A large volume pressure cell for high temperatures

Abstract

Studies of matter under very high pressure at synchrotron radiation sources are mostly done using pressure cells with single-crystal diamond anvils. In some cases the available volume (≤ 10^?3mm³)in such cells causes problems especially at high temperature and for crystal synthesis. To ensure sufficient homogeneity of pressure and temperature, the use of cells with large sample volumes (≥ 1 mm³) is necessary.

Existing devices for such measurements are compared with a novel setup which consists of a toroidal anvil arrangement and a lightweight (50 kg) press with 250 tonnes (2.5 MN) capacity. Preliminary tests of this instrument with synchrotron radiation are reported.

Presented at the IUCr Workshop on ‘Synchrotron Radiation Instrumentation for HighPressure Crystallography’. Daresbury Laboratory 20-21 July 1991     

Stochastic theory of large-scale enzyme-reaction networks: finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.     

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order Ω(-3∕2) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order Ω(-1∕2) and variance estimates accurate to order Ω(-3∕2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.     

Crystal structure of the quaternary alloy CuTaInSe3

The crystal structure of the quaternary compound CuTaInSe₃ belonging to the system (CuInSe₂)_1‐x(TaSe)_x with x= 0.5, was analyzed using X‐ray powder diffraction data. This material is isostructural with the CuFeInSe₃ compound, and crystallize in the tetragonal space group P42c (Nº 112), Z = 1, with unit cell parameters a = 5.7831(1) Å, c = 11.6227(4) Å, V = 388.71(2) ų. The Rietveld refinement of 18 instrumental and structural variables led to R_p = 8.0%, R_wp = 9.5%, R_exp = 6.3% and χ² = 1.5 for 4501 step intensities and 144 independent reflections. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Brownian motion of an asymmetrical particle in a potential field

It is well known that a free ellipsoidal Brownian particle exhibits anisotropic diffusion for short times which changes to isotropic at long times, and, that the long-time diffusion coefficient is an average of the translational diffusion coefficients along the different semiaxes of the particle. We show analytically that in the presence of external forces, the long-time diffusion coefficient is different from that of a free particle. The magnitude of the difference in the two diffusion coefficients is found to increase proportionately with the particle's asymmetry, being zero only for a perfectly spherical Brownian particle. It is also found that, for asymmetrical particles, the application of external forces can amplify the non-Gaussian character of the spatial probability distributions which consequently delays the transition to the classical behavior. We illustrate these phenomena by considering the quasi-two-dimensional Brownian motion of an ellipsoidal rigid particle in linear and harmonic potential fields. These two examples provide insight into the role played by particle asymmetry in electrophoresis and microconfinement due to a laser trap or due to intracellular macromolecular crowding.     

Temperature variation of the fundamental absorption edge in AgGaSe2

Optical absorption measurements were made in the temperature range 9–300 K on the chalcopyrite semiconductor compound AgGaSe₂ and the optical energy gap E_G determined as a function of temperature T. In order to obtain the values of E_G as a function of T, the Elliot-Toyozawa model [R.J. Elliot, J. Phys. Rev. 108 (1957) 1384; D.D. Sell, P. Lawaets, Phys. Rev. Lett. 26 (1971) 311] was employed to perform the analysis of the optical absorption spectra. The resulting E_G vs. T curve was fitted to a semi-empirical model that takes into account both the thermal expansion and the electron–phonon interaction contributions. The results have been used to estimate values of the deformation potentials of the valence and conduction bands of the compound.     

Pronounced variation in the collective dynamics of highly correlated lightest liquid alkali metal: Lithium

Recently measured inelastic X-ray spectra (IXS) of detailed coherent dynamical structure factor S(κ, ω) and hence the equilibrium collective dynamics, of the lightest liquid alkali metal, lithium at 475 K, have been successfully explained using the modified microscopic theory of the collective dynamics of a simple liquid, in a huge wave-vector, κ, range: 1.4 nm^?1 ≤ κ ≤ 110.0 nm^?1, ?κ is the linear momentum transfer. The role of single particle motion in the collective dynamics of the liquid changes from diffusive for smaller values of wave-vector, κ < 21 nm^?1 to that of a free particle for higher κ-values, 21 nm^?1 ≤ κ ≤ 110 nm^?1. The quantum correction due to detailed balance condition in S(κ, ω) for liquid Li, whose dynamics, unlike that of quantum liquid ⁴He, is essentially classical, yields results in better agreement with the corresponding experimental S(κ, ω) and the quantum correction becomes significant for higher values of κ and ω. The wave-vector dependent variation of longitudinal viscosity, η_l, is in good agreement with the corresponding results obtained from memory function approach. The wave-vector dependent variation of single characteristic relaxation time lies in between the variation of two relaxation times of memory function approach.     

Strong-coupling dynamics of a multicellular chemotactic system

Chemical signaling is one of the ubiquitous mechanisms by which intercellular communication takes place at the microscopic level, particularly via chemotaxis. Such multicellular systems are popularly studied using continuum, mean-field equations. In this Letter we study a stochastic model of chemotactic signaling. The Langevin formalism of the model makes it amenable to calculation via nonperturbative analysis, which enables a quantification of the effect of fluctuations on both the weak and the strongly coupled biological dynamics. In particular, we show that the (i) self-localization due to autochemotaxis is impossible. (ii) When aggregation occurs, the aggregate performs a random walk with a renormalized diffusion coefficient D(R) proportiuonal to epsilon-2N-3. (iii) The stochastic model exhibits sharp transitions in cell motile behavior for negative chemotaxis, behavior that has no parallel in the mean-field Keller-Segel equations.     

Space Dependent Mean Field Approximation Modelling

It is shown that the self-consistency condition which is the basic equation for calculating the mean-field order parameter of any mean-field model Hamiltonian can be replaced by the standard Metropolis Monte Carlo scheme. The advantage of this method is its ease of implementation for both the homogeneous mean-field order parameter and the heterogeneous one. To be specific, the mean-field version of the Ising model spin system is discussed in detail and the resulting magnetization is the same as in the case of solving the respective mean-field self-consistency equation. In addition, it is shown that if a high temperature phase of such system is quenched below critical temperature then the mean field experienced by spins develops into a network of domains in analogous way as it happens with the spins in the case of the exact many-body Hamiltonian system and the coarsening processes start to take place. To show that the introduced Metropolis Monte Carlo method works also in case of the continuous variables the order parameter for the Maier-Saupe model for nematic liquid crystals has been calculated.     

An efficient implementation of a QM�CMM method in SIESTA

We present the major features of a new implementation of a QM?CMM method that uses the DFT code Siesta to treat the quantum mechanical subsystem and the AMBER force field to deal with the classical part. The computation of the electrostatic interaction has been completely revamped to treat periodic boundary conditions exactly, using a real-space grid that encompasses the whole system. Additionally, we present a new parallelization of the Siesta grid operations that provides near-perfect load balancing for all the relevant operations and achieves a much better scalability, which is important for efficient massive QM?CMM calculations in which the grid can potentially be very large.