${\mathrm{SnO}}_{2}$ was investigated at pressures up to 49 GPa by angle-dispersive x-ray diffraction using an imaging plate. Three phase transitions were observed on compression. Rutile-type ${\mathrm{SnO}}_{2}$ underwent a second-order transition to a ${\mathrm{CaCl}}_{2}$-type phase at 11.8 GPa under hydrostatic conditions, as determined from the pressure dependence of the spontaneous strain. This transition was observed at significantly lower pressures under nonhydrostatic conditions. A second transition to an \ensuremath{\alpha}-${\mathrm{PbO}}_{2}$-type phase was observed to begin above 12 GPa under nonhydrostatic conditions; however, only a small amount of this phase was obtained. Both the \ensuremath{\alpha}-${\mathrm{PbO}}_{2}$-type and the ${\mathrm{CaCl}}_{2}$-type phases transformed to a modified fluorite-type phase, space group Pa3-bar, above 21 GPa. Upon decompression, retransformation was observed and the sample recovered under ambient conditions consisted of a mixture of the rutile-type and \ensuremath{\alpha}-${\mathrm{PbO}}_{2}$-type phases. The structures of the rutile, ${\mathrm{CaCl}}_{2}$ and modified fluorite type phases were refined in situ by the Rietveld method allowing the structural evolution of ${\mathrm{SnO}}_{2}$ to be followed as a function of pressure. The relationships between the high-pressure structures of ${\mathrm{SnO}}_{2}$ are discussed using group theory and potential transformation pathways identified. The transition sequence observed for tin dioxide has important implications for the high-pressure behavior of other rutile-structured compounds.

X-ray diffraction study of the phase transitions and structural evolution of tin dioxide at high pressure:ffRelationships between structure types and implications for other rutile-type dioxides

The sections in this article are


Introduction
Pressure-Driven Phase Transitions
Framework Flexion
Increase in Coordination Number
Pressure-Induced Ordering


Generating High Pressure
Dynamic Pressure Generation
Static Pressure Devices
Large-Volume Presses
Diamond Anvil Cells




Probing Phase Transformations in Materials at High Pressure
Volumetric Techniques
Spectroscopic Techniques
Microscopy
Raman and Infrared Spectroscopy
Mossbauer Spectroscopy
X-Ray Absorption Spectroscopy
NMR


Ultrasonic Sound Velocity
Diffraction Techniques
X-Ray Diffraction
Neutron Diffraction




Examples
Zincblende-Type Semiconductors
Si and Ge
GaAs
InSb


Materials in the B–C–N System
C
BN
CN
BC
BCN


H2O
Ice Ih, XI and Ic
Ice II
Ice III and Ice IX
Ice V, Ice IV and Ice XII
Ice VI, Ice VII, Ice VIII, Ice X
Amorphous Ice at High Pressure




Acknowledgements

High Pressure Phase Transformations

The second-order elastic constants of brucite were determined by Brillouin scattering to 15 GPa in a diamond anvil cell. The experiments were carried out using a 4:1 methanol-ethanol mixture as pressure medium, and ruby as a pressure standard. Two planes, one perpendicular to the c axis (basal plane) and the other containing the c axis (meridian plane), were measured at room pressure and 10 elevated pressures. Individual elastic stiffnesses, aggregate moduli, and their pressure derivatives were obtained by Þ tting the data to Eulerian Þ nite strain equations. The inversion yields individual elastic constants of C11 = 154.0(14) GPa, C33 = 49.7(7) GPa, C12 = 42.1(17) GPa, C13 = 7.8(25) GPa, C14 = 1.3(10) GPa, C44 = 21.3(4) GPa, and their pressure derivatives of (∂C11/∂P)0 = 9.0(2), (∂C33/∂P)0 = 14.0(5), (∂C12/∂P)0 = 3.2(2), (∂C13/∂P)0 = 5.0(1), (∂C14/∂P)0 = 0.9(1), (∂C44/∂P)0 = 3.9(1). Aggregate moduli and their pressure derivatives are KS0 = 36.4(9) GPa, G0 = 31.3(2) GPa, (∂KS/∂P)T0 = 8.9(4), (∂G/∂P)0 = 4.3(1) for the Reuss bound, and KS0 = 43.8(8) GPa, G0 = 35.2(3) GPa, (∂KS/∂P)T0 = 6.8(2), (∂G/P)0 = 3.4(1) for the Voigt-Reuss-Hill average. The ratio of the linear compressibility along the c and a axes decreased from 4.7 to 1.3 over the examined pressure range. The shear anisotropy (C66/ C44) decreased from 2.6(1) at ambient condition to 1.3(1) with increase of pressure to 12 GPa. Axial compressibilities and a compression curve constructed from our Brillouin data are in good agreement with previous X-ray diffraction data. The increased interlayer interactions and hydrogen repulsion that occurs as brucite is compressed produce a continuous variation of elastic properties rather than any abrupt discontinuities.

Single-crystal elasticity of brucite, Mg(OH)2, to 15 GPa by Brillouin scattering

The structural compression mechanism and compressibility of diaspore, AlO(OH), were investigated by in situ single-crystal synchrotron X-ray diffraction at pressures up to 7 GPa using the diamond-anvil cell technique. Complementary density functional theory based model calculations at pressures up to 40 GPa revealed additional information on the pressure-dependence of the hydrogen-bond geometry and the vibrational properties of diaspore. A fit of a second-order Birch–Murnaghan equation of state to the p–V data resulted in the bulk modulus B0 = 150(3) GPa and B0 = 150.9(4) GPa for the experimental and theoretical data, respectively, while a fit of a third-order Birch–Murnaghan equation of state resulted in B0 = 143.7(9) GPa with its pressure derivative B′ = 4.4(6) for the theoretical data. The compression is anisotropic, with the a-axis being most compressible. The compression of the crystal structure proceeds mainly by bond shortening, and particularly by compression of the hydrogen bond, which crosses the channels of the crystal structure in the (001) plane, in a direction nearly parallel to the a-axis, and hence is responsible for the pronounced compression of this axis. While the hydrogen bond strength increases with pressure, a symmetrisation is not reached in the investigated pressure range up to 40 GPa and does not seem likely to occur in diaspore even at higher pressures. The stretching frequencies of the O–H bond decrease approximately linearly with increasing pressure, and therefore also with increasing O–H bond length and decreasing hydrogen bond length.

High-pressure properties of diaspore, AlO(OH)

The existence of very short non-bonded H–H distances in β-Ni(OH)2 at ambient conditions, predisposes this compound towards a structural change at very low pressures. To investigate this, we have now carried out a high-pressure Raman scattering investigation on β-Ni(OH)2 up to 25 GPa. Our results show a monotonic stiffening of all the lattice modes and a small softening of hydroxyl symmetric stretch mode under pressure. Absence of any signature of a phase transformation up to 25 GPa and a reversible intrinsic broadening of the OH mode suggest that, even at the ambient conditions, β-Ni(OH)2 may be in the non-ideal CdI2 structure in which H-lattice is disordered.

High-pressure behavior of β-Ni (OH) 2 - a Raman scattering study

A phase transition from Ca(OH)2 I (portlandite) to Ca(OH)2 II at high pressure and temperature has been confirmed, using in situ x-ray diffraction in a multianvil high pressure device (DIA). The structure was determined at 9.5 GPa and room temperature from data collected after heating the sample at 300°C at 7.2 GPa in a diamond anvil cell. Both the Le Bail fit and preliminary Rietveld refinement suggest that the new phase, which reverts to Ca(OH), I during pressure release, has a structure related to that of baddeleyite (ZrO1); it is monoclinic (P21/c) with a= 4.887(2), b= 5.834(2), c = 5.587(2), β = 99.74(2)°. The coordination number of Ca increases from six to seven (5 + 2) across the transition. At 500°C, the phase boundary is bracketed at 5.7 ± 0.4 GPa by reversal experiments performed in the DIA.

The baddeleyite-type high pressure phase of Ca(OH)2

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The baddeleyite-type high pressure phase of Ca(OH)2