The four interior sulfur atoms are located at 0. 5, 0. 25, 0. 25 away from the nearest unit cell corners. There are 4 formula units of Sins per unit cell. Fig 1 : Sprightlier purple : Zinc & Yellow: Sulfur Fig 2 : Polyhedral Of sprightlier The arrangement of atoms can further be visualized by connecting the Sulfur bonds to form tetragonal polyhedral with Sulfur being enclosed in each of them. The normal of one of the faces can be calculated by finding the cross product of the two edge directions.Given that the directions of the cell edges corresponds to normal of the tetragonal face [1 x [1 = Using ATOMS, by expanding the number of unit cells, tooting the structure and observe down the [1 1 1] axis, stacking of tetragonal polyhedral are observed.
As the Zinc atoms are coordinated within its polyhedral, every polyhedral layer is a close packed structure with one atom being in contact with 6 other atoms. By separating it into individual layers, it can also observed that there are three different close packed layers that differ in spatial orientation 600 rotation apart.The three layers are given the fundamental BBC notation.
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Hence, a FCC structure follows an BBC stacking sequence. Fig 3: Upper right hand corner: Sprightlier polyhedral. Lower right hand ornery: Polyhedral viewed from [1 1 1] direction Hurwitz has a hexagonal structure with a basis of sins. There are 2 formula units of Sins per unit cell. The point coordinates of Zen atoms are at O, O, O & 1/3, 2/3, 0. 5 ; and S atoms at 1/3, 2/3 , 7/8. Similarly, each S is bonded with four Zen atoms.
Because of the atomic coordination, the polyhedral are tetragonal and they extend out of its unit cells.By extending the number of unit cells, stacking in the direction of c axis can be observed. Like sprightlier, every layer of polyhedral is close-packed. However, there are only two types of closed-packed layers. Hence for hexagonal structures, it has an BABY alternating sequence. Fig: Unit cell and polyhedral of Hurwitz With both structures having high symmetries and the ability to transform into one another at different temperatures, there is a possibility of high orientation relationship between the two Structures. Using ATOMS, it is observed that [1 1 1] sprightlier I |  Hurwitz.
Hexagonal layers are observed.The yellow atoms with a black line across represent S atoms on the same plane. Within each hexagonal ring, three S are on the same plane with a Zen atom directly below them. Fig 5: sophistries from [1 1 1] Paragraph 2 Fig 61 Hurwitz from  4 Zen or S atoms form a tetrahedron, depending on how we arrange the tetrahedrons, we get different structures or polytypic, the written and shapelier. First, we mainly look at a hexagonal unit cell and stack the Zen/S tetrahedrons accordingly. By varying the number of tetrahedrons, the arrangement of tetrahedrons in each layer, we get homogeneously 3 possibilities, either A, B or C layers.And by varying the BBC sequence we get different kinds of polytypic of the same period.
By varying the number of layers in each unit cell, we get polytypic of different period. Barman et al. Identified the 101_, ALL, ALL, 261_ and ALL. Fig 7 depicts the OIL structure.
As it is not a simple 31_ period stacking, a hexagonal (H) unit cell is used. From the paper, we know that the stacking sequence is (ABACA)(AC) or (8 2). The first 8 is in BBC cubic (C) stacking and last 2 of (H) stacking. For ALL it is a hexagonal unit cell.
For ALL, it is made up of three AL sequences, each different variant, resulting in overall period of ALL. 261- and ALL are hexagonal too. polytypic are named by their periodicity and the number Of consecutive stacking orders in one period. As mentioned earlier, there are 3 possible areas or ways (A/B/C) to arrange the tetrahedrons in a single layer. So a unit cell can consist of these few layers. However, there are some rules such that 2 consecutive layers cannot be the same and the first and end layers of a period cannot be the same. For example for 41, it cannot be (4) which is ABACA but can be (3 1) ABACA or (2 2) ABACA.Hence, polytypic can be stacked by different periodicity (more than 2 to over 20) and for each periodicity, there are different variants, hence there are a lot of possibilities.
For OIL it cannot be (10) which is BACCARAT, it can be (9 1) which is ABACAS-B, it can be 8 2) which is ABACA-ABA it can be (7 3) which is ABACA-CAB it can be (6 4) which is ABACA-BACK it can be (5 5) which is ABACA-CUBA It also can be (7 2 1) which is ABACA-CB-C or ABACA-CA-C and (5 3 2) which shows how complicated it can be if there are more and more semi-periods within the period.Hence there are a lot of possible OIL variants. Fig 7: Sins polytypic described by Barman et al. Paragraph 3 X-ray diffraction can be applied for the determination of crystallographic structures and the subsequent elucidation of layer sequences of polytypic. Despite its efficacy in crystallography, difficulties were faced in the termination of structures of vapor-phase grown Sins samples. This was due to the presence of uniform crystallographic regions with dimensions that are too small for accurate results.The result would usually consists of varied structures and I-dimensional stacking disorder.
To circumvent such a problem, x-ray crystallography can be complemented with electron diffraction as the latter allows for the study of tiny crystals. Moreover, electrons are more interactive with atoms. Through relating the observed X-ray diffraction intensity distribution with the intensity distributions of all geometrically Seibel layer sequences, the polyester’s layer sequence can be found. The layer sequence depends on the period m of the polytypic.As period m increases, the comparison becomes more difficult to conduct because the number of available layer sequences rises drastically. As such for higher polytypic, the number of layer sequences are limited to certain specifications by applying a proportionate relationship between the crystal structure and birefringence. On the other hand, for lower polytypic, taking measurements along (10. 1) columns would ultimately provide the period m.
Observing the OIL polytypic, which is a low polytypic, the diffraction spots appeared to be distinct and consistent.