Compressional behaviour of paulingite -A sub-nanosponge?

Introduction Paulingite is a rare zeolite, found in vesicles in basalt flows, with ideal chemical formula: (K,Na,Ca0.5,Ba0.5,)10(Al10Si32O84)\uf0d730H2O (Z = 16). Its crystal structure was solved and refined by Gordon et al. (1966) in the space group Im3m, showing the complex framework topology of this zeolite designated with the IZA-code \u201cPAU\u201d. A structural re-investigation was carried out later by Lengauer et al. (1997). The tetrahedral framework topology of paulingite is characterized by a connecting double 8-ring (D8R), which links alternatively the \uf061-cage (truncated cuboctahedron) and the \uf067-cage (gmelinite-type cage). The D8R, the \uf061-cage and the \uf067-cage represent the building-block units of the PAU framework. The main voids systems of the PAU framework are represented by two parallel (and independent) sets of a three-dimensional channel systems oriented along the principal axes and shifted \ubd, \ubd, \ubd against each other. Along the threefold axis of the PAU framework, a second type of a channel system exists, which is built up by the \uf061-cage and a modified form of the levyne-cage only observed in the paulingite topology (i.e., \uf070-cage) (Lengauer et al. 1997). The PAU framework type is considered as one of the most complex in the mineral world. In all the structure refinements so far reported, the Si/Al-distribution was modelled as completely disordered. A series of extra-framework sites were located. The long \u201cfree diameters\u201d of the channel systems make this zeolite a good candidate to explore the P-induced penetration of external molecular species in response to hydrostatic compression (e.g., Gatta 2008, 2010). Experimental Methods A sample of paulingite from Vina\u159ick\ue1 hora Hill near Kladno (Czech Republic) was used for our experiments. A sample from the same locality was previously used by Lengauer et al. (1997) for their chemical and crystallographic study. Electron microprobe analysis (in wavelength dispersive mode) along with thermo-gravimetric data yielded the following chemical formula: (Ca2.57K2.28Ba1.39Na0.38)(Alll.55Si30.59O84)x 27H2O (Lengauer et al. 1997). A single-crystal of paulingite, free of defects under polarized microscope, was selected for the in-situ diffraction experiment with a diamond anvil cell (DAC). Intensity diffraction data were first collected at room-conditions with a Stoe StadiVari diffractometer with an high-brilliance Incoatec Mo I\ub5s X-ray-source and a Dectris Pilatus 300K pixel detector. The structure refinement was performed in the space group Im3m using the structural model of Lengauer et al. (1997) to a R1 = 0.0802 for 2477 Fo > 4\uf073(Fo) and 255 refined parameters. The same crystal was used for the high-pressure (HP) experiment performed using an ETH-type DAC. The experiment was conducted using a mixture of methanol:ethanol = 4:1 as hydrostatic P-transmitting medium, along with a few ruby chips serving as P-calibrant. Unit-cell parameters were measured between 0.0001 (crystal in the DAC with no pressure medium) and 3.3(1) GPa. Two further in-situ HP synchrotron X-ray powder diffraction experiments were performed at the X7A beamline at the national synchrotron light source (NSLS) at Brookhaven National Laboratory (BNL). A gas-proportional position-sensitive detector was used. The wavelength of the incident beam was 0.60046(1) \uc5 as determined from a CeO2 standard. A modified Merrill\u2013Bassett DAC was used to generate HP-conditions. Two compression experiments with two different P-fluids were performed, i.e., with silicon-oil and a mix of methanol:ethanol:water = 16:3:1. The evolution of the cell parameters with P for all three pressure-transmitting media is shown in Fig. 1. Results and Discussion The evolution of the unit-cell parameters of paulingite with P based on our experiments with different P-media show a dramatic role played by the compression-fluid on the behavior of this zeolite (Figure 1). Due to its polymeric nature, silicon-oil can be unambiguously considered as a \u201cnon-penetrating\u201d P-medium. The compressional pattern obtained with silicon-oil describes the actual elastic behavior of paulingite (i.e., without any interference of the P-fluid). The Birch-Murnaghan equation of state truncated to the second-order was used to fit the experimental P-V data within the P-range investigated (i.e. 0.0001-2.5(1) GPa), giving the following isothermal bulk modulus: K0 = \uf0620-1 = V0(\uf0b6P/\uf0b6V) = 18(1) GPa (\uf0620 = 0.055(3) GPa-1). Paulingite appears to be one of the softest crystalline inorganic materials reported so far. The HP-data obtained using the mix methanol:ethanol = 4:1 and methanol:ethanol:water = 16:3:1 suggest that these molecules act as \u201cpenetrating\u201d media in response to the applied pressure. The P-induced penetration of external molecules through the cavities leads to a lower bulk compressibility of paulingite. The different compressibility of paulingite in methanol:ethanol = 4:1 and methanol:ethanol:water = 16:3:1 mix reflects the different penetrability of the media. Water is clearly the most penetrating molecule in response to the applied pressure, and so in general an hydrous medium tends to decrease significantly the compressional pattern of a porous material (Gatta 2008, 2010). Interestingly, the P-induced penetration of external molecules in paulingite structure does not lead to spectacular expansion (with a drastic discontinuity in the P-V behaviour), as observed for example in natrolite (Lee et al. 2002). The complexity of the paulingite structure did not allow to perform structure refinement at high pressure, hindering a description of the penetration mechanisms at the atomic scale. A series of further experiments are in progress in order to explore: 1) the reversibility of the P-induced penetration of aforementioned molecules and 2) the behavior of this zeolite as a \u201csub-nanosponge\u201d for other small molecules in response to hydrostatic pressure. Acknowledgment GDG acknowledges the Italian Ministry of Education, MIUR-Project: \u201cFuturo in Ricerca 2012 - ImPACT- RBFR12CLQD\u201d. References Gatta, G.D. (2008) Does porous mean soft? On the elastic behaviour and structural evolution of zeolites under pressure. Zeitschrift f\ufcr Kristallographie, 223, 160\u2013170. Gatta, G.D. (2010) Extreme deformation mechanisms in open-framework silicates at high-pressure: Evidence of anomalous inter-tetrahedral angles. Microporous and Mesoporous Materials, 128, 78\u201384. Gordon, E.K., Samson, S. and Kamb, W.B. (1966). Crystal structure of the zeolite paulingite. Science, 154, 1004-1007. Lee, Y., Vogt, T., Hriljac, J.A., Parise, J.B., and Artioli, G. (2002) Pressure-Induced Volume Expansion of Zeolites in the Natrolite Family. Journal of the American Chemical Society, 124, 5466-5475. Lengauer, C.L., Giester, G., and Tillmanns, E. (1997). Mineralogical characterization of paulingite from Vinarick\ue1 Hora, Czech Republic. Mineralogical Magazine, 61, 591-606

High-pressure polymorphism and structural transitions of norsethite, BaMg(CO3)2

In situ high-pressure investigations on norsethite, BaMg(CO3)2, have been performed in sequence of diamond-anvil cell experiments by means of single-crystal X-ray and synchrotron diffraction and Raman spectroscopy. Isothermal hydrostatic compression at room temperature yields a high-pressure phase transition at Pc 48 2.32 \ub1 0.04 GPa, which is weakly first order in character and reveals significant elastic softening of the high-pressure form of norsethite. X-ray structure determination reveals C2/c symmetry (Z = 4; a = 8.6522(14) \uc5, b = 4.9774(13) \uc5, c = 11.1542(9) \uc5, \u3b2 = 104.928(8)\ub0, V = 464.20(12) \uc53 at 3.00 GPa), and the structure refinement (R1 = 0.0763) confirms a distorted, but topologically similar crystal structure of the so-called \u3b3-norsethite, with Ba in 12-fold and Mg in octahedral coordination. The CO3 groups were found to get tilted off the ab-plane direction by ~16.5\ub0. Positional shifts, in particular of the Ba atoms and the three crystallographically independent oxygen sites, give a higher flexibility for atomic displacements, from which both the relatively higher compressibility and the remarkable softening originate. The corresponding bulk moduli are K0 = 66.2 \ub1 2.3 GPa and dK/dP = 2.0 \ub1 1.8 for \u3b1-norsethite and K0 = 41.9 \ub1 0.4 GPa and dK/dP = 6.1 \ub1 0.3 for \u3b3-norsethite, displaying a pronounced directional anisotropy (\u3b1: \u3b2 a-1 = 444(53) GPa, \u3b2 c-1 = 76(2) GPa; \u3b3: \u3b2 a-1 = 5.1(1.3) 7 103 GPa, \u3b2 b-1 = 193(6) GPa \u3b2 c-1 = 53.4(0.4) GPa). High-pressure Raman spectra show a significant splitting of several modes, which were used to identify the transformation in high-pressure high-temperature experiments in the range up to 4 GPa and 542 K. Based on the experimental series of data points determined by XRD and Raman measurements, the phase boundary of the \u3b1-to-\u3b3-transition was determined with a Clausius-Clapeyron slope of 9.8(7) 7 10-3 GPa K-1. An in situ measurement of the X-ray intensities was taken at 1.5 GPa and 411 K in order to identify the nature of the structural variation on increased temperatures corresponding to the previously reported transformation from \u3b1- to \u3b2-norsethite at 343 K and 1 bar. The investigations revealed, in contrast to all X-ray diffraction data recorded at 298 K, the disappearance of the superstructure reflections and the observed reflection conditions confirm the anticipated (Formula presented.) space-group symmetry. The same superstructure reflections, which disappear as temperature increases, were found to gain in intensity due to the positional shift of the Ba atoms in the \u3b3-phase

High-pressure behavior and crystal-fluid interaction under extreme conditions in paulingite [PAU-topology]

The compressional behavior and the P-induced crystal-fluid interaction of a natural paulingite-K have been explored on the basis of in-situ single-crystal and powder X-ray diffraction, and in-situ single-crystal Raman spectroscopy with a diamond anvil cell and a series of diverse pressure-transmitting fluids (i.e., silicone-oil, methanol:ethanol = 4:1, methanol:ethanol:water = 16:3:1). No evidence of any phase transition was observed within the P-range investigated, independent on the used P-fluids. The compressional behavior of paulingite is significantly different in response to the different nature of the P-fluids. A drastically lower compressibility is observed when the zeolite is compressed in methanol:ethanol or, even more noticeably, in methanol:ethanol:water mix. We ascribe this phenomenon to the different crystal-fluid interaction at high pressure: (1) silicone-oil is a "non-penetrating" P-medium, because of its polymeric nature, whereas (2) methanol-ethanol and water are "penetrating" P-fluids. The P-induced penetration processes appear to be completely reversible on the basis of the X-ray diffraction data alone. The Raman spectra collected after the high-pressure experiments show, unambiguously, that a residual fraction of methanol (and/or ethanol and probably even extra H2O) still resides in the zeolitic sub-nanocavities; such molecules are spontaneously released after a few days at atmospheric pressure. The actual compressibility of paulingite-K is that obtained by the compression experiment in silicone-oil, with an isothermal bulk modulus K0 = \u3b20-1 = 18.0(1.1) GPa. Paulingite appears to be one of the softest zeolite ever found

High-pressure structural behavior of \u3b1-Fe2O3 studied by single-crystal X-ray diffraction and synchrotron radiation up to 25 GPa

In situ X-ray diffraction experiments were carried out at pressures up to 25 GPa on a synthetic hematite (\u3b1-Fe2O3) crystal using synchrotron radiation in an angle-dispersive setup. Experiments were performed in diamond-anvil cells using neon as a pressure-transmitting medium. Single-crystal diffraction data were collected from omega scans and structural refinements were carried out for 10 pressure points. Bulk and linear incompressibilities were obtained from least-squares fits of refined data to the Eulerian strain based Birch-Murnaghan equation of state. Finite strain analysis suggests a truncation at second order, yielding results of K0 = 207(3), Ka0 = 751(17), and Kc0 = 492(8) for bulk and axial moduli, respectively. The a-axis is about 1.5 times stiffer than the c-axis. Compression of the main structural feature, the FeO6 octahedra, is quite uniform, with just slight changes of distortion parameters at higher pressures

Static elasticity of cordierite II: effect of molecular CO2CO_2 channel constituents on the compressibility

Two natural CO2-rich cordierite samples (1.00 wt% CO2, 0.38 wt% H2O, and 1.65 wt% CO2, 0.15 wt% H2O, respectively) were investigated by means of Raman spectroscopy and single-crystal X-ray diffraction at ambient and high pressures. The effect of heavy-ion irradiation (Au 2.2 GeV, fluence of 1 x 10(12) ions cm(-2)) on the crystal structure was investigated to characterize the structural alterations complementary to results reported on hydrous cordierite. The linear CO2 molecules sustained irradiation-induced breakdown with small CO2-to-CO conversion rates in contrast to the distinct loss of channel H2O. The maximum CO2 depletion rate corresponds to similar to 12 +/- A 5 % (i.e. similar to 0.87 and similar to 1.49 wt% CO2 according to the two samples, respectively). The elastic properties of CO2-rich cordierite reveal stiffening due to the CO2 molecules (non-irradiated: isothermal bulk modulus K (0) = 120.3 +/- A 3.7 GPa, irradiated: K (0) = 109.7 +/- A 3.7 GPa), but show the equivalent effect of hydrous cordierite to get softer when irradiated. The degree of anisotropy of axial compressibilities and the anomalous elastic softening at increasing pressure agrees with those reported for hydrous cordierite. Nevertheless, the experimental high-pressure measurements using ethanol-methanol reveal a small hysteresis between compression and decompression, together with the noticeable effect of pressure-induced over-hydration at pressures between 4 and 5 GPa

Puzzling calcite-III dimorphism : crystallography, high-pressure behavior, and pathway of single-crystal transitions

Abstract High-pressure phase transformations between the polymorphic forms I, II, III, and IIIb of CaCO3 were investigated by analytical in situ high-pressure high-temperature experiments on oriented single-crystal samples. All experiments at non-ambient conditions were carried out by means of Raman scattering, X-ray, and synchrotron diffraction techniques using diamond-anvil cells in the pressure range up to 6.5 GPa. The composite-gasket resistive heating technique was applied for all high-pressure investigations at temperatures up to 550 K. High-pressure Raman spectra reveal distinguishable characteristic spectral differences located in the wave number range of external modes with the occurrence of band splitting and shoulders due to subtle symmetry changes. Constraints from in situ observations suggest a stability field of CaCO3-IIIb at relatively low temperatures adjacent to the calcite-II field. Isothermal compression of calcite provides the sequence from I to II, IIIb, and finally, III, with all transformations showing volume discontinuities. Re-transformation at decreasing pressure from III oversteps the stability field of IIIb and demonstrates the pathway of pressure changes to determine the transition sequence. Clausius-Clapeyron slopes of the phase boundary lines were determined as: \u394P/\u394T = -2.79 \ub1 0.28 7 10-3 GPa K-1 (I-II); +1.87 \ub1 0.31 7 10-3 GPa K-1 (II/III); +4.01 \ub1 0.5 7 10-3 GPa K-1 (II/IIIb); -33.9 \ub1 0.4 7 10-3 GPa K-1 (IIIb/III). The triple point between phases II, IIIb, and III was determined by intersection and is located at 2.01(7) GPa/338(5) K. The pathway of transition from I over II to IIIb can be interpreted by displacement with small shear involved (by 2.9\ub0 on I/II and by 8.2\ub0 on II/IIIb). The former triad of calcite-I corresponds to the [20-1] direction in the P21/c unit cell of phase II and to [101] in the pseudomonoclinic C(Formula presented.) setting of phase IIIb. Crystal structure investigations of triclinic CaCO3-III at non-ambient pressure-temperature conditions confirm the reported structure, and the small changes associated with the variation in P and T explain the broad stability of this structure with respect to variations in P and T. PVT equation of state parameters was determined from experimental data points in the range of 2.20-6.50 GPa at 298-405 K providing (Formula presented.) = 87.5(5.1) GPa, (\u3b4KT/\u3b4T)P = -0.21(0.23) GPa K-1, \u3b10 = 0.8(21.4) 7 10-5 K-1, and \u3b11 = 1.0(3.7) 7 10-7 K-1 using a second-order Birch-Murnaghan equation of state formalism

Static elasticity of cordierite I : effect of heavy ion irradiation on the compressibility of hydrous cordierite

The effect of ion beam irradiations on the elastic properties of hydrous cordierite was investigated by means of Raman and X-ray diffraction experiments. Oriented single crystals were exposed to swift heavy ions (Au, Bi) of various specific energies (10.0-11.1 MeV/u and 80 MeV/u), applying fluences up to 5 7 1013 ions/cm2. The determination of unit-cell constants yields a volume strain of 3.4 7 10-3 up to the maximum fluence, which corresponds to a compression of non-irradiated cordierite at ~480 \ub1 10 MPa. The unit-cell contraction is anisotropic (e1 = 1.4 \ub1 0.1 7 10-3, e2 = 1.5 \ub1 0.1 7 10-3, and e3 = 7 \ub1 1 7 10-4) with the c-axis to shrink only half as much as the axes within the ab-plane. The lattice elasticity for irradiated cordierite (\u3c6{symbol} = 1 7 1012 ions/cm2) was determined from single-crystal XRD measurements in the diamond anvil cell. The fitted third-order Birch-Murnaghan equation-of-state parameters of irradiated cordierite (V0 = 1548.41 \ub1 0.16 \uc53, K0 = 117.1 \ub1 1.1 GPa, 02K/ 02P = -0.6 \ub1 0.3) reveal a 10-11 % higher compressibility compared to non-irradiated cordierite. While the higher compressibility is attributed to the previously reported irradiation-induced loss of extra-framework H2O, the anomalous elasticity as expressed by elastic softening (\u3b2 a-1, \u3b2 b-1, \u3b2 c-1 = 397 \ub1 9, 395 \ub1 28, 308 \ub1 11 GPa, 02(\u3b2-1)/ 02P = -4.5 \ub1 2.7, -6.6 \ub1 8.4, -5.4 \ub1 3.0) appears to be related to the framework stability and to be independent of the water content in the channels and thus of the ion beam exposure

On the approximability of the L(h, k)-labelling problem on bipartite graphs (Extended abstract)

Given an undirected graph G, an L(h, k)-labelling of G assigns colors to vertices from the integer set {0,.. lambda(h,k)}, such that any two vertices v(i) and v(j) receive colors c(v(i)) and c(v(j)) satisfying the following conditions: i) if v(i) and v(j) are adjacent then vertical bar c(v(i)) - c(v(j))vertical bar >= h; ii) if v(i) and v(j) are at distance two then vertical bar c(v(i)) - c(v(j))vertical bar >= k. The aim of the L(h, k)-labelling problem is to minimize lambda(h,k)- In this paper we study the approximability of the L(h,k)-labelling problem on bipartite graphs and extend the results to s-partite and general graphs. Indeed, the decision version of this problem is known to be DIP-complete in general and, to our knowledge, there are no polynomial solutions, either exact or approximate, for bipartite graphs. Here, we state some results concerning the approximability of the L(h,k)-labelling problem for bipartite graphs, exploiting a novel technique, consisting in computing approximate vertex- and edge-colorings of auxiliary graphs to deduce an L(h, k)-labelling for the input bipartite graph. We derive an approximation algorithm with performance ratio bounded by (4)/D-3(2), where, D is equal to the minimum even value bounding the minimum of the maximum degrees of the two partitions. One of the above coloring algorithms is in fact an approximating edge-coloring algorithm for hypergraphs of maximum dimension d, i.e. the maximum edge cardinality, with performance ratio d. Furthermore, we consider a different approximation technique based on the reduction of the L(h, k)-labelling problem to the vertex-coloring of the square of a graph. Using this approach we derive an approximation algorithm with performance ratio bounded by min(h, 2k)root n + o(k root n), assuming h >= k. Hence, the first technique is competitive when D O(n(1/4)) These algorithms match with a result in [2] stating that L(1,1) labelling n-vertex bipartite graphs is hard to approximate within(n1/2-)epsilon, for any epsilon > 0, unless NP=ZPP. We then extend the latter approximation strategy to s-partite graphs, obtaining a (min(h, sk)root n + o(sk root n))-approximation ratio, and to general graphs deriving an (h root n + o(h root n))-approximation algorithm, assuming h >= k. Finally, we prove that the L(h, k)-labelling problem is not easier than coloring the square of a graph