The New Polytype Structures Pd₈T₃ (T = As, Sb)

Abstract

The polytypic structure of Pd₈T₃ (T = As, Sb) compounds was revealed using the graph method. The topology of the layers and the regular sequence of their alternation are analyzed. The ordering of antimony and arsenic atoms by the positions at the nodes of layer-networks and the positional disorder in the sequence of alternating layers, which lead to the formation of different structural polytypes, are considered.

INTRODUCTION

From the example of the structures of a group of compounds with the general formula Pd₈T₃ (T = As, Sb), the application of graphs for description and analysis of the structures of platinoid minerals is considered. The group under consideration includes the following minerals: stillwaterite, Pd₈As₃ [1], arsenopalladinite, Pd₈As_2.5Sb_0.5 [2], and mertieite, Pd₈Sb_2.5As_0.5 [3], as well as the synthetic phase Pd₈Sb₃ [4, 5] (Table 1).

Table 1. Crystallochemical characteristics of compounds of the family Pd₈T₃ (T = As, Sb)

The compounds of the Pd₈As₃–Pd₈Sb₃ series are characterized by the absence of complete isomorphic miscibility. The structure of the mineral depends on the As/Sb ratio. In the Pd₈As₃–Pd₈Sb₃ series, three structural types are realized: Pd₈As₃, Pd₈As_2.5Sb_0.5, and Pd₈Sb₃, which have both common structural features and specific differences.

The structures of these compounds can be described as derivatives of the close packing, formed by pnictogen atoms, like arsenic or antimony, the voids of which are occupied with palladium atoms.

The theory of close packings has been applied to the description of mineral structures by many authors. Among them, it would be especially valuable to mention the so-called “Blue Book” by N.V. Belov “Structures of ionic crystals and metal phases” [6]. Belov considered possible variants of alternating layers of close packing and described simple binary compounds predominantly with ionic bonding. Belov’s ideas in relation to a large number of mineral species have been developed in Lima-de-Faria’s works [7–11]. Thomson introduces a quantitative parameter to estimate the distortion of the “anion skeleton” of close packing from the ideal one in silicate structures [12].

There are many examples of describing the structures of minerals and synthetic compounds in the form of nets and graphs in crystallochemistry. Without aiming to quote all of them, we will provide here some, in our opinion, key examples. In 1954, Wells [13, 14] used the concept of networks in the description and systematization of structures of compounds. Wells gives the basic principles of distinguishing 3D networks in structures—networks of connected points with three-dimensional periodicity: (1) each point is connected to three adjacent points, (2) the distance between two connected points is always smaller than to any other point, (3) the network has no loops.

Graph theory was applied by Smith and Rinaldi to describe tetrahedral frameworks [15, 16]. The principles developed by Smith served as a basis for the systematics covering a great number of synthetic silicates with framework-type structures consisting of tetrahedral rings. We are talking about zeolites, which, due to the presence of channels in their framework, capable of accommodating not only atoms but also whole molecules, have found extensive practical application as molecular sieves.

Moore [17] and Hawthorne [18] used graphs to describe minerals. Natural compounds of some classes, such as phosphates and sulfates, are characterized by the absence of polymerization of anionic polyhedra. Due to this, Moore [17], when developing the systematics of phosphates, relied on distinguishing clusters from octahedrally coordinated cations, considering the degree of their polymerization, types of bonding, and types of connection of cationic octahedra and anionic tetrahedra. Hawthorne [18, 19] undertook a topological analysis of the types of combining octahedral and tetrahedral polyhedra into clusters in the structures of oxides and oxysols and described them using graphs.

METHODS

In our approach to the description of the structures of palladium minerals, the structures are “resolved” into layers–nets of atoms. The choice of such a description for palladium minerals of the Pd₈T₃ group (T = As, Sb) is due to the peculiarity of their structure and the nature of the chemical bond. Palladium and arsenic (or antimony) atoms are distributed over different layers in the structure, which are parallel to the ab plane and alternate along the c axis in different ratios. If we consider atoms as nodes of networks and connect the nearest nodes (all atoms belonging to the same layer) with connectivity lines, then we obtain a network. The geometry of the distribution of lines and nodes in the network determines the topology of the layer of atoms. In fact, such a network is a two-dimensional graph, representing as a whole a set of networks with a certain sequence of their packing.

A similar principle was used in Pearson’s systematics [20], which, in our opinion, is the most fundamental generalization in the field of crystal chemistry of compounds with metallic bonding (intermetallides). Pearson analyzed the crystal chemical properties and systematized the structure of more than 500 metal phases based on distinguishing atomic nets.

The separation of atomic nets and the analysis of their topology allows us to formalize the description of the structure and identify patterns in the structure of palladium minerals. Let us consider the structures of compounds of the Pd₈T₃ (T = As, Sb).

The layers of arsenic and antimony atoms have the same topology in all structures of the Pd₈As₃–Pd₈Sb₃ series: these are triangular nets 3⁶. This is the topology of the layers in the close packing: the arrangement of the balls forming the packing corresponds to the arrangement of the nodes of the nets 3⁶. A schematic representation of the nets is shown in Fig. 1.

Fig. 1.

The scheme of net of pnictogen atoms in compounds of the Pd₈Т₃ family.

Structures of the family Pd₈T₃ (T = As, Sb) are formed by two types of triangular pnictogen net. The nodes of the networks Т are occupied by either arsenic atoms or antimony atoms. The nodes in networks of the first type are not equivalent as they have different symmetry (nodes T2 and T3 in Fig. 1). Such net are assigned the letter code “A.” It is in these layers that impurity atoms occupy the position T3. In networks of the second-type, all nodes (nodes T1 in Fig. 1) are equivalent and occupied by one type of atom. Such nets are assigned the letter code “B.” The expanded crystal chemical formula of compounds of this group is written as Pd₈T1_1.5T2₁T3_0.5. Layers A and B also differ in symmetry and are characterized by different groups of two-dimensional symmetry (Table 2).

Table 2. Symmetry of nets of pnictogens in the structures of the family Pd₈T₃ (T = As, Sb)

In general, there are several variants for occupying net nodes with atoms of two varieties. In the structures of the end members, all nodes of the nets are occupied by the same atoms. In compounds containing an admixture of the second component, a different degree of order‒disorder is realized. With complete disordering, the admixture of atoms of the second type is distributed over all T positions in the structure. With complete ordering, the admixture atoms completely occupy only one of the three T positions. Furthermore, in the case of a sufficient concentration of impurities, it is possible that one position is occupied by atoms of one type; the second one, by atoms of another type; and the third one, by atoms of two types.

RESULTS AND DISCUSSION

Four variants of filling the net nodes with arsenic and antimony atoms are realized in the Pd₈T₃ structures (T = As, Sb) (Table 3). All nodes are occupied by arsenic atoms in the stillwaterite structure: Pd₈As1_1.5As2₁As3_0.5. All nodes in the structure of the Pd₈Sb1_1.5Sb2₁Sb3_0.5 phase are occupied by antimony atoms. One of the three possible positions in mertieite (Pd₈Sb_1.5Sb₁As_0.5) is occupied by arsenic atoms. One of three positions in the arsenopalladinite structure Pd₈{As1₁As1$_{{0.5}}^{'}$}As2₁Sb3_0.5 is occupied by antimony atoms.

Table 3. Population density of nodes of pnictogen networks in the structures of the family Pd₈T₃ (T = As, Sb)

The layers of arsenic and antimony atoms in the structures of this family are located parallel to the plane ab of an elementary сell. Layers of types A and B alternate with each other with cells (Fig. 2).

Fig. 2.

The sequence of alternating layers of pnictogens in compounds of the Pd₈Т₃ family (arsenic atoms are indicated in black, antimony atoms are indicated in blue).

The sequence of alternating layers of pnictogens in  the structure of stillwaterite, a three-layer, distorted cubic close packing, is ABB… (Fig. 2, Table 4).

Table 4. The sequence of alternating layers in the structure of compounds of the family Pd₈T₃ (T = As, Sb)

The sequence of alternating layers of pnictogens in the structure of antimony-bearing Pd₈T₃ compounds is different: it is derived from hexagonal double-layer close packing: ABABAB….

The elemental cell of the arsenopalladinite structure includes two layers of pnictogens: AB… (Fig. 2, Table 4). However, the “ideal” hexagonal close packing is distorted: antimony and arsenic atoms are shifted from high-symmetrical positions with triclinic structure, and only the general topology of the layer 3⁶ is preserved.

In the structure of mertieite Pd₈Sb_2.5As_0.5 and in the pure antimony difference, Pd₈Sb₃ phase, one can observe the positional disorder. These compounds are isostructural and are characterized by a cell with a 12-layer sequence of the arrangement of pnictogen network: ABA'B 'A''BAB 'A'B''A'B… (Fig. 2, Table 4). There occurs the displacement of pnictogen layers in the ab plane relative to each other, and only the thirteenth layer repeats the first.

The c parameter of the elementary сell in compounds of this family is proportional to the distance between two adjacent layers of pnictogens, which is approximately 3.7 Å. In stillwaterite, which includes three layers of pnictogens in the elementary cell, the с parameter is 10.311 Å. As arsenopalladinite includes two layers of atoms-pnictogens, the с parameter is 7.5255 Å. Mertieite and the Pd₈Sb₃ phase include 12 layers of arsenic and antimony atoms, and the c parameter increases to 43.037 Å.

Pd atoms in Pd₈T₃ (Т = As, Sb) structures occur in voids of distorted close packing (CP) consisting of arsenic and(or) antimony atoms (Fig. 3).

Fig. 3.

The voids (vacant spaces) of the close packing consisting of antimony and arsenic atoms in the arsenopalladinite structure are occupied by palladium atoms (red balls).

Pd atoms in the stillwaterite Pd₈As₃ structure occupies the 8/9 octahedral and 8/9 tetrahedral voids of the CP. Pd atoms in the structures of arsenopalladinite Pd₈As_2.5Sb_0.5, mertieite, Pd₈Sb_2.5As_0.5, and the Pd₈Sb₃ phase occupy all octahedral positions and 5/6 of the tetrahedral ones of the CP.

Let us consider the arrangement of Pd atoms in structures of compounds of the family Pd₈T₃ (Т = As, Sb). Pd atoms are shifted from the geometric center of voids, some of them to the “lower” layer of pnictogens, the others, to the “upper” layer. Thus, there are two layers of Pd atoms between each pair of adjacent layers of pnictogens. This set can be called a structural module of the Pd₈T₃ compounds (Fig. 4).

Fig. 4.

The sequence of alternating layers of palladium atoms and layers of pnictogen atoms in the arsenopalladinite structure, projection onto plane bc (palladium atoms are red balls, arsenic atoms are black balls, antimony atoms are blue balls).

Three types of layers of Pd atoms with different topologies are distinguished: triangular nets 3⁶ (“d”), nets of triangles and pentagons (“e”), and nets of tetragons and triangles (“f  ”) (Fig. 5). Layers of Pd atoms are also located parallel to the plane ab of the cell and alternate towards the axis c. Here, a certain sequence of alternation is observed.

Fig. 5.

Topology of layers of palladium atoms in structures of the Pd₈Т₃ family.

Only the structure of stillwaterite, Pd₈As₃, includes all three types of layers of Pd atoms. The Pd layers in stillwaterite is characterized by the following sequence of layers: AdeBffBed…. The antimony varieties of Pd₈T₃ compounds have only two types of layers of palladium atoms in their structures: triangle nets (d) and combined nets made of triangles and pentagons (e). Arsenopalladinite, Pd₈As_2.5Sb_0.5, has only six layers in a cell: AdeBed…, Mertieite, Pd₈Sb_2.5As_0.5, and the synthetic Pd₈Sb₃ phase have a cell consisting of 36 layers: AdeBedA'deB 'edA''deBedA'deBedA'deB''edA'deBed… (Table 4).

The described properties of the structure of compounds of the family of Pd₈T₃ (Т = As, Sb) indicate that the structures are polytypic. The structure of the pure arsenic variety, stillwaterite, Pd₈As₃, is a trigonal polytype and a derivative of the three–layer closest cubic packing (CCP), the structure derivative from the NaCl-type CCP. The structure of the arsenopalladinite, Pd₈As_2.5Sb_0.5 is a triclinic polytype. Mertieite Pd₈Sb_2.5As_0.5 and Pd₈Sb₃ phases are rhombohedral polytypic varieties in the family studied. The structures of compounds containing antimony in their composition are derived from two-layer hexagonal close packing (HCP), the structure the NiAs-type HCP.