REVISED MANUSCRIPT
Nadia Curet(1,2), Marcello Merli(3), Silvana Capella(1), Piera Benna(1,2) and Alessandro Pavese(1,2)
Low pressure ferroelastic phase transition in rutile-type AX
2minerals:
cassiterite (SnO
2), pyrolusite (MnO
2) and sellaite (MgF
2)
(1)
Earth Sciences Department, University of Torino, Via Valperga Caluso 35, 10125 Torino, Italy
(2)
CrisDi Interdepartmental Center for Crystallography, Via P. Giuria 5, 10125 Torino, Italy
(3)
Earth and Sea Department, University of Palermo, Via Archirafi 36, 90123 Palermo, Italy
Corresponding author: Alessandro Pavese
E-mail: alessandro.pavese@unito.it Phone : ++39 011 6705180
Key-words: high-pressure diffraction; ferroelastic phase transition; cassiterite; pyrolusite; sellaite ORCID of the authors:
Nadia Curet 0000-0002-6300-7133 Marcello Merli 0000-0002-1819-4291 Silvana Capella 0000-0002-7652-2898 Piera Benna 0000-0002-1683-3707 Alessandro Pavese 0000-0003-4982-2382
Acknowledgements The authors are very grateful to Marco Ciriot (President of AMI, “Associazione Micromineralogica Italiana”) for supplying the natural samples and precise information about their geographic occurrences. Reviews from two anonymous referees greatly improved the manuscript; we are grateful to them for critical reading and useful suggestions. We sincerely thank Laurie Jayne Kurilla for giving valuable advice on the English language. The CrisDi and G Scanset Interdepartmental Centers of University of Torino are acknowledged. The present investigation was partly funded by the Italian Ministry for Education, University and Research through the MIUR-Project PRIN 2017 (2017L83S77).
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Abstract
The structural behavior of cassiterite (SnO2), pyrolusite (MnO2) and sellaite (MgF2), i.e. AX2
-minerals, has been investigated at room temperature by in situ high-pressure single-crystal diffraction, up to 14 GPa, using a diamond anvil cell. Such minerals undergo a ferroelastic phase transition, from rutile-like structure (SG: P42/mnm) to CaCl2-like structure (SG: Pnnm),
at 10.25, 4.05 and 4.80 GPa, respectively. The structural evolution under pressure has been described by the trends of some structure parameters that are other than zero in the region of the low-symmetry phase’s stability. In particular, three tilting angles (, ’, ABS) and the metric distortion of the cation-centred octahedron (quantified via the difference between apical-anion and equatorial-anion distances |Xax-Xeq|) are used to express the atoms’ readjustment, i.e. relaxation, taking place in the CaCl2-like structures under pressure. The
crystallographic investigation presented is complemented with an analysis of the energy involved in the phase transition using the Landau formalism and adopting the following definition for the order parameter: Q = 11-22, ij being the spontaneous strain tensor. The
dependence of , ’, ABS and |Xax-Xeq| on Q allows determination of a correlation
between geometrical deformation parameter and energy. Lastly, the relaxation mechanisms that exploits , ’, ABS and |Xax-Xeq| may be related to the ionic degree of bonding, the latter modelled via quantum mechanics and Bader theory. Sellaite, the mineral exhibiting the highest degree of ionic bonding among those investigated, tends to accomplish relaxation through pure rotation of the octahedron, rather than a metric distortion (|Xax-Xeq|), which would shorten inter-atomic distances thus increasing repulsion between anions.
Introduction
Rutile-type AX2-compounds have motivated a great deal of attention for several reasons. On
one hand, the outstanding physical and chemical properties of rutile, TiO2, boost researchers
to delve into the behaviour of rutile-isostructural minerals to better understand the
behaviour of TiO2, and to unearth possible analogies of other AX2-systems. Rutile exhibits a
complex phenomenology as a function of pressure and temperature. It undergoes phase transitions that lead to thirteen polymorphs (Liu et al. 2015). The TiO2-phases allow a variety
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of technological applications, which exploit properties such as the narrowing of the band gap in the S/N Nd-doped TiO2 (Umebayashi et al. 2002, 2003; Wang and Doren 2005) and the
photocatalytic activity induced by C4+ and S4+ dopant ions (Ohno et al. 2004a, 2004b). On the other hand, it is worth comparing rutile-like AX2 compounds’ behaviour with stishovite’s,
SiO2, the latter being of relevance to mantle mineral composition and providing an example
of crystal structure in which Si fits an octahedral coordination (Carpenter et al. 2000).
Altogether, in spite of their seeming “chemical simplicity”, rutile-type AX2-compounds exhibit
a complex physical behaviour. In such a view, high-pressure (HP) investigations are useful to bring to light differences between AX2-compounds, in particular exploring 1) their
physical-chemical mechanisms of structural relaxation under P and 2) the relationships between structural relaxation and energy, involving low- and high-symmetry phases, if phase transitions take place. Several investigations were performed by HP powder diffraction experiments on rutile-type AX2-compounds (Haines et al. 2000; Prakapenka et al. 2003; Shieh
et al. 2006; Grocholski et al. 2014). In such studies, the authors explored large ranges of pressure, often over 100 GPa. Conversely, few experiments on single-crystal are reported (Nakagiri et al. 1987; Ross et al. 1990), and little attention has been devoted to get insight into the behaviour of AX2-minerals in the low-pressure range. The latter aspect is relevant to
help understand the origins of a loss of stability and the ensuing structural relaxation
mechanism, which often makes the resulting high-pressure polymorph stable upon a wide P-range.
In the present investigation, we deal with low-pressure triggered ferroelastic phase transitions of AX2-minerals from rutile-type to CaCl2-type structure. We focus on SnO2
(cassiterite), MnO2 (pyrolusite; -MnO2) and MgF2 (sellaite), given that they a) exhibit
structural features that are complementary to each other (we shall discuss this aspect below), b) show bulk modulus values covering a wide range (K0 = 101(3) GPa in MgF2, K0 =
205(7) GPa in SnO2, K0 = 328(18) GPa in MnO2) and c) have chemical compositions that
involve both cation and anion replacements. The present study is carried out by in situ HP X-ray single-crystal diffraction, from room pressure to about 14 GPa. The structural evolutions of the minerals under investigation are interpreted in light of the Landau theory. The aim is
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to span the gap found in literature about a detailed structural analysis and phenomenological energy interpretation of the symmetry break from rutile-type to CaCl2-type structure, as a
function of composition. In the following, for the sake of simplicity we shall employ the names “cassiterite”, “pyrolusite” and “sellaite” to address both tetragonal and orthorhombic phases.
Rutile-type structure and earlier studies
Rutile-type structure AX2 compounds have tetragonal symmetry and space group P42/mnm,
with Z=2. The A-cation is located at 0,0,0 and the X-anion at x,x,0 (Vegard 1916). The resulting structure is simple: each A-cation is bonded to six X-anions in octahedral coordination and each X-anion is, in turn, bonded to three A-cations. Octahedral chains develop along [001] by a corner-sharing linking mechanism. Among the six cation-anion bonds stabilizing AX6-octahedra, two “axial” A-Xax bonds, perpendicular to the (110) plane,
have length R1, and the remaining four “equatorial” A-Xeq bonds have length R2. The R1 and
R2 lengths are slightly different from one another and this discrepancy causes a distortion of
the octahedron (Baur 1956; 1976; Baur and Khan 1971; Bolzan et al. 1997), which, in the case of ideal symmetry, should have R1 = R2. Plotng structural data of rutile-type AX2
oxide/halide compounds in terms of their c/a ratio versus anion x-coordinate, one finds that such structures lie in two distinct classes, as a function of the geometrical distortion of their octahedral building units: almost all halides fulfil the following inequality R1 < R2, whereas
most oxides are such that R1 > R2. This led the aforementioned authors to conclude that
bonding in some rutile-type oxides (TiO2, GeO2 and SnO2) could not be completely ionic, but
it would bear a covalent contribution. The four equatorial anions (Xeq) are located at the vertices of a rectangle in the (110) plane, whose longest side lies parallel to [001], whereas the shortest one is perpendicular to [001]. Such an arrangement is described by means of the rectangle’s side lengths and Xeq-A-Xeq angles.
All the rutile-type compounds investigated to-date reveal at high pressure a phase transition to the CaCl2-type orthorhombic structure, with space group Pnnm (Z=2), and
additional transitions at higher pressures. The space group Pnnm is a subgroup of P42/mnm 4 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 7
(Bärnighausen 1980) and no discontinuities in the cell edges and relative volumes have been observed, this pointing to the occurrence of a second order transition. The rutile-to-CaCl2
-type transition involves rotation of the AX6 octahedral chain about the twofold axis parallel
to z, yielding an orthorhombic distortion, which implies disappearance of the diagonal mirror planes of the rutile-type structure, and therefore of the fourfold screw axis (Baur 1994, 2007).
Two simple geometrical relationships hold between the latce parameters of the orthorhombic unit cell, anion’s coordinates and tilting-angles ( and ’) of the AX6
-octahedron (Bärnighausen et al. 1984; Range et al. 1987; see Fig. 1a):
tan (45° + ) = b(0.5− y)a (0.5−x ) (1a)
tan (45° - ’) = byax (1b)
where a and b are the latce parameters of the orthorhombic symmetry phase; x and y the factionary coordinates of the X-anion.
If =’0, then the octahedron rotates, whereas if ’0 then distortions occur (Haines et al. 1995), and the A-Xax bond is not perpendicular to the plane of the four equatorial anions anymore.
Previous works on synthetic SnO2 reveal that its structure exhibits R1 slightly longer
than R2 (Baur and Khan 1971). Hazen and Finger (1981) and Haines and Léger (1997) report
bulk modulus values of K0 = 218(2) GPa with k’ = 7, and K0 = 205(7) GPa with k’ = 7.4(2.0),
respectively. Rietveld refinements on X-ray powder diffraction patterns collected on a P-range such that the tetragonal symmetry is stable show that i) the oxygen’s x coordinate slightly decreases upon increasing pressure and ii) the axial Sn-O bonds are more
compressible than the equatorial ones (Haines and Léger 1997). The rutile-to-CaCl2-type
phase transition occurrence was estimated at P 11.8 GPa by extrapolation of the
spontaneous strain values versus pressure from Haines and Léger (1997), who experimentally observed at 12.6 GPa the appearance of the low-symmetry phase. Shieh et al. (2006) claim the occurrence of the CaCl2-type polymorph at 13.6 GPa. In their study, further transitions 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
were detected at higher pressure, i.e. to pyrite-type structure (Pa ´3 ) at 38 GPa, to ZrO2
-type structure (Pbca) at 64 GPa, and to cotunnite--type structure (Pnam) at 80 GPa, after heating. Hassan et al. (2013) predict a transition pressure at 11.6 GPa. According to Erdem et al. (2014), the same transition is supposed to take place at 7.59 GPa, and at 11.50 GPa there should occur a transformation more, to a -PbO2-type structure.
Pyrolusite (-MnO2) exhibits R1 > R2. Natural crystals are usually fine-grained and
literature reports a few structural characterizations (Kondrashev and Zaslavskii 1951; Wyckoff 1963). The HP behaviour of -MnO2 was studied on powdered samples in the range 0-46
GPa, and the rutile-to-CaCl2-type transition is placed between 0.3 and 1.9 GPa (Haines et al.
1995). The aforementioned authors claim a significant broadening of the h00 and 0k0 reflections, on such P-interval. However, unambiguous peak splitng of the mentioned reflections takes place only at pressures higher than 7.3 GPa. The orthorhombic phase of MnO2 yields a bulk modulus of K0 = 328(18) GPa with K’= 4(2), according to Haines et al.
(1995). By ab initio calculations, Li et al. (2006) predict that the rutile-type MnO2 structure
transforms to CaCl2-type structure at 5 GPa and then changes to pyrite-type at 20 GPa.
Sellaite (MgF2) is a fluoride with the rutile-type structure (Baur 1976), exhibiting, like
most fluorides, R2 > R1. Nakagiri et al. (1987) studied the high-pressure behaviour of MgF2 by
X-ray single-crystal diffraction experiments, using a Diamond Anvil Cell (DAC), up to 4.8 GPa. In the investigated range, the fluorine’s x coordinate slightly decreases under P and the gap between R1 and R2 widens, the octahedron becoming more and more distorted.
Notwithstanding all this, no phase transition was seen. Haines et al. (2001) located the rutile-to-CaCl2-type phase transition over 9 GPa, because of the observed broadening and
subsequent splitng of the h ≠ k diffraction peaks, and reported the following elastic
properties: K0 = 101(3) GPa with K’ = 4.2(1.1). At 14 GPa the aforementioned authors claim a
modified fluorite PdF2-type phase, space group Pa ´3 , Z=4. Kanchana et al. (2003) studied
the structural phase transition in MgF2 by calculations using the TB-LMTO method and
predicted the rutile-to-CaCl2-type transition at 10 GPa, and a further transition to cubic
PdF2-type at 14.1 GPa. Using density functional theory, Živković and Lukačević (2016) 6 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 11
calculated the pressure dependence of phonon modes’ frequencies and elastic constants, and they concluded that the rutile-to-CaCl2-type transition is a second-order phase
transition. Using the LDA-T approximation, the quoted authors foresaw the occurrence of a soft mode that tends to zero at 4.7 GPa, thus heralding the appearance of instability.
Experimental
Samples
The specimens under study are natural crystals from mines. Cassiterite was sampled from Panasqueira, Covilha, Castelo Branco (Portugal); pyrolusite from Upton Pyne, East Devon (England); sellaite from Suran, Ishlya, Beloretsk district, Bashkortostan (Bashkiria), Urals (Russia) (M. Ciriot Collection, Russo 2007). Chemical composition analyses were carried out by an electronic -probe on crystal fragments embedded into araldite. The resulting sections were polished and carbon coated. A JEOL JSM-IT300LV Scanning Electron Microprobe
equipped with Oxford INCA Energy 200 EDS SATW detector (WD 10, KV 15) was used to measure the chemical composition of each sample. Rhodonite (Mn), almandine-pyrope (Al, Mg), anhydrite (Ca), strontiofluorite (F) and metallic tin (Sn) were used as standards for the elements in parentheses. We can estimate an uncertainty of some 0.01 atom per formula unit, based on instrument calibration, lower detectability limit, and dispersion of the values related to the performed analyses. Considering such uncertainty, the compositions of the three specimens under investigation are approximated, as reported below
cassiterite SnO2 (average of 9 analyzes);
pyrolusite MnO2 (average of 11 analyzes);
sellaite Mg2+0.985 Ca2+0.015 F2 (average of 13 analyzes).
In situ HP-single crystal X-Ray Diffraction
After chemical characterization, single crystals of cassiterite, pyrolusite and sellaite were selected to perform in situ high-pressure X-ray diffraction measurements. The samples were chosen according to their optical features and size, and then tested with preliminary X-ray diffraction experiments at ambient conditions. The P42/mnm space group was confirmed for
all the specimens under investigation. The selected crystals (pyrolusite 1003030 Å3; cassiterite 1206020 Å3; sellaite 1209030 Å3) were placed in an ETH-DAC (Miletich et al.
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2000), using a 200 µm-hole stainless steel gasket, pre-indented to a thickness of about 80 µm. A 16:3:1 methanol:ethanol:water (M:E:W) mixture was used as a hydrostatic pressure-transmitng medium. Four 5 µm size ruby specimens were scattered over the HP-chamber hosting the sample, to i) measure pressure (Mao et al. 1986), ii) check/quantify occurrence of deviations from hydrostatic conditions and iii) provide an estimate of the uncertainty on P. As to point ii), the mix 16:3:1 M:E:W fails to provide fully hydrostatic conditions over 10.5 GPa (Angel et al. 2007; Klotz et al. 2009) therefore extra attention should be paid to data obtained at pressure above the mentioned threshold. The fluorescence lines of the ruby crystals were measured by a LABRAM HRVIS (Horiba Jobin Yvon Instruments) -Raman spectrometer (G. Scanset Center, University of Torino). The uncertainty on pressure,
estimated as e.s.d. of the P-determinations on the ruby crystals, is on average as large as 0.1 GPa. For cassiterite, a second crystal (906020 Å3) was studied, using a DAC equipped with a 150 µm-hole stainless steel gasket, pre-indented to a thickness of about 65 µm; this arrangement allowed us to achieve about 14 GPa.
X-ray diffraction intensities were measured with a Gemini R Ultra diffractometer (CrisDi Center, University of Torino), equipped with a Ruby CCD detector, using MoKα radiation and an X-ray tube operating at 50 kV and 40 mA. A total of 714 exposure frames (2 angle width 0.6°, exposure time = 40 s, detector-sample distance 82 mm) were collected at each
pressure, using four φ- and twelve ω-scans runs, thus covering as large an accessible reciprocal space portion as possible. The CrysAlisRedTM program (Rigaku Technologies) was used to fit the diffraction spots and integrate the related intensities. Structural refinements were carried out by the SHELX-97 package (Sheldrick 2008), adopting the low-symmetry space group even for tetragonal symmetry to follow the structural evolution under pressure (see the next section). In particular: the fractional coordinates of the anion were refined without restraints; the occupancy factors were fixed at their values from the chemical compositions; anisotropic (for cations) and isotropic (for anions) atomic displacement parameters were refined. At high pressure, in the case of some datasets (mostly for
pyrolusite and for cassiterite at P > 12 GPa), cations’ vibration motion, too, was modelled by isotropic ADPs, to preserve a reliable ratio between the number of independent data and the number of structural degrees of freedom. Unit-cell parameters and refinement details for
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cassiterite, pyrolusite and sellaite are presented in Tables 1-2-3, respectively (CIF files provided as electronic supplementary material).
Results and Discussion
Structures as a function of pressure
In the present study we follow the structural evolution versus pressure of each phase under investigation to help clarify the mechanism causing the symmetry break and estimate the transition pressure, about whose value uncertainty is still in debate in present literature. The low-symmetry phase’s space group, Pnnm, is a subgroup of P42/mnm. The symmetry break
relieves symmetry constraints and allows the following degrees of freedom: 1) the x,x,0 atomic coordinates of the X-anion change into x,y,0; x y measures the deviation of the anion from the [110] diagonal direction; 2) the a-c latce parameters change into a-b-c of the orthorhombic phase.
The additional crystallographic degrees of freedom enable a set of “deformation parameters”, i.e. observables that are zero in the high-symmetry phase and other than zero in the low-symmetry phase. We chose to use the appellation of “deformation parameters” to underline that they provide a deformation with respect to the high-symmetry phase, if one extends the latter into the stability field of the low-symmetry phase. Such deformation parameters are associated to the following atomic re-arrangements, related to the low-symmetry phase:
1) the four equatorial oxygen atoms of the octahedron no longer lie in the (110) plane, and the octahedron’s orientation can change. The Xax-Xeq distances are equal to each other in the high-symmetry phase, whereas in the low-symmetry phase they split into two sets of values and the related absolute difference is referred to by |Xax-Xeq|;
2) the A-Xax bond, which in the high-symmetry phase is normal to the (110) plane, can tilt in the low-symmetry phase. The tilting angle, Xax-A-Xeq, contributes to the description of the octahedral distortion. Hereafter we refer to the acute Xax-A-Xeq angle (Fig. 1b) by the acronym ABS (“Axial Bond Squareness”);
3) the and ’ angles, mentioned in the “Rutile-type structure and earlier studies” (Fig. 1a), can take values other than zero in the low-symmetry phase.
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The low-symmetry structure has two degrees of freedom more than the high-symmetry structure; this implies that only two deformation parameters are independent.
Notwithstanding, the deformation parameters express different ways adopted by a structure to respond to HP and relax accordingly. In this view, we shall pay special attention to |Xax-Xeq|, ABS, and ’, they will be termed “degrees of freedom”, for the sake of simplicity.
As stated above, we also conducted structural refinements using the Pnnm space group for the tetragonal phase. This means that the independent anion’s coordinates are x and y, instead of x only, as it occurs in the high-symmetry case. A comparatively modest number of degrees of freedom increases our confidence that correlations are reasonably low and unlikely to skew our results, which can be checked by comparing the results from
refinements in low-symmetry with those in high-symmetry structures. The choice to adopt the low-symmetry structure throughout the P-range explored is dictated by our aim to see the structure’s evolution from P42/mnm to Pnnm by recording the trend of deformation
parameters. This is carried out to monitor where and how such observables become
significantly other than zero and estimate the transition pressure value as the point at which an abrupt change of trend takes place. This approach is feasible due to the simplicity of the structure of the involved phase. Should the number of degrees of freedom of the low-symmetry phase be large, then correlations would occur and likely lead to incorrect
conclusions. Note that for each P-point we also determined the space-group according to the consolidated approach (see for instance: Marsh 1995; Baur and Fischer 2003) and performed structural refinements in high-symmetry structure, when it resulted in P42/mnm .
Tables 1a-b, 2a-b and 3a-b report the latce parameters, general refinement conditions and structure parameters related to the structural refinements of cassiterite, pyrolusite and sellaite, respectively. The quality of the pyrolusite crystal was slightly lower than cassiterite’s and sellaite’s, thus yielding larger figures of merit (R and wR2) and a smaller number of unique reflections suitable to structural refinements for MnO2.
Figures 2a, 2b, 2d, 2e, 3a, 3b, 3d, 3e and 4a, 4b, 4d, 4e display latce parameters,
|x-y|, ABS angles and |Xax-Xeq|, as a function of pressure, in cassiterite, pyrolusite and sellaite, respectively. Figures 2c and 3c show |-’| for cassiterite and pyrolusite; in the case of sellaite (Fig. 4c), and ’ are displayed individually, given that they provide a more effective
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recording of the phase transition than their absolute difference. In short, the suite of Figures 2, 3 and 4 displays geometric deformation parameters that, as stated above, become other than zero in the low-symmetry phase, because of the symmetry break. Figures 2b, 3b and 4b prove that cassiterite, pyrolusite and sellaite turn from tetragonal to orthorhombic symmetry in the intervals 10.2-10.5, 4.0-4.2 and 4.8-5.0 GPa, respectively.
In cassiterite, the tetragonal symmetry holds up to 10.2-10.3 GPa, and at 10.5 GPa the structure is substantially orthorhombic. The coordinates x and y of the oxygen (Fig. 2b) and the ABS angles of the octahedron (Fig. 2d) exhibit apparent changes of trend. In Fig. 2b on the P-interval 0-10.3 GPa, i.e. below the phase transition pressure, a 3-wide horizontal grey band is reported, where is the uncertainty on the x coordinate of the anion from structure refinements using the “actual” tetragonal P42/mnm space group. Fig. 2b shows that the |x
-y| difference values, from refinements using Pnnm, lie within the e.s.d obtained from
refinements employing tetragonal symmetry. At pressure higher than 10.5 GPa, the a and b unit-cell parameters have different compressibility and the gap between their values
increases as a function of P (Fig. 2a). A change of the c parameter’s trend is observable, too:
c decreases from 3.1826(5), at room conditions, to 3.1549(7) Å, at 10.3 GPa; at higher P, it
increases so as to achieve the figure of 3.1611(9) at 11.3 GPa (Fig. 2a). Such a behaviour, never reported in previous works, might be reflective of oscillations due to uncertainties around a plateau value. |Xax-Xeq| versus P records the phase transition, displaying an abrupt change of trend that takes place on the range 10.2-10.5 GPa (Fig. 2e). The and ’ angles are both very close to zero up to 10.2-10.3 GPa. At higher pressure, the octahedron distorts so that ’ > , even if the absolute - and ’-values are still comparatively small. | -’| (Fig. 2c) and ABS (Fig. 2d) exhibit trends characterized by a monotonic increase and decrease, respectively, of their values as a function of P, and such that d|-’|/dP 0.66 and dABS/dP -0.35 GPa-1.
In pyrolusite, the structural refinements suggest that the P42/mnm space group holds
up to 4.0-4.1 GPa. This is proven by the x-y absolute differences between coordinates obtained by refinements in the low-symmetry space group, which are 3-consistent with those from the high-symmetry space group. At 4.2 GPa the two x-y coordinates of the oxygen atom are significantly different from one another (Fig. 3b). At pressure higher than 4.2 GPa, the unit-cell parameters a and b difference widens. In particular a slightly increases, while b
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shortens, yielding dln(|a-b|)/dP 0.25 GPa-1 (Fig. 3a). Up to 4.0-4.1 GPa the and ’ angles are close to zero; at 4.2 GPa, and ’ become 5.5° and 3.4°, respectively (Fig. 3c). At higher
P they further increase in value, achieving 11.5° and 7.9°, respectively, at 9.2 GPa. Such
figures are in qualitative agreement with the values of 8.3° and 6.5° at 7.3 GPa, reported for and ’, respectively, by Haines et al. (1995). The difference between obtuse and acute ABS angles (Fig. 3d) and |Xax-Xeq| (Fig. 3e) change trends abruptly above 4.2 GPa, passing from 0 to 2.6° and 0.07 Å, respectively.
In sellaite, the space group P42/mnm holds up to 4.8 GPa, whereas it is replaced by
Pnnm at 5.0 GPa. At 5.0 GPa, i.e. in orthorhombic structure stability regime, i) the x-y
coordinates of the fluorine atom do not show significant difference from one another (0.3013(9) versus 0.3036(13), respectively; Fig. 4b. The x-y differences are consistent within 3 with the results from refinements in the highsymmetry space group, and ii) the a
-b cell edges are still undistinguisha-ble from one another within the experimental uncertainty
(4.553(5) and 4.551(8) Å, respectively; Fig. 4a). However, d(|x-y|)/dP changes from 0 to 0.01 GPa-1 (Fig. 4b) and dABS/dP from ≈ 0 to ≈ -0.16 GPa-1(Fig. 4d). In particular, at 5.0 GPa the ABS angle starts to increase, up to some 6 GPa. At higher P the x-y coordinates become significantly different from one another (for instance, at 10.2 GPa x and y coordinates are 0.315(2) and 0.288(3), respectively). The tilting angles and ’, become other than zero only at pressure over 6 GPa, and have values close to one another (Fig. 4c). At 10.2 GPa, and ’ are 3.1° and 3.2° respectively, in good agreement with the figures reported by Haines et al. (2001), who provide = 3.0(2)° and ’ = 2.8(2)°, at 10.4 GPa. Figure 4e displays a significant change of the |Xax-Xeq|-values, passing from high- to low-symmetry stability ranges.
However, in the low-symmetry phase P-region |Xax-Xeq| gives rather scattered figures, thus hinting that the relaxation mechanism exploited by sellaite is weakly correlated to the difference between equatorial and apical anions distances.
Figure 5 displays the trends of the average A-X distance, <A-X>, as a function of P. All of the minerals under investigation do not exhibit any discontinuity around the transition pressure (Ptr), and their <A-X>-values trend smoothly, within the experimental
uncertainties. If one examines the average R1-R2 values, calculated at P < Ptr (< R1-R2P< >)
and P > Ptr (< R1-R2P> >), cassiterite and pyrolusite give < R1-R2P> >/< R1-R2P< > 8.73 and
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5.46 respectively, at variance with sellaite yielding < |R1-R2|P> >/< |R1-R2|P< > 1.37. Note
that |R1-R2| values are associated with the distortion of the octahedron, but they are not
related to any symmetry break.
Altogether, cassiterite, pyrolusite and sellaite undergo the same symmetry-change, but adopt relaxation mechanisms that exhibit differences among them:
-- Cell parameters. The axial compressibilities, calculated as = - < (dai /dP) (1/ai) > (where ai
is the cell parameter), are for cassiterite: a = -3.0(4), b = 8(1), c = 2(2) ×10-3 GPa-1, for pyrolusite: a = -0.7(5), b = 3.6(5), c = 1(1) ×10-3 GPa-1 and for sellaite: a =1.2(3), b = 5.6(8), c = 2.8(3) ×10-3 GPa-1, respectively. Cassiterite and pyrolusite have a-edges that show at P > Ptr slightly increasing trends, characterized by absolute axial variations of 1.0 and 0.3%,
respectively. Conversely, sellaite’s a-edge decreases smoothly as a function of pressure, with an absolute axial variation of 0.6 %. Note that in the case of pyrolusite, a discontinuity seems to occur at Ptr, involving the a-edge. However, this does not affect the volume cell at such an
extent as to induce any unquestionable discontinuity on V (whose trend is not shown for the sake of brevity). All of the three minerals exhibit b-edges that shorten regularly under
pressure, accompanied by changes of slope with respect to the regime at P < Ptr. The c-edge
shows somewhat of a “saturation”, i.e. appearance of a “plateau”, just over Ptr, for cassiterite
and pyrolusite, whereas at higher pressure c decreases regularly. Sellaite, in turn, exhibits a smoothly decreasing c-trend, with axial variation as large as 1.5%. Note that the c-parameter length is equal to the octahedron’s edge whose ends are occupied by two X-anions. In this view, any shortening of c is associated with a nearing of two negative ions to one another and therefore with an increase of repulsion;
-- x and y coordinates. The |x-y| difference increases monotonically upon P (Fig. 2b, 3b and 4b) though at different rates: 0.014, 0.007 and 0.006 GPa-1 for cassiterite, pyrolusite e sellaite respectively;
-- AX6 octahedron rotation. In cassiterite, at P just over Ptr we observe ’0, which
becomes ’0 upon increasing pressure, with d|-’|/dP 0.66 GPa-1 (Fig. 2c). In pyrolusite, ’0 holds at P > Ptr (Fig. 3c), with d|-’|/dP 0.23 GPa-1. In sellaite, and 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375
’ begin to increase at P > 6 GPa, even if the transition is estimated to take place between 4.8 and 5.0 GPa; at higher P, and ’ increase preserving |-’| 0 (Fig. 4c);
-- AX6 octahedron distortion because of the A-Xax bond tilt, measured through the acute ABS
angle. In cassiterite, ABS regularly decreases, whereas in pyrolusite it changes little (Fig. 2d
and Fig. 3d). In sellaite, ABS decreases between 5 and 6 GPa, but it then inverts such trend and increases so that at 8 GPa its value is 90° (Fig. 4d);
-- AX6 octahedron distortion because of R1 R2. The average compressibility values of <A-X>
change little if estimated at P < Ptr versus P > Ptr, in all the minerals under investigation (Fig.
5). Cassiterite and pyrolusite give < R1-R2P> >/< R1-R2P< > ratios 8.73 and 5.46,
respectively. However, in cassiterite R1-R2P> gradually increases with P (R1 > R2), while in
pyrolusite the difference between R1 and R2 abruptly changes above the transition (R1 > R2)
and then remains almost constant. In sellaite, R1-R2P> and R1-R2P< have quasi-parallel
trends and the < R1-R2P> >/< R1-R2P< > ratio is as large as 1.37;
-- Xax-Xeq octahedron edge distortion. In cassiterite, |Xax-Xeq| shows the same trend of ABS (compare Figs. 2d and 2e), while in pyrolusite an analogy is observable between |Xax-Xeq| and |ω-ω’| (Figs. 3c and 3e). In sellaite, on the pressure range 5-7 GPa, the trend of |Xax-Xeq| is comparable with ABS’s (see Figs. 4d and 4e), whereas at higher pressure |Xax-|Xax-Xeq| shows a behavior somewhat similar to |ω-ω’|’s.
Phase transition energy and relaxation mechanism
The P42/mnm Pnnm tetragonal (tetr)-orthorhombic (orth) ferroelastic transition is such
that atetr aorth, btetr borth, ctetr corth around Ptr, and therefore its active representation,
(K), requires K = 0. Therefore, we focus on the relationships between irreducible representations of the point groups 4/mmm and mmm. B1g, which fulfills the Landau
constraint, is the only irreducible representation that coincides with the total-symmetric one for the sub-group mmm, whereas it does not for 4/mmm. Given that B1g is associated to a 1D vector space, the order parameter (OP) vector has one component only, which is referred
14 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 27
to by Q. Q, in turn, must change according to B1g under the action of the P42/mnm space
group operators.
A linear combination of the spontaneous strain components, ij, allows us to formulate
an expression that fulfills the requirements for an OP, namely: i) 0 Q 1; ii) Q = 0 in the region wherein the high-symmetry polymorph is stable; iii) Q 0 elsewhere; iv) Q transforms according to B1g. In particular, one can choose Q = 11 - 22 (Haines et al. 1995). Using the
Eulerian strain tensor as formulated by Pavese (2005), one easily shows that
ηii=1 2
[
(
ai ai ,0)
2 −1]
(2)where ai and ai,0 are the ith cell-edge of the low- and high-symmetry phases, respectively, at
P > Ptr. Note that ai,0 is extrapolated as a1,0 = a2,0 = (a+b)/2 from the high-symmetry phase’s
stability field into low-symmetry phase’s.
The Gibbs energy difference between low- and high-symmetry phases is modelled via a Landau-type expression, i.e.
∆ G=1 2
(
P−Pc)
A Q 2 +∑
j=2 N 1 2 j BjQ 2 j (3)where Pc is the “critical” pressure that we take as an estimate of the “transition” pressure,
i.e. Ptr. From eq. (3) and taking into account that
∂ ∆ G ∂ P =∆ V = A Q 2 (4 a) and that ∂ ∆ G ∂Q =0=Q
[
(
P−Pc)
A+∑
j =2 N BjQ2 j−2]
(4 b)one determines the A and Bj coefficients, via eq.(4a) and (4b).
The truncation order of the expansion (eq. 3), i.e. N, is chosen by analyzing the P-Q2 plot, using the following equation
P=Pc−
∑
j=2 N B j A Q 2 j−2In Figures 6a, b and c, the Q-P curves for cassiterite, pyrolusite and sellaite are shown, and allow us to determine Pc for each mineral, thus obtaining 10.25, 4.05 and 4.80 GPa, 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426
respectively. Table 4 reports the A and B coefficients determined for cassiterite, pyrolusite and sellaite. Such coefficients provide a reliable representation of G for Q 0.02,
corresponding to the explored P-interval. We pay special attention to the A-values, which on average give the largest contribution to the Gibbs energy difference between orthorhombic and tetragonal phases around the transition pressure. In particular, the average percentage contributions to G of the A-dependent terms of eq. (3) range from 58 to 65 %. An
inspection of Table 4 reveals that sellaite and pyrolusite share similar A-figures, whereas cassiterite has an A-value significantly different from the other two. In proximity of Pc and
assuming the same Q, cassiterite requires a P-Pc about eight times as large as
pyrolusite/sellaite’s to achieve the same G. The ratio of
low-symmetry-stabilizing-contributions (negative terms of G, eq. (3)) over high-symmetry-stabilizing-low-symmetry-stabilizing-contributions (positive terms of G, eq. (3)) ranges from 2-1.7, 2-1.9 and 2-1.3 for cassiterite, pyrolusite and sellaite, respectively. This is in keeping with sellaite as the first, among the three phases under investigation, that undergoes a further P-triggered transition (from Pnnm to Pa ´3 at about 14 GPa).
We focus on the behavior of |Xax-Xeq|, 90°-ABS, and ’ as a function of Q, to correlate such structure deformation parameters with OP, the latter being associated to the Gibbs energy difference between orthorhombic and tetragonal phases. In particular, we chose to quantify the sensitivity of the Y-parameter to Q by the following expression: Y = <Y>-1Y/Q,
in which <Y> is the average of Y on the explored P-range, whereas Y and Q express the difference of Y and Q between their figures at the maximum and minimum P-values achieved on the pressure interval stabilizing the low-symmetry phase. The percentage contribution of each Y provides the “relaxation rate” due to Y. The larger such quantity, the more the
structural relaxation exploits a mechanism of atomic re-adjustment that affects the related Y. In so doing, we observe that and ’ contribute to the cassiterite structural relaxation in terms of a “relaxation rate” over 60%, whereas the remainder is accounted for by |Xax-Xeq| and 90°-ABS. Pyrolusite distributes uniformly its relaxation over the four degrees of freedom. Sellaite re-accommodates its atoms in order to employ foremost and ’ (“relaxation rate” over 85%). 16 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 31
Ionic character of bonding in AX2-minerals
The ionic component quantification of the bonding in AX2-minerals helps understand why
such systems show different behaviours as a function of pressure. In the present case, a pivotal question is whether increasing pressure promotes an increase of the ionic character of bonding. This point provides a straightforward link between structure’s behaviour and bonding nature. For instance, one edge of the building octahedral unit is as long as c, parallel to [001] and at its ends lie two anions, as already stated. Any shortening of c implies an increase of the repulsion between X-species. Quantum-mechanics calculations were carried out by the HF/DFT-CRYSTAL14 program (Dovesi el al. 2014) to model the static electron density of the high- and low-symmetry phases under study, up to the highest P explored (Appendix 1). Using the Bader analysis (Bader 1990, 2007) implemented by the TOPOND program (Gat and Casassa 2014) we calculated the basin charges attributable to each atom, thus determining a net charge (Znet-charge = atomic number – basin charge) associated to the involved ions. Atomic basins are confined by “-surfaces” that fulfill the following
relationship
∫
0
Ω
∇ ρ(r)∙ n (r) dS=0
where (r) is the electron density, n(r) is a versor normal to Ω at r and dS is an infinitesimal surface element; the integration is carried out on a Ω–surface that defines the atomic basin, surrounding an atom. In this light, the net charge of the jth-atom is calculated by
Znet charge, j=Zatomic number, j−
∫
0Ω, j
(r ) dV
and Znet charge,j provides a measure of the oxidation state of “j”.
Leaving details aside, as they are out of the scope of the present paper (about the general methodology, see Merli and Pavese 2018), we determine the following average net charges: Znet charge,Mg = 1.77, Znet charge,F = -0.887, Znet charge,Sn = 2.59, Znet charge,O-cassiterite =
-1.295, Znet charge,Mn = 1.91, Znet charge,O-pyrolusite=-0.955 e. These net charge values suggest
ionic contributions to bonding of 66, 48 and 89%, in cassiterite, pyrolusite and sellaite, respectively. Such figures are calculated as net-charge/conventional-oxidation-state ratio. These results are in keeping with Baur (1956, 1976), Baur and Khan (1971) and Bolzan et al.
457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484
(1997), as to a deviation from the ionic character of the AO2-type oxides. The predicted net
charges show a quasi-negligible sensitivity to pressure, at least in the narrow range investigated. The relevant ionic character of bonding in sellaite might be related to its
tendency to adjust its structure foremost via and ’, which are ’ and lead therefore to pure rotation in combination with quasi-isotropic compression of the octahedron, instead of exploiting a metric distortion, i.e. |Xax-Xeq|, that would yield general increase of repulsion between anions.
Conclusions
Cassiterite (SnO2), pyrolusite (-MnO2) and sellaite (MgF2) share the same rutile-like
structure. They undergo a P42/mnm Pnnm ferroelastic phase transition triggered by
pressure at 10.25 0.1, 4.05 0.1 and 4.80 0.1 GPa, respectively. Such Ptr-figures are
estimated by the analysis of the order parameter (Q = 11-22) versus P, in combination with
those structure observables (90°-ABS, , ’, |Xax-Xeq|) that are other than zero in the region of the low-symmetry phase’s stability. The three minerals under investigation exhibit different relaxation mechanisms at P > Ptr. SnO2 exploits and ’, in terms of 60% of the
“relaxation rate”; MnO2 uses uniformly all of the available deformation parameters to
readjust its structure; MgF2 largely privileges and ’, i.e. 85% of the “relaxation rate”.
Altogether, and ’ are among the deformation parameters that are most employed for relaxation by all of the minerals investigated, in keeping with the reasonable expectation that AX2-minerals with Pnmm symmetry use degrees of freedom that distort octahedron as little
as possible. AlthoughR1-R2 0 on the whole P-range explored, yet comparing R1-R2at P
< Ptr with P > Ptr helps bring to light further details about deformation mechanisms. In
sellaite R1-R2changes little as a function of P, thus hinting at a more modest metric
distortion of the octahedron than in cassiterite and pyrolusite. This is related to sellaite yielding small -’ figures, i.e. the octahedron tends to re-adjust by a pure rotation and quasi-isotropic shrinking. All this seems consistent with a more marked ionic bonding occurring in sellaite (ionic contribution to bonding 89%, from Bader theory), than in
18 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 35
cassiterite ( 66%) and pyrolusite ( 49%). In fact, distorting the MgF6-octahedron is difficult,
as an asymmetric shortening of the anion-anion distances may lead to a significant increase of repulsion. The A-coefficients of the G Landau expansion (see eq. 3) yield -1.022(8), -8.21(1) and -9.2(2) 103 J/GPa/mol for cassiterite, pyrolusite and sellaite, respectively. Although the A-coefficients are significantly different between cassiterite and the couple pyrolusite-sellaite, they provide similar average contributions to the total G (58-65% of the total Gibbs energy difference). In proximity of Pc and assuming the same Q, we observe that
cassiterite requires a P-Pc about eight times as large as pyrolusite/sellaite’s to achieve the
same G. Therefore, even if the involved minerals share the same structure-type, they exhibit significantly different responses versus P, which substantiates the important role played by chemical composition.
Appendix 1
Quantum mechanics modelling
Static calculations were performed at a given pressure and 0 K by the HF/DFT-CRYSTAL14 program (Dovesi el al. 2014), which implements “Ab-initio Linear-Combination-of-Atomic-Orbitals” for periodic systems. Neither zero-point-energy nor thermal pressure were taken into account, as in the present case we pay attention only to the trend, at room temperature. Exchange and correlation functionals were chosen on the basis of the capacity to reproduce experimental cell parameters and energy gaps. For sellaite, a combination of the Exchange Second Order GGA functional (SOGGA) with the PBE correlation functional (Zhao and Truhlar 2008) was chosen, using 5% of HF exchange hybridization. For cassiterite and pyrolusite the one-parameter B1WC hybrid functional (Bilc et al. 2008), which combines WC exchange and PWGGA correlation functionals, was employed, with 18 and 8% of HF exchange hybridization, respectively. The following tolerance values were chosen to govern the accuracy of the integrals of the self-consistent-field-cycles: 10-8 for coulomb overlap, 10-8 for coulomb penetration, 10-8 for exchange overlap, 10-8 for exchange pseudo-overlap in direct space, 10
-16
for exchange pseudo-overlap in reciprocal space and 10-8 Ha threshold for SCF-cycles’ convergence. 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539
For all the structures under investigation, the Peintinger-Oliveira-Bredow (POB) basis sets (Peintinger et al. 2013), constituted by triple-ζ valence plus polarization functions, were used, with the exception of Sn (Sn_9763111-631 basis set available at
http://www.tcm.phy.cam.ac.uk/~mdt26/basis_sets/Sn_basis.txt).
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FIGURE CAPTIONS
Fig. 1 Graphical representation of tilting-angles of the AX6 octahedron in pyrolusite at P = 9.2
GPa (Pnnm space group); view along [001]. Small circles = A cations; large circles = X anions. (a) ω and ω’ tilt angles defined by Bärnighausen et al. (1984); thin lines
represent the (110) and (1 ´1 0) planes. (b) Acute and obtuse Xax-A-Xeq angles (ABS = “Axial Bond Squareness”, this work)
Fig. 2 Evolution of structure’s parameters in cassiterite with increasing pressure. Data reduction and refinements are carried out in Pnnm space group. Full symbols = below
Ptr; open symbols = above Ptr. Experimental uncertainties (bars) for almost all points
are smaller than symbols. (a) Unit-cell parameters: a (circles), b (squares) and c (diamonds). Above Ptr, a increases and b decreases with respect to atetr at the highest
pressure of the field of stability of the high-symmetry phase; c-edge shows somewhat of a “plateau”, whereas at higher P it decreases regularly. (b) Difference |x -y| between the coordinates of the oxygen atom. In the P range 0-10.3 GPa the values of |x -y| are lower than the uncertainties on the x coordinate of oxygen from refinements using tetragonal symmetry (0.001 < 3x < 0.003, horizontal grey band). (c) Difference |ω-ω’| between the two tilt angles. (d) ABS angles. Diamonds = acute-ABS; circles = obtuse-ABS. (e) Difference |Xax-<Xeq| between the two sets of values of Oax-Oeq distances. Above Ptr, the octahedron is distorted and the four Oeqs are not equidistant from Oax
anymore.
Fig. 3 Evolution of structure’s parameters in pyrolusite with increasing pressure. Data reduction and refinements are carried out in Pnnm space group. Full symbols = below
Ptr; open symbols = above Ptr. Experimental uncertainties (bars) for almost all points
are smaller than symbols. (a) Unit-cell parameters: a (circles), b (squares) and c (diamonds); above Ptr, a slightly increases and b decreases; c shows somewhat of a
“plateau”, whereas at higher P it decreases regularly. (b) Difference |x -y| between the coordinates of the oxygen atom. The horizontal grey band has the same meaning as used in Fig. 2b. (c) Difference |ω-ω’| between the two tilt angles. After transition, the
680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707
octahedral chain begins immediately to rotate and the tilt angles increase. (d) ABS angles. Diamonds = acute-ABS; circles = obtuse-ABS. (e) Difference |Xax-Xeq| between the two sets of values of Oax-Oeq distances. Above Ptr, the octahedron is distorted and
the four Oeqs are not equidistant from Oax anymore.
Fig. 4 Evolution of structure’s parameters in sellaite with increasing pressure. Data reduction
and refinements are carried out in Pnnm space group. Full symbols = below Ptr; open
symbols = above Ptr. Experimental uncertainties (bars) for almost all points are smaller
than symbols. (a) Unit-cell parameters: a (circles), b (squares) and c (diamonds). (b) Difference |x-y| between the coordinates of the fluorine atom. The horizontal grey
band has the same meaning as used in Fig. 2b. (c) Tilt angles (circles) and ’
(diamonds). (d) ABS angles. Diamonds = acute-ABS; circles = obtuse-ABS; dashed lines define the band where the ABS’s are equal to 90° within the uncertainty; grey region marks the pressure range where ABS’s are different from 90°. (e) Difference |Xax-Xeq| between the two sets of values of Fax-Feq distances; grey region marks the pressure range where the ABS angle results in a distortion of the octahedron (compare with Fig. 4d).
Fig. 5 Average cation-anion bond lengths as a function of pressure in cassiterite (circles),
pyrolusite (triangles) and sellaite (diamond). Full symbols = below Ptr; open symbols =
above Ptr. Experimental uncertainties (bars) for almost all points are smaller than
symbols. Data reduction and refinements are carried out in Pnnm space group
Fig. 6 Orthorhombic spontaneous strain Q after phase transition as a function of pressure. (a)
Cassiterite; calculated transition pressure Pc = 10.25 GPa. (b) Pyrolusite. Pc = 4.05 GPa.
(c) Sellaite. Pc = 4.80 GPa 26 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 51
Table 1a Cassiterite; unit-cell parameters and X-ray diffraction data-collection conditions: number of collected reflections, number of unique reflections and refinement figures of merit (e.s.d. in brackets) P (GPa) a (Å) b (Å) c (Å) V (ų) N. refl. Unique refl. R (%) Fo>4(Fo) RTOT (%) wR2 (%) 0.0001a 4.7363(6) 4.7363(6) 3.1826(5) 71.392(17) 489 81 3.43 3.51 7.34 0.3(1)a 4.7361(6) 4.7361(6) 3.1834(5) 71.407(16) 459 81 3.16 3.27 7.84 0.9(1)a 4.7319(6) 4.7319(6) 3.1808(5) 71.219(18) 447 78 3.36 3.41 8.48 1.1(1)a 4.7291(6) 4.7291(6) 3.1815(5) 71.152(17) 450 79 3.11 3.24 8.15 2.0(1)a 4.7211(6) 4.7211(6) 3.1788(5) 70.852(17) 462 84 3.61 3.73 8.92 2.6(1)a 4.7159(6) 4.7159(6) 3.1766(7) 70.637(17) 446 57 3.59 3.65 8.42 3.2(1)a 4.7110(7) 4.7110(7) 3.1766(5) 70.500(18) 444 54 3.55 3.67 8.37 4.1(1)a 4.7035(7) 4.7035(7) 3.1732(5) 70.200(18) 457 56 3.96 3.96 8.51 4.2(1)a 4.6998(6) 4.6998(6) 3.1719(4) 70.061(16) 457 75 3.29 3.32 6.27 6.2(1)a 4.6855(6) 4.6855(6) 3.1674(5) 69.537(17) 467 81 3.73 3.83 9.78 8.4(1)a 4.669(1) 4.669(1) 3.1615(5) 68.919(17) 465 78 3.52 3.68 7.60 9.2(1)a 4.6627(6) 4.6627(6) 3.1592(5) 68.684(16) 452 74 3.70 3.93 6.57 9.6(1)a 4.6605(7) 4.6605(7) 3.1591(5) 68.617(19) 458 60 2.38 2.46 6.44 10.0(1)a 4.6529(6) 4.6529(6) 3.1567(4) 68.340(16) 443 59 2.00 2.16 4.63 10.3(1)a 4.6541(9) 4.6541(9) 3.1549(7) 68.340(20) 461 64 3.16 3.37 7.32 10.5(1) 4.6579(18) 4.647(10) 3.1589(9) 68.37(15) 519 63 2.52 2.87 5.21 10.9(1) 4.6655(19) 4.630(10) 3.1599(9) 68.25(16) 515 61 2.35 2.71 5.57 11.3(1) 4.6755(18) 4.616(10) 3.1611(9) 68.22(15) 409 59 2.72 2.91 6.92 12.0(1)b 4.675(3) 4.589(6) 3.155(2) 67.68(11) 165 25 3.75 4.79 9.93 12.8(1)b 4.684(8) 4.560(10) 3.147(5) 67.22(13) 156 17 9.57 13.63 23.30 13.4(1)b 4.705(3) 4.548(6) 3.143(20) 67.25(11) 150 24 5.84 6.47 10.87
Data reduction and refinements are carried out in Pnnm space group, even in the case of actual tetragonal symmetry (a). N. refined parameters = 9 (up to P = 11.3 GPa).
b
Experiments were performed on a small crystal, obtaining fewer observed reflections. Sn-site refined with isotropic displacement parameters; N. refined parameters = 5. Given that pressure is above its threshold of hydrostaticity, we report such structure results for the sake of
completeness, but believe that only latce parameters are fully reliable.
731 732 733 734 735 736 737 738 739
Table 1b Cassiterite; x and y atomic coordinates of the O-anion, Sn-Oax (R1) and Sn-Oeq (R2)
bond distances, average <Sn-O> bond length, Oax-Sn-Oeq (ABS) and Oeq-Sn-Oeq angles
P (GPa) x y Sn-Oax (x2) R1 (Å) Sn-Oeq (x4) R2 (Å) <Sn-O> (Å) ABS (°) Oeq-Sn-Oeq (°) 0.0001 0.3058(6) 0.3049(7) 2.045(3) 2.057(2) 2.053(1) 90.03(3) 101.34(13) 0.3(1) 0.3060(7) 0.3053(9) 2.047(4) 2.056(2) 2.053(1) 90.02(4) 101.44(17) 0.9(1) 0.3060 (6) 0.3055(8) 2.046(3) 2.054(2) 2.051(1) 90.02(3) 101.48(15) 1.1(1) 0.3065(9) 0.3050(10) 2.045(5) 2.054(3) 2.051(1) 90.05(5) 101.52(19) 2.0(1) 0.3057(6) 0.3049(7) 2.038(3) 2.053(2) 2.048(1) 90.02(3) 101.44(14) 2.6(1) 0.3051(10) 0.304(2) 2.033(8) 2.053(5) 2.047(2) 90.02(1) 101.3(3) 3.2(1) 0.3049(9) 0.3066(19) 2.037(7) 2.049(4) 2.045(2) 89.94(7) 101.7(3) 4.1(1) 0.3048(11) 0.304(2) 2.026(8) 2.051(5) 2.043(3) 90.01(9) 101.4(4) 4.2(1) 0.3056(6) 0.3047(8) 2.028(3) 2.048(2) 2.041(1) 90.03(3) 101.54(14) 6.2(1) 0.3060(8) 0.3056(10) 2.026(4) 2.041(3) 2.036(1) 90.02(4) 101.81(18) 8.4(1) 0.3065(5) 0.3055(8) 2.021(3) 2.035(2) 2.030(1) 90.03(3) 101.96(13) 9.2(1) 0.3056(7) 0.3044(11) 2.012(4) 2.036(3) 2.028(1) 90.05(4) 101.74(18) 9.6(1) 0.3054 (8) 0.3067(17) 2.017(7) 2.032(4) 2.027(2) 89.96(6) 102.0(3) 10.0(1) 0.3063(4) 0.3071(12) 2.018(4) 2.027(3) 2.024(1) 89.97(4) 102.27(18) 10.3(1) 0.3063(6) 0.3061(14) 2.014(5) 2.030(3) 2.024(2) 89.98(5) 102.0(2) 10.5(1) 0.3059 (9) 0.3073(22) 2.017(8) 2.028(5) 2.025(3) 89.87(11) 102.3(4) 10.9(1) 0.3073(9) 0.303(2) 2.013(9) 2.030(5) 2.024(3) 89.82(11) 102.3(4) 11.3(1) 0.3093(7) 0.305(2) 2.016(8) 2.027(5) 2.023(2) 89.72(11) 102.5(3) 12.0(1) 0.319(3) 0.312(13) 2.07(4) 1.99(3) 2.014(13) 89.7(5) 105.2(2.0) 12.8(1) 0.347(10) 0.315(22) 2.169(19) 1.924(8) 2.006(5) 89.3(7) 113.4(1.0) 13.4(1) 0.366(4) 0.326(18) 2.27(6) 1.87(4) 2.004(18) 88.8(1.0) 114(3) 28 740 741 742 55
Table 2a Pyrolusite; unit-cell parameters and X-ray single crystal diffraction data collection conditions: number of collected reflection reflections, number of unique reflections and refinement figures of merit
P (GPa) a (Å) b (Å) c (Å) V (ų) N. Refl. Unique refl. R (%) Fo>4(Fo) RTOT (%) wR2 (%) 0.0001a 4.4311(19) 4.4311(19) 2.8805(6) 56.56(4) 228 31 8.57 9.57 19.77 0.1(1)a 4.423(2) 4.423(2) 2.8803(7) 56.35(4) 245 33 7.59 9.74 18.01 0.3(1)a 4.418(2) 4.418(2) 2.8793(7) 56.20(4) 372 33 8.13 9.42 17.70 0.9(1)a 4.418(2) 4.418(2) 2.8767(8) 56.15(5) 390 34 7.74 7.81 15.74 1.1(1)a 4.414(2) 4.414(2) 2.8734(8) 55.98(4) 383 34 8.45 9.53 17.84 2.0(1)a 4.411(3) 4.411(3) 2.8758(8) 55.95(5) 232 29 7.70 7.95 17.33 2.5(1)a 4.397(1) 4.397(1) 2.8691(4) 55.470(20) 300 48 7.48 7.61 15.10 2.6(1)a 4.3967(9) 4.3967(9) 2.8698(4) 55.476(17) 300 51 5.81 6.28 13.99 3.2(1)a 4.3920(9) 4.3920(9) 2.8661(4) 55.286(19) 291 49 5.58 5.73 13.18 4.1(1)a 4.3895(10) 4.3895(10) 2.8649(4) 55.200(20) 296 51 6.27 6.48 16.17 4.2(1) 4.395(10) 4.371(4) 2.8632(20) 55.00(14) 326 31 9.90 12.11 22.52 5.3(1) 4.392(14) 4.352(7) 2.863(5) 54.72(20) 184 28 9.22 11.26 18.57 6.2(1) 4.40(3) 4.3234(20) 2.8636(7) 54.47(12) 340 33 6.84 9.14 18.01 8.4(1) 4.41(3) 4.3047(17) 2.862(1) 53.33(13) 345 33 7.00 8.70 14.62 8.7(1) 4.409(7) 4.289(1) 2.8514(5) 53.929(9) 300 43 6.12 7.78 15.69 9.2(1) 4.41(1) 4.288(3) 2.845(2) 53.8(3) 340 32 5.99 9.71 14.14 10.8(1)b 4.408(13) 4.27(4) 2.84(3) 53.54(17) - - - -
-Data reduction and refinements are carried out in the Pnnm space group, even in the case of actual tetragonal symmetry(a).
b
The number of total reflections was sufficient for determination of the unit cell parameters, whereas the unique reflections were not enough for structural refinement
743 744 745 746 747 748 749
Table 2b Pyrolusite; x and y atomic coordinates of the O-anion, Mn-Oax (R1) and Mn-Oeq (R2)
bond distances, average <Mn-O> bond length, Oax-Mn-Oeq (ABS) and Oeq-Mn-Oeq angles
P(GPa) x y Mn-Oax (x2) R1 (Å) Mn-Oeq(x4) R2 (Å) <Mn-O> (Å) ABS (°) Oeq-Mn-Oeq (°) 0.0001 0.297(4) 0.309(20) 1.89(7) 1.90(4) 1.899(21) 88.8(8) 99.3(2.9) 0.1(1) 0.308(3) 0.302(12) 1.938(20) 1.868(13) 1.891(6) 90.7(5) 100.3(1.7) 0.3(1) 0.313(3) 0.297(13) 1.90(4) 1.89(3) 1.895(13) 90.5(5) 100.2(1.9) 0.9(1) 0.308(3) 0.294(11) 1.87(3) 1.91(2) 1.897(11) 89.3(4) 99.2(1.7) 1.1(1) 0.306(3) 0.305(12) 1.89(4) 1.89(2) 1.889(12) 91.1(5) 100.7(1.8) 2.0(1) 0.309(3) 0.302(13) 1.90(4) 1.89(3) 1.891(13) 90.8(5) 100.5(1.9) 2.5(1) 0.305(3) 0.303(3) 1.888(13) 1.884(9) 1.885(4) 90.13(14) 99.2(6) 2.6(1) 0.3040(19) 0.3038(21) 1.890(9) 1.883(6) 1.885(3) 90.15(10) 99.3(4) 3.2(1) 0.3030(19) 0.3060(21) 1.891(9) 1.878(6) 1.883(3) 90.24(10) 99.5(4) 4.1(1) 0.3007(21) 0.306(2) 1.883(11) 1.882(7) 1.883(3) 90.09(12) 99.1(5) 4.2(1) 0.336(14) 0.299(5) 1.97(5) 1.83(3) 1.876(14) 88.7(8) 103.1(2.1) 5.3(1) 0.319(14) 0.283(5) 1.86(5) 1.89(3) 1.882(15) 89.2(6) 98.4(2.0) 6.2(1) 0.339(12) 0.281(4) 1.92(4) 1.859(20) 1.879(12) 88.5(7) 100.8(1.6) 8.4(1) 0.347(11) 0.277(3) 1.94(4) 1.849(19) 1.880(11) 88.2(7) 101.4(1.4) 8.7(1) 0.335(6) 0.279(3) 1.899(22) 1.861(12) 1.874(6) 89.0(3) 100.0(9) 9.2(1) 0.358(11) 0.279(3) 1.98(4) 1.822(18) 1.874(11) 87.7(7) 102.7(1.4) 30 750 751 752 59
