In this paper we introduce and analyze a two-level Schwarz additive domain decomposition
method used as a preconditioner of a GMRES algorithm for solving unsymmetric systems arising
from the finite volume element or covolume methods for elliptic problems. The subproblems are
solved by inexact solvers. We show that the method converges for both circumcentric and barycentric
covolume methods. In the generous overlap case, the method is shown to be optimal, i.e., the
conditioner number is uniformly bounded in coarse and fine mesh sizes.
Lattice parameters of calcite were measured at simultaneous high pressures and temperatures up to 10 kbar and 500°C. Samples of Solnhofen limestone and distilled, deionized water were loaded in a hydrothermal diamond-anvil cell. In situ energy-dispersive X-ray diffraction was used to determine lattice parameters along five H2O isochores with densities of 1.040, 0.964, 0.760, 0.670, and 0.595 g/cm3 from 30 to 500°C; these densities correspond to the ice-melting temperature of -7.7 °C and the liquid-vapor homogenization temperatures 92.4,274.5, 318.9, and 344.6 °C, respectively. In addition, data along the P axis were collected by hydrostatic compression at room temperature and along the T axis by heating at atmospheric pressure. Our results show that anisotropic thermal expansion of calcite continues up to 10 kbar, therefore making it a good double internal X-ray standard. Both a and c lattice parameters are fitted to second-order polynomials of pressure, temperature, and a cross term.
Melanterite (FeSO4·7H2O)-rozenite (FeSO4·4H2O) and chalcanthite (CuSO4·5H2O)-bonattite (CuSO4·3H2O) equilibria were determined by humidity measurements at 0.1 MPa. Two methods were used; one is the gas-flow-cell method (between 21 and 98 °C), and the other is the humiditybuffer method (between 21 and 70 °C). The first method has a larger temperature uncertainty even though it is more efficient. With the aid of humidity buffers, which correspond to a series of saturated binary salt solutions, the second method yields reliable results as demonstrated by very tight reversals along each humidity buffer. These results are consistent with those obtained by the first method, and also with the solubility data reported in the literature. Thermodynamic analysis of these data yields values of 29.231 ± 0.025 and 22.593 ± 0.040 kJ/mol for standard Gibbs free energy of reaction at 298.15 K and 0.1 MPa for melanterite-rozenite and chalcanthite-bonattite equilibria, respectively. The methods used in this study hold great potential for unraveling the thermodynamic properties of sulfate salts involved in dehydration reactions at near ambient conditions.