- Email: [email protected]
Methodological reconstruction of dioctahedral 1:1 phyllosilicate polytypes
Applied Clay Science 146 (2017) 201–205
Contents lists available at ScienceDirect
Applied Clay Science journal homepage: www.elsevier.com/locate/clay
Research paper
Methodological reconstruction of dioctahedral 1:1 phyllosilicate polytypes a,⁎
a
Carlos E. Teixeira , Paulo R.G. Brandão , Ricardo W. Nunes a b
MARK
b
Metallurgy, Materials and Mining Engineering Departments, Federal University of Minas Gerais, Brazil Physics Department, Federal University of Minas Gerais, Brazil
A R T I C L E I N F O
A B S T R A C T
Keywords: Dioctahedral Polytype kaolinite Dickite Nacrite
The layered kaolin-group minerals are composed mainly by three polytypes: kaolinite, dickite and nacrite. The geometrical polytypic reconstruction of these phases regards both the topological properties of individual networks (e.g., OH network linked to the hexagonal siloxane surface) and energetic aspect of superposition of cations. Starting from early attempts made by Bookin and Newnham, Zvyagin, Dornberger-Schiff and Durovic proposed their own symbolic representation of these structures. This work used the symbolic proposal of Zvyagin to prepare a methodological strategy to build the 52 species of dioctahedral polytypes. Two examples are shown to demonstrate the methodology and the CIF file of all the structures are made available.
1. Introduction The kaolin-group minerals have the general chemical composition Al2Si2O5(OH)4 and the mineralogical polytypes most commonly observed at ambient temperature and pressure are kaolinite, dickite and nacrite. These minerals are characterized as dioctahedral 1:1 phyllosilicates associated to weathering and burial sedimentary environment (Beaufort et al., 1998; Cuadros et al., 2014), besides the hydrothermal possibilities (Kogure and Inoue, 2005). Since Pauling, 1930, several experimental studies resolving the structure of these minerals (Bailey, 1988; Bish and von Dreele, 1989; Bish, 1993; Blount et al., 1969; SenGupta et al., 1984; Young and Hewat, 1988; Zheng and Bailey, 1994; Zhukhlistov, 2008) were performed, being mostly based on X-ray and neutron diffraction data, collected from both powders and singlecrystal samples, along with Raman spectroscopic data. A thermodynamic study made by de Ligny and Navrotsky (1999), using dropsolution calorimetry, that explained the geological occurrence of halloysite, nacrite, and dickite, which are metastable phases, must be interpreted in terms of kinetics or as the result of a specific synthesis path, rather than resulting from changes in the thermodynamically stable phase assemblage. Polytypism is a special case of polymorphism, occurring only in layered structures. In the natural environment, it occurs in the progressive transition kaolinite ➔ dickite ➔ nacrite (Beaufort et al., 1998; Cuadros et al., 2014), but the geological observation is not conclusive about the phenomenon and its mechanisms (Beaufort et al., 1998). The small energy differences between different polytypes, as well as the anisotropy of the interatomic forces often cause polytypism to manifest
⁎
Corresponding author. E-mail address: [email protected] (C.E. Teixeira).
http://dx.doi.org/10.1016/j.clay.2017.06.001 Received 9 November 2016; Received in revised form 30 May 2017; Accepted 1 June 2017 0169-1317/ © 2017 Elsevier B.V. All rights reserved.
itself in the form of stacking fault formation rather than the formation of separate phases (Dera et al., 2003). The confining pressure is identified as the main thermodynamic factor that drives these transformations. Experimental studies were performed in the last decades (Dera et al., 2003; Johnston et al., 2002; Welch and Crichton, 2010) tried to state the phenomenon but it is not always limited to the mainly geological observational set-square. Dera et al. (2003) identified a isosymmetric reversible pressure-induced phase transformation between 1.9 and 2.5 GPa in dickite, calling the transformed phase as HP-dickite. Welch and Crichton (2010) have investigated the compressional behavior of kaolinite under static compression by synchrotron X-ray powder diffraction and identified transformations at 3.7 and 7.0 GPa. Many different theoretical studies can be found in the literature approaching different information about the mineral species. Structural and lattice energy (Hartman, 1983; Salah, 2011; Sato et al., 2004), elastic (Salah, 2011; Salah, 2012; Sato et al., 2005) and thermodynamic (Mercier and Le Page, 2008, 2010) approaches have provided a broad picture of application of theoretical methods on dioctahedral 1:1 polytypes investigation. The series of recent papers presented by Mercier and Le Page (2008, 2009, 2010, 2011) investigated the behavior of multiple polytype with the pressure, deriving pressure-paths and thermodynamic ordering of the structures. The authors used a polytype builder tool named Materials Toolkit (Le Page and Rodgers, 2005) to derive the structure species. The polytypism in phyllosilicates, dioctahedral and trioctahedral, was investigated in several past studies (Bailey, 1963; Bailey, 1969; Bookin et al., 1989; Newnham, 1961; Steadman, 1964). The work of Zvyagin (1961, 1967, 1988) and Zvyagin and Drifts (1996) introduced
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
the utilization of symbolic representation of translations to represent the different stacking sequence in layered phyllosilicates. Durovic (1974) and Dornberger-Schiff and Durovic (1975a, 1975b) have presented a general outline and analysis of symmetry of kaolin-type layers as order-disorder structures consisting of three sheets put together. Also, an alternative symbolic representation of the symmetry condition of existence of monoctahedral, dioctahedral and trioctahedral, and all the structure construction symbols were provided. Starting from this symbolic description this work will present a methodology to better describe the 1:1 polytypes clarifying the gap between the theoretical symbolic representation and the proper dioctahedral atomic configuration.
2. Methodology and results The stacking patterns of dioctahedral structures are described by Durovic (1974) and Dornberger-Schiff and Durovic (1975a, 1975b) as a sequence of packets Pn seated in their main planes. These packets are composed by three kinds of sheets:
Fig. 2.2. Geometrical identification of displacement between networks (Zvyagin, 1961).
i. A tetrahedral sheets consisting of the network of SiO4−4 and the OH− ions lying in the plane of the apical oxygen atoms. The plane space group is P(6) mm; ii. The octahedral sheets consists of the plane of octahedrally coordinated cations with plane space group P(3)1 m; iii. The third sheets, nominated OH-layer, consists of the plane of OH− ions completing the octahedral coordination of the cations with plane space group H(6) mm.
dimensional networks: tetrahedral and octahedral. The two-dimensional networks in the same layer and adjacent networks of neighboring layers can be displaced relative to each other in six different ways. These relative displacements are referred to the networks origins being these situated at the center of tetrahedral hexagons and the position of the vacant octahedral atom. Geometrically and analytically these displacement are identified as in Fig. 2.2 and Table 2.1: The two-dimensional networks within a layer and the neighboring networks of adjacent layers can be displaced linearly relative to each other. The intra (σi) and inter (τk) layer displacement can be fulfilled in six different ways as geometrically and analytically exemplified in the Fig. 1 and Table 2.1, respectively. Displacements of both types (σi and τk) are, generally speaking, independent so that any arbitrary structure will be defined by a sequence of values of σ and τ. The Zvyagin formulation has two implicitly assumptions:
These sheets are numbered as L0 , L1eL2 according to the appearance sequence in the structure. Thus the pairs of adjacent sheets (Lp; Lp + 1) and (Lq; Lq + 1) will be equivalent under the condition that Lp and Lq are also equivalent. Considering the pair (L3n; L3n + 1), the origin of L3n + 1 is displaced by a3 3 relative to the origin of L3n, being these taken conventionally in coincidence with the positions of (6) and (3)1 m symmetry, respectively. The clockwise rotations of both layers by 60o, 120o, 180o, 240o, or 300o around the hexagonal axis of L3n would bring this layer into coincidence with itself, but the origin of L3n + 1 will then occur displaced by < 1 > = − a1 3 , < 2 > = a2 3 … or < 5 > = − a2 3 , respectively, relative to the origin of L3n.; besides, the orientation of L3n + 1 would also change accordingly. The elementary displacements ± a1/3, ± a2/3 , ± a3/3 are denoted by the characters 0–5 in clockwise order starting with a3/3 in the Fig. 2.1. All pairs (L3n ; L3n + 1) are geometrically equivalent and the position of L3n + 2 relative to the preceding pair is uniquely determined by the geometrical rule of stacking in the structure. Zvyagin (1961, 1967, 1988) proposed a simpler interpretation reporting the stacking as made by layers composed of two types of two
i. The reading sequence of symbols imply that the layers are added one below another; ii. The two dimensional coordinate system should point horizontal right and vertical up. Taking into account these two implicit conditions and the symbolism derived by Zvyagin, it is possible two reconstruct the tridimensional atomic structure of dioctahedral phyllosilicates. However, it is precisely in the transition between these two types of representation that there is a spot of complexity. Structural reconstruction of atomic configuration of large structures is difficult and the correspondence between the symmetry requirements and the atomic positions themselves can be pervasive and obscure. The authors proceeded in this gap and developed a bidimensional schematic rendering that was capable of reproducing the atomic configuration and symmetry properties of the dioctahedral structures. Having as starting point the construction rules presented and using the octahedral vacancy as reference point the scheme of translations was performed. The internal structure of each layer is defined by the intralayer displacement vector σi that characterizes the position of the octahedral vacancy regarding the center of the tetragonal ring in the adjacent network. The rigid translation of the layer is resolved by combining the σi and τk of each layer. The complete stacking profile is defined by a collection of σiτk values that together define both the internal structure of each layer and the relative position between layers. From the construction of the two dimensional diagrams it is possible to indicate the correct position of the elements of symmetry relative to each structure. Therefore, the two-dimensional diagrams are the key
Fig. 2.1. Possible displacement of layers and packets (Dornberger-Schiff and Durovic 1975a).
202
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
Table 2.1 Analytical identification of displacement between networks (Zvyagin, 1961). Displacement symbol
Displacement
Displacement symbol
Displacement
Displacement symbol
Displacement
σ1 σ2 σ3 σ4 σ5 σ6
1,1 − 1,1 1,0 − 1,− 1 1,−1 − 1,0
τ1 τ2 τ3 τ4 τ5 τ6
−1,− 1 1,− 1 −1,0 1,1 −1,1 1,0
τ0 τ+
0,0 0,1
τ−
0,− 1
(2σ1) (2σ2) (2σ3) (2σ4) (2σ5) (2σ6)
Fig. 2.3. Schematic bidimensional representation of [100] (A) section and [010] (B) section.
point in the task of complexity reduction necessary to represent and rebuild dioctahedral structures. As example, the symbolic representation of the structure VIII.1 is σ1τ1σ5τ5σ1 and the individual slips of the layers are: σ1τ1 σ5τ5
(1,1) + (− 1,− 1) = (0,0) (1,− 1) + (−1.1) = (0,0)
These translations can be represented in the sections along [100] and [010] as illustrated in Fig. 2.3. The red crosses indicate the vacant octahedral position in each layer. It follows easily that the glide plane should be settled up in the middle of the “b” (or “y”) axes and the atomic configuration is stated in reference to this symmetry element. The set of translations is capable to reproduce the atomic configuration compatible with a specific symmetry element. The consequent crystal structure and the relevant crystallographic information (CIF file) are demonstrated in Fig. 2.4 and Table 2.2, respectively. Fig. 2.4 shows the atomic and symmetry elements positions inside the structure unit cell. The fractional coordinates of the unit formula with the geometry and symmetry information are listed in Table 2.2. This first case may suggest that the use of symbolism is immediate but this is not a so direct conclusion. Analyzing now the 6-layer structure II.9, represented by σ3τ6σ2τ5σ1τ4σ6τ3σ5τ2σ4τ1σ3, whose individual layers are translated relative to the previous one by
Fig. 2.4. Atomic and symmetry elements positions inside the VIII.1 unit cell according with the [100] (A) and [001] (B) perspective. Atoms colors are: oxygen (red), silicon (yellow), aluminum (pink) and hydrogen (gray). The glide planes are represented by the pink line in both sections. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2.2 CIF file with the main crystallographic information about the VIII.1 structure.
Al Al O O O O O O O O O Si Si H H H H
Al1 Al2 O1 O2 O3 O4 O5 OH1 OH2 OH3 OH4 Si1 Si2 OH1 OH2 OH3 OH4
Site fract x
Site fract y
Site fract z
Crystallographic information
0.33333 0.83333 0.25000 0.50000 0.75000 0.00000 0.50000 0.16667 0.66667 0.66667 0.00000 0.00000 0.50000 0.16667 0.66667 0.66667 0.00000
0.50000 0.66667 0.75000 0.50000 0.75000 0.83333 0.66667 0.66667 0.50000 0.83333 0.50000 0.83333 0.66667 0.66667 0.50000 0.83333 0.50000
0.23100 0.23100 0.00000 0.00000 0.00000 0.15400 0.15400 0.30100 0.30100 0.30100 0.15400 0.04200 0.04200 0.36743 0.36743 0.36743 0.08757
Cell length a Cell length b Cell length c Cell angle alpha Cell angle beta Cell angle gamma Cell group H-M Int Tables number
5.15 8.95 14.30 90 90 90 Cc 9
Symmetry operation x x x + 1/2 x + 1/2
y y y + 1/2 − y + 1/2
203
z z + 1/2 z z + 1/2
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
Fig. 2.5. Schematic bidimensional representation of [100] (A) section and [010] (B) section.
system and the atomic configuration should be stated in reference to this symmetry element. This case is far from being evident, but the atomic configuration could be found using the octahedral vacancy that serves to highlight the translations events between layers. The consequent crystal structure and the relevant crystallographic information (CIF file) are demonstrated in Fig. 2.6 and Table 2.3, respectively. Fig. 2.6 illustrates the atomic and symmetry elements positions inside the structure unit cell. The fractional coordinates of the unit formula with the geometry and symmetry information are listed in the Table 2.3. Generally the transition from the symbolic representation for specific structure configuration is though and pervasive and this work presented a simple methodology to rebuild the dioctahedral polytypes. Thus the scope of this investigation was drawing the correct links between the theoretical symmetry-based polytypes and the factual configuration sight in the 1:1 phyllosilicates. Polytypes with more symmetry elements can be rebuilt using the same methodology taking due care to harmonize the symmetry requirements of each one. Using the methodology presented here the authors built the 52 (36 non-equivalent and 16 enantiomorphs) dioctahedral polytypes whose symbolic representation is displayed in Table 2.4. According to Zvyagin (1961, 1988) and Dornberger-Schiff and Durovic (1975a) the three natural kaolin polytypes, kaolinite, dickite and nacrite, are represented by structures I.1, I.4 and II.2, respectively.
Fig. 2.6. Atomic and symmetry elements positions inside the II.9 unit cell according with the [100] (A) and [001] (B) perspective. Atoms colors are: oxygen (red), silicon (yellow), aluminum (pink) and hydrogen (gray). The three-fold screw axes are represented by the green and yellow lines in both sections. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
σ3τ6 σ2τ5 σ1τ4 σ6τ3 σ5τ2 σ4τ1
(1,0) + (1,0) = (− 1.0) (− 1.1) + (− 1.1) = (1,−1) (1,1) + (1,1) = (− 1,− 1) (− 1.0) + (− 1.0) = (1,0) (1,− 1) + (1,−1) = (− 1.1) (− 1,-1) + (− 1,-1) = (1,1)
3. Conclusion The symbolic representation introduced by Zvyagin was used to reconstruct the complete set of dioctahedral 1:1 phyllosilicate polytypes. The methodology proposed was capable to reconcile the atomic configuration of the individual networks and the theory of layer stacking. The natural polytypes, e.g., kaolinite, dickite and nacrite, were reconstructed with adherence between the geometric properties of them. The complete set of 52 dioctahedral polytypes was drafted and transcribed to CIF files.
The [100] and [010] bidimensional diagrams are represented in Fig. 2.5. The red crosses indicate the vacant octahedral positions in each layer and the purple parts are a consequence of the bidimensional periodicity and are inserted to make the understanding easy. In the orthogonal coordinate system the 6-fold screw axes should be pointed at coordinates (0.833, 0.167) and at (0.667, 0) at the trigonal Table 2.3 CIF file with the main crystallographic information about the II.9 structure.
Al Al Si Si O O O O O O O O O H H H H
Al1 Al2 Si1 Si2 O1 O2 O3 O4 O5 OH1 OH2 OH3 OH4 OH1 OH2 OH3 OH4
Site fract x
Site fract y
Site fract z
Crystallographic information
0.00000 − 0.66667 0.00000 − 0.33333 − 0.16667 − 0.66667 − 0.16667 0.00000 − 0.33333 − 0.33333 − 0.66667 0.00000 − 0.66667 − 0.33333 − 0.66667 0.00000 − 0.66667
0.00000 0.66667 0.33333 0.66667 0.00000 0.50000 0.50000 0.33333 0.66667 0.00000 0.33333 0.66667 0.00000 0.00000 0.33333 0.66667 0.00000
0.07692 0.07692 0.01399 0.01399 0.00000 0.00000 0.00000 0.05128 0.05128 0.10023 0.10023 0.10023 0.05128 0.12005 0.12005 0.12005 0.03147
Cell length a Cell length b Cell length c Cell angle alpha Cell angle beta Cell angle gamma Cell group H-M Int Tables number
5.15 5.15 42.90 90 90 120 P65 170
Symmetry operation x −y −x + y −x y x−y
y x−y −x −y −x + y x
204
z z + 2/3 z + 1/3 z + 1/2 z + 1/6 z + 5/6
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
Table 2.4 52 dioctahedral structures: 36 nonequivalents and 16 enantiomorphics. Id
Symbol
# layers
Space group
Id
Symbol
# layers
Space group
I.1 I.2 I.3 I.4 I.5 I.6 I.7 I.8 I.9 II.1 II.2 II.3 II.4 II.5 II.6 II.7 II.8 II.9 III.1 III.2 III.3 III.4 IV.1 IV.2 IV.3 IV.4
σ2τ− σ2 σ4τ+ σ4 σ3τ+ σ3τ− σ3 σ1τ+ σ5τ− σ1 σ1τ− σ5τ+ σ1 σ3τ+ σ5τ+ σ1τ+ σ3 σ3τ− σ5τ− σ1τ− σ3 σ3τ+ σ1τ− σ5τ0σ3 σ3τ+ σ5τ3σ1τ6σ3 σ4τ1σ5τ2σ4 σ1τ6σ2τ3σ1 σ3τ4σ6τ5σ3 σ1τ2σ4τ5σ1 σ5τ4σ2τ1σ5 σ3τ6σ4τ1σ5τ2σ6τ3σ1τ4σ2τ5σ3 σ3τ2σ4τ3σ5τ4σ6τ5σ1τ6σ2τ1σ3 σ3τ4σ2τ3σ1τ2σ6τ1σ5τ6σ4τ5σ3 σ3τ6σ2τ5σ1τ4σ6τ3σ5τ2σ4τ1σ3 σ1τ2σ2τ1σ1 σ3τ6σ6τ3σ3 σ3τ4σ4τ5σ5τ6σ6τ1σ1τ2σ2τ3σ3 σ3τ2σ2τ1σ1τ6σ6τ5σ5τ4σ4τ3σ3 σ6τ2σ6 σ3τ1σ3 σ3τ5σ3τ1σ3 σ1τ3σ5τ3σ1
1 1 2 2 2 3 3 3 3 2 2 2 2 2 6 6 6 6 2 2 6 6 1 1 2 2
P1 P1 Cc Cc Cc P31 P31 P32 P32 Cc Cc Cc P21 P21 P61 P61 P65 P65 Cc CcmP21 P61 P65 P1 P1 Cc Cc
IV.5 IV.6 V.1 V.2 V.3 V.4 V.5 V.6 VI.1 VI.2 VI.3 VI.4 VII.1 VII.2 VII.3 VIII.1 VIII.2 VIII.3 IX.1 IX.2 IX.3 X.1 X.2 X.3 XI.1 XII.1
σ3τ1σ5τ3σ1τ5σ3 σ3τ1σ1τ5σ5τ3σ3 σ1τ− σ2τ− σ1 σ3τ+ σ6τ− σ3 σ3τ− σ6τ+ σ3 σ3τ+ σ6τ+ σ3 σ3τ− σ4τ+ σ5τ− σ6τ+ σ1τ− σ2τ+ σ3 σ3τ+ σ2τ+ σ1τ+ σ6τ+ σ5τ+ σ4τ+ σ3 σ6τ0σ6 σ1τ0σ5τ0σ1 σ3τ0σ5τ− σ1τ+ σ3 σ3τ0σ1τ+ σ5τ− σ3 σ5τ− σ4τ− σ5 σ3τ+ σ4τ− σ5τ+ σ6τ− σ1τ+ σ2τ− σ3 σ3τ+ σ4τ −σ5τ+ σ6τ −σ1τ+ σ2τ − σ3 σ1τ1σ5τ5σ1 σ3τ3σ5τ5σ1τ1σ3 σ3τ3σ1τ1σ5τ5σ3 σ1τ5σ5τ1σ1 σ3τ5σ5τ1σ1τ3σ3 σ3τ1σ1τ5σ5τ3σ3 σ1τ0σ2τ0σ1 σ3τ0σ4τ+ σ5τ+ σ6τ0σ1τ− σ2τ− σ3 σ3τ0σ2τ− σ1τ− σ6τ0σ5τ+ σ4τ+ σ3 σ3τ3σ3 σ3τ0σ6τ0σ3
3 3 2 2 2 2 6 6 1 2 3 3 2 6 6 2 3 3 2 3 3 2 6 6 1 2
P31 P32 Cc P21 P21 Cc P61 P65 Cm Cc P31 P32 Cc P61 P65 Cc P31 P32 Cc P31 P32 Cc P61 P65 Cm CcmP21
Lett. 29 (16), 17–21. Kogure, T., Inoue, A., 2005. Stacking defects and long-period polytypes in kaolin minerals from a hydrothermal deposit. Eur. J. Mineral. 17 (3), 465–473. Le Page, Y., Rodgers, J.R., 2005. Quantum software interfaced with crystal-structure databases: tools, results and perspectives. J. Appl. Crystallogr. 38 (4), 697–705. de Ligny, D., Navrotsky, A., 1999. Energetic of kaolin polymorphs. Am. Mineral. 84 (4), 506–516. Mercier, P.H.J., Le Page, Y., 2008. Kaolin polytype revisited ab initio. Acta Crystallographica Section B 64, 131–143. Mercier, P.H.J., Le Page, Y., 2009. Ab initio exploration of layer slipping transformations in kaolinite up to 60 GPa. Mater. Sci. Technol. 25 (4), 131–143. Mercier, P.H.J., Le Page, Y., 2010. Kaolin polytype revisited ab initio at 10 GPa. Am. Mineral. 95, 1117–1120. Mercier, P.H.J., Le Page, Y., 2011. Rational ab initio modeling for low energy hydrogenbonded phyllosilicate polytypes. Eur. J. Mineral. 23 (3), 401–407. Newnham, R.E., 1961. A refinement of the dickite structure and some remarks on polymorphism in kaolin minerals. Mineral. Mag. 32 (252), 683–704. Pauling, L., 1930. The structure of chlorites. Proc. Natl. Acad. Sci. U. S. A. 16, 578–582. Salah, K.M., 2011. Theoretical study of kaolinite structure; energy minimization and crystal properties. World J. Nano Sci. Eng. 1 (2), 62–66. Salah, K.M., 2012. Elastic constant prediction of Nacrite: molecular dynamics simulations. Int J. Min. Eng. Miner. Process. 1 (3), 115–119. Sato, H., Ono, K., Johnston, C.T., Yamagishi, A., 2004. First-principle study of polytype structures of 1:1 dioctahedral phyllosilicates. Am. Mineral. 89, 1581–1585. Sato, H., Ono, K., Johnston, C.T., Yamagishi, A., 2005. First-principles studies on the elastic constants of a 1:1 layered kaolinite mineral. Am. Mineral. 90, 1824–1826. SenGupta, P.K., Schlemper, E.O., Johns, W.D., Ross, F., 1984. Hydrogen positions in dickite. Clay Clay Miner. 32 (6), 483–485. Steadman, R., 1964. The structures of trioctahedral kaolin-type silicates. Acta Crystallogr. 17, 924–927. Welch, M.D., Crichton, W.A., 2010. Pressure-induced transformations in kaolinite. Am. Mineral. 95, 651–654. Young, R.A., Hewat, A.W., 1988. Verification of the triclinic crystal structure of kaolinite. Clay Clay Miner. 36 (3), 225–232. Zheng, H., Bailey, S.W., 1994. Refinement of the nacrite structure. Clay Clay Miner. 42 (1), 46–52. Zhukhlistov, A.P., 2008. Crystal structure of nacrite from the electron diffraction data. Cystallography Reports. 53 (1), 76–82. Zvyagin, B.B., 1961. Polymorphism of double-layer minerals of the kaolinite type. Soviet Physics: crystallography 7, 38–51. Zvyagin, B.B., 1967. Electron diffraction analysis of clay mineral structures. In: Monographs in Geoscience. Springer US, pp. 1–356. Zvyagin, B.B., 1988. Polytypism of crystal structures. Comp. Math. Appl. 16, 569–591. Zvyagin, B.B., Drifts, V.A., 1996. Interrelated features of structure and stacking of kaolin mineral layers. Clay Clay Miner. 44, 297–303.
Acknowledgements The authors are grateful to the following institutions and offices: the Federal University of Minas Gerais (UFMG), the Post-Graduate Program in Metallurgical, Materials and Mining Engineering (PPGEM), the PostGraduate Program in Physics and to CAPES/PROEX. The co-author P.R.G. Brandão also acknowledges CNPq for a research grant. References Bailey, S.W., 1963. Polymorphism of the kaolin minerals. Am. Mineral. 48, 1196–1209. Bailey, S.W., 1969. Polytypism of trioctahedral 1:1 layer silicates. Clay Clay Miner. 17, 355–371. Bailey, S.W., 1988. X-ray diffraction identification of the polytypes of mica, serpentine, and chlorite. Clay Clay Miner. 36 (3), 193–213. Beaufort, D., Cassagnabere, A., Petit, S., Lanson, B., Berger, G., Lacharpagne, H., Johansen, J.C., 1998. Kaolinite-to-dickite conversion series in sandstone reservoirs. Clay Miner. 33, 297–316. Bish, D.L., 1993. Rietveld refinement of the kaolinite structure at 1.5 K. Clay Clay Miner. 41 (6), 738–744. Bish, D.L., Von Dreele, R.B., 1989. Rietveld refinement of non-hydrogen atomic positions in kaolinite. Clay Clay Miner. 37 (4), 289–296. Blount, A.L., Threadgold, I.M., Bailey, S.W., 1969. Refinement of the crystal structure of nacrite. Clay Clay Miner. 17, 185–194. Bookin, A.S., Drits, V.A., Plançon, A., Tchoubar, C., 1989. Stacking faults in kaolin-group minerals in the light of real structure features. Clay Clay Miner. 37 (4), 297–307. Cuadros, J., Vega, R., Toscano, A., Arroyo, X., 2014. Kaolinite transformation into dickite during burial diagenesis. Am. Mineral. 99, 681–696. Dera, P., Prewitt, C.T., Japel, S., Bish, D.L., Johnston, C.T., 2003. Pressure controlled polytypism in hydrous layered materials. Am. Mineral. 88, 1425–1429. Dornberger-Schiff, K., Durovic, S., 1975a. OD-interpretation of kaolinite-type structures I: symmetry of kaolinite packets and their stacking possibilities. Clay Clay Miner. 23, 219–229. Dornberger-Schiff, K., Durovic, S., 1975b. OD-interpretation of kaolinite-type structures II: the regular polytypes (mdo-polytypes) and their derivation. Clays and Clay Miner. 23, 231–246. Durovic, S., 1974. Notion of 'packets' in the theory of OD structures of M > 1 kinds of layers. examples: kaolinites and MoS2. Acta Crystallographica Section B. 30, 76–78. Hartman, P., 1983. Calculation of electrostatic interlayer bonding energy and lattice energy of polar phyllosilicates: kaolinite and chlorite. Clay Clay Miner. 31 (3), 218–222. Johnston, C.T., Wang, S., Bish, D.L., Dera, P., Agnew, S.F., Kenney, J.W., 2002. Novel pressure-induced phase transformations in hydrous layered materials. Geophys. Res.
205
Contents lists available at ScienceDirect
Applied Clay Science journal homepage: www.elsevier.com/locate/clay
Research paper
Methodological reconstruction of dioctahedral 1:1 phyllosilicate polytypes a,⁎
a
Carlos E. Teixeira , Paulo R.G. Brandão , Ricardo W. Nunes a b
MARK
b
Metallurgy, Materials and Mining Engineering Departments, Federal University of Minas Gerais, Brazil Physics Department, Federal University of Minas Gerais, Brazil
A R T I C L E I N F O
A B S T R A C T
Keywords: Dioctahedral Polytype kaolinite Dickite Nacrite
The layered kaolin-group minerals are composed mainly by three polytypes: kaolinite, dickite and nacrite. The geometrical polytypic reconstruction of these phases regards both the topological properties of individual networks (e.g., OH network linked to the hexagonal siloxane surface) and energetic aspect of superposition of cations. Starting from early attempts made by Bookin and Newnham, Zvyagin, Dornberger-Schiff and Durovic proposed their own symbolic representation of these structures. This work used the symbolic proposal of Zvyagin to prepare a methodological strategy to build the 52 species of dioctahedral polytypes. Two examples are shown to demonstrate the methodology and the CIF file of all the structures are made available.
1. Introduction The kaolin-group minerals have the general chemical composition Al2Si2O5(OH)4 and the mineralogical polytypes most commonly observed at ambient temperature and pressure are kaolinite, dickite and nacrite. These minerals are characterized as dioctahedral 1:1 phyllosilicates associated to weathering and burial sedimentary environment (Beaufort et al., 1998; Cuadros et al., 2014), besides the hydrothermal possibilities (Kogure and Inoue, 2005). Since Pauling, 1930, several experimental studies resolving the structure of these minerals (Bailey, 1988; Bish and von Dreele, 1989; Bish, 1993; Blount et al., 1969; SenGupta et al., 1984; Young and Hewat, 1988; Zheng and Bailey, 1994; Zhukhlistov, 2008) were performed, being mostly based on X-ray and neutron diffraction data, collected from both powders and singlecrystal samples, along with Raman spectroscopic data. A thermodynamic study made by de Ligny and Navrotsky (1999), using dropsolution calorimetry, that explained the geological occurrence of halloysite, nacrite, and dickite, which are metastable phases, must be interpreted in terms of kinetics or as the result of a specific synthesis path, rather than resulting from changes in the thermodynamically stable phase assemblage. Polytypism is a special case of polymorphism, occurring only in layered structures. In the natural environment, it occurs in the progressive transition kaolinite ➔ dickite ➔ nacrite (Beaufort et al., 1998; Cuadros et al., 2014), but the geological observation is not conclusive about the phenomenon and its mechanisms (Beaufort et al., 1998). The small energy differences between different polytypes, as well as the anisotropy of the interatomic forces often cause polytypism to manifest
⁎
Corresponding author. E-mail address: [email protected] (C.E. Teixeira).
http://dx.doi.org/10.1016/j.clay.2017.06.001 Received 9 November 2016; Received in revised form 30 May 2017; Accepted 1 June 2017 0169-1317/ © 2017 Elsevier B.V. All rights reserved.
itself in the form of stacking fault formation rather than the formation of separate phases (Dera et al., 2003). The confining pressure is identified as the main thermodynamic factor that drives these transformations. Experimental studies were performed in the last decades (Dera et al., 2003; Johnston et al., 2002; Welch and Crichton, 2010) tried to state the phenomenon but it is not always limited to the mainly geological observational set-square. Dera et al. (2003) identified a isosymmetric reversible pressure-induced phase transformation between 1.9 and 2.5 GPa in dickite, calling the transformed phase as HP-dickite. Welch and Crichton (2010) have investigated the compressional behavior of kaolinite under static compression by synchrotron X-ray powder diffraction and identified transformations at 3.7 and 7.0 GPa. Many different theoretical studies can be found in the literature approaching different information about the mineral species. Structural and lattice energy (Hartman, 1983; Salah, 2011; Sato et al., 2004), elastic (Salah, 2011; Salah, 2012; Sato et al., 2005) and thermodynamic (Mercier and Le Page, 2008, 2010) approaches have provided a broad picture of application of theoretical methods on dioctahedral 1:1 polytypes investigation. The series of recent papers presented by Mercier and Le Page (2008, 2009, 2010, 2011) investigated the behavior of multiple polytype with the pressure, deriving pressure-paths and thermodynamic ordering of the structures. The authors used a polytype builder tool named Materials Toolkit (Le Page and Rodgers, 2005) to derive the structure species. The polytypism in phyllosilicates, dioctahedral and trioctahedral, was investigated in several past studies (Bailey, 1963; Bailey, 1969; Bookin et al., 1989; Newnham, 1961; Steadman, 1964). The work of Zvyagin (1961, 1967, 1988) and Zvyagin and Drifts (1996) introduced
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
the utilization of symbolic representation of translations to represent the different stacking sequence in layered phyllosilicates. Durovic (1974) and Dornberger-Schiff and Durovic (1975a, 1975b) have presented a general outline and analysis of symmetry of kaolin-type layers as order-disorder structures consisting of three sheets put together. Also, an alternative symbolic representation of the symmetry condition of existence of monoctahedral, dioctahedral and trioctahedral, and all the structure construction symbols were provided. Starting from this symbolic description this work will present a methodology to better describe the 1:1 polytypes clarifying the gap between the theoretical symbolic representation and the proper dioctahedral atomic configuration.
2. Methodology and results The stacking patterns of dioctahedral structures are described by Durovic (1974) and Dornberger-Schiff and Durovic (1975a, 1975b) as a sequence of packets Pn seated in their main planes. These packets are composed by three kinds of sheets:
Fig. 2.2. Geometrical identification of displacement between networks (Zvyagin, 1961).
i. A tetrahedral sheets consisting of the network of SiO4−4 and the OH− ions lying in the plane of the apical oxygen atoms. The plane space group is P(6) mm; ii. The octahedral sheets consists of the plane of octahedrally coordinated cations with plane space group P(3)1 m; iii. The third sheets, nominated OH-layer, consists of the plane of OH− ions completing the octahedral coordination of the cations with plane space group H(6) mm.
dimensional networks: tetrahedral and octahedral. The two-dimensional networks in the same layer and adjacent networks of neighboring layers can be displaced relative to each other in six different ways. These relative displacements are referred to the networks origins being these situated at the center of tetrahedral hexagons and the position of the vacant octahedral atom. Geometrically and analytically these displacement are identified as in Fig. 2.2 and Table 2.1: The two-dimensional networks within a layer and the neighboring networks of adjacent layers can be displaced linearly relative to each other. The intra (σi) and inter (τk) layer displacement can be fulfilled in six different ways as geometrically and analytically exemplified in the Fig. 1 and Table 2.1, respectively. Displacements of both types (σi and τk) are, generally speaking, independent so that any arbitrary structure will be defined by a sequence of values of σ and τ. The Zvyagin formulation has two implicitly assumptions:
These sheets are numbered as L0 , L1eL2 according to the appearance sequence in the structure. Thus the pairs of adjacent sheets (Lp; Lp + 1) and (Lq; Lq + 1) will be equivalent under the condition that Lp and Lq are also equivalent. Considering the pair (L3n; L3n + 1), the origin of L3n + 1 is displaced by a3 3 relative to the origin of L3n, being these taken conventionally in coincidence with the positions of (6) and (3)1 m symmetry, respectively. The clockwise rotations of both layers by 60o, 120o, 180o, 240o, or 300o around the hexagonal axis of L3n would bring this layer into coincidence with itself, but the origin of L3n + 1 will then occur displaced by < 1 > = − a1 3 , < 2 > = a2 3 … or < 5 > = − a2 3 , respectively, relative to the origin of L3n.; besides, the orientation of L3n + 1 would also change accordingly. The elementary displacements ± a1/3, ± a2/3 , ± a3/3 are denoted by the characters 0–5 in clockwise order starting with a3/3 in the Fig. 2.1. All pairs (L3n ; L3n + 1) are geometrically equivalent and the position of L3n + 2 relative to the preceding pair is uniquely determined by the geometrical rule of stacking in the structure. Zvyagin (1961, 1967, 1988) proposed a simpler interpretation reporting the stacking as made by layers composed of two types of two
i. The reading sequence of symbols imply that the layers are added one below another; ii. The two dimensional coordinate system should point horizontal right and vertical up. Taking into account these two implicit conditions and the symbolism derived by Zvyagin, it is possible two reconstruct the tridimensional atomic structure of dioctahedral phyllosilicates. However, it is precisely in the transition between these two types of representation that there is a spot of complexity. Structural reconstruction of atomic configuration of large structures is difficult and the correspondence between the symmetry requirements and the atomic positions themselves can be pervasive and obscure. The authors proceeded in this gap and developed a bidimensional schematic rendering that was capable of reproducing the atomic configuration and symmetry properties of the dioctahedral structures. Having as starting point the construction rules presented and using the octahedral vacancy as reference point the scheme of translations was performed. The internal structure of each layer is defined by the intralayer displacement vector σi that characterizes the position of the octahedral vacancy regarding the center of the tetragonal ring in the adjacent network. The rigid translation of the layer is resolved by combining the σi and τk of each layer. The complete stacking profile is defined by a collection of σiτk values that together define both the internal structure of each layer and the relative position between layers. From the construction of the two dimensional diagrams it is possible to indicate the correct position of the elements of symmetry relative to each structure. Therefore, the two-dimensional diagrams are the key
Fig. 2.1. Possible displacement of layers and packets (Dornberger-Schiff and Durovic 1975a).
202
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
Table 2.1 Analytical identification of displacement between networks (Zvyagin, 1961). Displacement symbol
Displacement
Displacement symbol
Displacement
Displacement symbol
Displacement
σ1 σ2 σ3 σ4 σ5 σ6
1,1 − 1,1 1,0 − 1,− 1 1,−1 − 1,0
τ1 τ2 τ3 τ4 τ5 τ6
−1,− 1 1,− 1 −1,0 1,1 −1,1 1,0
τ0 τ+
0,0 0,1
τ−
0,− 1
(2σ1) (2σ2) (2σ3) (2σ4) (2σ5) (2σ6)
Fig. 2.3. Schematic bidimensional representation of [100] (A) section and [010] (B) section.
point in the task of complexity reduction necessary to represent and rebuild dioctahedral structures. As example, the symbolic representation of the structure VIII.1 is σ1τ1σ5τ5σ1 and the individual slips of the layers are: σ1τ1 σ5τ5
(1,1) + (− 1,− 1) = (0,0) (1,− 1) + (−1.1) = (0,0)
These translations can be represented in the sections along [100] and [010] as illustrated in Fig. 2.3. The red crosses indicate the vacant octahedral position in each layer. It follows easily that the glide plane should be settled up in the middle of the “b” (or “y”) axes and the atomic configuration is stated in reference to this symmetry element. The set of translations is capable to reproduce the atomic configuration compatible with a specific symmetry element. The consequent crystal structure and the relevant crystallographic information (CIF file) are demonstrated in Fig. 2.4 and Table 2.2, respectively. Fig. 2.4 shows the atomic and symmetry elements positions inside the structure unit cell. The fractional coordinates of the unit formula with the geometry and symmetry information are listed in Table 2.2. This first case may suggest that the use of symbolism is immediate but this is not a so direct conclusion. Analyzing now the 6-layer structure II.9, represented by σ3τ6σ2τ5σ1τ4σ6τ3σ5τ2σ4τ1σ3, whose individual layers are translated relative to the previous one by
Fig. 2.4. Atomic and symmetry elements positions inside the VIII.1 unit cell according with the [100] (A) and [001] (B) perspective. Atoms colors are: oxygen (red), silicon (yellow), aluminum (pink) and hydrogen (gray). The glide planes are represented by the pink line in both sections. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2.2 CIF file with the main crystallographic information about the VIII.1 structure.
Al Al O O O O O O O O O Si Si H H H H
Al1 Al2 O1 O2 O3 O4 O5 OH1 OH2 OH3 OH4 Si1 Si2 OH1 OH2 OH3 OH4
Site fract x
Site fract y
Site fract z
Crystallographic information
0.33333 0.83333 0.25000 0.50000 0.75000 0.00000 0.50000 0.16667 0.66667 0.66667 0.00000 0.00000 0.50000 0.16667 0.66667 0.66667 0.00000
0.50000 0.66667 0.75000 0.50000 0.75000 0.83333 0.66667 0.66667 0.50000 0.83333 0.50000 0.83333 0.66667 0.66667 0.50000 0.83333 0.50000
0.23100 0.23100 0.00000 0.00000 0.00000 0.15400 0.15400 0.30100 0.30100 0.30100 0.15400 0.04200 0.04200 0.36743 0.36743 0.36743 0.08757
Cell length a Cell length b Cell length c Cell angle alpha Cell angle beta Cell angle gamma Cell group H-M Int Tables number
5.15 8.95 14.30 90 90 90 Cc 9
Symmetry operation x x x + 1/2 x + 1/2
y y y + 1/2 − y + 1/2
203
z z + 1/2 z z + 1/2
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
Fig. 2.5. Schematic bidimensional representation of [100] (A) section and [010] (B) section.
system and the atomic configuration should be stated in reference to this symmetry element. This case is far from being evident, but the atomic configuration could be found using the octahedral vacancy that serves to highlight the translations events between layers. The consequent crystal structure and the relevant crystallographic information (CIF file) are demonstrated in Fig. 2.6 and Table 2.3, respectively. Fig. 2.6 illustrates the atomic and symmetry elements positions inside the structure unit cell. The fractional coordinates of the unit formula with the geometry and symmetry information are listed in the Table 2.3. Generally the transition from the symbolic representation for specific structure configuration is though and pervasive and this work presented a simple methodology to rebuild the dioctahedral polytypes. Thus the scope of this investigation was drawing the correct links between the theoretical symmetry-based polytypes and the factual configuration sight in the 1:1 phyllosilicates. Polytypes with more symmetry elements can be rebuilt using the same methodology taking due care to harmonize the symmetry requirements of each one. Using the methodology presented here the authors built the 52 (36 non-equivalent and 16 enantiomorphs) dioctahedral polytypes whose symbolic representation is displayed in Table 2.4. According to Zvyagin (1961, 1988) and Dornberger-Schiff and Durovic (1975a) the three natural kaolin polytypes, kaolinite, dickite and nacrite, are represented by structures I.1, I.4 and II.2, respectively.
Fig. 2.6. Atomic and symmetry elements positions inside the II.9 unit cell according with the [100] (A) and [001] (B) perspective. Atoms colors are: oxygen (red), silicon (yellow), aluminum (pink) and hydrogen (gray). The three-fold screw axes are represented by the green and yellow lines in both sections. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
σ3τ6 σ2τ5 σ1τ4 σ6τ3 σ5τ2 σ4τ1
(1,0) + (1,0) = (− 1.0) (− 1.1) + (− 1.1) = (1,−1) (1,1) + (1,1) = (− 1,− 1) (− 1.0) + (− 1.0) = (1,0) (1,− 1) + (1,−1) = (− 1.1) (− 1,-1) + (− 1,-1) = (1,1)
3. Conclusion The symbolic representation introduced by Zvyagin was used to reconstruct the complete set of dioctahedral 1:1 phyllosilicate polytypes. The methodology proposed was capable to reconcile the atomic configuration of the individual networks and the theory of layer stacking. The natural polytypes, e.g., kaolinite, dickite and nacrite, were reconstructed with adherence between the geometric properties of them. The complete set of 52 dioctahedral polytypes was drafted and transcribed to CIF files.
The [100] and [010] bidimensional diagrams are represented in Fig. 2.5. The red crosses indicate the vacant octahedral positions in each layer and the purple parts are a consequence of the bidimensional periodicity and are inserted to make the understanding easy. In the orthogonal coordinate system the 6-fold screw axes should be pointed at coordinates (0.833, 0.167) and at (0.667, 0) at the trigonal Table 2.3 CIF file with the main crystallographic information about the II.9 structure.
Al Al Si Si O O O O O O O O O H H H H
Al1 Al2 Si1 Si2 O1 O2 O3 O4 O5 OH1 OH2 OH3 OH4 OH1 OH2 OH3 OH4
Site fract x
Site fract y
Site fract z
Crystallographic information
0.00000 − 0.66667 0.00000 − 0.33333 − 0.16667 − 0.66667 − 0.16667 0.00000 − 0.33333 − 0.33333 − 0.66667 0.00000 − 0.66667 − 0.33333 − 0.66667 0.00000 − 0.66667
0.00000 0.66667 0.33333 0.66667 0.00000 0.50000 0.50000 0.33333 0.66667 0.00000 0.33333 0.66667 0.00000 0.00000 0.33333 0.66667 0.00000
0.07692 0.07692 0.01399 0.01399 0.00000 0.00000 0.00000 0.05128 0.05128 0.10023 0.10023 0.10023 0.05128 0.12005 0.12005 0.12005 0.03147
Cell length a Cell length b Cell length c Cell angle alpha Cell angle beta Cell angle gamma Cell group H-M Int Tables number
5.15 5.15 42.90 90 90 120 P65 170
Symmetry operation x −y −x + y −x y x−y
y x−y −x −y −x + y x
204
z z + 2/3 z + 1/3 z + 1/2 z + 1/6 z + 5/6
Applied Clay Science 146 (2017) 201–205
C.E. Teixeira et al.
Table 2.4 52 dioctahedral structures: 36 nonequivalents and 16 enantiomorphics. Id
Symbol
# layers
Space group
Id
Symbol
# layers
Space group
I.1 I.2 I.3 I.4 I.5 I.6 I.7 I.8 I.9 II.1 II.2 II.3 II.4 II.5 II.6 II.7 II.8 II.9 III.1 III.2 III.3 III.4 IV.1 IV.2 IV.3 IV.4
σ2τ− σ2 σ4τ+ σ4 σ3τ+ σ3τ− σ3 σ1τ+ σ5τ− σ1 σ1τ− σ5τ+ σ1 σ3τ+ σ5τ+ σ1τ+ σ3 σ3τ− σ5τ− σ1τ− σ3 σ3τ+ σ1τ− σ5τ0σ3 σ3τ+ σ5τ3σ1τ6σ3 σ4τ1σ5τ2σ4 σ1τ6σ2τ3σ1 σ3τ4σ6τ5σ3 σ1τ2σ4τ5σ1 σ5τ4σ2τ1σ5 σ3τ6σ4τ1σ5τ2σ6τ3σ1τ4σ2τ5σ3 σ3τ2σ4τ3σ5τ4σ6τ5σ1τ6σ2τ1σ3 σ3τ4σ2τ3σ1τ2σ6τ1σ5τ6σ4τ5σ3 σ3τ6σ2τ5σ1τ4σ6τ3σ5τ2σ4τ1σ3 σ1τ2σ2τ1σ1 σ3τ6σ6τ3σ3 σ3τ4σ4τ5σ5τ6σ6τ1σ1τ2σ2τ3σ3 σ3τ2σ2τ1σ1τ6σ6τ5σ5τ4σ4τ3σ3 σ6τ2σ6 σ3τ1σ3 σ3τ5σ3τ1σ3 σ1τ3σ5τ3σ1
1 1 2 2 2 3 3 3 3 2 2 2 2 2 6 6 6 6 2 2 6 6 1 1 2 2
P1 P1 Cc Cc Cc P31 P31 P32 P32 Cc Cc Cc P21 P21 P61 P61 P65 P65 Cc CcmP21 P61 P65 P1 P1 Cc Cc
IV.5 IV.6 V.1 V.2 V.3 V.4 V.5 V.6 VI.1 VI.2 VI.3 VI.4 VII.1 VII.2 VII.3 VIII.1 VIII.2 VIII.3 IX.1 IX.2 IX.3 X.1 X.2 X.3 XI.1 XII.1
σ3τ1σ5τ3σ1τ5σ3 σ3τ1σ1τ5σ5τ3σ3 σ1τ− σ2τ− σ1 σ3τ+ σ6τ− σ3 σ3τ− σ6τ+ σ3 σ3τ+ σ6τ+ σ3 σ3τ− σ4τ+ σ5τ− σ6τ+ σ1τ− σ2τ+ σ3 σ3τ+ σ2τ+ σ1τ+ σ6τ+ σ5τ+ σ4τ+ σ3 σ6τ0σ6 σ1τ0σ5τ0σ1 σ3τ0σ5τ− σ1τ+ σ3 σ3τ0σ1τ+ σ5τ− σ3 σ5τ− σ4τ− σ5 σ3τ+ σ4τ− σ5τ+ σ6τ− σ1τ+ σ2τ− σ3 σ3τ+ σ4τ −σ5τ+ σ6τ −σ1τ+ σ2τ − σ3 σ1τ1σ5τ5σ1 σ3τ3σ5τ5σ1τ1σ3 σ3τ3σ1τ1σ5τ5σ3 σ1τ5σ5τ1σ1 σ3τ5σ5τ1σ1τ3σ3 σ3τ1σ1τ5σ5τ3σ3 σ1τ0σ2τ0σ1 σ3τ0σ4τ+ σ5τ+ σ6τ0σ1τ− σ2τ− σ3 σ3τ0σ2τ− σ1τ− σ6τ0σ5τ+ σ4τ+ σ3 σ3τ3σ3 σ3τ0σ6τ0σ3
3 3 2 2 2 2 6 6 1 2 3 3 2 6 6 2 3 3 2 3 3 2 6 6 1 2
P31 P32 Cc P21 P21 Cc P61 P65 Cm Cc P31 P32 Cc P61 P65 Cc P31 P32 Cc P31 P32 Cc P61 P65 Cm CcmP21
Lett. 29 (16), 17–21. Kogure, T., Inoue, A., 2005. Stacking defects and long-period polytypes in kaolin minerals from a hydrothermal deposit. Eur. J. Mineral. 17 (3), 465–473. Le Page, Y., Rodgers, J.R., 2005. Quantum software interfaced with crystal-structure databases: tools, results and perspectives. J. Appl. Crystallogr. 38 (4), 697–705. de Ligny, D., Navrotsky, A., 1999. Energetic of kaolin polymorphs. Am. Mineral. 84 (4), 506–516. Mercier, P.H.J., Le Page, Y., 2008. Kaolin polytype revisited ab initio. Acta Crystallographica Section B 64, 131–143. Mercier, P.H.J., Le Page, Y., 2009. Ab initio exploration of layer slipping transformations in kaolinite up to 60 GPa. Mater. Sci. Technol. 25 (4), 131–143. Mercier, P.H.J., Le Page, Y., 2010. Kaolin polytype revisited ab initio at 10 GPa. Am. Mineral. 95, 1117–1120. Mercier, P.H.J., Le Page, Y., 2011. Rational ab initio modeling for low energy hydrogenbonded phyllosilicate polytypes. Eur. J. Mineral. 23 (3), 401–407. Newnham, R.E., 1961. A refinement of the dickite structure and some remarks on polymorphism in kaolin minerals. Mineral. Mag. 32 (252), 683–704. Pauling, L., 1930. The structure of chlorites. Proc. Natl. Acad. Sci. U. S. A. 16, 578–582. Salah, K.M., 2011. Theoretical study of kaolinite structure; energy minimization and crystal properties. World J. Nano Sci. Eng. 1 (2), 62–66. Salah, K.M., 2012. Elastic constant prediction of Nacrite: molecular dynamics simulations. Int J. Min. Eng. Miner. Process. 1 (3), 115–119. Sato, H., Ono, K., Johnston, C.T., Yamagishi, A., 2004. First-principle study of polytype structures of 1:1 dioctahedral phyllosilicates. Am. Mineral. 89, 1581–1585. Sato, H., Ono, K., Johnston, C.T., Yamagishi, A., 2005. First-principles studies on the elastic constants of a 1:1 layered kaolinite mineral. Am. Mineral. 90, 1824–1826. SenGupta, P.K., Schlemper, E.O., Johns, W.D., Ross, F., 1984. Hydrogen positions in dickite. Clay Clay Miner. 32 (6), 483–485. Steadman, R., 1964. The structures of trioctahedral kaolin-type silicates. Acta Crystallogr. 17, 924–927. Welch, M.D., Crichton, W.A., 2010. Pressure-induced transformations in kaolinite. Am. Mineral. 95, 651–654. Young, R.A., Hewat, A.W., 1988. Verification of the triclinic crystal structure of kaolinite. Clay Clay Miner. 36 (3), 225–232. Zheng, H., Bailey, S.W., 1994. Refinement of the nacrite structure. Clay Clay Miner. 42 (1), 46–52. Zhukhlistov, A.P., 2008. Crystal structure of nacrite from the electron diffraction data. Cystallography Reports. 53 (1), 76–82. Zvyagin, B.B., 1961. Polymorphism of double-layer minerals of the kaolinite type. Soviet Physics: crystallography 7, 38–51. Zvyagin, B.B., 1967. Electron diffraction analysis of clay mineral structures. In: Monographs in Geoscience. Springer US, pp. 1–356. Zvyagin, B.B., 1988. Polytypism of crystal structures. Comp. Math. Appl. 16, 569–591. Zvyagin, B.B., Drifts, V.A., 1996. Interrelated features of structure and stacking of kaolin mineral layers. Clay Clay Miner. 44, 297–303.
Acknowledgements The authors are grateful to the following institutions and offices: the Federal University of Minas Gerais (UFMG), the Post-Graduate Program in Metallurgical, Materials and Mining Engineering (PPGEM), the PostGraduate Program in Physics and to CAPES/PROEX. The co-author P.R.G. Brandão also acknowledges CNPq for a research grant. References Bailey, S.W., 1963. Polymorphism of the kaolin minerals. Am. Mineral. 48, 1196–1209. Bailey, S.W., 1969. Polytypism of trioctahedral 1:1 layer silicates. Clay Clay Miner. 17, 355–371. Bailey, S.W., 1988. X-ray diffraction identification of the polytypes of mica, serpentine, and chlorite. Clay Clay Miner. 36 (3), 193–213. Beaufort, D., Cassagnabere, A., Petit, S., Lanson, B., Berger, G., Lacharpagne, H., Johansen, J.C., 1998. Kaolinite-to-dickite conversion series in sandstone reservoirs. Clay Miner. 33, 297–316. Bish, D.L., 1993. Rietveld refinement of the kaolinite structure at 1.5 K. Clay Clay Miner. 41 (6), 738–744. Bish, D.L., Von Dreele, R.B., 1989. Rietveld refinement of non-hydrogen atomic positions in kaolinite. Clay Clay Miner. 37 (4), 289–296. Blount, A.L., Threadgold, I.M., Bailey, S.W., 1969. Refinement of the crystal structure of nacrite. Clay Clay Miner. 17, 185–194. Bookin, A.S., Drits, V.A., Plançon, A., Tchoubar, C., 1989. Stacking faults in kaolin-group minerals in the light of real structure features. Clay Clay Miner. 37 (4), 297–307. Cuadros, J., Vega, R., Toscano, A., Arroyo, X., 2014. Kaolinite transformation into dickite during burial diagenesis. Am. Mineral. 99, 681–696. Dera, P., Prewitt, C.T., Japel, S., Bish, D.L., Johnston, C.T., 2003. Pressure controlled polytypism in hydrous layered materials. Am. Mineral. 88, 1425–1429. Dornberger-Schiff, K., Durovic, S., 1975a. OD-interpretation of kaolinite-type structures I: symmetry of kaolinite packets and their stacking possibilities. Clay Clay Miner. 23, 219–229. Dornberger-Schiff, K., Durovic, S., 1975b. OD-interpretation of kaolinite-type structures II: the regular polytypes (mdo-polytypes) and their derivation. Clays and Clay Miner. 23, 231–246. Durovic, S., 1974. Notion of 'packets' in the theory of OD structures of M > 1 kinds of layers. examples: kaolinites and MoS2. Acta Crystallographica Section B. 30, 76–78. Hartman, P., 1983. Calculation of electrostatic interlayer bonding energy and lattice energy of polar phyllosilicates: kaolinite and chlorite. Clay Clay Miner. 31 (3), 218–222. Johnston, C.T., Wang, S., Bish, D.L., Dera, P., Agnew, S.F., Kenney, J.W., 2002. Novel pressure-induced phase transformations in hydrous layered materials. Geophys. Res.
205