so on. The properties of these materials are deeply affected and relayed on the charge communications when they syntheses, processed, decomposition and shaped.
In this essay we are concerning about the relationships between the charge transformations of the interfacial atoms and the interfacial stabilities. The interfacial stabilities, electronic properties and ultimate tensile stress of the TiB2/Cu have been studied in previous works. Therefore, we have taken the interfacial charge transformations into account to investigate the influences of the charge transformation vs. the interfacial stabilities of the TiB2/Cu. TiB2/Cu interfacial models were constructed via the TiB2 (0001) [32,33] and Cu (111) [34] surface, due to their low surface energies. In addition, we chosen three stacking ways of the Cu and two terminated atoms (Ti-terminated and B-terminated) of the TiB2 to construct the TiB2/Cu composites models. The three stacking sequences were considered for the Cu respective as "HCP", "MT" and "OT". In specific, the "HCP" stacking refers to the interfacial Cu atoms are on-top the first layer of TiB2 atoms, "MT" stacking refers to the interfacial Cu atoms reside atop the midpoint of the atomic connection of the first layer of TiB2 atoms and "OT" stacking means the interfacial Cu atoms reside atop the TiB2 second layer atoms. Namely, there were six TiB2(0001)/Cu(111) interfacial models generated for theoretical investigations. Therefore, six TiB2/Cu interfacial models are shown in Fig.   1, and they are labeled as TT-HCP, TT-MT, TT-OT, BT-HCP, BT-MT and BT-OT respectively. In order to eliminate the interactions between the surface atoms, a 15 Å vacuum layer was added along z directions for each surface. All calculations calculated via the first principles method to TiB2/Cu interfacial models under the periodic boundary conditions and plane wave basis set of the Cambridge Serial Total Energy Package (CASTEP) Code [ 35 , 36 ] . The Perdew-Burker-Enzerhof (PBE) functional generalized gradient approximation (GGA) [37] were deal with the exchange-correlation interactions in the all calculations. The Brillouin zone was sampled with the Monkhorst-Pack k-point grid [38] 11111 for all TiB2/Cu interfacial models, Cu(111) slab and TiB2 (0001) slab, respectively. The atoms of the TiB2/Cu were relaxed for acquiring the ground state by Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [ 39 ] . Nevertheless, the total energy tolerance, maximum force tolerance and maximal displacement calculating convergent details were applied as 1.0 × 10 -5 eV/atom, 0.03 eV/Å and 1.0 × 10 -5 Å, respectively. In addition, 500 eV was chosen as the cut-off energy for the plane wave as the expansion in reciprocal space. In order to calculate the electronic properties of the interfacial atoms, the 3d 10 4s 1 , 3s 2 3p 6 3d 2 4s 2 , and 2s 2 2p 1 valence electron configurations were applied to Cu, Ti and B atoms respectively. The total atoms for TT-TiB2/Cu, Cu (111) slab and TiB(0001) slab are 20 (21 for BT-TiB2/Cu),7 and 13 (14 for BT-TiB2(0001) slab), respectively.

The interfacial thickness of the TiB2(0001)/Cu(111).
The interfacial thickness is not referring to the distance of the interfacial atoms, but the range influenced by atomic electrons of the heterogeneous interface. Therefore, in this section, the PDOS is z axis coordinate of the 3 rd Ti layer atom while for BT-TiB2/Cu which is z axis coordinate of the 3 rd B atomic layer atom) and l Cu( z) is z axis coordinate of the 2 nd Cu layer atom. Hence, the interfacial thickness of the TiB2(0001)/Cu(111) have been predicted and their specific values are displayed in Table 2. In Table 2

The bond length and bond populations of theTiB2 and Cu cell
In order to investigate the electronic structure and bonding state of atoms performed on TiB2(0001)/Cu(111) interfaces, the Mulliken populations [40] are applied to study the electrons of interfacial atom and bond population of the TiB2(0001)/Cu(111), TiB2 cell and Cu cell, respectively.
The bond length and populations reflect the character and strength of the bond properties. Therefore, the overlap population could be an objective criterion for bonding state between the two atoms assessing the covalent or ionic nature of a bond [41] . The high value of the bond population indicates the formation of the covalent bond, while the small value implies the ionic interaction maintained between the two atoms. Herein, the ionic character can be measured by the effective ionic valence, namely, the difference between the formal ionic charge and the Mulliken charge on anion species.
Nevertheless, if the bond population value is 0 which indicates a perfect ionic bond, if the values greater than zero, which indicate an increasingly levels of covalence involved [ 42 ] . Therefore, and partial covalent properties. These results have been qualitative confirmed by partial density of the state (PDOS) in previous work, and the mechanism of formation of these bond also have been explained in theoretical study [23] .

The bond length and bond populations of the TiB2(0001)/Cu(111)
Since the heterogeneous interfaces have been formed in TiB2 (0001) Nevertheless, in Fig. 3  which is a hybrid bond with most metallic properties and partial covalent properties in TiB2 cell [43] . These results are accord well with the results of the Wad, γint, interfacial distance and interfacial thickness which have been discussed in previous work [23] .

The charge transformation of Ti and B atoms in TiB2 cell
The The valence electrons for neutral Ti, B and Cu atoms have been displayed in Table 3, and they are 12 e, 3 e and 11 e, respectively. Moreover, the outermost electrons for Ti, B atoms in TiB2 are different with their corresponding neutral atoms, and they are 10.9 e and 3.55 e for Ti and B atoms  [43] 3.54 [43] 10.82 [45] 3.59 [45] respectively. Therefore, contrasted to the neutral Ti atom, the Ti atom in TiB2 cell lost 1.1 e electrons which are equally shared by the two B atoms surrounded with. Compared with the neutral B atom, each B atom in TiB2 cell acquiring 0.55 e.

3.3.2The charge transformation performed in TiB2(0001)/Cu(111)
The electron density distribution, electron difference distribution and electron localized function have been discussed for the TiB2(0001)/Cu(111) in previous work [23] , the charge communication performing on interfacial regions of the TiB2(0001)/Cu(111) have been explicitly confirmed.
However, these results only qualitatively study the electron transformation on interfaces of the TiB2(0001)/Cu(111), while the quantitative study of the charge communication is not specifically discussed. Therefore, the changes of charge difference for each atom performing at the interfaces is still confused, and it is necessary to figure out the charge transformations of the specific atoms undertaking at the interfaces. Therefore, 3d 10 4s 1 , 3s 2 3p 6 3d 2 4s 2 , and 2s 2 2p 1 are applied as the valence electrons for Cu, Ti and B atoms in TiB2(0001)/Cu(111), respectively. Nevertheless, the specific atoms need to be figured out initially for different models, namely, for TT and BT-TiB2(0001)/Cu(111) models their specific chemical formula are Ti5B8Cu7 and Ti4B10Cu7, respectively. Since the formula of TT-TiB2(0001)/Cu (111)  and Cu atoms, so that the specific atoms lost or obtained charges can be finally determined.
Moreover, the electrons for each atom in TiB2(0001)/Cu(111) of six interfacial models have been calculated and which display in Table S1. to Table S6. The electrons of the ions in TiB2(0001)/Cu(111) calculated from the Table S1 to Table S6, and then the total results displayed in the Table 3. From the Table 3 Based on the specific values in Table 4, the interfacial charge transformations are carried out via the Eq. (4) and the Eq. (5), and the calculated lost charges mostly equal to the obtained charges within no more than 0.02 e difference. Taking TT-HCP for instance, however, the loss of the charge of the  Because the interfacial bonding and charge transformation are the key parameters for interfacial stability of the TiB2(0001)/Cu(111), the change of the electrons belonged to the orbit leading the hybridization of the orbitals . Therefore, the electrons belonged to 3d 10 4s 1 , 2p 6 3d 2 4s 2 and 2s 2 2p 1 for Cu, Ti and B atoms in TiB2(0001)/Cu(111) need to be analyzed to investigate specific changes of the oribits, respectively.

Orbital electrons transformation of the interfacial atoms of the TiB2/Cu
Since the TiB2 is an ionic crystal, which contains two types of the bond, i.e., the δ bond and the π bond. The δ bond are formed due to the sp 2 hybridization happened during the two Banionic acquiring the electrons. However, the 2pz orbital of the two Banionic not involving the hybridization and leading to the combination of the localized π bond [43] . According to the Table 6 Table 6, it can be found that the charges in 2px orbits equal to those in 2py orbits of Ti, B Cu atoms. For Ti and Cu atoms, the charges in 3dxy equal to those in 3dx 2 -y 2 , and it is similar to the charges in 3dzx, 3dzy orbits of Cu and Ti atoms in

Conclusion
In this work, the charge transformation of the interfacial atoms for TiB2/Cu were studies via the first principles. The relationship between the charge transformation and stabilities of the interfaces indicated that the bonding state and ways determined the stability of the heterogeneous interfaces, and main results can be generalized as below: (1) The interfacial thickness layers have been calculated for TiB2/Cu composites via the PDOS. The interfacial thickness layers of the TT-TiB2/Cu are higher than 0.715 nm, while those of the BT-TiB2/Cu are lower than 0.715 nm.

Data availability
The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request. Code availability N/A.