Reappraisal of Polytypism in Layered Double Hydroxides

Mar 28, 2017 - Recent diffraction studies on layered double hydroxides have shown that the three-layer polytypes that were thought to crystallize in ...
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Reappraisal of Polytypism in Layered Double Hydroxides: Consequences of Cation Ordering in the Metal Hydroxide Layer Latha Pachayappan, Supreeth Nagendran, and P. Vishnu Kamath* Department of Chemistry, Central College, Bangalore University, Bangalore 560 001, India S Supporting Information *

ABSTRACT: Recent diffraction studies on layered double hydroxides have shown that the threelayer polytypes that were thought to crystallize in rhombohedral symmetry are actually one-layer polytypes of monoclinic symmetry. However, the prevailing Bookin and Drits (1993) scheme of polytypism, which is based on the widely accepted cation-disordered structure model, fails to predict the occurrence of low symmetry (monoclinic and orthorhombic) polytypes among the layered double hydroxides. In this work, a cation-ordered metal hydroxide layer (layer group p3̅12/m or c12/m1) is chosen as the basic building block. Application of the structural synthon approach enables the description of the complete universe of polytypes comprising 1H, 1M1−7, 2H, 2O, 3R, 3H, 6H, and 6R among others (M: monoclinic; O: orthorhombic). These polytypes are characterized by their unique stacking vectors. The polytypes of large unit cell volume are obtained by a combination of two or more stacking vectors. This work has relevance to the understanding of several mineral structures, especially those with large unit cells.

1. INTRODUCTION Graphite is the simplest layered material, wherein each layer comprises a hexagonal mesh of covalently bonded carbon atoms. The carbon atoms in this two-dimensional (2-D) array are close packed. The hexagonal arrays are stacked one above another in a graphite crystal. Two distinct stacking sequences are possible: (a) ···ABAB··· of hexagonal symmetry and (b) ··· ABCABC··· of rhombohedral symmetry. As the two stacking sequences have comparable enthalpy, a random intergrowth of the two polytypic modifications results in turbostratic disorder.1 The situation becomes more complicated when the layer is two atoms thick as in the structure of mineral brucite Mg(OH)2. The divalent hydroxides M(OH)2 (M = Mg, Fe, Co, Ni) crystallize in the CdI2 structure (C6 type), wherein the hydroxyl ions are hexagonally close packed and M(II) ions occupy alternative layers of octahedral interstitials.2 The ionocovalently bonded metal hydroxide layers are stacked one above another and held together by weak van der Waals forces. Given the weak bonding between successive layers, the question arises: In how many ways can the metal hydroxide layers be stacked? This question was answered by Bookin and Drits (1993) who evolved a systematic scheme for predicting the complete universe of possible polytypes. This scheme was founded on the fact that the hydroxyl ions in the metal hydroxide layer are close packed which enables the structure of the M(OH)2 layer to be described by the symbol AbC [A, C: close packed hydroxyl ion positions; b: octahedral interstitial position of M(II)] or more simply as AC. Many different stacking sequences can be envisaged, to yield one, two, three..., etc. layered polytypes. Some illustrative examples are AC − AC − AC − AC

1H © XXXX American Chemical Society

AC = CA = AC = CA

2H1

(ii)

AC − AB − AC − AB

2H 2

(iii)

AC − BA = AC − BA

2H3

(iv)

AC = CB = BA = AC

3R1

(v)

AC − BA − CB − AC

3R 2

(vi)

Periodic combinations of repeating motifs obtained from different polytypes generate yet more polytypes, and in the case of CdI2 several hundreds of polytypes have been described.3 Different n-layer polytypes differ from each other in the local symmetry of the interlayer sites generated. They could be trigonal prismatic represented by the symbol “=” or octahedral represented by the symbol “−” in the Bookin and Drits (1993) scheme. This scheme of polytype description is commonly applicable to all single cation layered phases. For instance, among the binary LiMO2 (M = Ni, Co) oxides, the 3R1 modification is given the symbol P3 (P: prismatic interlayer site; 3: three-layered polytype), and 3R2 modification is given the symbol O3 (O: octahedral interlayer site).4 For a given aparameter, the free volume of a prismatic interlayer site is greater than that of the octahedral site, whereby polytypes that enclose prismatic sites would be enthalpically not favored. Consequently, despite these numerous possibilities, Mg(OH)2 crystallizes exclusively in the structure of the 1H polytype (P3̅m1; a0 = 3.14 Å; c0 = 4.71 Å) and does not exhibit any polytypism. Ni(OH)2 on the other hand crystallizes with a plethora of stacking faults, which manifest themselves by the nonuniform broadening of reflections in the powder X-ray Received: January 17, 2017

(i) A

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diffraction (PXRD) pattern. The first attempt to explain the broadening was made by Delmas and Tessier (1997),5 who took into account the effect of growth and deformation faults on the line shape of reflections in the PXRD pattern. Later work6 interpreted the faulted structure to arise from a random intergrowth of different polytypes. Intergrowths of different polytypes lead to characteristic nonuniform broadening of the h0l reflections in the PXRD pattern of nickel hydroxide. This general scheme of classification of planar faults has been extended to the layered double hydroxides (LDHs).7 The LDHs have a double cation metal hydroxide layer [MII1−xM′IIIx(OH)2]x+, obtained by isomorphous substitution of a fraction, x (0.2 ≤ x ≤ 0.33), of the divalent cations by trivalent (Al3+, Cr3+, Fe3+) cations.8 The general understanding is that the cations within the metal hydroxide are disordered, whereby the divalent and trivalent cations are distributed statistically in all six coordinated cation sites within the metal hydroxide layer. In this model, the LDH is treated like a (pseudo)single cation hydroxide. Numerous structure refinements have been carried out using the (pseudo)single cation structure model and are recently reviewed.9,10 Most of these structures belong to the 3R1 polytypic modification. A large number of mineral structures have also been refined using the same structure model.11 In all these, the a-parameter, a0 ≈ 3.11 Å, is comparable to that of the single cation metal hydroxide, M(OH)2 (M = Mg2+, Ni2+). On the basis of chemical considerations, the (pseudo)single cation structure model is untenable for the LDHs, given the large difference in the ionic radii, charge, and polarizing powers of the divalent and trivalent cations. Recent studies12−15 on highly ordered LDHs have shown that the trivalent cations are in an ordered arrangement relative to the positions of the divalent cations within the metal hydroxide layer, resulting in the generation of a supercell with a-parameter: a = √3 × a0 ≈ 5.33 Å for the composition x = 0.33 (a0 = a-parameter of a single cation hydroxide). As a consequence of cation ordering, the following structural features of the metal hydroxide layer may be noted.15 (i) There are three intralayer nonbonded OH···OH distances within the array of hydroxyl ions of the metal hydroxide layer. Thereby, the hydroxyl ions are not close packed and cannot be described by positions, A, B, and C. (ii) The cation coordination is distorted compared to that of cations in a (pseudo)single cation metal hydroxide. (iii) The crystal symmetry of the LDH is either hexagonal (P3̅) or reduced to monoclinic (C2/m). The emerging consensus on the cation-ordered structure calls for a complete reappraisal of the universe of possible polytypes in LDH systems. This paper attempts to describe the complete universe of polytypes that could arise from a cationordered double hydroxide layer of the composition x = 0.33. This work is illustrative in nature, and the approach outlined here can be extended not only to LDHs of other compositions, but also to any class of layered materials.

solids. The diffraction intensity is computed by integrating the intensity emanating from each layer over an infinite stacking, in a recursive manner. All the simulations are carried out using the metal hydroxide layer extracted from the published structure of the [Zn4Al2(OH)12](SO4)·6H2O LDH.18 The PXRD patterns are computed for a basal spacing of 7.50 Å to facilitate comparison with experimental patterns of the widely reported carbonate-intercalated LDH phases. The intercalated atoms were removed, and all the simulated patterns reported here correspond to LDH phases with an empty interlayer. The anions and water molecules in the interlayer are either disordered or occupy general positions (x, y, z) of high degeneracy. Consequently the contribution of the interlayer atoms to the diffraction profile is minimal19 and does not affect the relative intensities of the non-00l reflections significantly. For the purpose of simulations in this work, the Laue symmetry is declared UNKNOWN, and the position parameters of all the symmetry related atoms are input. Code DIFFaX then evaluates the Laue symmetry. The computed Laue symmetry helps to verify that the layer is correctly defined. Different polytypes are characterized by their respective stacking vectors. The stacking vectors define the interlayer relationship. When more than one stacking vector is used, a probability is defined for the use of each. An illustrative input file used for the simulation of the PXRD pattern of the 1H polytype is included in the Supporting Information as File S1. In each simulation the calculated Bragg reflections are broadened using a Lorentzian profile function with a fwhm = 0.2° 2θ. All simulations are performed for the wavelength of a Cu Kα (λ = 1.5418 Å) source. Different polytypes are identified by the relative intensities of the non-00l reflections. 2.1. Evaluation of the Interlayer Site Symmetry. Code SYMGROUP20 was used to evaluate the local symmetry around any given site within the LDH crystal. To find the coordination symmetry of the metal, the Cartesian coordinates of the six hydroxyl ions coordinated to the metal were input. Code SYMGROUP evaluates a score for each possible symmetry element Cn (n = 1−6), planes of symmetry (m), and inversion center (i). A score zero indicates the exactness of symmetry. Any deviation from the ideal symmetry manifests in a score > 0. The larger the score, the more likely that the corresponding symmetry element is absent. To evaluate the local symmetry of an interlayer site, the coordinates of six nearest hydroxyl ions, three each from adjacent layers, were used. In a typical evaluation, a collection of symmetry elements are found to have a score = 0. These symmetry elements determine the exact point group of the local symmetry. In many evaluations, a collection of symmetry elements was found to have closely matching scores with a small but nonzero value. These symmetry elements point to an approximate point group symmetry. In such cases, other symmetry elements generally have scores, an order of magnitude higher, discounting their existence. Thereby, although the procedure relies on the application of an arbitrarily chosen cut off score, the determination of the cut off was generally not difficult.

3. RESULTS AND DISCUSSION One of the defining features of polytypism is the invariance of the structure in two dimensions. Among the LDHs, the metal hydroxide layer remains invariant across all LDH systems of a given composition. The cation-disordered metal hydroxide layer, which comprises the fundamental building block of the Bookin and Drits scheme of polytypism belongs to the layer

2. SIMULATIONS Different polytypes have distinct PXRD patterns. PXRD patterns of the different theoretically possible polytypes were simulated using code DIFFaX.16,17 Within the scope of the DIFFaX formalism, a crystal is treated as a stacking of 2-D arrays of atoms, an approach that is ideally suited for layered B

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group p32̅ /m1.21 In this layer group, all the metal atoms occupy a single crystallographic site, and the array of hydroxyl ions is perfectly hexagonal. There is a 3̅ axis passing through each metal atom normal to the layer. A typical cation-ordered metal hydroxide layer belongs to the layer group p3̅12/m (Figure 1). In this layer group, the divalent

reflections. The (0, 0, 1) stacking vector generates a onelayer polytype (ah = √3 × a0 ≈ 5.35 Å; ch = 7.50 Å; h: hexagonal) of hexagonal symmetry (polytype 1H) belonging to the P3̅ space group (Table S1). This is a well-known structure, which is used as a model for the refinement of the structures of the [Zn−Cr−SO4]0.33,13 [Cu−Cr−SO4]0.33,14 and [Zn−Al− SO4]0.3318 LDHs. The PXRD patterns simulated for the stacking vectors (1/3, 2/3, 1/3) and (2/3, 1/3, 1/3) differ from that of the 1H polytype in the appearance of additional reflections of low intensity. The differences though minor are of great significance as they reveal the correct crystal symmetry. All the reflections generated, including the minor ones, could be indexed to a three-layered cell (ar = ah = 5.35 Å; cr ≈ 3 × ch = 22.52 Å; r: rhombohedral, Table S1), with the reflection conditions (−h + k + l) = 3n, indicative of rhombohedral crystal symmetry (polytype 3R). In the 1H polytype, the stacking sequence of the metal ions is ···Al3+···Al3+ ···Al3+··· (Zn2+··· Zn2+···Zn2+···) along the c-crystallographic axis, also the stacking direction. In the 3R polytypes, the stacking sequence is ···Al3+···Zn2+···Zn2+···Al3+···. This difference in the structure accounts for the differences in the PXRD patterns of the 1H and 3R polytypes. Within the Bookin and Drits scheme, applicable to (pseudo)single cation metal hydroxides, there are two rhombohedral polytypes which essentially differ in the local symmetry of the interlayer site (D3h for 3R1, and D3d for 3R2). A SYMGROUP analysis of the local symmetry of the interlayer sites in the present case reveals the existence of two sites (a and b in Table 1) in the 1H polytype, having the D3d and D3 symmetries, respectively. The interlayer site, a, of D3d symmetry is preserved in the 3R polytypes. The other site, b, suffers a distortion and symmetry lowering to C3v [stacking vector (2/3, 1/3, 1/3)] or C3 [stacking vector (1/3, 2/3, 1/3)] in the 3R polytypes. This difference suggests that there could indeed be two different polytypes of rhombohedral symmetry even among the cation-ordered LDHs. A close look at the simulated PXRD patterns generated by the two stacking vectors shows differences in the relative intensities of the weak reflections. For instance, when the stacking vector (1/3, 2/3, 1/3) is used, the h0l family of reflections is lower in intensity compared to the h-hl family. When the (2/3, 1/3, 1/3) stacking vector is used, the situation is reversed and the h0l reflections are more intense than the h-hl family of reflections (see inset in Figure 2). Such a reversal in the relative intensities of select families of reflections seen here is evocative of the polytypism in single cation phases, wherein the 0kl reflections are more intense in the 3R1 polytype, and h0l reflections are more intense in the 3R2 polytype. However, the differences in the present instance being minor, for all practical purposes, PXRD is unlikely to distinguish between the two rhombohedral polytypes which we choose to label as 3R and 3R′. The [Ca−Al−Cl]0.33 LDH crystallizes in the structure of the 3R polytype.22 An entirely new series of polytypes are generated by introducing a mirror plane between adjacent metal hydroxide layers halfway in the interlayer gallery. If the symbol P is assigned to the metal hydroxide layer and Ρ̅ is assigned to its mirror image, the stacking of Ρ̅ layer over P with the (0, 0, 1) stacking vector also conserves the 3-fold symmetry (3̅ or 3) along the stacking direction. The resultant PXRD pattern (Figure 3) is indexed to a two-layer cell of hexagonal symmetry (2H), where ah = 5.35 Å and ch = 15.01 Å. This structure is reported for the 2H-chlormagaluminite mineral.23 The PXRD patterns simulated using the stacking vectors (1/3, 2/3, z) or

Figure 1. (a) Structure of a single layer of [Zn−Al]0.33 LDH, and (b) the corresponding representation of the layer group p3̅12/m.

and trivalent cations occupy two crystallographically distinct sites. The unit mesh has Al3+ ions in the corner, and the two Zn2+ ions occupy (1/3, 2/3) and (2/3, 1/3) positions along the diagonal. The 2-D array of hydroxyl ions is nonuniformly distended, by virtue of a 3̅ axis that passes through the Al3+ ions, whereas a 3-axis passes through the Zn2+ ions normal to the layer. The coordination around Zn2+ is lowered from the ideal D3d symmetry. 3.1. Polytypes Generated by a Single Stacking Vector. 3.1.1. Polytypes of High Symmetry. Different polytypes differ from one another in the manner in which the metal hydroxide layers are stacked. In keeping with the structural synthon approach,21 the preferred stacking sequences are those which conserve the principal symmetry elements of a single metal hydroxide layer in the crystal. A coincidence of the 3-fold axes (3̅ or 3) of successive metal hydroxide layers can be realized if the layers are stacked using the stacking vectors (0, 0, 1), (1/3, 2/3, z), or (2/3, 1/3, z) where z = 1/3. The simulated PXRD patterns of the resultant crystals (Figure 2) are very similar owing to the coincidence of most of the major Bragg

Figure 2. Simulated PXRD patterns of the [Zn−Al] LDH using the stacking vectors (a) (0, 0, 1) (polytype 1H), (b) (1/3, 2/3, z) (polytype 3R′), and (c) (2/3, 1/3, z) (polytype 3R). Rectangular boxes highlight the additional reflections generated by a rhombohedral cell of larger volume. Inset shows patterns (b) and (c) on an expanded scale in the 2θ range 18−22° to illustrate the reversal in intensities. C

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Table 1. Interlayer Site Symmetries Computed by Code SYMGROUP for Different Sites in the 1H, 3R, and 3R′ Polytypesa 1H (0, 0, z)

3R (2/3, 1/3, z)

3R′ (1/3, 2/3, z)

symmetry

a

b

a

b

a

b

C2 C3 C4 C6 i m S2 S3 S4 S6 point group

0.00000*(3) 0.00000*(1) 19.69743 22.60414 0.00000*(1) 0.00000*(3) 0.00000*(1) 3.76736 12.05916 0.00000*(1) D3d

0.02731*(3) 0.00000*(1) 12.38395 29.69325 0.52568 0.49751 0.52568 3.28634 12.22698 0.52568 D3

0.00000*(3) 0.00000*(1) 12.59228 29.43410 0.00000*(1) 0.00000*(3) 0.00000*(1) 5.19840 12.59228 0.00000*(1) D3d

0.53463 0.00000*(1) 15.13679 28.60011 0.55594 0.02052*(3) 0.55594 4.50991 15.30725 0.55594 C3v

0.00000*(3) 0.00000*(1) 10.84590 29.15993 0.00000*(1) 0.00000*(3) 0.00000*(1) 5.62229 10.84590 0.00000*(1) D3d

0.32140 0.00000*(1) 16.39730 27.14936 0.56724 0.23992 0.56724 3.24700 14.09441 0.56724 C3

Scores marked with * are considered for point group determination. The number in parentheses gives the number of corresponding symmetry elements.

a

(2) Translations that eliminate the 3̅ axis and results in the coincidence of inversion centers along the stacking direction, and (3) Translations that lead to the intersection of 3̅ axis with the 21 screw axis (see layer group representation in Figure 1). Two stacking vectors that lead to the coincidence of the 3̅ axis of the metal hydroxide layer with the (pseudo) 3-fold axis of the adjacent layer are (1/3, 0, z) and (2/3, 0, z) (z = 1). Both the patterns are indexed to a one-layered unit cell of monoclinic symmetry (c-stacking) with am = ah, bm = √3 × ah, cm = 7.72 Å, β = 103°; m: monoclinic (Table S2). However, the two patterns differ from each other in the relative intensities of select reflections (Figure 4). They are therefore referred as 1M1 Figure 3. Simulated PXRD patterns of the [Zn−Al] LDH in the 2θ range 32−59° for the PΡ̅ stacking using the stacking vectors (a) (0, 0, 1) (polytype 2H) and (b) (1/3, 2/3, z)/(2/3, 1/3, z) (polytype 6R). The reflections marked by */# are those that cannot be assigned to the closely related 1H/3R polytypes, respectively.

(2/3, 1/3, z) for P and Ρ̅ layers are indexed to a six-layer supercell (Figure 3). The hkl indices satisfy the rhombohedral condition, and we label this polytype as a 6R, where ar = 5.35 Å and cr = 45.03 Å. 3.1.2. Polytypes of Low Symmetry. Within the Bookin and Drits scheme applicable to the (pseudo)single cation phases, all the polytypes described have hexagonal/rhombohedral crystal symmetry. No polytypes of lower crystal symmetry are envisaged. Within the structural synthon formalism,24 polytypes of lower symmetry can be generated by systematically eliminating the principal symmetry elements, 3 or 3̅, in the present case, while at the same time preserving other symmetry elements. This can be done by translating successive layers along the a (or b)-axis. Such translations [(a/n, 0, 1) or (0, b/n, 1), n = 2, 3, 4, etc.] remove the coincidence of the 3-fold axes of adjacent layers, while retaining the in-plane 2-axes perpendicular to the a (or b) crystallographic axis. The very large number of possible translations can be classified in the following way.

Figure 4. Simulated PXRD patterns of the [Zn−Al] LDH using the stacking vectors (a) (1/3, 0, z) (polytype 1M1) and (b) (2/3, 0, z) (polytype 1M2). Inset shows the patterns on an expanded scale in the mid-2θ range to illustrate the complementarity in the intensities of different pairs of reflections.

(1/3, 0, 1) and 1M2 (2/3, 0, 1) respectively. In the 1M1 polytype the 13l family of reflections has a higher intensity than the 20l family of reflections. The relative intensities of these two families of reflections are reversed in the powder pattern of the 1M2 polytype (Figure 4). In this sense, the PXRD pattern of 1M1 is complementary to that of 1M2. These observations

(1) Translations that lead to the coincidence of the 3̅ axis of a metal hydroxide layer with the (pseudo)3-fold axis present at the “O” atom of the adjacent layer. D

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enable a fingerprint identification of the corresponding polytypes. The interlayer relationship of the 1M1 polytype can also be realized by the translation (2/3, 2/3, 1). Similar equivalences can be obtained for the 1M2 polytype as well. The equivalent stacking vectors are summarized below:24 (a) (1/3, 0, z) ≈ (0, 1/3, z) ≈ (2/3, 2/3, z) 1M1 polytype (b) (2/3, 0, z) ≈ (0, 2/3, z) ≈ (1/3, 1/3, z) 1M2 polytype From a structural point of view, the two polytypes differ from one another in the local symmetry of the interlayer sites. The 1M1 polytype encloses two interlayer sites with C2h and C2 point group symmetries, respectively. In the 1M2 polytype, there is a reduction in the symmetry of the interlayer site to Cs (Table 2). Figure 5. Simulated PXRD patterns of the [Zn−Al] LDH using the stacking vectors (a) (1/2, 0, z) (polytype 1M3) and (b) an equal mix of (1/3, 0, z) and (2/3, 0, z) (polytype 2O). The region in the rectangular box is shown in the inset. The peaks encircled in the inset indicate the reflections absent in pattern (a).

Table 2. Interlayer Site Symmetries Computed by Code SYMGROUP for Different Sites in the 1M1 and 1M2 Polytypesa 1M1 (1/3, 0, z)

1M2 (2/3, 0, z)

symmetry

a

b

a

b

C2 C3 C4 C6 i m S2 S3 S4 S6 point group

0.04379*(1) 0.73208 14.62526 25.17983 0.00000*(1) 0.04379*(1) 0.00000*(1) 5.46319 14.62526 0.73208 C2h

0.04379*(1) 0.73207 14.69951 26.94190 0.54905 0.20941 0.54905 5.28018 12.73883 0.73207 C2

0.36919 0.38306 25.81911 26.20460 6.22813 0.04048*(1) 6.22813 0.44690 12.46576 6.41966 Cs

0.20175 0.36155 21.63030 28.84451 5.87842 0.17017 5.87842 0.42181 13.91914 6.05920

a Scores marked with * are considered for point group determination. The number in parentheses gives the number of corresponding symmetry elements.

1M1 and 1M2 constitute the first subgroup of polytypes of low symmetry that are obtained by adopting the structural synthon approach. Recent work based on structure refinement using powder data has indeed shown that the carbonate-LDHs and certain select sulfate-intercalated LDHs adopt the structure of the 1M2 polytype.15,25,26 We next describe the second subgroup of translations that retain the coincidence of inversion symmetry along the stacking direction. This is done by bringing about the intersection of the 3̅ axis of one metal hydroxide layer with the inversion center of the adjacent metal hydroxide layer using the stacking vector (1/ 2, 0, z) along a or (0, 1/2, z) (z = 1) along b. The simulated PXRD pattern (Figure 5) is indexed to a monoclinic cell with β = 109° (Table S2) and is referred to as 1M3. The same interlayer relationship is also obtained by the (1/2, 1/2, 1) translation. The unit mesh in the a−b plane remains the same as in 1M1 and 1M2 polytypes. In this structure, the interlayer site has only a mirror plane symmetry by virtue of the local symmetry which is Cs. Similarly, (1/4, 0, z) and (3/4, 0, z) (z = 1) result in the intersection of the 3-fold axis of the metal hydroxide layer with the 21 screw of the adjacent layer. These stacking vectors yield powder patterns (Figure 6) which are indexed to a cell with a stacking angle β ≈ 100° (Table S2). The stacking vector (1/4, 0, 1) generates prominent 13l (l = 1, 2, 3) and −15l (l = 1, 2) reflections (polytype 1M4), whereas the stacking vector (3/4, 0,

Figure 6. Simulated PXRD patterns of the [Zn−Al] LDH using the stacking vectors (a) (1/4, 0, z) (polytype 1M4) and (b) (3/4, 0, z) (polytype 1M5). Inset shows the patterns on an expanded scale in the mid-2θ range to illustrate the complementarity in the intensities of different pairs of reflections.

1) generates prominent −13l (l = 1, 2, 3) and 15l reflections (polytype 1M5). The (1/4, 0, z) stacking vector is very unique in that it generates a 4-coordinate interlayer site (Figure 7) together with two different 6-coordinate sites. SYMGROUP analyses show that the 4-coordinate interlayer site has C3v symmetry, while the 6-coordinate sites are of C2h and C2 point group symmetries (Table S3). In contrast the stacking vector (3/4, 0, z) generates an interlayer site of Cs symmetry. Similar analysis can be continued for higher values of n. 3.2. Structural Synthon Approach to Polytypes of Monoclinic Symmetry. The (a/n, 0, z) [or (0, b/n, z)] translations are expected to yield polytypes defined by n-layer orthogonal cells of hexagonal/rhombohedral symmetry. However, as seen in the earlier section (Table S2), these polytypes can be indexed to a single layer cell with a nonorthogonal stacking angle (Scheme 1). The stacking angle turns out to be the β crystallographic angle of the equivalent monoclinic cell and varies from 100 to 110° for n values from 2−4. The monoclinic cell is topotactically related to the hexagonal cell E

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Figure 8. (Top) Structure of a single layer of [Zn−Al] LDH showing the choice of the unit mesh used to define a unit cell of monoclinic symmetry and (bottom) the corresponding representation of the layer group c12/m1.

Figure 7. (a) Four-coordinate and 6-coordinate sites generated in the interlayer by the stacking vector (1/4, 0, z) (polytype 1M4) and (b) projection of the cages along the stacking direction.

Table 3. Equivalent Stacking Vectors between the Synthons of Hexagonal and Monoclinic Symmetry

Scheme 1

hexagonal (0, 0, 1) (1/3, 2/3, z) and (2/3, 1/3, z) (1/3, 0, z) (2/3, 0, z) (1/2, 0, z) and (1/2, 1/2, z) (1/4, 0, z) (3/4, 0, z)

[110]h ∥ [010]m (h: hexagonal; m: monoclinic). The corresponding unit mesh within the metal hydroxide layer is defined am = ah; bm = √3 × ah. The b-parameter is the Al3+··· Al3+ distance along the body diagonal of the hexagonal mesh. The unit mesh extracted from the published monoclinic structure model of the [Zn−Al−CO3]0.33 LDH (CCDC No. 1402449) belongs to the layer group c12/m1 (Figure 8). The PXRD patterns generated by applying the structural synthon approach to this synthon are similar to those obtained from the hexagonal mesh (Figure 1) and thereby reflect the topotactic relationship between the two synthons. This provides evidence that the metal hydroxide layer remains invariant irrespective of the crystal symmetry, except for the minor distortions in the hydroxyl array. The stacking vectors obtained from the monoclinic mesh and the equivalent vectors obtained from the hexagonal mesh are given in Table 3. The translation of the successive P and Ρ̅ layers along a (or b)-axis [stacking vectors (a/n, 0, 1)/(0, b/n, 1)] generates a 2nlayer orthogonal unit cell of high symmetry which can also be described by a two-layer unit cell of monoclinic symmetry (polytype 2M). For instance, the simulated pattern generated by the use of the stacking vector (1/3, 0, 1) is indexed to a sixlayer cell of hexagonal symmetry. The pattern can also be indexed to a two-layer cell of monoclinic symmetry where the β corresponds to the angle made by the stacking vector to the metal hydroxide layer (simulations not shown). The monoclinic cells are preferred because of their smaller volume. 3.3. Polytypes Generated by a Combination of Two or More Stacking Vectors. New polytypes with large periodic

monoclinic (0, 0, 1) and (1/2, 1/2, z) (0, 1/3, z), (0, 2/3, z), (1/2, 1/6, z) and (1/2, 5/6, z) (1/3, 0, z) (2/3, 0, z) (1/2, 0, z), (0, 1/2, z), (1/4, 1/4, z), (1/4, 3/4, z), (3/4, 1/4, z), and (3/4, 3/4, z) (1/4, 0, z) (3/4, 0, z)

lengths can be generated by the simultaneous use of two or more stacking vectors in equal proportions. As an illustration the stacking vectors that preserve the 3-fold symmetry of the hexagonal structural synthon are considered first. When the (0, 0, 1) stacking vector is alternated with (1/3, 2/3, 1), the simulated pattern includes many minor reflections, which cannot be indexed to either the 1H or the 3R polytypes. However, the pattern can be indexed to a six-layer polytype (cr′ = 45.04 Å) (Table S1) of rhombohedral symmetry (polytype 6R′). A similar pattern was obtained by the combination of the stacking vectors (0, 0, 1) with (2/3, 1/3, 1). The use of all the three stacking vectors (0, 0, 1), (1/3, 2/3, 1), and (2/3, 1/3, 1) results in a PXRD pattern that is indexed to a three-layered cell of hexagonal symmetry (polytype 3H) (Table S1). However, it should be borne in mind that differences between the powder patterns of these polytypes are too slight to be experimentally observed. But these structure models merit consideration while interpreting single crystal data. A combination of (0, 0, 1) and (1/3, 0, 1) generates a powder pattern which can be indexed to six-layer hexagonal cell (polytype 6H1). An identical pattern was obtained by the use of a single stacking vector (1/6, 0, 1) (Figure 9) and indexed to monoclinic cell with β = 96° (Tables S2 and S3; polytype 1M6). It is once again demonstrated that an n-layer orthogonal cell can be reduced to a single layer nonorthogonal cell of monoclinic symmetry. The use of (0, 0, 1) and (2/3, 0, 1) yields a complementary PXRD pattern with reversal in the relative intensities of select family of reflections (polytype 6H2/ F

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(composition x = 0.33), which expands the universe of possible polytypes to include polytypes of monoclinic and orthorhombic symmetry not envisaged earlier. This approach based on the identification of the layer group of the synthon is general and applicable to other compositions as well. For instance, when x = 0.25, cation ordering yields a metal hydroxide layer with a = 2 × a0 (layer group p3̅2/m1). The new polytypes incorporate interlayer sites of characteristic local symmetry. Polytype selection is mediated by the intercalated anion, as the local symmetry of the interlayer site and the molecular symmetry of the anion have a group-subgroup relationship. This work identifies new polytypes as potential targets for future synthetic efforts by the appropriate choice of the anion.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b00071. File S1. DIFFaX input file used for the simulation of the 1H polytype. Table S1. Calculated 2θ values and the corresponding indices of the 1H, 3R, 6R′, and 3H polytypes. Table S2. Calculated 2θ values and the corresponding indices of the 1M1/1M2, 1M3, 1M4/ 1M5, 1M6/1M7 polytypes. Table S3. Interlayer site symmetries computed by code SYMGROUP for different sites in the 1M4 and 1M6 polytypes (PDF)

Figure 9. PXRD patterns of the [Zn−Al] LDH simulated using (a) an equal mix of stacking vectors (0, 0, 1) and (1/3, 0, z) (polytype 6H1), (b) the stacking vector (1/6, 0, z) (polytype 1M6), (c) an equal mix of stacking vectors (0, 0, 1) and (2/3, 0, z) (polytype 6H2), and (d) the stacking vector (5/6, 0, z) (polytype 1M7).

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1M7). The same interlayer relationships can also be obtained by using the stacking vectors (5/6, 5/6, 1) (1M6) and (1/6, 1/6, 1) (1M7). In all these cases, the unit mesh is invariant whether defined along the hexagonal or monoclinic axes. Extending this approach, numerous new six-layer polytypes can be generated by combining (1/3, 0, 1) with (1/3, 2/3, 1)/ (2/3, 1/3, 1) and by combining (2/3, 0, 1) with (1/3, 2/3, 1)/ (2/3, 1/3, 1). It is further possible to generate nine-layer polytypes. Polytypes of Orthorhombic Symmetry. When the stacking vector (1/3, 0, 1) is alternated with (2/3, 0, 1), the resulting crystal has a two-layer cell of orthorhombic symmetry (polytype 2O) with co ≈ 2 × cm (o: orthorhombic). On inspection, the PXRD pattern of 2O is remarkably similar to that of 1M3 (Figure 5). This is understandable as the use of the stacking vector (1/3, 0, z) alternatively with (2/3, 0, z) yields an average mutual shift of (1/2, 0, z) over a large length scale. However, the polytype 2O has a larger unit cell than 1M3. This results in the appearance of additional reflections in the PXRD pattern of 2O, which are not observed in 1M3 (see inset in Figure 5). In principle, a series of orthorhombic polytypes can be generated by the alteration of any stacking vector (1/n, 0, 1) with the corresponding (n−1/n, 0, 1). 3.4. Polytypes of Large Cell Size. Within the Bookin and Drits scheme, polytypes with large cell size such as 6H/6R, etc. are constructed by ordered intergrowths of two or more twolayer/three-layer polytypes. Still larger polytypes are envisaged by an ordered mix of extended motifs extracted from polytypes with shorter periodic lengths. In the present scheme, polytypes of large periodic lengths can be understood in terms of a single metal hydroxide layer stacked by a combination of two or more stacking vectors.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Supreeth Nagendran: 0000-0002-9843-0214 P. Vishnu Kamath: 0000-0002-3549-7024 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.P. and P.V.K. thank the Department of Science and Technology (DST), Government of India, for financial support under the WOS-A scheme and SERB, respectively. S.N. is a recipient of the UGC-SRF (NET) fellowship. P.V.K. is a Ramanna Fellow of the DST.

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REFERENCES

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4. CONCLUSION In conclusion, a new scheme of polytypism of LDHs is proposed based on a cation-ordered metal hydroxide layer G

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DOI: 10.1021/acs.cgd.7b00071 Cryst. Growth Des. XXXX, XXX, XXX−XXX