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.     

Experimental delineation of the “e” ⇌ I\bar 1 and “e” ⇌ C\bar 1 transformations in intermediate plagioclase feldspars

Approximately 125 hydrothermal annealing experiments have been carried out in an attempt to bracket the stability fields of different ordered structures within the plagioclase feldspar solid solution. Natural crystals were used for the experiments and were subjected to temperatures of ～650°C to ～1,000°C for times of up to 370 days at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =600 bars, or \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =1,200 bars. The structural states of both parent and product materials were characterised by electron diffraction, with special attention being paid to the nature of type e and type b reflections (at h+k=(2n+1), l=(2n+1) positions). Structural changes of the type C \(\bar 1\) → I \(\bar 1\) , C \(\bar 1\) → “e” structure, I \(\bar 1\) → “e” and “e” structure → I \(\bar 1\) have been followed. There are marked differences between the ordering behaviour of crystals with compositions on either side of the C \(\bar 1\) ? I \(\bar 1\) transition line. In the composition range ～ An₅₀ to ～ An₇₀ the e structure appears to have a true field of stability relative to I \(\bar 1\) ordering, and a transformation of the type I \(\bar 1\) ? e has been reversed. It is suggested that the e structure is the more stable ordered state at temperatures of ～ 800°C and below. For compositions more albite-rich than ～ An₅₀ the upper temperature limit for long range e ordering is lower than ～ 750°C, and there is no evidence for any I \(\bar 1\) ordering. The evidence for a true stability field for “e” plagioclase, which is also consistent with calorimetric data, necessitates reanalysis both of the ordering behaviour of plagioclase crystals in nature and of the equilibrium phase diagram for the albite-anorthite system. Igneous crystals with compositions of ～ An₆₅, for example, probably follow a sequence of structural states C \(\bar 1\) → I \(\bar 1\) → e during cooling. The peristerite, Bøggild and Huttenlocher miscibility gaps are clearly associated with breaks in the albite, e and I \(\bar 1\) ordering behaviour but their exact topologies will depend on the thermodynamic character of the order/disorder transformations.     

Deformation and transformation in experimentally shock-loaded quartz

Single crystals of quartz, shock-loaded along the a axis to pressures of 22 Gpa, 24 GPa, 26 GPa and 30 GPa were examined by high-voltage transmission electron microscopy (TEM), scanning electron microscopy (SEM) and X-ray diffraction. Asymmetric broadenings of X-ray lines indicate spatial inhomogeneity of shock effects. X-ray streaking angles in the reciprocal lattice planes h0 \(\bar h\) l, 0k \(\bar k\) l and hki0 indicate a slight tilting deformation by rotation about [00.1] in (0001). TEM reveals glass lamellae which are mostly in (01 \(\bar 1\) 2) orientation, and are correlated with optical planar elements and with surface steps seen in SEM. No dislocations are found. There are (0001) lamellar features, probably Brazil twins. The (01 \(\bar 1\) 2) glass lamellae develop directly from bands of quartz in which intense deformation has produced a fine-scale lamellar to blocky structure, possibly also originating by twinning. Relics of crystalline structure are found in almost completely vitrified lamellae. Stishovite occurs in heavily deformed parts of the 22 GPa and 24 GPa specimens, in patches of densified glass distinct from the sharply bounded lamellae. The nucleationless, pervasive transformation of lamellae to glass, with preservation of their sharp boundaries, is attributed to defect coalescence analogous to vitrification by radiation damage (metamictization). Some patchy glass may be due to melting.     

Thermodynamics of plagioclases I: Theory of the I\bar 1 - P\bar 1 phase transition in anorthite and Ca-rich plagioclases

Landau theory of the \(P\bar 1 - I\bar 1\) phase transition in Ca-rich plagioclases reveals the sensitivity of the phase transition behaviour to a) Al, Si disorder, b) structural replacement of Ca by Na, and c) inhomogeneities of lattice strains. The following effects are predicted:

1. A tricritical phase transition exists in fully ordered anorthite. Al, Si disorder and Na, Ca exchange lead to second order phase transitions.
2. The transition temperatures depend sensitively on the degree of Al, Si disorder and the chemical composition of the Ca-rich plagioclases. Increasing Na-content decreases the transition temperatures.
3. The thermal evolution of c and d reflections depends on the homogeneity of the crystal and do not necessarily reflect the temperature evolution of the macroscopic lattice strain. A simple quadratic dependence of the X-ray scattering intensity on the order parameter exists only for fully ordered, homogeneous anorthite.

The role of inhomogeneous Al, Si distributions and lattice relaxations are discussed including possible structural modulations.     

High-temperature 29Si MAS NMR spectroscopy of anorthite (CaAl2Si2O8) and its P\bar 1-I\bar 1structural phase transition

We present ²⁹Si MAS NMR data for a well-ordered natural anorthite, obtained in situ at temperatures of from 25 to 500° C, which follow the changes in the aluminosilicate framework through the P $\bar 1$ -I $\bar 1$ structural phase transition. Pairs of peaks due to sites offset by approximately 1/2 [111] converge through the P $\bar 1$ phase and only four peaks are present above about 241° C. The variation of the peak positions with temperature and correlations based on structural data for the P $\bar 1$ and I $\bar 1$ phases allow assignment of all the MAS-NMR peaks to crystallographic sites. A Landau-type analysis gives an expression that relates the separation of pairs of con verging peaks to the local order parameter for the P $\bar 1$ -I $\bar 1$ transition, from which we determine its temperature dependence. Data for the best-constrained set of peak positions give for the order parameter critical exponent β = 0.27±0.04, consistent with previous results indicating that the P $\bar 1$ -I $\bar 1$ transition in pure anorthite is tricritical. No significant change in the ²⁹Si spin-lattice relaxation rate occurs across the P $\bar 1$ -I $\bar 1$ transition.     

The order-disorder transition in gallium analogue of albite,NaGaSi3O8

The order-disorder transformation in NaGaSi₃O₈ was studied at \(P_{H_2 O} \approx 100\) bar using a hydrous sodium gallium silicate gel and synthetic Ga-albites of various degrees of order as initial materials. The structural state of the gallium albites was determined by the angle separation in X-ray powder patterns of 131 and 1 \(\bar 3\) 1, and of \(\bar 2\) 04 and 060 peaks. The direction of order-disorder transformations was found to change sharply at 938 (±3)°C. This indicates a first order phase transition in NaGaSi₃O₈ as in albite, of which it is the structural analogue.     

The calcium oxotellurate(IV) nitrates Ca5Te4O12(NO3)2(H2O)2 and Ca6Te5O15(NO3)2

Single crystals of two novel calcium oxotellurate(IV) nitrates were grown under hydrothermal conditions and were structurally characterized by X-ray diffraction. Ca $_5$ Te $_4\text {O}_{12}$ (NO $_3$ ) $_2$ (H $_2$ O) $_2$ [ $Cc$ , $Z=4$ , $a=25.258(3)$ Å, $b=5.7289(7)$ Å, $c=17.0066(19)$ Å, $\beta =124.377(2)^{\circ}$ , $R[F^2 > 2\sigma (F^2)]=0.043$ , 4083 $F^2$ data, 281 parameters] can be described as a non-classic order/disorder (OD) structure, which fulfills the basic principle of OD theory, viz. local equivalence of polytypes, but does not strictly follow the vicinity condition (VC) of OD theory. The structure is made up from an alternating stacking of non-polar layers composed of isolated [TeO $_3$ ] units and Ca $^{2+}$ ions and polar layers containing NO $_3^-$ ions and water molecules. The electron lone-pairs of the [TeO $_3$ ] units protrude into the free space of the anion/water layers. The crystal under investigation was a non-classic OD-twin of domains of a maximum degree of order (MDO). At the twin plane a fragment of the second MDO polytype is located. The main building blocks of Ca $_6$ Te $_5\text {O}_{15}$ (NO $_3$ ) $_2$ [ $P2_1/c$ , $Z=4$ , $a=15.494(2)$ Å, $b=5.6145(7)$ Å, $c=39.338(4)$ Å, $\beta =142.480(5)^{\circ}$ , $R[F^2 > 2\sigma (F^2)]=0.043$ , 3026 $F^2$ data, 307 parameters] are isolated [TeO $_3$ ] units and Ca $^{2+}$ ions which are connected to a three-dimensional framework perforated by channels in which the N atoms of the nitrate anions are located and the electron lone-pairs of the [TeO $_3$ ] units protrude. The structure can topologically be derived from the structure of Ca $_5$ Te $_4\text {O}_{12}$ (NO $_3$ ) $_2$ (H $_2$ O) $_2$ by removing the water molecules and connecting the CaTeO $_3$ layers with additional [TeO $_3$ ] units and Ca $^{2+}$ ions.     

Thermodynamics of plagioclase II: Temperature evolution of the spontaneous strain at the I\bar 1 \leftrightarrow P\bar 1 phase transition in anorthite

The temperature dependence of the lattice parameters of pure anorthite with high Al/Si order reveals the predicted tricritical behaviour of the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition at T _c ^* =510 K. The spontaneous strain couples to the order parameter Q° as x _i∝S _xQ ⁱ Q°² with S _xQ ¹ =4.166×10^?3, S _xQ ² =0.771×10^?3, S _xQ ³ =?7.223×10^?3 for the diagonal elements. The temperature dependence of Q° is $$Q^{\text{o}} = \left( {1 - \frac{T}{{510}}} \right)^\beta ,{\text{ }}\beta = \tfrac{{\text{1}}}{{\text{4}}}$$ A strong dependence of T _c ^* , S _xQ ⁱ and β is predicted for Al/Si disordered anorthite.     

Equilibrium thermodynamics of Al/Si ordering in anorthite

Variations in the equilibrium degree of Al/Si order in anorthite have been investigated experimentally over the temperature range 800-1535° C. Spontaneous strain measurements give the temperature dependence of the macroscopic order parameter, Q, defined with respect to the \(C\bar 1 \rightleftharpoons I\bar 1\) phase transition, while high temperature solution calorimetric data allow the relationship between Q and excess enthalpy, H, to be determined. The thermodynamic behaviour can be described by a Landau expansion in one order parameter if the transition is first order in character, with an equilibrium transition temperature, T _tr, of ～2595 K and a jump in Q from 0 to ～0.65 at T_tr. The coefficients in this Landau expansion have been allowed to vary with composition, using Q=1 at 0 K for pure anorthite as a reference point for the order parameter. Published data for H and Q at different compositions allow the calibration of the additional parameters such that the free energy due to the \(C\bar 1 \rightleftharpoons I\bar 1\) transition in anorthite-rich plagioclase feldspars may be expressed (in cal. mole^-1) as: \(\begin{gathered}G = \tfrac{1}{2} \cdot 9(T - 2283 + 2525X_{Ab} )Q^2 \\ {\text{ + }}\tfrac{1}{4}( - 26642 + 121100X_{Ab} )Q^4 \\ {\text{ + }}\tfrac{1}{6}(47395 - 98663X_{Ab} )Q^6 \\ \end{gathered}\) where X _Ab is the mole fraction of albite component. The nature of the transition changes from first order in pure anorthite through tricritical at ～An₇₈ to second order, with increasing albite content. The magnitude of the free energy of \()\) ordering reduces markedly as X _Ab increases. At ～700° C incommensurate ordering in crystals with compositions ～An₅₀–An₇₀ needs to have an associated free energy reduction of only a few hundred calories to provide a more stable structure. These results, together with a simple mixing model for the disordered ( \()\) ) solid solution, an assumed tricritical model for the incommensurate ordering and published data for ordering in albite have been used to calculate a set of possible free energy relations for the plagioclase system. The incommensurate structure should appear on the equilibrium phase diagram, but its apparent stability with respect to the assemblage albite plus anorthite at low temperatures depends on the values assigned to the mixing parameters of the $$$$ solid solution.     

Alpha-radioactivity-related upper age limit for thermoluminescence dating?

A systematic underestimation of the age of mineralisation by the thermoluminescence (tl) technique has been observed in a variety of samples older than Quaternary although their naturaltl was not saturated. The samples included calcites, oozes, lime stones, shales, gypsum, basalts and dolerites. It is shown that thetl build-up in nature reaches a dynamic equilibrium level much ahead of the lifetime of thetl trap concerned and is solely determined by the alpha radioactivity of the sample; the validity fortl dating does not exist once such an equilibrium is reached. For the samples considered, the limiting Paleo-alpha dose fortl dating validity works out to be about 150 kilorads; beyond this dose, thetl age and the geological age bears a ratio given by \(t'/t = a\left[ {\smallint _0^t \dot D_\alpha dt} \right]^{ - b} \) wherea andb are constants and \(\dot D_\alpha \) is the annual alpha irradiation rate in the sample. For a suite of samples withb≠1, relative dating seems possible by thetl technique. It may be generalised that samples with 1ppm level of U, Th content cannot betl dated if they are older than about 500 kiloyears even though theirntl trap lifetimes may be 100 myrs; conversely, a 1000 myr-old sample can betl dated only if its U, Th content is much less than ppb levels and itstl trap lifetime greater than 10¹⁰ years.     

X-ray diffraction study of the orientational order/disorder transition in NaNO3: Evidence for order parameter coupling

The orientational ordering transition R \(R\bar 3m - R\bar 3c\) in NaNO₃ near 552 K has been investigated using x-ray diffraction techniques. NaNO₃ is a model system for CaCO₃ and other minerals with orientational disorder of triangular molecules in a simple NaCl-type matrix. The temperature evolution of the integrated intensities of the superlattice reflection \(\bar 1\) 23 and the fundamental reflection 110 are discussed in terms of Landau theory of two coupled order parameters. It is shown that the known phenomenological critical exponent (Poon and Salje 1988) and the anomalous thermal expansion at T > T _tr (Reeder et al. 1988) can be understood as the result of a Z point instability which mainly describes the NO ₃ ^- disorder, and a second order parameter linked with the spontaneous strain of this phase transition.     

Experimental study of subsolidus phase relations and mixing properties of pyroxene and plagioclase in the system Na2O-CaO-Al2O3-SiO2

In the system Na₂O-CaO-Al₂O₃-SiO₂ (NCAS), the equilibrium compositions of pyroxene coexisting with grossular and corundum were experimentally determined at 40 different P-T conditions (1,100–1,400° C and 20.5–38 kbar). Mixing properties of the Ca-Tschermak — Jadeite pyroxene inferred from the data are (J, K): $$\begin{gathered} G_{Px}^{xs} = X_{{\text{CaTs}}} X_{{\text{Jd}}} [14,810 - 7.15T - 5,070(X_{{\text{CaTs}}} - X_{{\text{Jd}}} ) \hfill \\ {\text{ }} - 3,350(X_{{\text{CaTs}}} - X_{{\text{Jd}}} )^2 ] \hfill \\ \end{gathered} $$ The excess entropy is consistent with a complete disorder of cations in the M2 and the T site. Compositions of coexisting pyroxene and plagioclase were obtained in 11 experiments at 1,190–1,300° C/25 kbar. The data were used to infer an entropy difference between low and high anorthite at 1,200° C, corresponding to the enthalpy difference of 9.6 kJ/mol associated with the C \(\bar 1\) =I \(\bar 1\) transition in anorthite as given by Carpenter and McConnell (1984). The resulting entropy difference of 5.0 J/ mol · K places the transition at 1,647° C. Plagioclase is modeled as ideal solutions, C \(\bar 1\) and I \(\bar 1\) , with a non-first order transition between them approximated by an empirical expression (J, bar, K): $$\Delta G_T = \Delta G_{1,473} \left[ {1 - 3X_{Ab} \tfrac{{T^4 - 1,473^4 }}{{\left( {1,920 - 0.004P} \right)^4 - 1,473^4 }}} \right],$$ where $$\Delta G_{1,473} = 9,600 - 5.0T - 0.02P$$ The derived mixing properties of the pyroxene and plagioclase solutions, combined with the thermodynamic properties of other phases, were used to calculate phase relations in the NCAS system. Equilibria involving pyroxene+plagioclase +grossular+corundum and pyroxene+plagioclase +grossular+kyani te are suitable for thermobarometry. Albite is the most stable plagioclase.     

X-ray and electron-optical investigation of synthetic high-temperature plagioclases

High-temperature plagioclases NaAlSi₃O₈(Ab)-CaAl₂Si₂O₈(An) have been prepared by dry devitrification of glasses. X-ray powder photographs were taken to follow the time-temperature dependence of indicators of structural state and to determine the lattice parameters of the plagioclases as well as their K-exchanged equivalents. Transmission electron microscopy (TEM) has been used to study the anorthite-type antiphase domain textures. The results are as follows:

1. TEM and X-ray powder data suggest to subdivide the high-temperature plagioclase series into three structural regions: (a) An0 to An30–40: monalbite/analbite to high albite-type structures, (b) An60–70 to An100: anorthite-type structures, (c) An30–40 to An60–70: transitional structures assumed to represent the early stages in the development of the structural complexities found in chemically intermediate low temperature plagioclases.
2. b-Antiphase domains typical for the anorthite-type structure could be imaged in samples ranging between An100 and An67.5, whereas c-antiphase domains have only been found in An90 and An100. The b-domains developed during isothermal crystallization, rather than cooling. The transition from the anorthite-type structure (S.G.I \(\bar 1\) ) to an intermediate C \(\bar 1\) -type structure at An60–70 appears to be a gradual one.
3. The relative contribution of various structural and chemical influences on the cell edges and angles is discussed in detail. It is shown that the nonlinear variation of γ with An content is due to incomplete Al,Si disorder in the high series.

     

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.     

The thermodynamics of the I \overline{1} –P \overline{1} phase transition in Ca-rich plagioclase from an assessment of the spontaneous strain

In-situ powder diffraction measurements between 90 and 935?K on four anorthite-rich plagioclase samples (An₁₀₀, An₉₆Ab₄, An₈₉Ab₁₁ and An₇₈Ab₂₂) were used to determine the detailed evolution of these samples through the $I \overline{1} $ – $P \overline{1} $ phase transition. The c-type reflections indicative of $P \overline{1} $ symmetry were detected only in An₁₀₀, An₉₆Ab₄, whereas deviations in the evolution of the unit-cell parameters with temperature were observed in all samples, most prominently in the β unit-cell angle. The c-type reflections disappear at ~510 and ~425?K in An₁₀₀ and An₉₆Ab₄ respectively, and their intensity decreases according to a tricritical trend $ I^{2} \propto \left( {T - T_{\text{c}} } \right) $ . The cell parameter changes were used to determine the spontaneous strains arising from the transition which were modelled with Landau theory, allowing for low-temperature quantum saturation, in order to determine the thermodynamic behaviour. In An₁₀₀ tricritical behaviour was observed [T _c?=?512.7(4)?K; θ_s?=?394(4)] in good agreement with previous studies, and the c-type superlattice reflections indicative of $P \overline{1} $ symmetry persist up to the T _c determined from the spontaneous strain, and then disappear. The evolution of the spontaneous strain in An₉₆Ab₄ is tricritical at low temperatures [T _c?=?459(1) K, θ_s?=?396(5)] up to the temperature of disappearance of c-type reflections, but becomes second order beyond ~440?K. In An₈₉Ab₁₁ the strain displays second-order behaviour throughout [T _c?=?500(1) and θ_s?=?212(5)], and the c-type reflections are not detected in the powder diffraction patterns at any temperature. The apparent discrepancy between the absence of c-type reflections in temperature ranges where the cell parameters display significant spontaneous strain is resolved through consideration of the sizes of the anti-phase domains within the crystals. It is deduced that the tricritical phase transition occurs in well-ordered crystals with large domains in which the behavior of individual domains is dominant (i.e. in pure anorthite) or where the $P \overline{1} $ distortions within the domains are large enough to dominate the structural coherency strains between the domains. When both the magnitude of the $P \overline{1} $ pattern of displacements of the tetrahedral framework become smaller and the influence of the structural coherency between anti-phase domains becomes significant, the thermodynamic behavior becomes 2nd-order in character, the c-type reflections disappear, and the orientation of the spontaneous strain changes.     

The effect of Al/Si disorder on the I \bar 1-P \bar 1Co-Elastic phase transition in Ca-rich plagioclase

The influence of Al/Si disorder in the anorthite tetrahedral framework upon the I \(\bar 1\) -P \(\bar 1\) displacive transition of that framework has been investigted at high-temperature by powder X-ray diffraction. The temperature-dependence of the order parameter in a heat-treated (disordered) anorthite and a Ca-rich plagioclase has been determined from spontaneous strain measurements. Both samples show appreciable disorder, with Q _od = 0.88 in both cases. In each, the critical exponent β appears to be intermediate between values for classical tricritical (1/4) and second-order (1/2) phase transitions. This critical behaviour is consistent with a Landau potential in which the coefficient of the quartic term is positive but smaller than the coefficient of the sixth order term, corresponding to a second-order phase transition close to a tricritical point. There does not appear to be any defect strain tail near T _c and inhomogeneities in Q _od appear to be on rather a short length scale in these samples. The role of changing Q _od appears to be more important than that of changing composition (albite component). The data are interpreted using a model of a homogeneous field due to changing Q _od which renormalizes the transition temperature, T _c ^* , and the fourth order coefficient, B _eff, in the Landau expansion. The results are consistent with classical Landau behaviour, and demonstrate the care which must be taken in interpreting apparently non-classical critical exponents for phase transitions close to a tricritical point.     

Species of plated dinosaur Stegosaurus (Morrison Formation, Late Jurassic) of western USA: new type species designation needed

Stegosaurus armatus Marsh 1877, based on a partial tail and a very large dermal plate from the Morrison Formation (Late Jurassic) of Morrison, Wyoming, USA, is a nomen dubium. Valid Morrison stegosaur species (with possible autapomorphies, dermal “armor” considered if present), with most holotypes consisting of a disarticulated partial postcranial skeleton at most, include: Hypsirhophus discurus Cope 1878 (characters of incomplete vertebrae, a dorsal and a caudal; Garden Park near Cañon City, Colorado); Stegosaurus ungulatus Marsh 1879 (half skeleton with partial skull; three pairs of small flat dermal spines adjacent to terminal tail spikes; Quarry 12, Como Bluff near Como station, Wyoming; syntype is holotype of S. duplex Marsh 1887, half skeleton lacking armor; Quarry 11, Como Bluff); Diracodon laticeps Marsh 1881b (just partial dentaries with few teeth, diastema between predentary and tooth 1; Quarry 13, Como Bluff); Stegosaurus sulcatus Marsh 1887 (pair of ?tail spikes with greatly enlarged base; Quarry 13, Como Bluff); S. longispinus Gilmore 1914 (characters of distal caudal vertebrae, tail spikes: two pairs, sub-equal bases, transversely flattened, very elongate; Alcova, Wyoming); and Hesperosaurus mjosi Carpenter, Miles &; Cloward, 2001 (?Stegosaurus mjosi; partial articulated skeleton with skull, no limbs, several plesiomorphic and autapomorphic characters, dorsal plates longer than tall; Wyoming). However, the well known valid nominal species, S. stenops Marsh 1887 (12 autapomorphies, three alternating flat plates adjacent to terminal tail spikes; Garden Park), is based on a virtually complete articulated skeleton lacking only the terminal caudal vertebrae and first pair of tail spikes. It includes 17 dermal plates, is still exposed as preserved on the block, and is the current basis for Stegosaurus. The International Commission on Zoological Nomenclature (ICZN) will be petitioned to designate S. stenops Marsh 1887 as the new type species of Stegosaurus Marsh 1877 in order to conserve Stegosauria Marsh 1877 and Stegosauridae Marsh 1880 (also Stegosauroidea, Stegosaurinae).     

A new ophiuroid (Geocoma schoentalensis sp. nov.) from the Middle Jurassic of northwestern Switzerland and remarks on the family Aplocomidae Hess 1965

A new ophiuroid species from the Hauptrogenstein Formation (Middle Jurassic, Bajocian) of the Rehhag ridge near Schöntal, northwestern Switzerland, is described based on 34 specimens. The impression of an indeterminate astropectinid sea star has also been found. The fully articulated specimens have been smothered by mobile oolitic dunes or sandwaves. The site can be genetically classified as an obrution deposit and belongs to the widely recognized “Hauptrogenstein type”. The remains are assigned to the genus Geocoma d’Orbigny 1850, best known from the type species, G. carinata (Münster), from the Tithonian Plattenkalk of Zandt. As suggested by Kutscher (1997) this species also includes Ophiocten kelheimense Boehm 1889, now documented by numerous well-preserved specimens from the Plattenkalk of Hienheim. Kutscher assigned the Hienheim specimens to the genus Sinosura Hess 1964 and used both names though G. carinata has priority. Despite rather small differences Sinosura is retained as a valid genus besides Geocoma, and both are placed in the family Aplocomidae Hess 1965. Geocoma and Sinosura share small adpressed arm spines with Aplocoma d’Orbigny 1852. Aplocoma is represented by a number of Triassic and Jurassic species, and the subfamily Aplocominae is proposed herein for the three genera. A second subfamily, Ophiopetrinae, is proposed for the genera Ophiopetra Enay &; Hess 1962 and Ophiohybris Hess 1964, and is characterized by larger, erect arm spines.     

Standing stock and estimated production rates of phytoplankton and zooplankton in Narragansett Bay,Rhode Island

Seasonal changes in phytoplankton biomass and production, total zooplankton biomass, and biomass and potential production rates of the two dominant copepods, Acartia hudsonica (formerly called Acartia clausi) and Acartia tonsa are described for several stations in Narragansett Bay, R.I. Plankton in the bay behaved as a single population with simultaneous changes occurring at the upper bay (Station 5) and the lower bay (Station 1). Phytoplankton biomass was higher in the upper bay ( \(\bar x\) =16.95 mg chl a·m^?3) than in the lower bay ( \(\bar x\) =6.37 mg chl a·m^?3) and these 0269 0101 V differences in biomass were reflected in the phytoplankton production rates. The zooplankton, which was dominated by A. hudsonica in the spring and early summer and A. tonsa during summer and fall, showed no such consistent differences between the stations. Mean A. hudsonica biomass (St 1, \(\bar x\) ;=82.7 mg dry wt·m^?3; St 5, _ \(\bar x\) ;=95.2 mg dry wt·m^?3) exceeded that of A. tonsa (St 1, \(\bar x\) ;=56.7 mg dry wt·m^?3; St 5, \(\bar x\) ;=60.0 mg dry wt·m^?3). Potential production rates of the two Acartia 0269 0101 V spp. were strongly temperature dependent. Despite the higher biomass levels of A. hudsonica, low temperatures resulted in lower potential production rates ( \(\bar x\) ; St 1=7.25 mg C·m^?3 day^?1; \(\bar x\) ; St 5=10.77mg C·m^?3 day^?1) and biomass doubling times of up to 9.6 days. Potential production rates of A. tonsa at summer temperatures were high ( \(\bar x\) ; St 1=19.0 mg C·m^?3 day^?1; \(\bar x\) ; St 5=22.9 mg C·m^?3 day^?1) and biomass doubling times were generally less than one day.     

A dynamical model for the I\bar 1 - P\bar 1 phase transition in anorthite,CaAl2Si2O8

The non-ferroic triclinic to triclinic \(I\bar 1 - P\bar 1\) phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R ₁ ⁺ representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R ₁ ⁺ order parameter of the high symmetry triclinic phase \(P\bar 1_0\) (or equivalently \(I\bar 1\) ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b^* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R ₁ ⁺ order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x₀,y₀,z₀) of \(P\bar 1_0\) (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x₀, y₀, z₀), an opposite displacement at (x₀+1,y₀+1,z₀+1), and the same displacement at ( \(\bar x\) ₀+1, \(\bar y\) ₀+1, \(\bar z\) ₀+1) of \(P\bar 1_0\) . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).