An analytical model for the prediction of rip spacing in intermediate beaches

Considering the diversity of rip currents based on the classification of Castelle et al. (2016), it is crucial to study the characteristics of each individual rip current type, which are classified based on different dominant controlling forces and physical driving mechanisms. In this study, an analytical model was presented to predict the spacing of channel rip currents \((S_{\mathrm{rip}})\) in intermediate beaches using the equations of continuity and momentum. Then, the analytical model predictions were compared with the results of numerical simulations calibrated with field studies of other researchers, that showed good agreements. The main results of this study showed that rip spacing was simultaneously related to the characteristics of wave and bed in the surf zone. In addition, it was shown that due to inevitable changes of the hydrodynamic and morphological conditions of rip channel in the beach, the parameter \(H_{b0}/h_{c}\) (where \(H_{b0}\) is the wave height before approaching the sand bar and \(h_{c}\) is channel depth) is an important factor in predicting the rip current situation and the changes of the beach state with time.     

The R{\overline{3}} c \to R{\overline{3}} m transition in nitratine, NaNO3, and implications for calcite, CaCO3

The temperature dependences of the crystal structure and superstructure intensities in sodium nitrate, mineral name nitratine, NaNO₃, were studied using Rietveld structure refinements based on synchrotron powder X-ray diffraction. Nitratine transforms from $R{\overline{3}} c\;\hbox{to}\;R{\overline{3}} m$ at T _c = 552(1) K. A NO₃ group occupies, statistically, two positions with equal frequency in the disordered $R{\overline{3}} m$ phase, but with unequal frequency in the partially ordered $R{\overline{3}} c$ phase. One position for the NO₃ group is rotated by 60° or 180° with respect to the other. The occupancy of the two orientations in the $R{\overline{3}} c$ phase is obtained from the occupancy factor, x, for the O1 site and gives rise to the order parameter, S = 2x ? 1, where S is 0 at T _c and 1 at 0 K. The NO₃ groups rotate in a rapid process from about 541 to T _c, where the a axis contracts. Using a modified Bragg–Williams model, a good fit was obtained for the normalized intensities (that is, normalized, NI^1/2) for the (113) and (211) reflections in $R{\overline{3}} c\hbox {\,NaNO}_{3},$ and indicates a second-order transition. Using the same model, a reasonable fit was obtained for the order parameter, S, and also supports a second-order transition.     

Perception of the rip current hazard on Galveston Island and North Padre Island,Texas, USA

The hazard posed by a rip current depends in part on the ability of beach users to identify a rip current and to associate surf conditions with the potential for rip currents. Understanding which visual features beach users associated with rip currents is an important step in the development of appropriate programs and educational materials aimed at improving the ability of beach users to identify a rip current. A face-to-face survey (n = 392) was conducted to assess the ability of beach users to identify a rip current using five near eye-level photographs that simulate the view of the beach and surf zone as the respondent approached the beach. The survey was conducted on three heavily used public beaches in Texas (Galveston, Port Aransas, and Corpus Christi) at the height of the summer beach season in 2012. Only 13 % of respondents correctly selected the photograph showing the most hazardous conditions and correctly identified the precise location of the rip current on the photograph. The majority of beach users (87 %) incorrectly indicated that the photograph with the heaviest surf represented the most hazardous surf conditions and greatest potential for the development of rip currents, or failed to identify rip currents in photographs. Respondents who were able to correctly identify the rip current tended to recognize the breaking wave pattern, areas of darker water, or the proximity to structures as key visual characteristics of rip currents and also had higher self-reported abilities to swim in rough water and escape a rip current.     

Soil responses near Delhi ridge and adjacent regions in Greater Delhi during incidence of a local earthquake

In this study, soil response was carried out for the Greater Delhi region. A folded Proterozoic formation was identified as Delhi ridge, passes through its central part along SSW–NNE direction, and appears to be a main geomorphic feature for the study area. The Delhi ridge is an exposed quartzite rock of about 10–100 m wide and ~25 km long with gentler dipping both toward east and west. We have considered the exposed part as an outcrop side near the ridge axis and the dipping area as rigid base away from the ridge axis for ground motion study during the occurrence of the 25 November 2007 earthquake with magnitude M _L 4.3 (Richter scale) that occurred at Delhi–Haryana State boundary. The degree of shaking was very strong and reported major cracks in the buildings near the epicenter area. We have studied the soil response parameters at the surface level, considering horizontally stratified soil layers above rigid base. The equivalent linear method was used for soil response analysis at 25 sites in Greater Delhi area. The peak amplification factors vary from 3.2 to 5.9 and peak resonance frequency varies from 1.2 to 5.3 Hz. The correlation among the peak amplification factor (A) and frequency (f) was empirically established as A = 0.36f + 3.60. Increasing peak amplification factor was found at sites with increasingly thicker alluvium deposit with lower frequency contains ground motion and vice versa. Seismic zoning map was also reconstructed for peak amplification factors and predominant periods for the study area for the mitigation purposes of earthquake damage. The average shear wave velocity up to 30 m soil depth is also obtained for site classification. The average velocity to 30 m [ $ \overline{{V_{\text{s}} }} (30) $ ] is a widely used parameter for classifying sites for predicting their potentiality to amplify seismic shaking. A lower value [ $ \overline{{V_{\text{s}} }} (30) $ ] thus yields a more conservative estimate of ground motion, which generally increases as $ \overline{{V_{\text{s}} }} (30) $ decreases. Present estimate of $ \overline{{V_{\text{s}} }} (30) $ varies from 315 to 419 m/s. In this study, we have identified two site classes C and D, as per National Earthquake Hazard Reduction Program. The city planner or engineers can directly use these data for site-specific assessment during retrofitting of the existing structure, demolition of the old buildings and design a new structure to avoid major destruction of the buildings due to future earthquake.     

Fitting matrix-valued variogram models by simultaneous diagonalization (Part I: Theory)

Suppose that ¯(x₁),...,¯Z(x_n). are observations of vector-valued random function ¯(x). In the isotropic situation, the sample variogram γ^*(h) for a given lag h is $$\bar \gamma ^ * (h) = \frac{1}{{2N(h)}}\mathop \sum \limits_{s(h)} (\overline Z (x_1 ) - \overline Z (x_1 )) \overline {(Z} (x_1 ) - \overline Z (x_1 ))^T $$ where s(h) is a set of paired points with distance h and N(h) is the number of pairs in s(h).. For a selection of lags h₁, h₂, .... h_k such that N (h₁) > O. we obtain a ktuple of (semi) positive definite matrices $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ . We want to determine an orthonormal matrix B which simultaneously diagonalizes the $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ or nearly diagonalizes them in the sense that the sum of squares of offdiagonal elements is small compared to the sum of squares of diagonal elements. If such a B exists, we linearly transform $\overline Z (x)$ by $\overline Y (x) = B\overline Z (x)$ . Then, the resulting vector function $\overline Y (x)$ has less spatial correlation among its components than $\overline Z (x)$ does. The components of $\overline Y (x)$ with little contribution to the variogram structure may be dropped, and small crossvariograms fitted by straightlines. Variogram models obtained by this scheme preserve the negative definiteness property of variograms (in the matrix-valued function sense). A simplified analysis and computation in cokriging can be carried out. The principles of this scheme arc presented in this paper.     

The P–V–T equation of state of CaPtO3 post-perovskite

Orthorhombic post-perovskite CaPtO₃ is isostructural with post-perovskite MgSiO₃, a deep-Earth phase stable only above 100 GPa. Energy-dispersive X-ray diffraction data (to 9.4 GPa and 1,024 K) for CaPtO₃ have been combined with published isothermal and isobaric measurements to determine its P–V–T equation of state (EoS). A third-order Birch–Murnaghan EoS was used, with the volumetric thermal expansion coefficient (at atmospheric pressure) represented by α(T) = α₀ + α₁(T). The fitted parameters had values: isothermal incompressibility, $ K_{{T_{0} }} $  = 168.4(3) GPa; $ K_{{T_{0} }}^{\prime } $  = 4.48(3) (both at 298 K); $ \partial K_{{T_{0} }} /\partial T $  = ?0.032(3) GPa K^?1; α₀ = 2.32(2) × 10^?5 K^?1; α₁ = 5.7(4) × 10^?9 K^?2. The volumetric isothermal Anderson–Grüneisen parameter, δ _T , is 7.6(7) at 298 K. $ \partial K_{{T_{0} }} /\partial T $ for CaPtO₃ is similar to that recently reported for CaIrO₃, differing significantly from values found at high pressure for MgSiO₃ post-perovskite (?0.0085(11) to ?0.024 GPa K^?1). We also report axial P–V–T EoS of similar form, the first for any post-perovskite. Fitted to the cubes of the axes, these gave $ \partial K_{{aT_{0} }} /\partial T $  = ?0.038(4) GPa K^?1; $ \partial K_{{bT_{0} }} /\partial T $  = ?0.021(2) GPa K^?1; $ \partial K_{{cT_{0} }} /\partial T $  = ?0.026(5) GPa K^?1, with δ _T  = 8.9(9), 7.4(7) and 4.6(9) for a, b and c, respectively. Although $ K_{{T_{0} }} $ is lowest for the b-axis, its incompressibility is the least temperature dependent.     

Transmission electron microscopy of experimentally deformed chalcopyrite single crystals

Two crystals of natural chalcopyrite, CuFeS₂, experimentally deformed at 200° C have been studied by means of transmission electron microscopy (TEM). The activated glide planes are (001) and {112}. The dislocations in (001) have the Burgers vector [110] and a predominating edge character. They are split into two colinear partials b=1/2[110] and can cross split into {112}. The dislocations in {112} consist of straight segments along low index lattice lines. They are often arranged in dipoles generating trails of loops. Few dislocations with b=1/2[ \(\overline {11} \) 1] and [1 \(\bar 1\) 0] are present and dislocations with b=[0 \(\bar 2\) 1] occur in low angle subgrain boundaries. From weak beam contrasts it is presumed that most of the dislocations gliding in {112} have b=1/2〈3 \(\overline {11} \) 〉. They are dissociated into up to four partials. Microtwins and different types of stacking faults in {112} also occur. Models of the dissociation of dislocations are discussed.     

Petrological cannibalism: the chemical and textural consequences of incremental magma body growth

The textures of minerals in volcanic and plutonic rocks testify to a complexity of processes in their formation that is at odds with simple geochemical models of igneous differentiation. Zoning in plagioclase feldspar is a case in point. Very slow diffusion of the major components in plagioclase means that textural evidence for complex magmatic evolution is preserved, almost without modification. Consequently, plagioclase affords considerable insight into the processes by which magmas accumulate in the crust prior to their eventual eruption or solidification. Here, we use the example of the 1980–1986 eruptions of Mount St. Helens to explore the causes of textural complexity in plagioclase and associated trapped melt inclusions. Textures of individual crystals are consistent with multiple heating and cooling events; changes in total pressure (P) or volatile pressure ( $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O ) are less easy to assess from textures alone. We show that by allying textural and chemical analyses of plagioclase and melt inclusions, including volatiles (H₂O, CO₂) and slow-diffusing trace elements (Sr, Ba), to published experimental studies of Mount St. Helens magmas, it is possible to disambiguate the roles of pressure and temperature to reconstruct magmatic evolutionary pathways through temperature–pressure–melt fraction (T– $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O –F) space. Our modeled crystals indicate that (1) crystallization starts at $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O  > 300 MPa, consistent with prior estimates from melt inclusion volatile contents, (2) crystal cores grow at $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O  = 200–280 MPa at F = 0.65–0.7, (3) crystals are transferred to $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O  = 100–130 MPa (often accompanied by 10–20 °C of heating), where they grow albitic rims of varying thicknesses, and (4) the last stage of crystallization occurs after minor heating at $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O  ~ 100 MPa to produce characteristic rim compositions of An₅₀. We hypothesize that modeled $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O decreases in excess of ~50 MPa most likely represent upward transport through the magmatic system. Small variations in modeled $P_{{{\text{H}}_{ 2} {\text{O}}}}$ P H 2 O , in contrast, can be effected by fluxing the reservoir with CO₂-rich vapors that are either released from deeper in the system or transported with the recharge magma. Temperature fluctuations of 20–40 °C, on the other hand, are an inevitable consequence of incremental, or pulsed, assembly of crustal magma bodies wherein each pulse interacts with ancestral, stored magmas. We venture that this “petrological cannibalism” accounts for much of the plagioclase zoning and textural complexity seen not only at Mount St. Helens but also at arc magmas generally. More broadly we suggest that the magma reservoir below Mount St. Helens is dominated by crystal mush and fed by frequent inputs of hotter, but compositionally similar, magma, coupled with episodes of magma ascent from one storage region to another. This view both accords with other independent constraints on the subvolcanic system at Mount St. Helens and supports an emerging view of many active magmatic systems as dominantly super-solidus, rather than subliquidus, bodies.     

Depth dependence and exponential models of permeability in alluvial-fan gravel deposits

To determine depth dependence of permeability in various geologic deposits, exponential models have often been proposed. However, spatial variability in hydraulic conductivity, K, rarely fits this trend in coarse alluvial aquifers, where complex stratigraphic sequences follow unique trends due to depositional and post-depositional processes. This paper analyzes K of alluvial-fan gravel deposits in several boreholes, and finds exponential decay in K with depth. Relatively undisturbed gravel cores obtained in the Toyohira River alluvial fan, Sapporo, Japan, are categorized by four levels of fine-sediment packing between gravel grains. Grain size is also analyzed in cores from two boreholes in the mid-fan and one in the fan-toe. Profiles of estimated conductivity, $ \overline{K} $ , are constructed from profiles of core properties through a well-defined relation between slug-test results and core properties. Errors in $ \overline{K} $ are eliminated by a moving-average method, and regression analysis provides the decay exponents of $ \overline{K} $ with depth. Moving-average results show a similar decreasing trend in only the mid-fan above ～30-m depth, and the decay exponent is estimated as ≈0.11 m^?1, which is 10- to 1,000-fold that in consolidated rocks. A longitudinal cross section is also generated by using the profiles to establish hydrogeologic boundaries in the fan.     

X-ray single-crystal and Raman study of knorringite,Mg3(Cr1.58Mg0.21Si0.21)Si3O12, synthesized at 16 GPa and 1,600 °C

The crystal structure of a knorringite-type compound, Mg₃(Cr_1.58Mg_0.21Si_0.21)Si₃O₁₂, synthesized in a multi-anvil press at P = 16 GPa and T = 1,600 °C, was refined from single-crystal X-ray diffraction data up to R = 2.36 % for 314 independent reflections. Garnet was found to be cubic and have space group Ia $\overline{3}$ d, with the unit cell parameters a = 11.5718 (1) Å, V = 1,549.54 (2) Å³. The knorringite crystal studied contains 21 mol% of majorite end-member. The structural characterization of knorringitic garnet is important because the study of its thermodynamic constants provides new constraints on thermobarometry of peridotitic garnet assemblages of the lowermost upper mantle. The Raman spectra of synthetic knorringite have been obtained for the first time.     

Origin of birefringence in andradite from Arizona, Madagascar, and Iran

The crystal structure of four birefringent andradite samples (two from Arizona, one from Madagascar, and one from Iran) was refined with the Rietveld method, space group $Ia\overline{3} d$ , and monochromatic synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Each sample contains an assemblage of three different cubic phases. From the electron-microprobe (EMPA) results, fine-scale intergrowths in the Arizona-2 and Madagascar samples appear homogeneous with nearly identical compositions of {Ca_2.99Mg_0.01}_Σ3[ ${\text{Fe}}_{1.99}^{3 + }$ ${\text{Mn}}_{0.01}^{3 + }$ ]_Σ2(Si_2.95Al_0.03 ${\text{Fe}}_{0.02}^{3 + }$ )_Σ3O₁₂, Adr₉₈ (Arizona-2), and Adr₉₇ (Madagascar). Both samples are near-end-member andradite, ideally {Ca₃}[ ${\text{Fe}}_{2}^{3 + }$ ](Si₃)O₁₂, so cation ordering in the X, Y, or Z sites is not possible. Because of the large-scale intergrowths, the Arizona-1 and Iran samples contain three different compositions. Arizona-1 has compositions Adr₉₇ (phase-1), Adr₉₃Grs₄ (phase-2), and Adr₈₇Grs₁₁ (phase-3). Iran sample has compositions Adr₈₆Uv₁₂ (phase-1), Adr₆₉Uv₃₀ (phase-2), and Adr₇₆Uv₂₂ (phase-3). The crystal structure of the three phases within each sample was modeled quite well as indicated by the Rietveld refinement statistics of reduced χ² and overall R (F ²) values of, respectively, 1.980 and 0.0291 (Arizona-1); 1.091 and 0.0305 (Arizona-2); 1.362 and 0.0231 (Madagascar); and 1.681 and 0.0304 (Iran). The dominant phase for each sample has the following unit-cell parameters (Å) and weight fractions (%): a = 12.06314(1), 51.93(9) (Arizona-1); 12.04889(1), 52.47(1) (Arizona-2); 12.06276(1), 52.21(8) (Madagascar); and 12.05962(2), 63.3(1) (Iran). For these dominant phases, the distances and site occupancy factors (sofs) in terms of neutral atoms at the Ca(X), Fe(Y), and Si(Z) sites are as follows: <Ca–O> = 2.4348, Fe–O = 2.0121(6), Si–O = 1.6508(6) Å; Ca(sof) = 0.955(2), Fe(sof) = 0.930(2), and Si(sof) = 0.917(2) (Arizona-1); <Ca–O> = 2.4288, Fe–O = 2.0148(7), Si–O = 1.6476(7) Å; Ca(sof) = 0.953(2), Fe(sof) = 0.891(2), and Si(sof) = 0.927(2) (Arizona-2); <Ca–O> = 2.4319, Fe–O = 2.0220(6), Si–O = 1.6460(6) Å; Ca(sof) = 0.955(2), Fe(sof) = 0.941(2), and Si(sof) = 0.939(2) (Madagascar); and <Ca–O> = 2.4344, Fe–O = 2.0156(8), Si–O = 1.6468(8) Å; Ca(sof) = 0.928(2), Fe(sof) = 0.908(2), and Si(sof) = 0.932(3) (Iran). The sofs based on the EMPA results are similar to those obtained from the Rietveld refinement. Each phase in the HRPXRD results can be correlated with a specific chemical composition. For example, the Iran sample composition Adr₆₃Uv₃₀ corresponds to phase-3 that has the smallest unit-cell parameter; Adr₇₆Uv₂₂ corresponds to phase-1 that has the intermediate cell value; and Adr₈₆Uv₁₃ corresponds to phase-2 that has the largest unit-cell parameter. The bond distances compare well with those obtained from radii sum. The three different cubic phases in each sample cause strain that arises from the mismatch of the cubic unit-cell parameters and give rise to birefringence.     

Transmission electron microscopic study of experimentally deformed k-feldspar single crystals

A set of sanidine single crystals were previously deformed at 700° C in a Griggs triaxial press with different crystallographic orientations of the core so as to induce dislocation glide of different slip systems respectively. Deformed crystals have been studied by transmission electron microscopy (TEM) and the activated slip systems have been characterized for two orientations. (010)[001] and (001)1/2[ \(\overline 1 \) 10] systems expected for one orientation (main stress nearly parallel to [012]) are observed, whereas the (001)[100] system expected for the other orientation (main stress nearly parallel to [101]) is never observed. In the latter specimen the deformation is rather difficult and occurs through unexpected systems characterized as (110)1/2[1 \(\overline 1 \) 2] and (1 \(\overline 1 \) 1)1/2[110]. In all the samples studied the deformation is heterogeneous, exhibiting dislocation configurations related to temperature variations.     

Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures

Iron-rich orthopyroxene plays an important role in models of the thermal and magmatic evolution of the Moon, but its density at high pressure and high temperature is not well-constrained. We present in situ measurements of the unit-cell volume of a synthetic polycrystalline end-member orthoferrosilite (FeSiO₃, fs) at simultaneous high pressures (3.4–4.8 GPa) and high temperatures (1,148–1,448 K), to improve constraints on the density of orthopyroxene in the lunar interior. Unit-cell volumes were determined through in situ energy-dispersive synchrotron X-ray diffraction in a multi-anvil press, using MgO as a pressure marker. Our volume data were fitted to a high-temperature Birch–Murnaghan equation of state (EoS). Experimental data are reproduced accurately, with a  $\varDelta P$ Δ P  standard deviation of 0.20 GPa. The resulting thermoelastic parameters of fs are: V ₀ = 875.8 ± 1.4 Å³, K ₀ = 74.4 ± 5.3 GPa, and $\frac{{\text d}K}{{\text d}T} = -0.032 \pm 0.005\,\hbox{GPa K}^{-1}$ d K d T = - 0.032 ± 0.005 GPa K - 1 , assuming ${K}^{\prime}_{0} = 10 $ K 0 ′ = 10 . We also determined the thermal equation of state of a natural Fe-rich orthopyroxene from Hidra (Norway) to assess the effect of magnesium on the EoS of iron-rich orthopyroxene. Comparison between our two data sets and literature studies shows good agreement for room-temperature, room-pressure unit-cell volumes. Preliminary thermodynamic analyses of orthoferrosilite, FeSiO₃, and orthopyroxene solid solutions, (Mg_1?x Fe _x ) SiO₃, using vibrational models show that our volume measurements in pressure–temperature space are consistent with previous heat capacity and one-bar volume–temperature measurements. The isothermal bulk modulus at ambient conditions derived from our measurements is smaller than values presented in the literature. This new simultaneous high-pressure, high-temperature data are specifically useful for calculations of the orthopyroxene density in the Moon.     

Coherent elastic energies of exsolution boundaries in peristerite and böggild intergrowths

Elastic energy calculations based upon the coherent model of Willaime and Brown [Acta Cryst. A30, 316–331 (1974)] have been carried out for some exsolution textures in peristerite and Böggild intergrowths. For peristerites it is demonstrated that substitution of K for Na moves the orientation of the exsolution lamellae from (08 \(\overline {\text{1}} \) ) to about ( \(\overline {\text{1}} \) , 21, \(\overline {\text{2}} \) ) in agreement with observations. An electron microscope study of exsolution textures in labradorite and andesine plagioclases has been carried out and information about small structural differences in these lamellar structures has been obtained from elastic energy calculations.     

Flow rule in a high-cycle accumulation model backed by cyclic test data of 22 sands

The flow rule used in the high-cycle accumulation (HCA) model proposed by Niemunis et al. (Comput Geotech 32: 245, 2005) is examined on the basis of the data from approximately 350 drained long-term cyclic triaxial tests (N = 10⁵ cycles) performed on 22 different grain-size distribution curves of a clean quartz sand. In accordance with (Wichtmann et al. in Acta Geotechnica 1: 59, 2006), for all tested materials, the “high-cyclic flow rule (HCFR)”, i.e., the ratio of the volumetric and deviatoric strain accumulation rates \(\dot{\varepsilon}_{\rm{v}}^{{\rm acc}}/\dot{\varepsilon}_{\rm{q}}^{{\rm acc}}\) , was found dependent primarily on the average stress ratio η ^av = q ^av/p ^av and independent of amplitude, soil density and average mean pressure. The experimental HCFR can be fairly well approximated by the flow rule of the modified Cam-clay (MCC) model. Instead of the critical friction angle \(\varphi_{\rm{c}}\) which enters the flow rule for monotonic loading, the HCA model uses the MCC flow rule expression with a slightly different parameter \(\varphi_{\rm{cc}}\) . It should be determined from cyclic tests. \(\varphi_{\rm{cc}}\) and \(\varphi_{\rm{c}}\) are of similar magnitude but not always identical, because they are calibrated from different types of tests. For a simplified calibration in the absence of cyclic test data, \(\varphi_{\rm{cc}}\) may be estimated from the angle of repose \(\varphi_{\rm{r}}\) determined from a pluviated cone of sand (Wichtmann et al. in Acta Geotechnica 1: 59, 2006). However, the paper demonstrates that the MCC flow rule with \(\varphi_{\rm{r}}\) does not fit well the experimentally observed HCFR in the case of coarse or well-graded sands. For an improved simplified calibration procedure, correlations between \(\varphi_{\rm{cc}}\) and parameters of the grain-size distribution curve (d ₅₀,   C _u) have been developed on the basis of the present data set. The approximation of the experimental HCFR by the generalized flow rule equations proposed in (Wichtmann et al. in J Geotech Geoenviron Eng ASCE 136: 728, 2010), considering anisotropy, is also discussed in the paper.     

Transmission electron microscopy on meteoritic troilite

Phase transitions and associated domains of meteoritic troilite (FeS) have been studied by means of transmission electron microscopy (TEM). Three polymorphs have been found, two of which can be described by superstructures of the NiAs-type structure (A, C subcell). The P \(\overline 6\) 2c (√3A, 2C) polymorph, stable at room temperature, displays antiphase domains with the displacement vector 1/3< \(\overline {\text{1}}\) 10>. In situ heating experiments showed that the P \(\overline 6\) 2c polymorph changes at temperatures of 115°–150° C into an orthorhombic pseudohexagonal transitional phase with the probable space group Pmcn (A,√3A, C). It contains antiphase domains with the displacement vector 1/2 [110] and twins with a threefold twin-axis parallel c. When heated above 210° C the transitional phase transforms into the high-temperature modification with NiAs structure (P6 ₃/mmc). All observed phase transitions are reversible. The occurrence of antiphase and twin domains, respectively, agrees with the symmetry reductions involved in the subsolidus phase transitions. This is demonstrated by group-subgroup relationships among the space groups P6 ₃/mmc, Pmcn, and P \(\overline 6\) 2c.     

A critical look at representations of urban areas in global maps

According to the UN, the number of urban dwellers is expected to increase from roughly 3.2 billion today to more than 4.9 billion by 2030. An accurate and regularly updated estimate of the extent and spatial distribution of urban land is an important first step in our search for realistic responses to the ecological and social consequences of what promises to be the most rapid urbanization in world history. By employing circa-2000 satellite remote sensing imagery, geographic information systems, and census data, six groups from government and academia in both the EU and the US have created global maps that can be used to describe urban land. We compare these maps from global to sub-national scales, for the first time applying Discrete Global Grids to the problem of global-scale map comparison. Although most of these maps share common data inputs, they differ by as much as an order of magnitude in their estimates of the total areal extent of the Earth’s urban land (from 0.27 to 3.52 million km²). A sub-national analysis of the spatial distribution of urban land reveals that inter-map correlations are highest in North America ( $ \ifmmode\expandafter\bar\else\expandafter\=\fi{r} $  = 0.90), intermediate in Europe, South and Central America, and Sub-Saharan Africa ( $ \ifmmode\expandafter\bar\else\expandafter\=\fi{r} $  = 0.78), and lowest in Asia ( $ \ifmmode\expandafter\bar\else\expandafter\=\fi{r} $  = 0.63). Across most regions, our analysis uncovers a degree of variance that is high enough to call into question the consistency of each group’s approach to urban land, pointing to the need for both a common urban taxonomy and a global urban assessment effort.     

Crystal structure of K-substituted gonnardite: separation of local water–cation assemblages

K-substituted gonnardite, K_2.18Na_0.04Ca_0.02[Al_2.26Si_2.74O₁₀]·2.2H₂O, was studied by X-ray powder diffraction method. The structure was refined with the Rietveld technique in the tetragonal space group $I\overline{4} 2d$ with a = 13.65409(16), c = 6.56928(11) Å, V = 1224.74(2) ų, Z = 4. Most of K⁺ cations (1.94 apfu) statistically occupy three nearest positions to be considered as the split one. “Excess” cations are located in the position non-typical for K⁺. Statistics in the cation distribution is defined by the occupation of the additional position. Based on a crystal chemical positional model (C₂R₂A₂) [T₅O₁₀], the separation of the local water–cation assemblages from an average statistical pattern has been suggested.     

High-pressure elastic behavior of Ca4La6(SiO4)6(OH)2 a synthetic rare-earth silicate apatite: a powder X-ray diffraction study up to 9.33 GPa

The compression behavior of a synthetic Ca₄La₆(SiO₄)₆(OH)₂ has been investigated to about 9.33 GPa at 300 K using in situ angle-dispersive X-ray diffraction and a diamond anvil cell. No phase transition has been observed within the pressure range investigated. The values of zero-pressure volume V ₀, K ₀, and $K_{0}^{'}$ refined with a third-order Birch–Murnaghan equation of state are V ₀ = 579.2 ± 0.1 Å³, K ₀ = 89 ± 2 GPa, and $K_{0}^{'} = 10.9 \pm 0.8$ . If $K_{0}^{'}$ is fixed at 4, K ₀ is obtained as 110 ± 2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a0 = 79 ± 2 GPa) is more compressible than the c-axis (K _c0 = 121 ± 7 GPa). A comparison between the high-pressure elastic response of Ca₄La₆(SiO₄)₆(OH)₂ and the iso-structural calcium apatites is made. The possible reasons of the different elastic behavior between Ca₄La₆(SiO₄)₆(OH)₂ and calcium apatites are discussed.     

Deformation mechanisms in experimentally deformed single crystals of pyrrhotite,Fe1−xS

Single crystals of hexagonal and monoclinic pyrrhotite, Fe_1?xS, have been experimentally deformed by uniaxial compression at 300 MPa confining pressure, and at a strain rate of 1 × 10^?5 s^?1 in the temperature range from 200° C to 400° C. Very high anisotropy characterizes the mechanical behaviour of the crystal structure. During compression parallel to thec-axis, when no slip system may be activated, the maximum strength is observed. One or two degrees of non-parallelism between [c] and σ₁ results in slip on the basal plane, illustrating the very low resistance of the lattice against shear in this plane. At σ₁ Λ(0001)=45°, i.e. when maximum resolved shear stress is attained on the basal plane, the strength reaches a minimum. Thecritical resolved shear stress (CRSS) increases from less than 4.7 MPa at 400° C to 52 MPa at 200° C. A new slip system, \((10\overline 1 0)\parallel \left\langle {1\overline 2 10} \right\rangle \) prism slip, is described. It is activated only at high angles (>70°) between σ₁ and [c]. The CRSS of the prism slip ranges from 7 MPa (400° C) to 115 MPa (200° C). Twinning on \((10\overline 1 2)[(10\overline 1 2):(1\overline 2 10)]\) , earlier reported by several authors, has been produced only at the highest temperature either as secondary feature during pressure release (compression ‖[c]) or in heterogeneously strained areas (compression ⊥[c]). As twinning and prism slip attain their maximum values of the Schmidt factor under nearly equal stress conditions it is postulated that the former of the two deformation modes has the higher shear resistance.