Elastic Strain Model Research Articles

Experimental study of the partitioning of some platinum group elements (Pd and Ir) between orthopyroxene and silicate melt

Past experiments and observations on natural samples have largely focused on the roles of olivine and chromite in controlling the behaviour of the platinum-group elements (PGE) during melting and solidification, whereas other phases, such as pyroxene, have gone largely uncharacterized. To address this, experiments have been done to measure the partitioning of Pd (with a subset of results for Ir), between orthopyroxene and silicate melt at 1340 °C, 0.1 MPa and log fO2 of FMQ − 1 to FMQ + 6 (FMQ = Fayalite-Magnetite-Quartz). The X-ray Absorption Near-Edge Structure (XANES) was measured in a subset of experiment glasses. Glass concentrations of Pd (corrected to unit Pd activity) increase from ∼6 to ∼650 ug/g over the fO2 range of experiments. The slope of the solubility-fO2 relation is consistent with Pd1+ as the dominant oxidation state, with evidence for Pd0 and Pd2+ at the lowest and highest experiment fO2, respectively. Consistent with this result, the XANES reveal spectral features similar to Pd0 and Pd2+ spectral reference materials (specRM) at the most reduced and oxidized synthesis conditions, respectively. Other lines of evidence require the presence of a third melt species, here interpreted to be Pd1+. Values of orthopyroxene/melt partition coefficients for Pd (DPdOpx/melt) are 0.0051 (+/−0.006) at log fO2 < ΔFMQ + 3, increasing with fO2 to a maximum of 0.013 at ∼FMQ + 6. Sodium partition coefficients, expected to be similar to Pd, range from 0.0061 (+/−0.00061) at FMQ + 3, increase to 0.007–0.009 at higher fO2, but with no clear systematic trend. A value for DIrOpx-melt of ∼0.6 was measured at ∼FMQ + 4, indicating significantly more compatible behaviour for Ir relative to Pd. Partitioning results are interpreted in the context of the Blundy-Wood elastic strain model in which the variation in partitioning is related to ionic radius mismatch to an optimal crystallographic site size. Based on the trend in ionic radius with oxidation state, the estimated ionic radius of Pd1+ in octahedral coordination is similar to Na1+, and comparison to previous orthopyroxene-melt partitioning experiments suggests DPd1+opx/melt and DNaopx/melt should be nearly identical, consistent with the results of this study. The ionic radius of VI-fold Pd2+ is close to the optimal M2 site size, so an increased proportion of this species with fO2 accounts for the larger values of DPdopx/melt at the highest fO2 investigated. The much larger partition coefficient for Ir is consistent with the presence of Ir2+, whose estimated ionic radius is close to Fe2+ and Mg2+, as well as predictions for the optimal M1 site size. With the assumption that DPdopx/melt = DNaopx/melt, combined with a revised value for the Pd content of the primitive mantle, a melting model is presented that better reproduces the Pd concentration of high degree melts from sulfide-free mantle sources.

Probing strain modulation in a gate-defined one-dimensional electron system

Gate patterning on semiconductors is routinely used to electrostatically restrict electron movement into reduced dimensions. At cryogenic temperatures, where most studies are carried out, differential thermal contraction between the patterned gate and the semiconductor often lead to an appreciable strain modulation. The impact of such modulated strain to the conductive channel buried in a semiconductor has long been recognized, but measuring its magnitude and variation is rather challenging. Here we present a way to measure that modulation in a gate-defined GaAs-based one-dimensional channel by applying resistively-detected NMR (RDNMR) with in-situ electrons coupled to quadrupole nuclei. The detected strain magnitude, deduced from the quadrupole-split resonance, varies spatially on the order of $10^{-4}$, which is consistent with the predicted variation based on an elastic strain model. We estimate the initial lateral strain $\epsilon_{xx}$ developed at the interface to be about $3.5 \times 10^{-3}$.

Towards Isotropic Vortex Pinning in YBCO Films with Double-doping BHO-Y2O3 and BZO-Y2O3 Artificial Pining Centers

Strong and isotropic vortex pinning landscape is demanded for high field applications of YaBa2Cu3O7-x (YBCO) epitaxial thin films. Double-doping (DD) of artificial pinning centers (APCs) of mixed morphologies has been identified as a viable approach for this purpose. This work presents a comparative study on the transport critical current density Jc (H, θ) of 3.0 vol.%Y2O3+2.0 (or 6.0) vol.% BaZrO3 (BZO DD) and 3.0 vol.%Y2O3+ 2.0 (or 6.0) vol.% BaHfO3 (BHO DD) films. Based on the elastic strain model, BaHfO3 (BHO) nanorods have lower rigidity than their BaZrO3 (BZO) counterparts, which means their c-axis alignment is more susceptible to the local strain generated by the secondary dopant of Y2O3. Considering the increasing strain field with higher BZO (or BHO doping), the higher susceptibility may result in a large portion of the BHO APCs moving away from perfect c-axis alignment and enhancing isotropic pinning with respect to the H orientation. This is confirmed since the BHO DD films illustrate a less pronounced Jc peak at H//c-axis and hence more isotropic Jc(θ) than their BZO DD counterparts. At 9.0 T, the variation of the Jc across the entire θ range (0-90 degree) is less than 18% for the BHO DD film, in contrast to about 100% for the 2.0 vol.% BZO DD counterpart. At the higher BHO concentration of 6.0 vol.%, this higher tunability of the Y2O3 leads to increased ab-plane aligned BHO APCs and hence enhanced Jc at H//ab-plane.

Transformational dynamics of BZO and BHO nanorods imposed by Y2O3 nanoparticles for improved isotropic pinning in YBa2Cu3O7-δ thin films

An elastic strain model was applied to evaluate the rigidity of the c-axis aligned one-dimensional artificial pinning centers (1D-APCs) in YBa2Cu3O7-δ matrix films. Higher rigidity was predicted for BaZrO3 1D-APCs than that of the BaHfO3 1D-APCs. This suggests a secondary APC doping of Y2O3 in the 1D-APC/YBa2Cu3O7-δ nanocomposite films would generate a stronger perturbation to the c-axis alignment of the BaHfO3 1D-APCs and therefore a more isotropic magnetic vortex pinning landscape. In order to experimentally confirm this, we have made a comparative study of the critical current density Jc (H, θ, T) of 2 vol.% BaZrO3 + 3 vol.%Y2O3 and 2 vol.%BaHfO3 + 3 vol.%Y2O3 double-doped (DD) YBa2Cu3O7-δ films deposited at their optimal growth conditions. A much enhanced isotropic pinning was observed in the BaHfO3 DD samples. For example, at 65 K and 9.0 T, the variation of the Jc across the entire θ range from θ=0 (H//c) to θ=90 degree (H//ab) is less than 18% for BaHfO3 DD films, in contrast to about 100% for the BaZrO3 DD counterpart. In addition, lower α values from the Jc(H) ∼ H-α fitting were observed in the BaHfO3 DD films in a large θ range away from the H//c-axis. Since the two samples have comparable Jc values at H//c-axis, the improved isotropic pinning in BaHfO3 DD films confirms the theoretically predicted higher tunability of the BaHfO3 1D-APCs in APC/YBa2Cu3O7-δ nanocomposite films.

(Invited) Ab Initio Studies of Strain Effects on Perovskite Oxygen Vacancy Formation and Migration Energetics

Oxygen active materials are capable of rapidly transporting oxygen and exchanging it with the environment and have a wide range of applications, including solid oxide fuel cells, gas separation membranes, oxygen sensors, chemical looping devices, and memristors. Recent work has shown that epitaxial strain can play a significant role in altering the transport of oxygen through oxygen active materials, particularly in fluorite structured compounds. However, transition metal perovskites are an important class of oxygen active materials that have received only limited attention. In this work we use ab initio methods to model the coupling of biaxial epitaxial strain with oxygen vacancy formation and migration energetics in a range of transition metal perovskites. We focus on materials of the form LaBO3, where B = [Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Ga]. We predict the formation volume and strain response of oxygen vacancy formation energy, demonstrating that non-linear coupling of strain and vacancy formation can yield responses qualitatively different than those expected from simple elasticity arguments. In particular, as first observed in Ref. [1], we show that in some cases the vacancy can weaken the bonding and lower the elastic constants, which allows the formation of a vacancy to reduce the strain energy. This effect leads to stabilization of the vacancy under both compressive and tensile strain, even though the vacancy has positive formation volume. We also predict the migration volume and the strain response of oxygen migration energetics, here finding that values are quite consistent with a simple elastic strain model.[2] We find that tensile (compressive) biaxial strain reduces (enhances) the oxygen vacancy migration barrier approximately linearly across the systems studied (Figure 1). The average decrease in migration energy is 66 meV per percent strain for a single selected hop, with a low of 36 and a high of 89 meV decrease in migration barrier per percent strain across all the systems studied. In general we find that the oxygen transport kinetics can be altered by orders of magnitude in perovskites through strain effects on both vacancy content and migration energetics. These effects could play a significant role on materials performance at interfaces and in thin-film devices. [1] W. Donner, C. L. Chen, M. Liu, A. J. Jacobson, Y. L. Lee, M. Gadre, and D. Morgan, Epitaxial Strain-Induced Chemical Ordering in La0.5Sr0.5CoO3-delta Films on SrTiO3, Chemistry of Materials 23, p. 984-988 (2011). [2] T. Mayeshiba and D. Morgan, Strain Effects on Oxygen Migration in Perovskites, Phys. Chem. Chem. Phys. 17, p. 2715-2721 (2015 ). Figure 1

Non-Linear Numerical Simulation of Coiling by Elastic Finite Strain Model

The coiling process under traction is considered, with an incoming residual stress profile (that can be sufficiently compressive to make the strip buckle): a flatness defect. This paper details a 3D non-linear numerical simulation taking into account the contact of the strip on itself, with a perfect contact law. The model relies on elastic behavior at finite strain because of large rotations. Even though the behavior is elastic, the yield Von Mises criterion is computed and gives information about flatness defects (plastic zones are approximated by zones where the yield stress is exceeded). Furthermore, the paper aims at very short computation times. The modeling strategy relies (for each time step) on two analytical sub-steps. Numerical minimization procedure is used in order apply weak boundary conditions. Results are discussed with respect to a comprehensive Finite Element simulation and good agreement is observed.

The effect of lattice strain on the diameter of BaZrO3 nanorods in epitaxial YBa2Cu3O7−δ films

An elastic strain model has been applied in an effort to understand the effect of the lattice strain on the diameter of the BaZrO3 (BZO) nanorods self-assembled into aligned arrays along the c-axis in BZO-doped epitaxial YBa2Cu3O7−δ (YBCO) thin films. The calculated elastic energy of the strained BZO/YBCO composite lattice suggests that the diameter of the nanorods is approximately independent of the doping concentration of BZO as long as the density of the nanorods is sufficiently large. An experimental confirmation was carried out using transmission electron microscopy on YBCO thin films with BZO doping varying from 2% to 6% volume concentration. The diameter of the BZO nanorods was indeed found to be approximately constant in the range of 5.2–5.9 nm. The increase of the doping concentration therefore simply leads to an increase of the nanorod density, which links directly to the matching field of the effective pinning and is consistent with the transport Jc results measured for these samples.

Built‐in elastic strain and localization effects on GaAs luminescence of MOVPE‐grown GaAs–AlGaAs core–shell nanowires

Abstractmagnified imageThe core photoluminescence emission of MOVPE‐grown GaAs–Al0.33Ga0.67As core–shell nanowires is studied as function of the relevant geometrical parameter of these nanostructures, namely the shell‐thickness to core‐radius ratio hs/Rc. The energy of the dominant emission peak was compared with values of the GaAs heavy‐ and light‐hole excitons redshifted by a uniaxial tensile strain, the latter calculated assuming perfect coherence at the core/shell interface and elastic energy equilibrium within the nanowires. Good agreement is obtained for hs/Rc &lt; 1, the intrinsic strain‐free excitonic emission being identified at 1.510 eV, and further ascribed to bound heavy‐hole excitons. For hs/Rc &gt; 1 increasingly larger redshifts (up to ∼9 meV in excess of values calculated based on our elastic strain model) are observed, and tentatively ascribed to shell‐dependent exciton localization effects.magnified imageExperimental and calculated bound exciton peak energies for GaAs–Al0.33Ga0.67As core–shell nanowires as function of their shell‐thickness to core‐radius ratio hs/Rc. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Clinopyroxene–melt trace element partitioning and the development of a predictive model for HFSE and Sc

Clinopyroxene–melt trace element partitioning experiments were carried out in the system Na2O–CaO–MgO–Al2O3–SiO2 at pressures of 1, 2.3 and 3 GPa and temperatures of 1508 to 1811 K, to investigate the effects of temperature (T), pressure (P) and composition (X) on partition coefficients. Of particular interest were elements entering the octahedral M1-site. Ion probe analyses of run products produced crystal–melt partition coefficients (D) for 16 elements (Na, Ca, Al, Cl, Sc, Ti, Fe, Zr, In, La, Ce, Nd, Sm, Ho, Yb and Hf). With the exception of D Na, partition coefficients for all elements studied decrease with increased P and T, despite the concomitant increase in the Al content of the T-site. Fitting partition coefficients for isovalent series of cations to the elastic strain model of Blundy and Wood (1994) produced values for the site radius (r 0), effective elastic modulus (E) and strain-free partition coefficient (D 0). At each pressure, E values for the M1 and M2-sites increase with increasing Al concentration in the T-site $$ \left( {X_{\text{Al}}^{T} } \right) $$ . For a given bulk composition, E values decrease with increased T. The decrease in E with increasing T accounts for the remarkable constancy of the degree of fractionation between chemically similar elements, e.g. $$ D\left( {{\frac{\text{Zr}}{\text{Hf}}}} \right) $$ , over the range of pressures studied here. $$ E_{{{\text{M}}1}}^{4 + } $$ for our experiments is found to be higher than predicted by the Hazen and Finger (1979) relationship between elastic moduli and interatomic distance. This is explained by deformation of the M1-site polyhedron leading to relative displacement and kinking of the clinopyroxene T-site chains. We developed expressions for $$ E_{{{\text{M}}1}}^{4 + } $$ , $$ r_{{0,{\text{M}}1}}^{4 + } $$ , D Sc and D Ti as functions of P, T and composition. We show the feasibility of using calculated D Ti values in the prediction of D Zr and D Hf. Scandium and Ti partition coefficients were modelled based on the thermodynamic description for the crystal–melt exchange reaction and in terms of the energetics of the different charge-imbalanced configurations produced by insertion of a heterovalent trace cation. The resulting equations produce values of D Sc and D Ti that are within a factor of 2 of other experimentally determined values. Fits of the equations along the lherzolite solidus show that D Sc remains compatible in clinopyroxene at high pressure and that ratios of Zr/Hf and Ti/Eu should vary subtly with the pressure at which melting occurred.

Laboratory Investigation of Effective Stresses' Influence on Petrophysical Properties of Sandstone Reservoirs During Depletion

Abstract An increase in effective stresses takes place in reservoirs as a consequence of fluid production, a well-known phenomenon in both shallow and deep reservoirs. It may seem reasonable to assume that permeability and porosity decrease as pore pressure declines, since both effective radial and axial stresses become intensified during reservoir depletion. However, laboratory results show that this is not always the case. Porosity certainly decreases as a result of the compaction process, which allows the breakage of grain-to-grain cement bonds. Grain particles will become more compacted as both lateral and axial effective stresses increase. On the other hand, permeability shows no definite trend. In this paper, a series of delicate experimental procedures were conducted to reveal some of the most intriguing phenomena in pore collapse and their impact on permeability. Sandstone samples were tested using a triaxial set-up. Based on the experimental results of this study, in weak reservoir formations, pore collapse does not occur suddenly. Rather, rocks gradually compact as grain-to-grain cement bonds break down. It was found that permeability indeed changes as effective stresses increase. However, the pathway to permeability was found to be much more complex than previously stipulated. It was discovered that enhancement or damage to permeability is not a function of pore collapse alone. Other factors, such as stress path, initial porosity, particle size, particle shape and particle distribution play a major role in determining what type of alteration in permeability occurs and to what magnitude that alteration would be. Introduction Traditionally, petrophysical properties data are very crucial for reserves assessment and fluid flow characterization of petroleum reservoirs. A great deal of money and effort are usually allocated in order to accurately estimate these properties. Permeability and porosity are among those properties and are by far the most important. Porosity is the key for reserves estimates while permeability is the main parameter to predict flow rates, design drawdown and, therefore, wellbore completion. Until recently, the common belief was that, once determined, these properties remain constant throughout the production life of the reservoir. Studies(1–3), including this paper, showed that this is not a realistic assumption. During the pressure depletion process, as production from the reservoir continues, effective stresses within the reservoir increase. It is understood that the effect of reservoir stresses on porosity and permeability of the reservoir is more severe when porosity and permeability are high, although some experimental studies like Hubbert and Willis(4), Voight and St. Pierre(5) and Rosepiler(6) showed this effect is still significant, even at low porosity and permeability. It is also understood that stress paths have a large influence on horizontal and vertical permeability, and also on porosity. The elastic uniaxial strain model is mostly used in reservoir engineering to describe production-induced changes in horizontal stress due to pore pressure decline (pressure depletion). It predicts the total horizontal stress by using overburden stress, reservoir pressure decrease and material mechanical parameters. The principal assumption in this model is that there is no lateral deformation (zero horizontal strain condition) during the depletion process.

Development of quaternary Fe-based bulk metallic glasses

Fe-based bulk metallic glasses have been designed using several modeling criteria. Quaternary alloys were successfully developed in the Fe-rich compositional region where the only solutes used were Cr, Nb, and B. Furthermore, the exceedingly high level of Fe, exceeding 75 wt.% in some alloys, makes this series of alloys, compositionally very close to conventional steel alloys. Therefore, their production using conventional facilities and materials is more easily attainable than previously developed bulk metallic glasses. The modeling criteria used, simultaneously analyzes the thermodynamics and kinetics of the vitrification behavior in a potential glass-forming alloy. A liquidus model, which determines and ranks the presence of deep eutectics, is used to determine the optimal compositional region. This criterion is cross-checked with an elastic strain model. Alloys compositionally located near a deep eutectic, while simultaneously containing a topology that induces significant elastic strain in a developing crystalline lattice exhibits experimentally good glass forming ability.

Derivation of the center-wavelength shift of narrow-bandpass filters under temperature change

We derive a simple equation to predict the center-wavelength shift of a Fabry-Perot type narrow-bandpass filter by using the conventional characteristic matrix method and the elastic strain model as the temperature varies. We determine the thermal expansion coefficient of substrate from the zero-shift condition of the center wavelength of the filter. The calculated shifts are in a good agreement with the experimental ones, in which the narrow-bandpass filters are prepared by plasma ion-assisted deposition on four substrates with different thermal expansion coefficients.

Crystal chemical controls on rare earth element partitioning between epidote-group minerals and melts: an experimental and theoretical study

We have experimentally determined the partitioning of REE (rare earth elements) between zoisite and hydrous silicate melt at 1,100 °C and 3 GPa. All REE behave moderately compatible in zoisite with respect to the melt and all $$ D_{REE}^{zo/melt} $$ show a smooth parabolic dependence on ionic radius. The partitioning parabola peaks at Nd $$ \left( {D_{Nd}^{zo/melt} = 4.9} \right) $$ , and the compatibility slightly decreases towards La $$\left( {D_{La}^{zo/melt} = 3.9} \right)$$ and decreases by half an order of magnitude towards Yb $$\left( {D_{Yb}^{zo/melt} = 1.1} \right)$$ . Application of the elastic strain model of Blundy and Wood (1994) to the available zoisite and allanite REE mineral/melt partitioning data and comparison with partitioning pattern calculated from a combination of structural and physical data (taken from the literature) with the elastic strain model suggest that in zoisite REE prefer the A1-site and that only La and Ce are incorporated into the A2-site in significant amounts. In contrast, in allanite, all REE are preferentially incorporated into the large and highly co-ordinated A2 site. As a result, zoisite fractionates the MREE effectively from the HREE and moderately from the LREE, while allanite fractionates the LREE very effectively from the MREE and HREE. Consequently, the presence of either zoisite or allanite during slab melting will lead to quite different REE pattern in the produced melt.

Experimental constraints on the partitioning of rhenium and some platinum-group elements between olivine and silicate melt

We have performed partitioning experiments to assess the role of olivine in controlling the behavior of rhenium and the platinum group elements (PGEs) during basalt petrogenesis. Olivines were crystallized from an iron-bearing basalt at 1 bar (105 Pa) and log fO2 of −2.6, −4.9 and −7.4 (FMQ +4.3, +2 and −0.5, respectively). In situ analyses of olivine and glass by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) reveal a homogeneous distribution of Ru, Rh, Pd, Re, and Pt, but significant Os heterogeneity at the μm scale. This latter behavior arises from the presence of undissolved Os micronuggets suspended in the melt, and included in olivine crystals. Olivine–melt partition coefficients (Ds) for Re and the PGEs follow the order: DRh>DRu≫DPd∼DRe∼DPt. With decreasing fO2, Rh and Ru become more compatible, with maximum partition coefficients of ∼2.6 and ∼2, respectively, at log fO2 of −4.9. In contrast, D values for Pd become smaller with decreasing fO2, to a value of ∼0.006 at log fO2 of −7.4. Olivine–melt partitioning of Rh, Ru, Pd, Re and Pt derived from our experiments is confirmed by the behavior of these elements in lavas that have evolved by olivine fractionation. An elastic strain model predicts the olivine–melt partitioning of these elements, excepting our measured value of DPt, which is much lower. The fO2 dependence on partitioning implies that at higher fO2 some portion of PGEs exist in higher valence states than predicted from their solubility.

The effect of Ca-Tschermaks component on trace element partitioning between clinopyroxene and silicate melt

We have studied the influence of Ca-Tschermaks (Calcium Tschermaks or CaTs) content of clinopyroxene on the partitioning of trace elements between this phase and silicate melt at fixed temperature and pressure. Ion probe analyses of experiments carried out in the system Na 2O–CaO–MgO–Al 2O 3–SiO 2, at 0.1 MPa and 1218°C, produced crystal-melt partition coefficients ( D) of 36 trace elements (Li, Cl, Sc, Ti, V, Cr, Fe, Co, Ge, Sr, Y, Zr, Nb, Mo, Ru, Rh, In, Sn, Sb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta and W), for clinopyroxene compositions between 10 and 32 mol% CaTs. Partition coefficients for 2+ to 5+ cations show, for each charge, a near parabolic dependence of log D on ionic radius of the substituting cation, for partitioning into both the M1 and M2 sites of clinopyroxene. Fitting the results to the elastic strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal-melt partition coefficients from elastic moduli. Nature 372, 452–454] we obtain results for the strain-free partition coefficients of theoretical cations ( D 0), with site radius r 0, and for the site's Young's Modulus ( E). In agreement with earlier data our results show that increasing ivAl concentration in cpx is matched by increasing D, E M1, E M2 and D 0 for tri-, tetra- and pentavalent cations. The degree of fractionation between chemically similar elements (i.e. Ta/Nb, Zr/Hf) also increases. In contrast, D values for mono-, di- and hexavalent cations decrease with increasing ivAl in the cpx. The large suite of trace elements used has allowed us to study the effects of cation charge on D 0, r 0 and E. We have found that D 0 and r 0 decrease with increasing cation charge, e.g. r 0=0.66 Å for 4+ cations and 0.59 Å for 5+ cations substituting into M1. Values of E M1 and E M2 increase with cation charge as well as with increasing ivAl content. The increase in E M2 is linear and close to the trend set by Hazen and Finger [Hazen, R.M., Finger, L.W., 1979. Bulk modulus-volume relationship for cation–anion polyhedra. J. Geophys. Res. 84 (10) 6723–6728] for oxides. E M1 values are much higher and do not fit the trend predicted by the Hazen and Finger relationship.

Trace element partitioning between wollastonite and silicate-carbonate melt

AbstractWe have performed an experimental study of the influence of varying size and charge on cation partitioning between wollastonite and silicate-carbonate melt in the system CaCO3-SiO2. The experimental conditions (3 GPa, 1420°C) lie close to the wollastonite II tc/I tc phase boundary. Results for 1+, 2+, 3+ and 4+ partitioning show parabolic dependence of partition coefficients on ionic radius, which can be fitted to the elastic strain model of Blundy and Wood (1994), wherein partitioning is described using three parameters: site radius (r0), site elasticity (apparent Young's Modulus) and the ‘strain-free’ partition coefficient (D0) for an element with radiusr0. The apparent Young's Modulus of the Ca site in wollastonite, obtained from modelling the 2+ partitioning data, is 99±3 GPa, similar to the bulk-crystal value for the polymorph wollastonite I tc.r0decreases with increasing charge on the substituent cation, whileD0also shows an approximately parabolic dependence on charge, with a maximum for 2+ cations. Partition coefficients for divalent cations Zn, Co, Fe, Cd, Mn and Pb are lower than would be predicted from their ionic radii alone, indicating a preference for the melt. This may be a consequence either of cation-carbonate complexation in the melt, or of the more distorted nature of cation co-ordination environments in melts.

Trace element partitioning between amphibole, phlogopite, and basanite melt

We have measured amphibole-melt and phlogopite-melt partition coefficients ( D) for 22 trace elements in experimentally crystallized natural basanites with the ion microprobe. The synthesized phases display an exceptional degree of homogeneity for both major and trace elements, as demonstrated by the ratio of the standard deviation to the mean counting statistics uncertainty of the measurements. In pargasitic hornblende, actinides are highly incompatible ( D = 0.001), LILE and HFSE are mildly incompatible ( D = 0.04 – 0.2and0.1 – 0.2, respectively), and REE partition coefficients vary from 0.05 to 0.6, with a maximum near Ho. Except for the LILE ( D = 0.1 – 3.7), phlogopite partition coefficients are generally lower, especially the REE ( D ≈ 0.01). The partitioning results are consistent with a model in which the variation in partition coefficient with ionic radius results from the crystal lattice strain induced by the size misfit of the substituting trace element. This result predicts a decrease in Young's Modulus ( E) with increasing size of the cation sites in the crystal lattice, and E derived for the largest site in both amphibole and phlogopite agree well with experimentally determined bulk mineral values. The ability to model partitioning with an elastic strain model provides an important link between trace element partitioning and the macroscopic properties of minerals. Relative to an anhydrous peridotite, partial melting of an amphibole or phlogopite bearing peridotite will result in no Th-U fractionation, slight LILE depletions, and, aside from Ti, no significant HFSE depletions. Thus, barring the addition of any slab components besides H 2O, partial melting of hydrated peridotite is not a plausible explanation for any of the geochemical features commonly associated with subduction zone magmas.

Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition

Four types of single-cavity, thin-film, narrow-bandpass filter whose full width at half-maximum ranges from 0.5 to 1.1 nm are produced by ion-assisted deposition of alternating TiO(2)/SiO(2) or Ta(2)O(5)/SiO(2) layers upon eight substrates having differing coefficients of linear expansion, and the temperature stability of their center wavelengths is examined in the 1540-nm wavelength region. The temperature stability is shown to be greatly dependent on the coefficient of linear expansion of the substrate upon which the filter is deposited. For the eight substrates whose coefficients of linear expansion range from 0 to 142 × 10(-7)/°C, the temperature stability of the filters ranges from +0.018 to -0.005 nm/°C. Calculations based on a newly developed elastic strain model reveal that the main reason temperature stability of the center wavelengths exhibits substrate dependency is due to a reduction in film packing density brought about by volumetric distortion of the film, which is caused by stress induced from the substrate.

Misfit dislocations in finite lateral size Si1-xGex films grown by selective epitaxy

In this paper, the reduction of misfit dislocation density on small pads of selectively grown Si1-xGex films is studied experimentally and theoretically. The experiments were performed mainly on Si1-xGex layers with x=0.12 grown on patterned substrates with pad sizes of 10×10 to 104×104 μm2. The misfit dislocations were detected by optical and transmission electron microscopy. It was observed that on small pads, misfit dislocations are generated at a significantly higher critical thickness than on extended areas, while pads of size 10×10 μm2 or smaller showed no evidence of misfit dislocations at all. The theoretical analysis was performed in two steps. First, an elastic strain model was used to calculate the pad size dependence of the critical thickness. The main hypothesis of the model is that the density of misfit dislocations is solely affected by the elastic relaxation at the edges of small epitaxial areas. This equilibrium model can explain only the experimentally observed absence of misfit dislocations on small pads; however, it predicts a critical thickness for finite sizes much lower than the observed one. Second, a kinetic approach was further performed, in which the relaxation is supposed to be due to nucleation of misfit dislocations at defects and self-multiplication. The best fit with the experimental results was obtained for time constants for generation from defects of 600 min and for self-multiplication of 7 min and a gliding velocity of 12 μm/min. While the onset of relaxation seems to be due generation at defects, the self-multiplication process determines to a great extend the density of misfit dislocations.

DNA flexibility variation may dominate DNase I cleavage.

In a previous experimental study, we proposed that the bending and torsional stiffness of DNA display a systematic sequence dependence. Subsequently, we developed an elastic strain model to quantify the sequence dependence of the bending and torsional rigidity in terms of nearest neighbor interactions and used that model to analyze the sequence dependence of the 434 repressor binding to its operator. The analysis presented here shows that, in the absence of significant local variation of DNA secondary structure, DNase I cleavage is strongly correlated with local variation in the bending flexibility as calculated from our elastic strain model and that the agreement is also quantitatively significant. It is proposed that analysis using elastic strain models will provide a preliminary set of biochemical and chemical tools to explore the relation between DNA flexibility and the binding of other proteins.