Abstract
In this research work, we have explored the physical and topological properties of the crystal structure of metal-insulator transition superlattice (GST-SL). In recent times, two-dimensional substantial have enamored comprehensive considerations owing to their novel ophthalmic and mechanical properties for anticipated employment. Recently, some researchers put their interest in modifying this material into useful forms in human life. Also, Metal-Insulator Transition Superlattice (GST–SL) is useful in form of a thin film to utilize as two-dimensional (2D) transition metal dichalcogenides (TMDs). Moreover, we have defined the computed-based bond properties such as the degree constructed topological indices and their heat of formation for single crystal and monolayered structure of Ge-Sb-Te. Also, this structure is one of the most interesting composites in modern resources of science.
1. Introduction
The germanium , Antimony , Tellurium , and some other elements are present as metalloids. These metalloids lead to heat, electricity intermediates, metals, and they form large structure oxides. Metalloids are normal elements that have divided properties among metal and nonmetals, present in the Earth’s outside layer [1], which occurred in an environment with a combination of organic and inorganic mixtures and other normal synthetics. The unpredictable modern abuse of these elements and possible dangers to humans are restricted in free use [2].
Some researchers put their interest in modification this material into useful forms in human life for different fields such as the alloy in form of a thin film is utilized as then the two-dimensional (2D) transition metal dichalcogenides (TMD) were discovered comparable applications in numerous fields [3]. These are made of cationic elements such as transition metals, group (, ), and group [4]. Moreover, the anionic elements of chalcogenides (, , , ) are essential in numerous fields. Moreover, to improve the bandgap energy of Ge–Sb–Te (GST), the physico-chemical properties are useful for sensing, in nonvolatile RAM, thermoelectric, and face change properties [5, 6]. The 2D TMDs are mainly dissimilar to pure transition bulk compounds and show new properties [7, 8]. Phase change material properties of complex with a group of chalcogenides are promising technology and well known for so many years [9, 10].
A chemical graph is an ordered pair of two finite sets and , where is the set of vertices (atoms) and is the set of edges (bonds) in chemical graph [11]. The valence of molecules is usually portrayed by the vertex degrees [7, 12].
The number of edges affiliated with a vertex is identified as the degree of the vertex [13]. In this study, it is indicated by . Among different categories of topological indices, we will deliberate about degree-based topological indices depending on degree of end vertices of a graph, (see Table 1). For detailed study and application of these indices, see [24–27], respectively. In current circumstances, the basic aim of graph theory is the elaboration and enforcement of many contemporary scientific theories in assorted branches of chemistry. The QSPR/QSAR study is one of the essential reasons for broadening graph theory to chemistry [28].
2. Structure of
Another kind of material named superlattice (GST-SL) has attracted large attention because of its ultralow power utilization. This superb exhibition has been ascribed to a special information storage system such as crystalline to crystalline stage change as compared to previous references [10, 29]. 1D semiconductor nano stares, attributable to their low dimensionality, display novel properties that discover application in numerous gadget fields [30]. The working rule of ordinary gadgets depends on the changes between the metastable and amorphous crystalline stages set off either by optical. The thin film is deposited by femtosecond, picosecond, and nanosecond laser ablation [31, 32].
To this point, numerous investigations have been distributed over the most recent couple of years, proposing various distinctive atomic arrangements either for the amorphous and glasslike structure of the conceivable GST compounds or highlight by three unique stoichiometries, specifically (most common for PMC s) [33], , and . The bulk GST intensifies two distinctive glasslike polymorphs: a metastable stage with rock salt design and a stable ground state structure at marginally low energy having a hexagonal/rhombohedral structure [34].
It is shown that the imperfection is restricted into two atomic layers of , , and shows confirmed stacking flaws. In-situ analysis demonstrated that the and Te bilayers can be effectively reconfigured into such bilayer stacking shortcomings with ensuring the arrangement of another van der Waals hole, showing a component of underlying reconfiguration of the building block in layered compounds [35]. The enormous distinction of dielectric capacities between the amorphous and glass-like structure of -based stage change materials ( s) utilized in-memory storage gadgets likewise influences their Schottky barrier heights (s) and consequently their electric gadget properties. Here, the s of each structure of , , , and are found by thickness of useful supercell computations [2].
The worldwide substance stoichiometry of the material and the local substance stoichiometry of individual layer blocks are needed to have a protecting band hole as per the electron checking model examination. The electron property can be changed by changing the local stoichiometry, for example, creating flaws around van der Waals holes (Figure 1) [10]. Moreover, the unite cell and generalized structure of are depicted in Figure 2.
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After some basic computation, we can see that and . The principle strategy utilized here is the way to deal with edge partitioning and vertice degree calculating (see Table 2).
2.1. Computations of Results for
(i)The general Randi index of . For , we have(ii)The atom bond connectivity index of . The ABC index with the help of Tables 1 and 2 is(iii)The geometric arithmetic index of . The GA index with the help of Tables 1 and 2 is(iv)The first Zagreb index of . The first Zagreb index by using Tables 1 and 2 is(v)The second Zagreb index of . The second Zagreb index by using Tables 1 and 2 is(vi)The hyper Zagreb index of . The hyper Zagreb index by using Tables 1 and 2 is(vii)The forgotten index of . The forgotten index calculated by using Tables 1 and 2 is(viii)The augmented Zagreb index of . The augmented Zagreb index with the help of Tables 1 and 2 is(xi)The Balaban index of . It is easy to see that the Balaban index by using Tables 1 and 2 is(x)The redefined first Zagreb index of . The redefined first Zagreb index with the help of Tables 1 and 2 is(xi)The redefined second Zagreb index of . The redefined second Zagreb index by using Tables 1 and 2 is(xii)The redefined third Zagreb index of . The Redefined third Zagreb index by using Tables 1 and 2 is:
3. Applications and Discussion of Computed Results
The geometric arithmetic index gives improved prediction as compared to other descriptors. We can easily see that the heat formation of is lower as the values of increases. The first and the second Zagreb indices are established to appear within specific estimated expressions for the total -electron energy [7, 20]. The augmented Zagreb index gives better correlation for measuring the strain energy of molecules.
The computed numerical results of Randi indices are portrayed in Tables 3 and 4. The graphical illustration of for is characterized in Figures 3 and 4.
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We can use equation (14) for the transformation of Randi c indices into the approximate heat of formation for .
The computed numerical results of ABC index and GA index are portrayed in Table 5. The graphical illustration of these indices is characterized in Figure 5. The transformation of ABC index and GA index into the approximate heat of formation of at any level can be estimated with the help of the following equation:
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The computed numerical results for the first and the second Zagreb indices are shown in Table 6, while their graphical illustration is shown in Figure 6. The transformation of the first and the second Zagreb indices into the approximate heat of formation of at any level can be exercised with the help of the equation as follows:
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Numerical comparison of hyper Zagreb index and forgotten index is shown in Table 7, while graphically, their comparison is shown in Figure 7 Equation (17) can be employed for the transformation of hyper and forgotten indices into the approximate heat of formation of at any cubic level.
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Numerical results for AZI and indices are shown in Table 8, while Figure 8 illustrates the results graphically. For the transformation of augmented Zagreb index and Balaban index into the approximate heat of formation of at any level can be exercised with the help of the equation as follows:
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Numerical results of redefined Zagreb indices are shown in Table 9, while Figure 9 illustrates these indices graphically. The transformation of redefined Zagreb entropies into the approximate heat of formation of at any cubic level can be employed by using the equation as follows:
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4. Conclusion
In this paper, some degree constructed topological indices are computed which can be used to find out different physicochemical properties. More preciously, we have computed the Randi index, the atom bond connectivity index, the geometric arithmetic index, the first and second Zagreb indices, and the Balaban index. We also determined a relation between the degree constructed topological indices with heat of formation, and then, we discussed the crystal structure of (GST) and also its applications in different fields. The heat of formation and the entropy measure are computed in this study, which is useful to analyze the thermodynamic properties of the metal-insulator transition. We illustrated the comparison between the degree constructed topological indices and heat of formation, which leads us to know the physicochemical properties of this two-dimensional material GST.
Data Availability
The data used to support the findings of this study are cited at relevant places within the text as references.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
This work was equally contributed by all writers.