High-temperature behavior and structural studies on Ca₁₄Al₁₀Zn₆O₃₅

1 Introduction

In a paper on the incorporation of zinc oxide in the phases relevant for the cement-making process, Bolio and Glasser [1] reported the phase relationships in the system CaO–ZnO–Al₂O₃. The results of their comprehensive experimental study pointed to the existence of two ternary phases only: Ca₃Al₄ZnO₁₀ and Ca₆Al₄Zn₃O₁₅, respectively. The melting points of both compounds were specified as 1350 °C ± 25 °C as well as 1260° ± 25 °C. Independently, Barbanyagre et al. [2] confirmed the results concerning the presence of two ternary phases. However, they suggested that the composition of the second compound does not exactly lie on the Ca₃Al₂O₆–ZnO join but rather corresponds to Ca₁₄Al₁₀Zn₆O₃₅. Their proposed chemical formula was finally confirmed by the results of a single-crystal structure analysis.

According to ref. [2], Ca₁₄Al₁₀Zn₆O₃₅ crystallizes in the acentric cubic space group F23. The crystal structure can be described as a complex framework based on corner sharing [AlO₄]- and [ZnO₄]-tetrahedra. Unfortunately, no more detailed analysis of the net including the distributions of the aluminum and zinc cations on the different T-sites has been performed. This is somewhat surprising, because the differences in scattering power for X-rays between Al and Zn should be more than sufficient to distinguish these two species in a single-crystal structure analysis. In the course of an ongoing project on the system CaO–Al₂O₃–ZnO, we decided to re-investigate the cubic acentric crystal structure in more detail including a so-far missing topological analysis of the rather unusual tetrahedral framework. Furthermore, the evolution of the structure at elevated temperatures has been studied by in-situ single-crystal diffraction.

2 Experimental details

3 Results

3.1 Description of the crystal structure

Basically, our results confirm the structural features presented in ref. [2], except for the inverse chirality and the cation distributions on the four crystallograpically independent tetrahedral positions. The structure of Ca₁₄Al₁₀Zn₆O₃₅ can be described as a tetrahedral framework of corner sharing [(Zn,Al)]O₄-units. Site occupancy refinements indicated that the T1 site is the main sink for zinc (80.8 (4)% Zn & 19.2 (4)% Al). While the Zn-Al distribution on T3 is almost balanced (55.8 (3)% Zn & 44.2 (3)% Al), the remaining two tetrahedral positions show a strong preference for Al: T2: 9.0 (3)% Zn & 91.0 (2)% Al; T4: 100% Al. Notably, an unconstrained optimization of the Al/Zn populations under the assumption of full occupancy of the T-sites resulted in an almost ideal chemical composition. For the final calculations, we therefore introduced a restraint that fixed the total Al and Zn content to 40 and 24 atoms in the unit cell. Notably, the refined occupancies for the ambient-temperature structure conformed to the values obtained for the subsequent high-temperature data sets within two standard uncertainties, i.e. the Al–Zn distributions are virtually temperature independent. As can be seen from Table 2, all tetrahedra reside on special Wyckoff-positions with site-symmetry groups 23, 3 or 2.

According to Shannon [12], the effective ionic radius of Zn²⁺ for fourfold coordination (r _Zn = 0.60 Å) is considerably larger than the value for Al³⁺ (r _Al = 0.39 Å). Therefore, it is not surprising that the increasing Zn-content within the sequence T4-T2-T3-T1 is directly reflected in an increase of the average T–O distances (see Figure 1). The evolution of the <T–O>-values as a function of the Zn-concentration, X _Zn, can be adequately described by the following linear expression, where R corresponds to the correlation coefficient:

⟨ T − O ⟩ = 1.752 12 − 0.245 25 × X Zn / Å , R = 0.989.

Figure 1:

Evolution of the average T–O distances for the four independent T-sites as function of their Zn-concentrations.

The values for the individual T–O distances are within crystallochemically acceptable ranges. However, the four tetrahedra show pronounced differences concerning their deviations from regularity. Numerically, the degree of distortion can be expressed by the quadratic elongation QE and the angle variance AV [13]. For the four different tetrahedra these values are as follows: T1: QE = 1.007, AV = 28.808; T2: QE = 1.004, AV = 16.941; T3: QE = 1.026, AV = 91.725; T4: QE = 1.000, AV = 0.000. Due to the high site-symmetry, the pure aluminum tetrahedron around T4 is undistorted, while the [T3O₄]-unit shows the largest distortion.

Concerning the connectivity within the framework, four- (T2, T3, T4) as well as six- (T1) connected tetrahedra can be distinguished. Notably, the net contains one bridging oxygen (O1) simultaneously linking four [T1O₄]-units – a structural feature that has not been observed in silicate or alumosilicate frameworks. The four T1-O1-T1 angles are identical and have a value of 109.47°. The resulting tetrahedral configuration around O1 allows for a maximum spatial separation of the four tetrahedra sharing a common vertex. A projection along [100] of the complex network of [TO₄]-moieties is presented in Figure 2. Due to the high symmetry in combination with the large number of different T-sites it is difficult to achieve a concise visual description of the net. A detailed topological analysis of the framework including additional graphical aspects will be presented in a separate section.

Figure 2:

Projection of the tetrahedral framework parallel to [100]. Color coding: T1: green, T2: orange, T3: blue, and T4: pink. Red spheres represent oxygen atoms.

Charge compensation in the structure is achieved by the incorporation of additional aluminum and calcium cations occupying four large cavities of the tetrahedral network located around the 4b sites at (½,½,½). The corresponding cations are coordinated by six to seven oxygen anions and form a bulky cluster of general composition [AlO₆][Ca₁₄O₃₆] (see Figure 3). At the heart of the clusters are [M4O₆]-octahedra which are exclusively occupied by Al³⁺. They are surrounded by a total of fourteen Ca²⁺-ions distributed among the sites M1, M2 and M3. In more detail, eight inner (M2, M3) and six more distant (M1) calcium positions can be distinguished. The calcium cations in turn provide linkage between the octahedra and the tetrahedral framework, i.e. the central [M4O₆]-groups are isolated from the enclosing tetrahedra.

Figure 3:

Projection of a single heteropolyhedral cluster along [100]. The Al-dominated central [M4O₆]-octahedron is indicated in yellow. Large blue spheres: Calcium atoms. Red spheres represent oxygen atoms.

3.2 Thermal expansion

The temperature dependency of the lattice parameter a and the unit-cell volume V of Ca₁₄Al₁₀Zn₆O₃₅ is given in Table 1. On increasing temperature, a continuous behavior is observed. For processing of the data the TEV software [14] has been used. First, the evolution of the parameter was fitted to polynomials of different orders. The direct comparison of the coefficients of determination (CoD) as well as visual inspection of the resulting curves indicated that second order polynomial were sufficient to describe the temperature dependences. Actually, the following polynomials were obtained:

a T = 14.844 3 + 1.041 2 × 10 − 4 T + 5.781 2 × 10 − 8 T 2 / Å CoD : 0.999

V T = 3270.9 2 + 0.069 1 × T + 4.0 1 × 10 − 5 T 2 / Å 3 CoD : 0.998

Figure 4A and B shows the evolution of the corresponding normalized lattice parameter and volumes a/a ₀ and V/V ₀, respectively. In the next step, the polynomial for a and its derivative were employed for the determination of the thermal expansion coefficient α in the infinitesimal limit using the formalism of Paufler and Weber [15]. Of course, for a cubic material the second rank tensor α_ij describing thermal expansion degenerates to a scalar property. The values for α calculated between 25 and 800 °C in steps of 25 °C (see Figure 5) show an increase from 0.72 × 10⁻⁵/°C⁻¹ (at 25 °C) to 1.32 × 10⁻⁵/°C⁻¹ (at 790 °C).

Figure 4:

Temperature dependence of (a) the normalized unit-cell parameter a/a ₀ and (b) the cell volume V/V ₀.

Figure 5:

Temperature dependence of the thermal expansion coefficient α calculated for the infinitesimal temperature limit.

An alternative way to characterize the lattice strain induced by thermal expansion is the calculation of the finite Lagrangian strain tensor η which has been determined from the lattice parameters at 25 °C and 790 °C using the program WinStrain [16]. For a cubic material, η has only one independent component η ₁₁ = η ₂₂ = η ₃₃ = 0.0092 while the remaining three components are strictly zero. Dividing the strain by the temperature difference ΔT = 765 °C one obtains an estimation for average thermal expansion <α> = 1.2 × 10⁻⁵/°C⁻¹ valid in the relevant temperature interval.

4 Discussion

A detailed topological characterization of the framework including coordination sequences, extended point symbols as well as tiling analysis has been performed with the help of the program ToposPro [17]. Therefore, the whole crystal structure is described by a graph composed of the vertices (T-sites containing Al/Zn and O atoms) and edges (bonds) between them. The nodes of the graph can be classified according to their coordination sequences {N _k } [18]. They represent a set of integers {N _k } (k = 1,…, n), where N _k is the number of sites in the kth coordination sphere of the Al/Zn or O- atom that has been selected to be the central one. The corresponding values for the four symmetrically independent T-sites up to n = 10 (without the oxygen nodes) are summarized in Table 4. Furthermore, the corresponding extended point symbols [19] listing all shortest circuits for each angle for any non-equivalent atom have been determined. The results for the four symmetry independent T-sites are also summarized in Table 3.

Another interesting aspect in the construction and classification of tetrahedral frameworks is to look for certain stable configurations of T-atoms that occur in different types of nets and, therefore, reflect transferable properties. These configurations are the so-called composite building units or CBUs [20]. In the literature, several types of CBUs have been proposed including, for example, secondary building units (SBUs [21]) or natural building units (NBUs [22]) which are also referred to as natural tiles. An overview of the different terms and definitions can be found in the review paper of Anurova et al. [23], for example. When compared to previous definitions of building units, tilings of three-periodic nets based on natural tiles have a couple of advantages, the most important one is related to the fact that there exists a strict mathematical algorithm for their derivation. A natural tiling represents the minimum number of cages that are not the sums of smaller cages which form a unique partition of space [22]. Individual faces of the tiles (cages) are made from so-called essential rings [22]. The concept of natural tilings has been applied to the current framework in Ca₁₄Al₁₀Zn₆O₃₅ and the results of the calculations are summarized in Table 5.

Table 5:

Summary of the tiling characteristics observed in the tetrahedral net of Ca₁₄Al₁₀Zn₆O₃₅.^a

Tiling signature: 4 [63]+[34]+[64]+[316. 616]	Transitivity: [4 4 4 4]
Tile 1	Tile 2
Face symbol: [63]	Face symbol: [34]
V, E, F: 8, 9, 3	V, E, F: 4, 6, 4
Volume of the tile: 23.16 Å3	Volume of the tile: 4.05 Å3
Color code: yellow	Color code: green
Wyckoff site: 16d (0.102, 0.102, 0.102)	Wyckoff site: 4c (¼, ¼, ¼)
Tile 3	Tile 4
Face symbol: [64]	Face symbol: [316. 616]
V, E, F: 10, 12, 4	V, E, F: 42, 72, 32
Volume of the tile: 41.11 Å3	Volume of the tile: 680.38 Å3
Color code: violet	Color code: blue
Wyckoff site: 4d (¼, ¾, ¼)	Wyckoff site: 4b (½, ½, ½)

1. ^aV: vertices; E: edges; F: faces. The color code refers to color of the tiles in Figure 6.

Four different natural tiles can be distinguished by their face symbols [19] which encode the faces of which the tiles are made up. The general terminology is [a ^m .b ⁿ .c ^o … ] indicating that a tile consists of m faces representing a polygon with a vertices, n faces forming a polygon with b corners, and so on. Notably, the present network involves both very simple tiles ([3⁴]) with 4 vertices as well as complex tiles such as ([3¹⁶. 6¹⁶]) with a total of 42 vertices. Three of the tiles ([3⁴], [6⁴] and [6³]) within the present net have been already observed as NBUs in zeolite-type framework structures [24] and are also denoted as t-sod-a-1, t-hes and t-kah, respectively. According to a statistical evaluation [23], t-kah actually represents the most frequent natural tile in zeolites. To the best of our knowledge the present [3¹⁶. 6¹⁶] tile has not been described before. The arrangement of the natural tiles within the tetrahedral network is given in Figure 6.

Figure 6:

Arrangement of the four different natural tiles in the tetrahedral network of Ca₁₄Al₁₀Zn₆O₃₅. Grey spheres correspond to the nodes (T-sites) of the net. Colors refer to the color code given in Table 5.

The derived volumes of the four cages range from 4.05 (for [3⁴]) to 680.38 ų (for [3¹⁶. 6¹⁶]). It is the latter tile that encloses the large void hosting the aforementioned heteropolyhedral cluster cations. The tiling signature and the transitivity of the tiling are also listed in the header of Table 5. The tiling signature enumerates all non-equivalent tiles written using their face symbols. The four integers defining the transitivity indicate that the present tiling has 4 types of vertexes (first number), 4 types of edges, 4 types of faces and 4 types of tiles (last number).

The trends of the average bond distances for the different polyhedra around the M- and T-sites are given in Figure 7A–C. Notably, the dependence of the structural parameters from temperature can be adequately described by linear functions. The resulting rates of increase, i.e. the slopes, ∂d/∂T, can be used for the calculation of mean thermal expansion coefficients of the average bond distances: <α> = (1/d _amb ) × ∂d/∂T/°C⁻¹ where d _amb is the average value for a particular coordination polyhedron at ambient conditions: <M1-O>: <α> = 1.45 × 10⁻⁵/°C⁻¹, <M2-O>: <α> = 1.55 × 10⁻⁵/°C⁻¹, <M3-O>: <α> = 1.28 × 10⁻⁵/°C⁻¹, <M4-O>: <α> = 1.31 × 10⁻⁵/°C⁻¹, <T1-O>: <α> = 1.05 × 10⁻⁵/°C⁻¹, <T2-O>: <α> = 0.36 × 10⁻⁵/°C⁻¹, <T3-O>: <α> = 0.61 × 10⁻⁵/°C⁻¹, and <T4-O>: <α> = 0.41 × 10⁻⁵/°C⁻¹. Actually, the polyhedra belonging to the heteropolyhedral cluster show the largest expansion rates. The corresponding values for the four tetrahedra are significantly smaller. Furthermore, the Zn-enriched positions (T1, T3) expand more than the remaining two Al-dominated sites (T2, T4).

Figure 7:

Temperature dependence of the average M–O and T–O distances: (a) Ca-sites M1–M3, (b) Al-site M4 and (c) (Al/Zn) positions T1–T4.

Temperature induced microscopic structural distortions can be analyzed using the concept of overall thermal strain which can be considered to be the sum of (1) a lattice deformation and (2) an inner deformation [25, 26]. While the former modifies the unit-cell metric without changing the fractional atomic coordinates the latter has the opposite effect.

In order to get insight into the influence and magnitude of the inner strain we determined the vector field representing the shifts between the atomic coordinates obtained from the refinements at ambient temperature and at 790 °C, respectively. Furthermore, the sets of coordinates both were referred to the unit cell for the structure stable at 25 °C. The necessary calculations have been performed with the program AMPLIMODES [27]. In summary one can say that the cations and anions are affected by only very small displacements. Due to the occupation of special Wyckoff-sites without any positional degree of freedom, the positions M4, T4 and O1 are not influenced at all. Negligible shifts are observed for the positions M1, T1, T2 and O2. For the remaining sites the following displacement magnitudes have been calculated: M2: 0.012 Å, M3: 0.010 Å, T3: 0.011 Å, O3: 0.012 Å, O4: 0.017 Å, and O5: 0.015 Å. In combination with the program VESTA, the output of AMPLIMODES was also employed for the visualization of the distortion field. Figure 8A–C shows graphical representations of the shifts which can be attributed to the aforementioned six positions. For sake of a better visualization the different vector sets have been scaled with a common factor. Figure 8A shows the small fragment of the structure, where four [T1O₄]-groups are linked by a common O1 corner. The displacements of each of the three O4-atoms belonging to a single [T1O₄]-group are located in the corresponding basal planes of the tetrahedra. The shift pattern can be approximated by rotations around the relevant T1-O1 vectors. Figure 8B in turn exhibits a 10-membered tetrahedral ring within the framework with an alternating sequence of [T2O₄]- and [T3O₄]-units. While the T3-and O3-atoms are shifted concordantly parallel to the cubic body-diagonals, the O5 oxygen atoms show a rotational movement around the T3-O3 vector. Simultaneously, the O5-displacements are connected with an opening of the T3-O5-T2 bridging angle. The two O4 atoms belonging to the same tetrahedron are effected by opposite shifts within the O4-T2-O4 plane which basically decrease the O4-T2-O4 bond angle. The oxygen displacements around the invariant T4-site have not been shown. As described above, the four symmetrically equivalent O3-atoms simply move along the four body-diagonals increasing the T4-O3 distances by the same amount. In Figure 8C, the displacements in a part of the heteropolyhedral cluster including the central [M4O₆]-octahedron as well as one of the adjacent M1, M2 and M3 positions are presented.

Figure 8:

Graphical representation of the most prominent shift vectors reflecting the inner strain due to thermal expansion. Calculations are based on the differences between the structural models determined at 25 and 790 °C. (a): Group of four [T1O₄]-tetrahedra linked by a common O1 atom; (b): 10-Membered ring containing [T2O₄]- and [T3O₄]-units; (c) part of the heteropolyhedral cluster.

Notably, M4 and its six nearest O2 neighbors exhibit either no or extremely small changes in their relative coordinates. On the other hand, the evolution of the <M4-O> distances as a function of temperature indicated, that the [M4O₆]- octahedron has expansion rates comparable to those of the polyhedra around M1–M3. This is a clear indication, that the impact of the lattice strain has to be considered as well.

Catti et al. [28] presented a relationship where the influence of the overall thermal strain on the bond distances can be numerically separated into the contributions from lattice and inner deformations. Correcting for an obvious typographic error in Catti’s paper, the equation reads as

where d i j ′ and d _ij are the distances between a pair of atoms i and j at high and low temperatures, Δ G represents the change of the metric tensor G ′ − G (reflecting the lattice strain contribution) and Δ x _i  =  x ′ _i − x _i are the changes in the fractional coordinates (reflecting the inner strain component). Consequently, the contribution of the inner strain Δ(d ²)_inner for each bond can be directly obtained from the differences between the squared observed interatomic distances Δ(d ²) and the lattice part Δ(d ²)_lattice. From the calculation of the individual values we determined the average values for coordination polyhedra. For the sites M1–M4 the lattice strain is the dominating effect representing between 72% (for M2) and 88% (for M4) of the total thermal strain. Furthermore, Δ(d ²)_inner as well as Δ(d ²)_lattice were always >0. By contrast, the T-sites exhibit negative values for Δ(d ²)_inner. This indicates, that the T–O bonds expand less than expected from lattice strain alone.

Most of the atoms in the asymmetric unit of Ca₁₄Al₁₀Zn₆O₃₅ occupy special Wyckoff-positions. This observation prompted us to look for potential pseudo-symmetries within the crystal structure. For this purpose, the program PSEUDO [29] was used which is accessible via the Bilbao Crystallographic Server. The program checks if a structure S of space group H is pseudosymmetric for a supergroup G > H. As a first step of the analysis, a left coset decomposition of G with the respect to H is performed: G = e × H + g₂ × H + … + g_n × H, where the operations {e, g₂, …, g_n) are the coset representatives. Subsequently, the input structure S is transformed into the image g_i × S. Both structures are compared and in case that the shifts between corresponding atoms in S and g_i × S are below a certain threshold, pseudosymmetry is indicated. In the present case, the tests were performed for all minimal supergroups of H = F23. Only for G = F-43m a positive result was obtained. For this supergoup, the symmetry operation m[_1–10] has been selected for the coset decomposition. Notably, the substructure containing the positions M1–M4, T1–T4 as well as O1–O3 fulfills the symmetry requirements of the supergroup F-43m exactly. The remaining two oxygen sites, however, show pronounced deviations from the higher symmetry with displacement of 0.887 Å (for O4) and 0.844 Å (for O5).

The crystal structure of Ca₁₄Al₁₀Zn₆O₃₅ shows a close relationships to several synthetic inorganic compounds including Ca₁₄Ga₁₀Co₆O₃₆ [30] or Ca_12.6Ga_8.8Al_2.6Mn₆O₃₆ [31] and minerals such as tululite (Ca₁₄(Fe³⁺,Al) (Al,Zn,Fe³⁺, Si,P,Mn,Mg)₁₅O₃₆). Tulilite is a rather exotic mineral phase, which was identified in medium-temperature (800–850 °C) combustion metamorphic marbles from central Jordan [32].

A very detailed comparison of the crystal structures of Ca₁₄Al₁₀Zn₆O₃₅ and Ca₁₄Ga₁₀Co₆O₃₆ has been already presented in the paper of Grins et al. [30] and will not be repeated here. Using our atom labels one can summarize that in Ca₁₄Ga₁₀Co₆O₃₆ (i) the [T4O₄]-units are disordered among two positions where the corresponding oxygen atoms are located on the corners of a cube and (ii) the [T1O₄]- and [T3O₄]-groups are only partially occupied as well. A result of the disorder is an increase in space group symmetry from F23 to F432. Furthermore, the O1 anions simultaneously linking four adjacent tetrahedra are fully occupied for Ca₁₄Ga₁₀Co₆O₃₆ (Wyckoff-site 8c of F423) whereas in the present compound the corresponding site is half empty, i.e. oxygen atoms occur on Wyckoff-sites 4c of F23, whereas the ordered O1-vacancies are located in the centers of the [6⁴]-cages at Wyckoff-site 4d. This feature also explains the slightly lower oxygen content of Ca₁₄Al₁₀Zn₆O₃₅ (35 versus 36 oxygen atoms per formula unit). For tululite, split positions for some of the tetrahedra as well as additional oxygen atoms have been observed as well. However, modeling of the structure in a potentially higher-symmetrical space group was not deemed necessary by the authors [32].

5 Conclusions

Notably, Khramtsov et al. [33] found indications that the phase relationships in the system CaO-ZnO-Al₂O₃ may be more complicated than described in the previous studies [1, 2]. Ca₁₄Al₁₀Zn₆O₃₅ (or Ca₁₂Al_8.57Zn_5.14O₃₀) may be part of a more complex solid-solution series with general composition Ca₁₂Al_9−y Zn_5+x O_32±δ with x = 5–5.76 and y = 8.1–8.73. The authors listed a sequence of powder diffraction patterns which were claimed to represent different members of the series. Unfortunately, more detailed structural investigations have not been performed. Attempts aiming on the growth of single-crystals with different compositions could prove a fruitful investigation shedding more light on the response of the cubic structure to Al-Zn-substitutions and their interplay with the oxygen vacancies.

From an application point of view, Ca₁₄Al₁₀Zn₆O₃₅ has been investigated as a host material for the development of new phosphors. Doping with Mn⁴⁺ [34], Bi³⁺,Sm³⁺ [35] or Bi³⁺,Mn⁴⁺ [36] resulted in ceramic materials with interesting luminescence properties. However, the acentric-chiral point group 23 of the cubic material offers the potential for applications in the fields of piezoelectricity or acousto-optics, for example. Similar to technologically relevant Bi₁₂GeO₂₀ having the same crystal class, the compound may be useful in non-linear optics for building Pockels cells [37, 38 37,38]. Tests on the magnitude of the piezoelectric or electro-optic coefficients could be another direction for future research activities.