- Nano Express
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Theoretical Calculations of Refractive Properties for Hg3Te2Cl2 Crystals
© Bokotey. 2016
- Received: 11 October 2015
- Accepted: 10 May 2016
- Published: 16 May 2016
This paper reviews the optical properties, such as refractive index, optical dielectric constant, and reflection coefficient of the Hg3Te2Cl2 crystals. The applications of the Hg3X2Y2 crystals as electronic, optical, and optoelectronic devices are very much determined by the nature and magnitude of these fundamental material properties. The origin of chemical bonding in the crystals is very important for definition of the physical and chemical properties. The main structural feature of the Hg3X2Y2 crystals is the presence of covalent pyramids [XHg3] and linear X-Hg-X groups. Optical properties are calculated according to the model proposed by Harrison. The refractive index in the spectral region far from the absorption edge is determined within the generalized single-oscillator model. The calculated results are found to be in good agreement with experimental data.
- Corderoite structure
- Wyckoff positions
- Refractive index
The crystal structure of mercury chalcogenhalogenides possesses a lot of features which promote the appearance of structural instabilities. All chalcogenchlorides and Hg3Te2Br2 are crystallized in the corderoite structure and described by the T5-I213 space symmetry group [1–3]. The main feature of synthesized and natural mercury chalcogenhalogenides is the formation of numerous polymorphic modifications and existence of isomorphic substitutions in chalcogen and halogen anion sublattices. Interest in them is caused by the ability to form continuous raw of solid solutions that allows them for different variations of physical and chemical properties. Hg3X2Y2 crystals are characterized by physical properties such as optical activity, high refractive index, transparency in visible and IR-range, photoconductivity, and electrooptical effect. Hg3X2Y2 (X = S, Se, Te; Y = F, Cl, Br, I) compounds, their synthesis and polymorphism are investigated in Refs. [1–10]. Optical activity and refractive index are studied in Refs. [1, 10–14]. Raman and IR spectra are investigated in Refs. [2, 15, 16]. The detailed research results of absorption edge are presented in Refs. [17–19]. These structural and optical properties of mercury chalcogenhalogenides crystals can be combined in modelling of physical and chemical characteristics of nanomaterials for nonlinear optic devices.
The present paper is aimed at the theoretical studies of the refractive index and reflection coefficient in Hg3Te2Cl2 crystals. It should be noted that the refractive index is one of the fundamental properties of a material because it is closely related to the electronic polarizability of ions and the local field inside the material. Besides that, theoretical study of refractive index gives more detailed information about crystals properties. The refractive index evaluation is of considerable importance for applications in integrated optic devices, where materials refractive index is the key parameter for device design. The calculated results are compared with available experimental data. Such results are obtained for the first time.
Structure of Hg3X2Y2 Crystals
A special feature of all modifications of Hg3X2Y2 (X = S, Se, Te; Y = F, Cl, Br, I) compounds is a stronger ordering of the anions, as compared to the cations, owing to the strong covalent Hg–X bonds, which form various configurations with virtually the same «fixed» bond-lengths. The studied structures consist of strong covalent and connected pyramids [XHg3] and linear X–Hg–X groups which in different structural types form different spatial connections. At the same time, the presence of the «hinge-joint» bonds in the covalent –X–Hg–X–Hg–X– radical results in the appearance of many polymorphic modifications . The structure of the α-Hg3S2Cl2 type is realized in the cases, when the chalcogen anion size is more than halogen anion size S2− (0.182 nm), Se2− (0.193 nm), Te2− (0.211 nm) >Cl− (0.181 nm); Te2− (0.211 nm) >Br− (0.196 nm) .
Crystal data of Hg3Te2Cl2
Formula units per cell
Ratio of anions radii X 2−/Hal−
There are two types of chemical bonds in investigated crystals: the covalent—between mercury and chalcogen atoms and ionic—between mercury and halogen atoms [18–20]. The Hg–Cl bond length is 2.99 Å, while the Hg–Te bond length is 2.65 Å. Besides that, many interesting chemical bond aspects connected with existence of intrinsic defects. As Hg–Te is the main chemical bond, such structure interpretation reflects physical and chemical properties of the Hg3Te2Cl2 crystals.
For calculation of the refractive index, the Harrison bonding-orbital method was used [20, 21]. Using the Harrison bonding-orbital theory is irreplaceable for calculation of parameters, which describe the structure of energy bands, as well as for understanding the physical nature of this structure. The essence of bonding-orbital method consists in the description of the localized charges on the basis of interactions between electronic orbitals of structure atoms. As follows from the theory, analysis of covalent and ionic crystals is almost always based on the description of electron conditions in crystal in the form of linear combination of electronic orbitals. The complex approach to the investigation of optical properties includes some steps: neglect all matrix elements between bonding and anti-bonding states; reduce Hamiltonian matrix to two matrixes, one of which is constructed on valence band conditions, and another—on conductive band conditions; use Wannier functions for zeroing of matrix elements between bonding and anti-bonding states in matrix. As the result, one can obtain the diagonal matrix elements, which correspond to Wannier energy levels, as well as matrix elements between the bonding states, responsible for splitting of these levels in bands.
Most optical properties of semiconductors are integrally related to the particular nature of their electronic band structures. Band structure is in turn related to the type of crystallographic structure, the particular atoms, and their bonding. Both the valence band and conduction band states are important for prediction of the refractive index or optical dielectric constant.
The crystal optical investigations provide an important information concerning the nature and the properties of Hg3X2Y2 crystals. The refractive index is a very important physical parameter related to the microscopic atomic interactions. From the theoretical stand point, there are basically two different approaches in viewing this subject: on one hand, considering the crystal as a collection of an electric field, the refractive index will be related to the density and the local polarizability of these entities. On the other hand, considering the crystalline structure represented by a delocalized picture, the refractive index will be closely related to the energy band structure of the material, thorough quantum-mechanical analysis required is complicated and the results obtained are very particular [22–24]. The refractive index in the spectral region far from the absorption edge was determined within the generalized single-oscillator model. It makes possible to find the energies of filled electronic states using the Hartree–Fock values  for the valence levels in complex crystals. The approach becomes particularly useful when it is simplified by including only nearest-neighbor couplings and using universal parameters, which allows direct prediction of all properties .
Calculated parameters of Hg3Te2Cl2 crystals
V 2, eV
V 3, eV
It should be noted that theoretical calculations using complex approach always give underestimated values in comparison with experimental data. Refractive index varies from 3.06 at 4650 Å to the vicinity of the absorption edge, then starts to level off and reaches 2.68 at 7000 Å  for Hg3Te2Cl2 crystals. The calculated value of the refractive index is n theor = 2.3. A good agreement is observed with experiment . This is verified by the calculation of the optical dielectric constant which depends on the refractive index.
The refractive index calculations of the Hg3Te2Cl2 crystals using the Harrison bonding-orbital method are presented. Satisfactory agreement between experimental data and calculation results is obtained. It is shown that this approximation allows to analyze the optical properties of the Hg3X2Y2 (X = S, Se, Te; Y = F, Cl, Br, I) crystals. It is evident that structural features, covalent Hg–X chemical bonds of the Hg3X2Y2 crystals reflect their physical and chemical properties. Optical properties play a vital role in understanding the structure and the nature of chemical bonding in the crystals. Refractive index is very important magnitude that decided the optical and electronic behavior of crystals used for possible applications. It can be concluded from the present and previous studies that Hg3Te2Cl2 crystals are perspective nanomaterials for application in nonlinear optical devices. Finally, it should be noted that results obtained in this paper confirm the possibility of their application for analysis of the optical properties of complex compounds.
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