^{1,2,3,4,a)}, Gordon J. Kearley

^{5}, John L. Provis

^{4,6}and Daniel P. Riley

^{7,8}

### Abstract

The structure of kaolinite at the atomic level, including the effect of stacking faults, is investigated using inelastic neutron scattering (INS) spectroscopy and density functional theory (DFT) calculations. The vibrational dynamics of the standard crystal structure of kaolinite, calculated using DFT (VASP) with normal mode analysis, gives good agreement with the experimental INS data except for distinct discrepancies, especially for the low frequency modes (200 – 400 cm−1). By generating several types of stacking faults (shifts in the a , b plane for one kaolinite layer relative to the adjacent layer), it is seen that these low frequency modes are affected, specifically through the emergence of longer hydrogen bonds (O–H⋯O) in one of the models corresponding to a stacking fault of −0.3151 a − 0.3151 b . The small residual disagreement between observed and calculated INS is assigned to quantum effects (which are not taken into account in the DFT calculations), in the form of translational tunneling of the proton in the hydrogen bonds, which lead to a softening of the low frequency modes. DFT-based molecular dynamics simulations show that anharmonicity does not play an important role in the structural dynamics of kaolinite.

The authors would like to thank Dr. Stewart Parker and Dr. Timmy Ramirez-Cuesta for assistance with sample loading, data acquisition, and data reduction on TOSCA at ISIS, Rutherford Appleton Laboratory, UK, and Dr. Neil J. Henson for assistance and valuable discussions regarding VASP. The authors acknowledge the use of Los Alamos National Laboratory Institutional Computing resources for the calculations performed in this work. The participation of C.E.W. in this work was supported by Los Alamos National Laboratory, which is operated by Los Alamos National Security LLC under (U.S.) Department of Energy (DOE) Contract No. DE-AC52-06NA25396. Furthermore, C.E.W. gratefully acknowledges the support of the (U.S.) Department of Energy through the LANL/LDRD Program. This work was funded in part by the Australian Research Council (ARC) (including some funding via the Particulate Fluids Processing Centre, a Special Research Centre of the ARC), and in part by a studentship paid to Claire White by the Centre for Sustainable Resource Processing via the Geopolymer Alliance. Travel funding for the experiments at ISIS was provided through the ANSTO Access to Major Research Facilities Program.

INTRODUCTION

MATERIAL AND METHODS

RESULTS AND DISCUSSION

Kaolinite structure and INS data

Influence of stacking faults

Contributions from the different types of H-atoms

Does anharmonicity play a role?

Assessment of kaolin polymorphs

Possible existence of adsorbed water

Influence of hydrogen bonding strength (distance)

CONCLUSIONS

### Key Topics

- Stacking faults
- 21.0
- Hydrogen bonding
- 19.0
- Density functional theory
- 15.0
- Crystal defects
- 9.0
- Tunneling
- 8.0

## Figures

Schematic representation of kaolinite (depicted as a P1 unit cell). The 1:1 layering of silica and alumina sheets is labeled, as are the two types of H-atoms present (inner H-atoms and inner surface H-atoms).

Schematic representation of kaolinite (depicted as a P1 unit cell). The 1:1 layering of silica and alumina sheets is labeled, as are the two types of H-atoms present (inner H-atoms and inner surface H-atoms).

Experimental INS spectrum of kaolinite (KGa-1b) and the calculated spectrum of the standard kaolinite structure 3 using normal coordinate analysis with force constants calculated by DFT (DFT-NCA).

Experimental INS spectrum of kaolinite (KGa-1b) and the calculated spectrum of the standard kaolinite structure 3 using normal coordinate analysis with force constants calculated by DFT (DFT-NCA).

Experimental and calculated INS spectra of kaolinite. The calculated spectra are for the DFT-NCA INS of kaolinite (denoted “Kao calc.”) and the different translation models of the stacking faults (denoted “t 1 calc.,” “t 2 calc.,” and “t 0 calc.”).

Experimental and calculated INS spectra of kaolinite. The calculated spectra are for the DFT-NCA INS of kaolinite (denoted “Kao calc.”) and the different translation models of the stacking faults (denoted “t 1 calc.,” “t 2 calc.,” and “t 0 calc.”).

Experimental and calculated INS spectra of kaolinite. The calculated spectrum is the DFT-NCA INS spectrum of kaolinite (denoted “Kao calc.”), and the contributions of the different types of H-atoms in the structure (denoted “inner” and “inner surf.,” see Figure 1 for definition) to this calculated spectrum are shown separately.

Experimental and calculated INS spectra of kaolinite. The calculated spectrum is the DFT-NCA INS spectrum of kaolinite (denoted “Kao calc.”), and the contributions of the different types of H-atoms in the structure (denoted “inner” and “inner surf.,” see Figure 1 for definition) to this calculated spectrum are shown separately.

Experimental INS spectrum of kaolinite and the calculated spectrum of the t 0 supercell. The calculated spectrum is the DFT-NCA INS spectrum of the t 0 kaolinite supercell (denoted “t 0 calc.”) and the contributions of the different types of H-atoms to this calculated spectrum are given according to layers (layer 1 or 2, denoted “inner 1” and “inner 1 surf.,” see Figure 1 for definition of H-atoms).

Experimental INS spectrum of kaolinite and the calculated spectrum of the t 0 supercell. The calculated spectrum is the DFT-NCA INS spectrum of the t 0 kaolinite supercell (denoted “t 0 calc.”) and the contributions of the different types of H-atoms to this calculated spectrum are given according to layers (layer 1 or 2, denoted “inner 1” and “inner 1 surf.,” see Figure 1 for definition of H-atoms).

Experimental INS spectrum of kaolinite and the calculated spectrum of the t 0 supercell. The calculated spectrum is the DFT-MD INS of the t 0 kaolinite supercell (denoted “t 0 MD calc.”) and the contributions to this calculated spectrum are given for the different types of H-atoms in the structure according to layers (layer 1 or 2, denoted “inner 1” and “inner 1 surf.,” see Figure 1 for definition).

Experimental INS spectrum of kaolinite and the calculated spectrum of the t 0 supercell. The calculated spectrum is the DFT-MD INS of the t 0 kaolinite supercell (denoted “t 0 MD calc.”) and the contributions to this calculated spectrum are given for the different types of H-atoms in the structure according to layers (layer 1 or 2, denoted “inner 1” and “inner 1 surf.,” see Figure 1 for definition).

Experimental INS spectrum of kaolinite (KGa-1b) and the DFT-NCA calculated INS spectra of dickite 43 and nacrite. 44

Thermally induced weight loss for KGa-1b kaolinite.

Thermally induced weight loss for KGa-1b kaolinite.

Stacked plot of the calculated partial pair distribution functions of the oxygen-hydrogen correlation for kaolinite (denoted “Kao”) and the different translation models of the stacking faults (denoted “t 1”, “t 2,” and “t 0”) in the hydrogen bonding region (O–H⋯O).

Stacked plot of the calculated partial pair distribution functions of the oxygen-hydrogen correlation for kaolinite (denoted “Kao”) and the different translation models of the stacking faults (denoted “t 1”, “t 2,” and “t 0”) in the hydrogen bonding region (O–H⋯O).

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