Sieverts law

A diatomic gas, nitrogen for instance, dissociates into atoms when it dissolves in a metal. 

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Pressure-composition-temperature and thermodynamic relationships of of the titanium-molybdenum-hydrogen (deuterium) system are reported. 0-TiMo exhibits Sieverts Law behavior only in the very dilute region, with deviations toward decreased solubility thereafter. Data indicate that the presence of Mo in the 0-Ti lattice inhibits hydrogen solubility. This trend may stem from two factors for Mo contents >50 atom %, an electronic factor dominates whereas at lower Mo contents, behavior is controlled by the decrease in lattice parameter with increasing Mo content. Evidence suggests that Mo atoms block adjacent interstitial sites for hydrogen occupation. Thermodynamic data for deuterium absorption indicate that for temperatures below 297°C an inverse isotope effect is exhibited, in that the deuteride is more stable than the hydride. There is evidence for similar behavior in the tritide. 

Pressure-composition-temperature (P-C-T) relationships were reported for hydrogen and deuterium in a-titanium. Both systems obey Sieverts Law in the dilute region (10) i.e., the square root of equilibrium pressure is linearly proportional to the solute content. McQuillan (3) extended the hydrogen P-C-T data into the 7-phase. For a maximum equilibrium hydrogen pressure of 500... 

P-C-T Determinations Low Pressure Studies. Absorption isotherms obtained for the reaction of hydrogen with TiMo are shown in Figure 3 for 590°-392°C. These temperatures are above the decomposition temperature of /J-TiMo (see Figure 2) consequently, decomposition of the solid solution plays no role here. These data follow Sieverts Law only in the very dilute region—to hydrogen-to-metal ratios (H/M) of about 0.02. Thereafter, deviations in the direction of decreased solubility are observed. Data in the region of Sieverts Law can be used to determine the relative partial molar enthalpy and entropy at infinite dilution (47). From Sieverts Law (Equation 1), where Ks is a tempi/2 = Ksn (1)... 

Metal/hydrogen systems have been treated successfully by the assumption that, at low hydrogen concentrations, deviations from Sieverts Law result from an elastic interaction energy among the absorbed hydrogen atoms. The interaction is attractive in nature since including a hydrogen atom into an interstitial site results in a local expansion of the metal lattice. It is well known that lattice dilation exerts an attractive interaction with interstitial solute atoms. Under this... 

Deuterium absorption isotherms were determined similarly for TiMo. The temperature range examined was the same as that for hydrogen absorption, but the range of deuterium contents was significantly smaller, extending only to D/M zz 0.01. The data are presented in Figure 6. It is evident that Sieverts Law is... 

Sieverts Law c = Ks4p, where c is the subsurface concentration (solubility) of the dissolved atom in the solid metal, P is the partial pressure of the diatomic gas (sometimes replaced by the fugacity, j), and Ks is the solubility constant (temperature dependent), which is the chemical equilibrium constant between the molecular species in the gas phase and the atomic species within the metal lattice. This empirical relation was first demonstrated by Sieverts in 1929 for the solubility of hydrogen in iron. Departures from this law occur at high gas pressures and/or high concentrations of dissolved atoms. 

The hydrogen concentration in the a-phase (C ) is pressure dependent and frequently follows Sieverts law, i.e. CH=kP 2 where k is a temperature-dependent constant and P is the dihydrogen pressure. As the dihydrogen pressure is increased, saturation occurs and the metal hydride starts to form. Conversion of the saturated solution phase to hydride continues as hydrogen is added. The pressure remains constant while this conversion takes place in accordance with the Phase Rule ... 

Fig. 8.9 Hydrogen flux data from a 100 xm thick unalloyed ptdladium foiL Sieverts Law is followed very well, and the square root dependence implies that hydrogen is transported through the membrane in a dissociated form. The membrane, sealed by copper gaskets, was essentially 100% selective towards hydrogen with no leak to helium detected. Permeability at 440°C was 1.9 x 10 mol m- s-> Pa- -5...

Fig. 8.10 Hydrogen flux data of a composite membrane incorporating a Group IVB-VB material. Sieverts Law is followed very weU and a permeability at 440°C of 2.3 10 mol m s Pa was achieved. The membrane, sealed with copper gaskets, was essentially 100% selective towards hydrogen showing no detectable leak to helium. The disk withstood 33 bar differential pressure (Copyright Wiley-VCH Verlag, GmbH Co. KGaA, 2006. Adapted with permission from [8], Nonporous Inorganic Membranes.)...

Fig. 13.3 Hydrogen flux as a function of the difference in the square roots of the shell (P) and tube (Po) side pressures (Sieverts law) for Pd membrane on the PSS support with media grade 0.2 p,m...

The decomposition of alkali hydrides at higher temperatures evolves a hydrogen partial pressure even on dilute solutions in alkali metals, which obey Sieverts law ... 

In Sieverts law, nn is the hydrogen mole fraction in the solution, Ph the partial pressure of hydrogen on this solution and Ks the Sieverts constant. The value of this constant is dependent on the temperature as expressed in Eq. (21). 

The equation used to describe flux is derived from a combination of Pick s and Sieverts laws where the difference between the square root of hydrogen partial pressure on the feed and permeate sides of the membrane creates the driving force for hydrogen flux [168,169] ... 

For the 500 pm thick membrane, the thickest membrane employed, data falls fairly well on the Sieverts Law line, which is interpreted as implying that bulk diffusion of dissociated hydrogen is the rate limiting step. Experimentally measured permeability for the 500 pm membrane was 3.2 x 10 mol m" s" Pa" . As the higher feed pressures were approached (13.1 bar partial pressure hydrogen, 34 bar total pressure with heUum), some deviations from Sieverts Law were observed. These are attributed to gas phase diffusion limitations, as discussed below. 

When the membrane thickness was halved, from 500 pm to 250 pm, the hydrogen flux doubled, in accord with Sieverts Law, and the measured permeability remained at 3.2 x 10 mol m s Pa implying that bulk diffusion was the rate limiting step at lower feed pressures and that this value of permeabiUty was characteristic of the bulk membrane material. At higher feed pressures, larger deviations from Sieverts Law were seen, which is again attributed to gas phase diffusion Umitations. Evidence for this is shown in Eig. 4.4. If the concentration of hydrogen in the feed is increased from 40 mol% to 60, 80 or 100 mol%, the data... 

Figure 4.4 Data showing that observed deviations from Sieverts Law in membranes with very high permeabiiity arise from iimitations due to gas phase diffusion in the hydrogen feed. By increasing concentrations of hydrogen in the feed, the data returns to the Sieverts Law iine.

For further decrease in membrane thickness from 250 to 127 pm, the flux data shown in Fig. 4.3 no longer increase as predicted by Sieverts Law, and the permeability decreases to 2.4 x 10 mol m s Pa Arrhenius behavior also changes... 

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