Lattice Strain Parameters Research Articles

A REE-based zircon geothermometer based on improved lattice strain modeling of zircon-melt REE partition coefficients

Several methods for tracing geological processes based on the rare earth element (REE) concentrations in zircon have been proposed in recent years. Application of these methods requires quantitative knowledge of the partition coefficients (D) for the REE between zircon and co-existing phases, which may be melt, fluid, or other minerals. Precisely determining the DREE of zircon, however, is challenging. This is especially true for the light rare earth elements, which generally occur in very low concentrations in zircon. This difficulty can be overcome by modeling DREE using a prediction function based on the crystal lattice strain model. The prediction function is defined by three empirically derived lattice strain parameters: the apparent Young's Modulus E of the Zr site in which the REE resides; the ionic radius r0 of a (fictive) REE optimally fitting into this site; and the maximum partition coefficient D0 of this optimally fitting REE. In principle, these three parameters can be determined by fitting the prediction function to sets of measured DREE. The ionic radii of the REE, however, are all larger than r0 for zircon, commonly resulting in strain model fits yielding physically unrealistic values of r0, in particular. Here, we use a compilation of zircon-melt REE partition coefficients from the literature to establish a new empirical relationship between r0 and E, which is used as an additional constraint during lattice strain model curve fitting. Lattice strain parameters for literature DREE data sets of natural and synthetic zircon samples are calculated using our constraint resulting in a new parametrization of the inverse temperature dependence of D0. This parametrization enables quantitative estimates of REE-based crystallization temperatures of magmatic zircons, complementing estimates based on Ti-in-zircon geothermometry.

Three-dimensional (3D) and two-dimensional (2D) lead iodide-based perovskite materials: A comparison of material stability and ammonia gas sensitivity

Despite enormous attention on lead halide perovskite, the stability of material is of major concern that is in critical needs of attention. Lead iodide-based CH3NH3PbI3 (3D) perovskite (MIP) and (H2C=C(CH3)CO2CH2CH2NH3)2PbI2Cl2 (2D) perovskite (AMP) were synthesised and investigated for different days under various storage conditions. After few days, the original surface morphology of both samples changed and small scattered particles were found. RMS (roughness) of MIP decreased from 51.78 to 18.00 nm, while AMP showed otherwise (from 37.70 to 95.52 nm). The increase in roughness favours the diffusion of ammonia gas molecules into perovskite and consequently increases gas response properties. Based on roughness, FWHM, crystallite size, crystallinity and lattice strain parameters, it can be concluded that 2D AMP exhibited better sensing properties than 3D MIP although the finding shows superior stability of 3D over 2D due to the self-crystallization of 3D perovskite materials.

Trace element partitioning in zoned clinopyroxene as a proxy for undercooling: Experimental constraints from trachybasaltic magmas

Sector-zoned clinopyroxene records kinetic effects imposed by variable degrees of magma undercooling, ΔT, and can be utilised to track the dynamics of magmatic systems. The partitioning of trace elements into sectors grown in different crystallographic orientations can be used as a proxy for ΔT. However, an experimental assessment of the relationship between trace element zoning and ΔT has been lacking to date. Here we present trace element data from a series of undercooling crystallisation experiments on a primitive trachybasalt from Mt. Etna (Italy), at conditions of crustal storage (400 MPa, NNO + 2), and ΔT ranging from 23 to 173 °C. Changes in ΔT were modulated by varying both resting and liquidus temperatures, the latter via the melt-H2O content of the experiments. The resting temperature was retained for 24 h to ensure the attainment of near-equilibrium conditions.High-resolution elemental mapping reveals the distribution of trace elements in individual clinopyroxene zones. Increasing ΔT drives a shift from polyhedral morphologies with Al-rich prism and Al-poor hourglass sectors (ΔT = 23–25 °C), to skeletal (ΔT = 75–123 °C) and dendritic (ΔT = 132–173 °C) crystals with Al-rich skeletons and Al-poor overgrowths. Aluminium-rich zones have higher concentrations of rare earth elements (REE) and high field strength elements (HFSE) than Al-poor zones across all investigated ΔT conditions, and overall, Al, REE and HFSE contents increase with ΔT. This indicates that tetrahedral aluminium (TAl) and associated charge-balancing mechanisms govern the incorporation of REE and HFSE within clinopyroxene. Lattice strain parameters for REE in the M2 site indicate the incorporation of light relative to heavy REE in clinopyroxene is controlled by competing effects between the strain-free partition coefficient, D0, and the optimum cation radius, r0. Critically, the middle and heavy REE switch from incompatible to compatible with increasing ΔT. Used to model fractional crystallisation, our data demonstrate that fractionation of clinopyroxene at low ΔT controls pre-eruptive melt evolution. Importantly, this indicates crystallisation of clinopyroxene in the deep portions of Mt. Etna’s plumbing system is not rapid and is unlikely to result in the early formation of dendrites.We develop a parameterisation of ΔT based on REE partitioning between experimental clinopyroxene and coexisting melt, which can be applied to sector-zoned augite crystallising from mafic alkaline magmas, to reconstruct dynamic processes and thermal pathways during magma transport and storage. Applied to sector-zoned clinopyroxene microphenocrysts and groundmass microcrysts from the 1974 eccentric eruption at Mt. Etna, our parameterisation tracks an increase in ΔT with magma ascent and eruption, following recharge of Cr-rich mafic magma at depth. Sector-zoned clinopyroxene can track ΔT variations leading to volcanism at Mt. Etna and could be applied to quantify magma dynamics in other active volcanoes.

Influence of lattice strain on Er3+ ions activated magnesium zirconium phosphate phosphors: Morphological, structural, and photoluminescence properties

Rare earth ions doped alkaline metal zirconium phosphors have recently received significant attention in several applications including light-emitting diodes (LEDs) based solid-state lighting, solar panels, barcode readers and fluorescent labels focusing on the ultraviolet (UV) to visible (Vis) spectrum photoluminescence (PL) properties. Near-infrared (NIR) PL properties of rare earth ions doped magnesium zirconium phosphate (MZP) nanophosphors characteristics have not been investigated and considered as good candidates for optical amplifier and photonics applications. In this study, erbium doped magnesium zirconium phosphate (Er3+doped MgZr4(PO4)6) nanophosphors containing 0.0, 0.25, 0.5, 0.75 and 1.0 mol% Er3+ were synthesised using a sol–gel technique. The samples prepared were calcined at 900 °C. Nanopowders of the samples were examined by the transmission electron microscopy (TEM), X-ray diffraction (XRD), and Raman spectroscopy to determine the surface morphology, particle size, crystallographic phase, crystalline structure, and lattice strain. Increasing in the Er3+-ion concentrations do not have significant influence on the crystallite size, with an average crystallite size range from ∼ 28 nm to 32 nm. However, the lattice strain parameter of the Er3+ doped MZP samples decreased slightly as compared to the pure undoped MgZr4(PO4)6. The Er3+dopant was found to influence the photoluminescence properties measured at room temperature under a 980 nm excitation source. Systematic analysis revealed the presence of broad emission band corresponding to the 4I13/2→4I15/2transition. The results showed that 0.5 mol% Er3+doped sample exhibits a full width half maximum (FWHM) value of 38 nm with a long photoluminescence lifetime of 5.47 ms. The results obtained clearly demonstrates that 0.5 mol% Er3+ doped MgZr4(PO4)6 nanophosphors has a huge potential for integrated photonic applications such as lighting, biosensing, compact waveguide amplifiers, and lasers with emission properties in the IR region.

Trace element partitioning between wollastonite and alkaline silicate magmas

The partitioning of trace elements between wollastonite and melt provides a choice tool for understanding differentiation processes and trace element fractionation in alkaline-rich and silica-undersaturated magmatic systems at crustal conditions, but very few data are currently available. Here we provide the first partition coefficients and associated lattice strain parameters between wollastonite and silicate magmas of Oldoinyo Lengai (Tanzania). Trace element partitioning of isovalent cations shows a parabolic dependence between the partition coefficients and ionic radii explained by the lattice strain model with the site radius (r0) decreasing with increasing charge from r01+ = 1.2 Å to r05+ = 0.6 Å. Bivalent cations are moderately incompatible (DMg = 0.12 and DSr = 0.5) to compatible (DMn = 1). High field strength elements such as Zr and Nb are strongly incompatible in wollastonite (D < 0.01), and rare earth element (REE) partition coefficients increase with decreasing ionic radius from DLa = 0.19 to DLu = 2.8. The crystallization of wollastonite could eventually strongly influence REE fractionation (and more specifically the light-heavy REE ratios) during magmatic differentiation of alkali-rich foiditic melts and should therefore be considered to fully understand trace element evolution and partitioning in alkaline and silica-undersaturated magmas.

DOUBLE FIT: Optimization procedure applied to lattice strain model

Modeling trace element partition coefficients using the lattice strain model is a powerful tool for understanding the effects of P-T conditions and mineral and melt compositions on partition coefficients, thus significantly advancing the geochemical studies of trace element distributions in nature. In this model, partition coefficients describe the strain caused by a volume change upon cation substitution in the crystal lattice. In some mantle minerals, divalent, trivalent, and tetravalent trace element cations are mainly substituted in one specific site. Lattice strain model parameters, for instance in olivine and plagioclase, are thus fit for one crystal site. However, trace element cations can be substituted in two sites in the cases of pyroxenes, garnets, amphiboles, micas, or epidote-group minerals.To thoroughly study element partitioning in those minerals, one must consider the lattice strain parameters of the two sites. In this paper, we present a user-friendly executable program, working on PC, Linux, and Macintosh, to fit a lattice strain model by an error-weighted differential-evolution-constrained algorithm (Storn, R., and Price, K. 1997. Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341–359). This optimization procedure is called DOUBLE FIT and is available for download on http://celiadalou.wixsite.com/website/double-fit-program. DOUBLE FIT generates single or double parabolas fitting experimentally determined trace element partition coefficients using a very limited amount of data (at minimum six experimental data points) and accounting for data uncertainties. It is the fastest calculation available to obtain the best-fit lattice strain parameters while accounting for the elastic response of two different sites to trace element substitution in various minerals.

A predictive thermodynamic model for element partitioning between plagioclase and melt as a function of pressure, temperature and composition

One-atmosphere experiments in the system diopside-albite-anorthite (Di-Ab-An) have been used to explore the controls on plagioclase-melt partitioning of trace elements (Li, K, Rb, Cs, Mg, Zn, Sr, Ba, La, Sm, Y). By performing experiments along isotherms it was possible to isolate compositional controls from those of temperature. The lattice strain model accounts for variations in partition coefficients (<i>K</i>_<i>p</i>(i)) for isovalent series of cations (<i>i</i>^<i>n</i>+) and the experimental data are used to optimize the lattice strain parameters so that partition coefficients for <i>n</i> = 1 to 3 can be derived from <i>K</i>_<i>p</i>(Na), <i>K</i>_<i>p</i>(Ca), and <i>K</i>_<i>p</i>(La), respectively, at the conditions of interest. The optimized lattice strain parameters have magnitudes and compositional and thermal dependences that are consistent with elastic data for plagioclases. <i>K</i>_<i>p</i>(La) is parameterized via an exchange reaction involving CaAl₂Si₂O₈ and the La-feldspar component La_0.5Na_0.5Al₂Si₂O₈. The free energy change of this reaction is small, but well constrained by the data, such that for a given <i>P-T-X K</i>_<i>p</i>(La) can be derived from a combination of <i>K</i>_<i>p</i>(Na) and <i>K</i>_<i>p</i>(Ca). In the case where <i>K</i>_<i>p</i>(Na) and <i>K</i>_<i>p</i>(Ca) are independently constrained, the models reproduce the experimental values of 749 <i>K_p</i>s for Li, Mg, K, Rb, Sr, Y, Cs, Ba, and REE (obtained from 91 individual experiments varying over five orders of magnitude) within a factor of 1.5 for 53 percent of the data and a factor of 2 for 74 percent of the data. The isothermal experimental data reveal that additional compositional effects, arising from non-ideal mixing in plagioclase and in melt, also influence <i>K</i>_{<i>p</i>(<i>i</i>)}. A thermodynamic model based on the free energy of fusion of albite (NaAlSi₃O₈) and anorthite (CaAl₂Si₂O₈), and taking into account plagioclase and melt non-ideality in Di-Ab-An, is developed to express <i>K</i>_<i>p</i>(Na), <i>K</i>_<i>p</i>(Ca) as functions of pressure (<i>P</i>), temperature (<i>T</i>) and composition (<i>X</i>). The thermodynamic models are extended to a wider compositional range by means of an empirical parameterization of 919 <i>K</i>_<i>p</i>(Na) and 920 <i>K</i>_<i>p</i>(Ca) from a database of 991 published experiments. These models are able to reproduce 919 measured partitioning values for Li, Na, Mg, Ca, K, Rb, Sr, Y, Cs, Ba, and REE (from 91 experiments) with 47 percent of the model values within a factor of 1.5 of the measured values and 69 percent within a factor of 2 for any <i>P-T-X</i> condition. The models can also be used to constrain the dependence of the chemical potential of trace cations in plagioclase solid solutions (μ_i^pl) for use in diffusion chronometry where the fully equilibrated trace element concentration profile must be known in order to calculate timescales. It is shown that μ_i^pl is not adequately described by existing empirical models used to predict <i>K_p</i> as a function of anorthite because of the conflating effects of <i>T</i> and <i>X</i> in the polythermal experimental datasets from which those models were derived.

Vibronic Effects in Cu(II)-Doped Ba2Zn(HCO2)6·4H2O

The temperature-dependent electron paramagnetic resonance (EPR) spectrum of approximately 1% Cu(II) ions doped into Ba 2Zn(HCO2)6 x 4 H2O was analyzed at the Q-band frequencies over the temperature range 100-350 K to obtain structural information about the local environment. It can be concluded that the host crystal imparts a large orthorhombic strain which mainly corresponds to a tetragonal compression imposed onto the Cu(II)O6 species. This results in a copper center which adopts an orthorhombically distorted elongated geometry with the elongated axis perpendicular to the direction of the tetragonal compression due to the host crystal. There are two possible axes of elongation, and these represent two conformers separated by approximately 320 cm(-1). The thermal population of the higher energy level averages the g values, giving the observed temperature-dependent EPR spectra. The averaging process is between vibronic levels that are localized at two different minima of a single ground-state potential energy surface. These vibronic levels correspond to vibrational levels having different electronic properties. The determination of the host lattice strain parameters from the Cu(II) EPR spectra means that the guest ion is used as a probe of the environment of the Zn(II) site. The structural data derived from the lattice strain parameters are correlated with those from the Ba 2Zn(HCO2)6 x 4 H2O crystal structure.

Principal band gaps and bond lengths of the alloy (Al xGa 1− x) 1− zIn zP yAs 1− y lattice matched to GaAs

The principal band gaps ( E( Γ) ,E( L), and E( X)) and bond lengths ( d( x, y, z))of the alloy (Al x Ga 1− x ) 1− z In z P y As 1− y (where, 0 < x + z < 1, and 0 < y < 1) are calculated over the entire composition range based on the first order correlated function expansion (CFE) scheme. Defining the lattice strain parameter as ϵ = | d ⁡ ( x , y , z ) − d ⁡ ( 0 , 0 , 0 ) | d ⁡ ( 0 , 0 , 0 ) × 100 % , it is found that a good quality of alloy (defining ϵ < ∼ 0.5%) can be obtained in the composition region : 0 < x < ∼ 0.3, 0 < y < ∼ 0.2 and 0 < z < ∼ 0.1. The first order CFE lattice matching relations and corresponding band gaps for the alloy on the GaAs substrate are also determined. It is found that the principal band gaps of the alloy (Al x Ga 1− x ) 1− z In z P y As 1− y lattice matched to GaAs covers band gap ranges: 1.45 eV E < ( Γ) 2.69 eV, 1.80 eV < E( L) < 2.38 eV, and 1.97 eV < E( X) < 2.20 eV, while the direct band gap covers from 1.45 eV to 2.05 eV. Our theoretical prediction was compared with the existing experimental data.

Trace-element partitioning between garnet, clinopyroxene and Fe-rich picritic melts at 3 to 7 GPa

We have determined mineral-melt partition coefficients (D values) for 20 trace elements in garnet-pyroxenite run products, generated in 3 to 7 GPa, 1,425–1,750°C experiments on a high-Fe mantle melt (97SB68) from the Parana-Etendeka continental-flood-basalt (CFB) province. D values for both garnet (∼Py63Al25Gr12) and clinopyroxene (∼Ca0.2Mg0.6Fe0.2Si2O6) show a large variation with temperature but are less dependent on pressure. At 3 GPa, Dcpx/liq values for pyroxenes in garnet-pyroxenite run products are generally lower than those reported from Ca-rich pyroxenes generated in melting experiments on eclogites and basalts (∼Ca0.3–0.5Mg0.3–0.6Fe0.07–0.2Si2O6) but higher than those for Ca-poor pyroxenes from peridotites (∼Ca0.2Mg0.7Fe0.1Si2O6). Dgrt/liq values for light and heavy rare-earth elements are ≤0.07 and >0.8, respectively, and are similar to those for peridotitic garnets that have comparable grossular but higher pyrope contents (Py70–88All7–20Gr8–14). 97SB68 DLREEgrt/liq values are higher and DHREEgrt/liq values lower than those for eclogitic garnets which generally have higher grossular contents but lower pyrope contents (Py20–70Al10–50Gr10–55). D values agree with those predicted by lattice strain modelling and suggest that equilibrium was closely approached for all of our experimental runs. Correlations of D values with lattice-strain parameters and major-element contents suggest that the wollastonite component and pyrope:grossular ratio exert major controls on 97SB68 clinopyroxene and garnet partitioning, respectively. These are controlled by the prevailing pressure and temperature conditions for a given bulk-composition. The composition of co-existing melt was found to have a relatively minor effect on 97SB68 D values. The variations in D values displayed by different mantle lithologies are subtle and our study confirms previous investigations which have suggested that the modal proportions of garnet and clinopyroxene are by far the most influential factor in determining incompatible trace-element concentrations in mantle melts. The trace-element partition coefficients we have determined may be used to place high-pressure constraints on garnet-pyroxenite melting models.

Dynamic behavior of the Jahn-Teller distorted Cu(H(2)O)(6)(2+) ion in Cu(2+) doped Cs(2)[Zn(H(2)O)(6)](ZrF(6))(2) and the crystal structure of the host lattice.

The temperature dependence of the X- and Q-band EPR spectra of Cs(2)[Zn(H(2)O)(6)](ZrF(6))(2) containing approximately 1% Cu(2+) is reported. All three molecular g-values vary with temperature, and their behavior is interpreted using a model in which the potential surface of the Jahn-Teller distorted Cu(H(2)O)(6)(2+) ion is perturbed by an orthorhombic "strain" induced by interactions with the surrounding lattice. The strain parameters are significantly smaller than those reported previously for the Cu(H(2)O)(6)(2+) ion in similar lattices. The temperature dependence of the two higher g-values suggests that in the present compound the lattice interactions change slightly with temperature. The crystal structure of the Cs(2)[Zn(H(2)O)(6)](ZrF(6))(2) host is reported, and the geometry of the Zn(H(2)O)(6)(2+) ion is correlated with lattice strain parameters derived from the EPR spectrum of the guest Cu(2+) complex.

EPR of dynamic Jahn-Teller distortion in CuII doped magnesium Tutton's salt

The dynamic Jahn-Teller distortion in single crystals of CuII doped magnesium Tutton's salt, MgK2(SO4)2·6H2O was studied by EPR spectroscopy. The directions of the g tensor axes were found to coincide with those of A at room temperature as well as at 113 K and were correlated with the MgO directions in the lattice. Two spatially distinct sites of copper were detected in the crystal. The g and A values were also calculated from the polycrystalline samples at various temperatures. A dx2-y2 ground state has been assigned for CuII, as in the isomorphous zinc Tutton's salt. The Silver and Getz model was applied to understand the dynamics of Jahn-Teller (JT) activity. The system was found to undergo dynamic JT distortion at all temperatures. At low temperatures, the [Cu(H2O)6]2+ ion has three possible degenerate vibronic states corresponding to three possible directions for the long axis of the octahedron. The energy separations between the three inequivalent JT valleys were estimated as δ1,2 = 90 and δ1,3 = 370 cm−1. The lattice strain parameter V2 and the JT stabilization energy EJT were also estimated as 19,140 and 1030 cm−1 respectively. From the EJT value, the JT distortion present in the system was classified as a case of “strong” coupling.

Effects of promoter oxides on the reduction of nickel oxide

Bulk nickel oxide samples promoted with 2–3 wt.% CuO, Ag 2O, Al 2O 3 and ZrO 2 were tested for reducibility in hydrogen using three independent techniques: magnetization measurements, thermal gravimetric reduction and temperature-programmed reduction. All three showed the same trend. Reducibility, as measured by the extent of reduction at a given temperature, follows the order CuO ≈ Ag 2O ≫ none ≫ Al 2O 3 ≫ ZrO 2. X-ray diffraction indicated the absence of any promoter crystallites larger than 2.5 nm. This and the variation of derived lattice strain parameters are consistent with their successful incorporation into the NiO lattice. Lattice parameters and crystallite sizes were essentially the same. A model is proposed in which the initial stage of nickel oxide reduction is nucleation of nickel clusters, aided or hindered by the presence of more or less easily reduced cation-oxygen bonds in the surface. The conflict about the role of silver in promoting reduction of nickel oxide has been resolved. A steam reforming-type catalyst was tested for activity during self-reduction with and without promotion by Ag 2O. Moderate improvement in reducibility occurred but not when the catalyst was precalcined at 400 °C, showing that decomposition to silver metal destroys the effect.

The determination of crystallite-size and lattice-strain parameters in conjunction with the profile-refinement method for the determination of crystal structures

It is shown that the current status of the least-squares profile-refinement method, for the determination of crystal structures from X-ray and neutron powder diagrams, allows the simultaneous determination of crystallite-size and lattice-strain parameters. As profile-shape functions the Voigt, pseudo-Voigt and Pearson VII functions are considered. Formulae are obtained enabling structure refinement and size-strain analysis in the same computer run.

Thermal conductivity of near-stoichiometric (U, Pu, Nd)O 2 and (U, Pu, Eu)O 2 solid solutions

The thermal conductivities of near-stoichiometric [(U 0.8Pu 0.2),R]O 2 solid solutions containing RO 1.5(R = Nd or Eu) up to 10 mol% were determined by the laser flash method in the temperature range 700–1900 K. The thermal conductivities for the solid solutions up to about 1550 K. satisfied the phonon conduction equation K = (A + BT) −1 . The thermal conductivity decreased gradually with the increase of the rare earth content. This decrease was mainly caused by the lattice defect thermal resistance. The measured defect thermal resistivities ( = A) were in good agreement with the calculated results based on the lattice defect model in which U 4+, U 5+, Pu 4+ and R 3+ ions were considered as phonon scattering centers. The lattice strain parameter ϵ = 97 and 103 were obtained for (U, Pu, Nd)O 2 and (U, Pu, Eu)O 2 solid solutions, respectively. The lattice strain effect on the thermal resistivity was about 15 times larger than the mass difference one.

Thermal conductivity of stoichiometric (Pu, Nd)O 2 and (Pu, Y)O 2 solid solutions

The thermal conductivities of stoichiometric (Pu, R)O 2 solid solutions containing RO 1.5 (R = Nd and Y) up to 10 mol% were determined by the laser flash method in the temperature range 700–1400 K. The thermal conductivities for all solid solutions satisfied the phonon conduction equation K = ( A + BT) −1 within ± 6%. The lattice defect thermal resistivities (= A) increased gradually with the neodymium or yttrium content, while the intrinsic lattice thermal resistivities (= BT) were nearly equal to that measured for PuO 2. The measured thermal conductivities were consistent with the results of the lattice defect model calculation in which Pu 4+, Pu 5+ and R 3+ ions were considered as phonon scattering centers. The lattice strain parameters ϵ = 85 and 93 were obtained for (Pu, Nd)O 2 and (Pu, Y)O 2 solid solutions, respectively.