Energy band theory insulator, conductor, and semiconductor.

Elastic properties

            In order to conclude the influence on the substance by applied stress, elastic constants such as C11, C12, and C44. Such constants play a major role in finding information on the rigidity and stability of the material. The numerical first-principle approximation technique established by Charpin and incorporated in WIEN2K (King-Smith, et al., 1994) is used for the measurement of the rigidity and resilience of specific materials to calculate stress components for small strains. Table 4.2 shows the measured values C11, C12 and C44. The following expression is used to study mechanical stability (Muller et al., 1979).

            The mechanical consistency of these compounds is shown in a cubic step in the above criterion for certain products. Factor A for anisotropy, which provides information on wave speed in a crystal. In the engineering sciences this factor is important and is very much associated with persuading micro cracks in materials. Factor of anisotropy in the following expression in cubic antiperovskite crystals:

            A is equivalent to unity for completely isotropic material. The divergence from the unit gives details of the degree of elastic anisotropy of the Crystal measure A value (Ahmed et al., 2015) shown in Table 4.2, the anisotropic XNNi3 (X= Sn, Cu, Mg) factor values vary from the unity. In line with Table 4.2. The anisotropic values measured for the compounds analyzed are 0.62 for SnNNi3, 0.24 for CuNNi3 and 0.37 in MgNi3, respectively. We have also calculated Kleinman parameters in table 4.2, Kleinman parameter (ξ), which describes Kleinman’s relatively large cation position and anion value representing less bond resistance, and a smaller value is a big bond resistance. Table 4.2 tabulates and measures the values by interpreting expression.

            Table 4.2 indicates that MgNNi3 has greater resistance to bonding than other compounds tested. We have also measured the ratio of Poisson and Young’s compound element that provide information concerning the material’s strength and rigidity. It is noted from Table 4.2 that SnNNi3 is harder than MgNNi3 and CuNNi3. For fragile material, the value of Poisson is small, but for ductile it is indicated by 0.33 (Bannikov et al., 2010). Pugh provides the critical value for ductile and brittle transformation to predict the ductile and brittle behavior of solids. In Table 2 we concluded SnNNi3, MgNni3, and CuNNi3 that if the material appears brittle, otherwise ductile, all of the material is ductile (GB / G > 0.5). This ratio is 0.38251, 0.21221 and 0.35016 for Sn Ni3, CuNNi3 and MgNNi3, indicating this ductile in nature, according to Table 2.2. Table 2.2. Additional information is also given as the Pugh reference the critical value is 0.5 higher for brittle materials else material is labeled as ductile. For this law, the critical value is more than 0.5. XNNi3 (X= Sn, Cu, Mg) elastic constants are measured using key compounds. The following expressions are used to calculate other elastic parameters (e.g. shear modulus G, youth modulus, Poisson relation and bulk modulus B) using the following constants (C11, C12, C44) (Bannikov et al., 2010).

     ..…………………………… (4.7)

      ………………….….. (4.8)

Poisson’s ratio is also indicated by bonding and rigidity of materials. Inter atomically interacting structures have a value of μ near 0.25, and the value of μ is 0.1 to 0.33 for covalent or metallic materials. The determined Poisson ratio values are provided in table 4.2, which demonstrate that compounds (X= Sn, Cu, Mg) are primarily made from clustered inputs that suggest that these materials are ionic in nature.

Table 4.2: The optimized structural parameters , independent elastic constant Cij, bulk modulus B, shear modulus G , tetragonal shear modulus G’, Pugh ratio G/B , Young’s modulus Y, Poission ratio v, Zenger’s anisotropy index A and  Kleinman parameter,€ of XNNi3 (X= Sn, Cu, Mg)

ParameterSnNNi3  CuNNi3  MgNNi3  
 Current  WorkExperimental WorkAdditional workCurrent workExperimental WorkAdditional WorkCurrent  WorkExperimental WorkAdditional work
B  (Gpa)215.1238.9228.2209.2211.9216.9189.9194.1195.1
G  (Gpa)79.9363.953.941.254.979.160.063.957.3
G’ (Gpa)107.1151.0177.190.976.174.1107.196.283.8
Y   (Gpa)214.1177.1151.1115.1153.1211.2160.9157.2172.8

a Ref ( I. Shein, et al., 2010) b Ref (Bannikov, V., I. Shein, et al., 2010).

4.3 Electronic Properties

            Electrons of an individual nuclear-linked atom can only have those energy levels. When two atoms are brought closer together than one other, though, they are separated into two sub-levels called states. Under the power of the powers of other stable atoms. The smaller the electrons, the larger the difference will be. The permissible energy states are discrete and tightly separated, forming a continuous sequence. There are a large energy states in between two allowable energy bands that cannot be filled by electrons. These are called the forbidden states of energy and the range between two consecutive allowable bands of energy is called the forbidden gap in energy. The electrons are called valence electrons in most of the external orbits. The electron bands are known as the valance band. It may not be fully or partially filled, but never empty. The area above the valence strip is considered a driving line. Free electrons are occupied. Because they’re the main driver. Also they are called electrons of conduction. Both empty and partly complete can be used for the conduction band. The band is called the filled band below the valance band. It doesn’t play a part in conducting. It is because of the electrons in an atom that are bound. Figure 4.2 shows insulator, conductor, and semiconductor according to the
energy band theory.

Figure 4.2: Energy band theory insulator, conductor, and semiconductor.

            Insulators are materials that are strongly and closely bound with the valance electron to its atoms. These have an empty steering strip, a filled valance strip and have a large energy gap of several volts. Drivers are the materials in which we have a lot of free electrons. They’ve got; a partially filled lead band, a partially filled valance band and no energy difference. Semiconductors are the materials with electrical characteristics between insulators and conductors. They have a partially filled valve band (at room temperature), a partially filled conductor band and a small power gap (1ev). A single semiconductor is an insulator of 0k. For modern measurements, SCF (auto-compatible field) checks these properties for electrical and magnetic properties of these XNNi3 compounds (X= Sn, Cu, Mg) are used.

Thanks to their particular band arrangement, each substance has different electrical properties. WC-GGA (Wu-Cohen06) and GGA+U potentials are used for test spin polarized electronic band configurations. The electronic performance of XNNi3(x= SN, Cu, Mg) compounds is determined with symmetrical lattice parameters of dual cell structure. Figures with strong symmetry directions in the first areas of Brillouin, 4.2-4.9 for GGA+U show the determined band structures of XNNi3 in both spin channels. According to our results all substances with mixed valence bands and bands are metallic. The previous SnNNi3 analysis estimated the behavior of the metal in CuNNi3 and MgNNi3. The latest predictions also revealed metallic behavior, as previous measurements were focused on the optimization of single cells and current estimates are based on the optimization of double cells. There is no theoretical study of double-cell optimization properties of SnNi3, CuNNi3 and MgNNi3, and other researchers will examine our findings on these compounds in future. We measured the entire (TDOS) and partial state (PDOS) density of XNNi3 compounds (X= Sn, Cu, Mg), in order to test the role of various ion states in the electronic band structure. The GGA and GGA+U determined TDOS and PDOS are shown as shown below respectively. In all states including s, p, d and f atomic conditions Sn, N, and Ni the presence of the SnNNi3 Fig is shown in spin-down and spin-up networks. For spin-ups, states d and p have highest conductive band currency while the states and f have extreme valence band attendance for spin, s, p, d and f and maximum conductive band turnout for fermi levels Figure (4.10). GGA+U method and GGA method shows the metallic comportment of SnNNi3. The CuNNi3 TDOS and PDOS appear in a certain number. In Spin up d. p. and d. f. states have the largest participation in conductive band and a partial involvement in a conductive band only, in Spin up d. p. and f. The charge density of the electron is the electric charge of a body or area of a space per unit volume. The electron charge density plans will help to tell the bonding structure of the solids as a related enforce (Perdew et al., 1986) The electron density of the compounds XNNi3 (X= Sn, Cu, Mg) is calculated as shown in Figure 4.13. These figures still describe its bonding nature of metals like (X = Sn, Cu, Mg) and Nitrogen (N) and Ni. Figure 4.13 shows the calculated densities in plane (110). For PtNNi3, it is completely ionic if the bond between N and Ni is spin up and down. Although there is a minor polarization in the plane of (110) and a weak covalent bond among Sn and Ni, as shown in Fig (a) it spins and spins along Sn and Ni. For spin-up in the plane, the boundary of N with Ni in CuNNi3 is ionized absolutely (110). While there is a strong polarization and minor covalent relation in the (110) plane between Cu and Ni to spin up and down the Cu and Ni boundary, as shown in Figure 4.3. For a spin in planes (110), the relation between N and Ni is entirely ionic in MgNNi3. While the plane (110) of Ag and Ni is strongly polarized and weakly covalent, it flips and spins between Mg and Ni.

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