0. Hydrogen bonding in minerals under pressure
Bjoern Winkler
Goethe University Frankfurt a. M.

1. Contents Motivation Methods diffraction spectroscopy modelling
Examples
diaspore
the hydrogarnet substitution
nominally anhydrous minerals: wadsleyite

2. Motivation
Hydrogen bonding plays an important role in a very large number of processes
Numerous aspects are studied
structure and dynamics of hydrogen bonds in hydrous phases
incorporation of hydrogen (“water”) into nominally anhydrous phases
where are the hydrogen atoms ?
how much water can be incorporated ?
effects of anharmonicity
Test for theories
Metadynamics will not work for incommensurate phases, chemically complex systems etc..)

3. The Hydrogen Bond

4. Applicability of diffraction techniques
single crystal x-ray in DAC:
large P range – but hydrogens difficult to localize
single crystal neutron in DAC:
moderate P - neutron Laue diffraction (feasibility study worked on
x-ray powder diffraction at P: 
neutron powder diffraction: deuteration necessary, limited P- range

5. IR spectroscopic characterisation
n(OH) ~ cm-1
powder and single crystal IR spectroscopy as well-established tools, but quantitative measurements require calibration
correlations between n(OH) and d(O...O), d(O-H), d(H...O) at ambient pressure well established (Libowitsky (1999) and references therein)

6. Modelling of hydrogen bonded systems
Force field (empirical potential) models don’t work too well for hydrous silicates and related materials
Parameter-free approach
modeling of crystals: periodic boundary conditions
density functional theory (DFT)
athermal limit, Born-Oppenheimer Approximation
lattice dynamics from DFPT or finite displacement approach
plane waves + pseudopotentials or LCAO basis set
Metadynamics will not work for incommensurate phases, chemically complex systems etc..)

7. Example I: diaspore, a-AlOOH

8. Diaspore, a-AlOOH O H Pbnm, Z = 4 a = 4.401(1) Å b = 9.421 (4) Åc
Diaspore, a-AlOOH
Pbnm, Z = 4
a = 4.401(1) Å
b = (4) Å
c = 2.845(1) Å
V = (8) ų
intermediate H-bond
relatively high symmetry
relatively small unit cell
simple chemistry
Busing and Levy 1958

9. single crystal diffraction
High pressure
single crystal diffraction
Single-crystal structure analysis of AlO(OH) at 50 GPa: hydrogen atoms cannot be located (Friedrich et al., 2007, Am. Min)
a-AlOOH to d- AlOOH at ~18 GPa Diaspore metastable 30 GPa (and reflections still narrow)
Diaspore crystal
(30 x 20 x 10 µm³) at 52 GPa

10. Compressibility (experiment and model)
a/a0
b/b0
c/c0
V/V0
Exp. and DFT:
B0 = 151(2) GPa
Literature:
GPa
Exp.: Open symbols with error bars
DFT: Filled symbols
B. Winkler et al. (2001) Eur. J. Mineral 13, 343.
A. Friedrich et al. (2007) PCM 34, 145.
A. Friedrich et al. (2007) Am. Mineral. 92, 1640

11. Diaspore structural behaviour very well predicted
calc.: Winkler et al (2001)
exp.: Friedrich et al. (Phys. Chem. Min, 2007; Am. Min., 2007)
predict smooth decrease of a to 9.5o at 50 GPa

12. Hydrogen bond stretching motions
of diaspore, AlOOH

13. Pressure-induced shift of n(OH)
predicted shift does not follow correlation established at ambient pressure
but: O-H...O is slightly kinked in diaspore
no experimental data yet

14. Hydrogen bonding in diaspore
prediction of dispersion relation for OH-stretching frequencies shows unexpectedly large wave vector dependence: implies non-local dynamics

15. European Synchrotron Radiation Facility
linear accelerator
ESRF in Grenoble, France.*
booster synch.
storage ring
beamline
sketch of main functional parts**
circumference 844 m energy 6 GeV 40 beamlines * **

16. How to do the experiment?
kin
E, Q
Q=(1.1;1.1;1.1)
kout

17. IXS set-up E E Spot size: 30 x 60 m2 (H x V) sample detector
Monochromator
Si(n,n,n) – reflection, n = 7 -13
Q = °
1 tunable by temperature E f
Q = 4 /  sin()
Analyzer
Si(n,n,n) – reflection, n = 7 -13
Q = 89.98°
2 constant
 = 2 d(T) sin
d/d = E/E = -(T)T
 = at RT

19. Diaspore

20. IXS of hydrogen bonding in diaspore, AlOOH
there is dispersion of the OH-stretching vibration – this is not a fully localised mode dispersion can be rationalized by simple electrostatic model of the H-H interaction
Winkler B. et al., PRL, 2008

21. Example II: katoite

22. The hydrogarnet substitution
Garnets: X3[Y2Z3]O12
X – 8-fold coordinated
Y – 6-fold coordinated
Z – 4-fold coordinated
O – 4-fold coordinated
Grossular:Ca3[Al2Si3]O12
Pyrope: Mg3[Al2Si3]O12

23. Compressibility of garnets

24. Compressibility of garnets

25. The hydrogarnet substitution
Katoite: end-member ‘hydrogrossular’
model for ‘hydrogarnet substitution’
SiO4 replaced by (OH)4
is there an unusual pressure- induced behaviour of the OH bond ?
Nobes et al. (2000) Am. Min., 85,

26. Katoite Compressibility well described
compression mechanism for Al,Ca,O in agreement with experiment
O-H…O shows ‘conventional’ behaviour
hydro-pyrope always unstable w.r.t. components due to small size of Mg
Nobes et al. (2000) Am. Min., 85,
prompted new experiments by Lager et al., 2005

28. Katoite Fluorinert: Lager & van Dreele, 1996
Theory: Nobes et al., 2000a, 2000b
DAC: Lager et al., 2002
SME: Lager et al., 2005

29. Theory: Nobes et al., 2000a, 2000b
SME: Lager et al., 2005
Katoite

30. Katoite – IR (Lager et al., 2005)

31. Example III: zoisite

32. Zoisite
two structurally closely related silicates: ‚orthozoisite‘ and ‚clinozoisite‘
orthozoisite - nearly linear OH...O
clinozoisite - kinked OH...O (167°)
hydrogen bond has intermediate strength (n(OH) ~ 3100 cm-1 )

33. Zoisite pressure-induced shifts are very different:
Winkler et al. (1989)
orthozoisite dn/dP = -34 cm-1/GPa
Bradbury and Williams (2003)
clinozoisite dn/dP = -5 cm-1/GPa
generally: dn/dP = cm-1/GPa
some exceptions with (small) blue shifts
Winkler et al. (1989)

34. Model calculations DFT based
plane wave basis set / norm conserving pseudopotentials and DFPT using the CASTEP code
atom centered basis set (TZ2P) and finite displacement approach using SIESTA code
athermal limit
no correction for anharmonicity
anharmonicity will generally red-shift the stretching frequency (by ~100 cm-1)
GGA will generally blue-shift the OH-stretching frequency
recent study (Balan et al., 2008) has shown that this results in fortuitous error cancellation

35. Results
very good agreement between independent models and between models and experiment for structures, elastic behaviour and lattice dynamics
pressure-dependence of n(OH) of zoisite is indeed ‚anomalous‘
theo: -35 cm-1/GPa,
exp: -34 cm-1/GPa
linear bond: 2.5% elongation of O-H at 10 GPa in orthozoisite
kinked bond in clinozoisite remains kinked, only 0.5% elongation
doesn‘t follow structure-frequency
correlation
Winkler et al., Phys. Chem. Min (2008)

36. Example IV: wadsleyite

37. Wadsleyite - structure
-Mg2SiO4 - stable in the transition zone ( km depth)
structure orthorhombic or slightly monoclinic (Smyth et al. 1997)
structure with fully ordered H-defects suggested by Smyth (1994)

38. Elastic constants relaxed structure with total energy E0 and volume V0
after straining the crystal, the energy is
V is the volume of the strained crystal
and
is the pressure taken at V0
is the elastic energy proportional to the strains
The elastic constants are then

39. Elasticity of hydrous wadsleyite
earlier study (Kiefer et al., 2001) used DFT-LDA + ‚thermal correction‘ for anhydrous wadsleyite
here : DFT-GGA, both hydrous and anhydrous wadsleyite
most drastic change in c55
B decreases by 15%
exp: Holl et al., 2008 get a decrease in B by 12% for partial hydration

40. Wadsleyite - phonons
exp. (Kohn et al., 2002, Deon and Kochmüller, 2008)
complex IR-spectra between
3200 – 3700 cm-1
DFT model:
IR active modes at 3240 cm-1
and 3265 cm-1
‚OH-flip‘ induces significant changes (modes at and 3590 cm-1)
pressure dependence:
nearly linear red-shift of ~ 2 cm-1/GPa

41. Example V: molar absorption coefficients

44. Take home messages
Diffraction studies for the localisation of hydrogen positions in minerals are demanding
Don’t use spectroscopy-structure correlation established at ambient pressure to infer hydrogen positions at high pressures
DFT models work very well for hydrogen bonds
(if all assumptions are fulfilled reasonably well and the structural model is appropriate)
Recent developments: allow to predict intensity changes of Raman and IR spectra as a function of pressure, compute molar absorption coefficients

45. Acknowledgements Frankfurt group, especially D. Wilson, A. Friedrich
ESRF: Michael Krisch and Alexei Bosak
Keith Refson, Victor Milman, Julian Gale, R. Nobes, E.V. Akhmatskaya, J. White
HydroMin collaboration: E. Balan, K. Wright, M. Blanchard, S. Delattre, M. Lazzeri, F. Mauri, J. Ingrin
Funding: DFG, BMBF, DAAD, ESF, CECAM, Psi-k