Entropy terms in statistical thermodynamic analysis formula for non-stoichiometric interstitial compounds

ABSTRACT: A series of statistical thermodynamic analyses were made since 1974 for different types of non-stoichiometric interstitial compounds MXx under simplifying a priori assumption of constant interaction energy E(X-X) between nearest neighbour interstitial atoms X within a homogeneity composition range of MXx at arbitrary temperature T [K]. Mode of distribution of X atoms in interstitial sites in MXx lattice is represented by number θ of available interstitial sites for occupation by X atoms per M atom and the value of θ is determined to fulfil the a priori assumption. Mode of atomic configuration would yield major contribution to entropy term ∆S that appears in conventional thermodynamic expression of Gibbs free energy of formation, ∆G, in form of T∆S. In the statistical thermodynamic formulation, contribution of tightly bound electron appearing in form of RT ln fX where fX refers to atomic partition function of X atom in the MXx lattice and R the universal gas constant. Judging from this mathematical form of the term, R ln fX is considered to represent entropic contribution from tightly bound electron to X atom in MXx lattice. In the published series of works on statistical thermodynamic analysis for non-stoichiometric interstitial compounds, calculated values for R ln fX were reported but they were not reviewed with serious attention because R ln fX was considered merely as a secondary factor compared to principal factor E(X-M) referring to interaction energy between X and M in MXx lattice that represents enthalpy ∆H in conventional thermodynamic term. In this review article, consideration is given exclusively to the factor R ln fX evaluated in statistical thermodynamic approach to non-stoichiometric interstitial compounds.info:eu-repo/semantics/publishedVersio

Statistical Thermodynamic Analysis for Isothermal Hydrogenation Performances of Mg2-yPryNi4Intermetallics (y = 0.6, 0.8, 1.0)

Isothermal hydrogenation performances of intermetallic Mg2-yPryNi4 alloys with y = 0.6, 0.8 and 1.0 reported by Terashita et al.were analyzed on the basis of statistical thermodynamics under a simplifyinga priori assumption of constant nearest neighbourH-H interactionE(H-H) in a given phase at arbitrary T aiming at characterizing basic aspects of state of H atoms in the interstitial sites in H-storage alloy. To fulfill this a priori assumption, number θ of available interstitial sites per metal atom was chosen by preliminary search attempt at the onset of the statistical thermodynamic analysis. Primary H solution in Mg2-yPryNi4 was analyzed by the model with θ = 0.15. The chosen value 0.15 for the model analysis was close to be 1/6 (≈ 0.167) which was half of 1/3 (=[Mg + Pr]/[Mg + Pr + Ni])implying that about half of the (Mg + Pr)-related interstitial sites were provided as the available sites for occupation by H atoms in the primary H solution of Mg2-yPryNi4. On the other hand, hypo-stoichiometric M4H3 type hydride of Mg2-yPryNi4 was analyzed by the model with θ = 0.75 and θ' = 0.333 where ' refers to the lower limiting composition of the phase. This model yielded situation with E(H-H) = 0 for any Mg2-yPryNi4examined. Chosen value of θ' = 0.333 appeared to imply that the filling of Ni-related interstitial sites by H atoms started after preferential full occupation of the (Mg + Pr)-related interstitial sites by H atoms in the two-phase equilibrium range at invariable p(H2) plateau during H-charging

Suppressed hydrogen (H) solubility in body centered cubic vanadium (V) by alloying with molybdenum (Mo), chromium (Cr), iron (Fe) or cobalt (Co) appreciated in terms of statistical thermodynamics

Equilibrium isothermal pressure-composition relationships reported for H solubility in body centered cubic (bcc) V1-yMyHx (M = Cr, Mo, Fe or Co) by Suzuki et al. recently on this journal were analyzed with statistical thermodynamics under a priori assumption of constant H-H interatomic interaction energy E(H-H) within homogeneity composition range of bcc V1-yMyHx phase at arbitrary temperature T. Results of the present statistical thermodynamic analysis showed that detected H solubility suppression for the examined V1-yMyHx was consistently interpreted in terms of decrease of available number ? for occupation by H atoms per metal atom in the V1-yMy lattice from ? = 0.55 determined for bcc VHx in the earlier work of the author. The extent Q of stabilization of H atoms in the V1-yMy lattice through formation of H-V and H-M bonds was one of principal parameters determined by the statistical thermodynamic analysis. It was intriguing to note that Q(V1-yMyHx) with M = Fe and Co became less negative than Q(VHx) in pure bcc VHx implying that the extent of stabilization of H atoms in V1-yMy lattice with M = Fe or Co increased with reference to that in pure VHx in spite of decreased ? from that (0.55) in VHx. On the other hand, Q(V1-yMyHx) with M = Cr and Mo became less negative (that is decreased stability of H) than Q(VHx) corresponding straightforwardly to the detected decrease of ? value from that in VHx. Noting the promoted H permeability reported for V1-yFey membrane by Suzuki et al., search for alloying element M that induced H solubility drop form that in the bcc V but with effect of enhancing stability of H in the V1-yMy lattice was concluded to be a pragmatic guideline for the screening of alloying constituent towards development of V-based H permeation membrane material

Hydrogen absorption in epitaxial bcc V (001) thin films analysed by statistical thermodynamics

Andersson, Aits and Hjörvarsson of Uppsala Universitymeasured hydrogen uptake in epitaxial bcc (body centred cubic) vanadium (V) (001) thin films of thickness, 50 nm and 100 nm, over temperature range between 443 K and 513 K. The reported equilibriumpressure–temperature–composition (P–T–C) relationships for the epitaxial bcc V (001) thin films showed appreciable extent of enhancement ofH solubility comparedwith that for bulk bcc V. In this work, the reported equilibriumP–T–C relationships for the epitaxial bcc V(001) thin films by Andersson et al.were analysed in terms of statistical thermodynamics for H2 gas partial pressure p(H2) upto100 Pa andH/V mole atom ratio x in VHx up to 1. The present analysis results showed that, up to x=0.75, the state of H in the V latticewas comparable to that in bulk VHx specimen but that, in the range of x higher than 0.75, state of H in the thin film with the constrained basal plane condition was evidently distinguishable from that in non-constrained bulk VHx. This was concluded to be the consequence of the tetragonal distortion of the bcc lattice with biaxially constrained condition at the bottom surface of the VHx (001) thin film in the range of x exceeding 0.7

Chemical Activities, a(H) and a(X), of Constituents in H2X Type Gas Molecules (X = O or S) at Arbitrary Degree of Dissociation

Chemical activities, a(X) and a(H), of constituents, X and H, in H2X type gas molecules (X = S or O) were evaluated as functions of temperature T and extent α of dissociation adapting a thermodynamic analysis procedure developed by Katsura for interpreting enhanced a(N) and a(H) in NH3 gas molecules with suppressed α by flowing. Present analysis results showed that both H2S and H2O gas molecules are chemically rather inert even at comparatively low α unlike nitrogen-family tri-hydrides XH3 that were proved to yield high chemical activity of each constituent in a state being away from thermodynamic equilibrium. The parameter α referring to the extent of dissociation of HnX type gas molecules appears to be a significant parameter in evaluating the chemical activities, a(X) and a(H), in the HnX gas molecules that are remained non-dissociated

Roles of unstable chemical species and non-equilibrium reaction routes on properties of reaction product: a review

Chemical species might be held in a state being away from equilibrium state, at least temporarily, as represented by non-graphitic carbon and gaseous ammonia NH3 with suppressed extent of dissociation by flowing. Such chemical species X in unstable state would possess chemical activity a(X) considerably higher than that of the same element in equilibrium (reference) state. In case of carbon, a(C) of amorphous carbon is higher than that of graphite (equilibrium state of C; a(C) = 1). Thus, when metal M is reacted with excess C, carbon content x' in carbide MC x' in equilibrium with amorphous carbon becomes higher than x in MC x in equilibrium with graphite. In case of uranium carbo-nitride UC x N1–x in equilibrium with excess free C under given conditions of temperature T and N2 gas partial pressure p(N2), x' in UC x' N1–x' in equilibrium with amorphous carbon was experimentally demonstrated to be higher than x in UC x N1–x in equilibrium with graphite. Gaseous ammonia NH3 with suppressed extent of dissociation by flowing would yield very high nitrogen activity a(N) and modestly high hydrogen activity a(H) while NH3 dissociated to N2 and H2 to reach equilibrium state in closed reaction chamber would yield a(N) and a(H) to be represented by respective partial pressures, p(N2)1/2 and p(H2)1/2, in the gas phase. Synthesis of mono-nitride MoN of Mo in N2 gas was reported to be impossible even at high pressure up to 300 atm in autoclave but MoN co-existing with sub-nitride Mo2N might be synthesized in flowing NH3 gas at normal pressure. As such, unstable chemical species might allow us to synthesize novel reaction product that cannot be prepared by using stable chemical species alone in the reactant. However, special care must be taken in usage of unstable chemical species. For example, in case of non-graphitic carbon, graphitization might proceed with considerably fast rate when the reaction temperature is set to be well above 2000 K and thence no effect of high a(C) might be gained at reaction temperature exceeding 2000 K. On the other hand, in case of flowing NH3 gas, extent a of dissociation of NH3 gas would depend on the position along the flow path of NH3 gas stream (i.e., a tends to rise inevitably on going from the up-stream side to the down-stream side) as well as on the NH3 gas flow rate (i.e., a at specific position in the flow path tends to rise with diminishing NH3 gas flow rate). On the other hand, rapid solidification processing with cooling rate reaching to 106 K/s has been employed for refinement of microstructure of alloys and for extension of solubility limit as well as for formation of amorphous phases. Rapid solidification is considered as ultra-fast quenching process of high temperature micro structure, or more precisely, retention of atomistic configuration in molten state of multi-component system through extraction of heat with very high rate to inhibit atom diffusion processes to reach inherent equilibrium state defined uniquely as functions of temperature T and alloy composition. On the other hand, under certain mode of operation of solar furnace using concentrated solar beam as the reaction heat source, rapid heating to reach reaction temperature around 2000 K from ambient temperature within order of a second or even less is realized. During carbide synthesis from tungsten (W) under such operation mode of solar furnace, the authors detected evidence of formation of W m C n phases that did not correspond to the phase anticipated by referring to available equilibrium binary W–C phase diagram at the processing temperature. This experimental evidence is tentatively appreciated in terms of small energetic differences among WmCn phases with varying m/n ratios. That is, once certain W mCn phase is formed during rapid heating of W/C powder mixture, the formed phase would remain stable at the processing temperature T even if it is not the genuine equilibrium phase at T without being transformed to the genuine equilibrium phase at the specified T due to smallness of driving force for the phase transformation from a meta-stable phase W m C n to the genuine equilibrium phase W m C n. As such, deliberate usage of chemical species or processing route being away from equilibrium state might be of pragmatic convenience to synthesize novel compound of a given chemical constitution that cannot be prepared from reaction using stable chemical constituents alone or quasi-equilibrium processing route. Aspects regarding roles of unstable chemical species (non-graphitic carbon, uncracked ammonia gas) and non-equilibrium reaction routes (ultra-fast cooling/heating) on properties (chemical composition, micro structure) of reaction product are reviewed integrally from generalized standpoint of usage of non-equilibrium state for synthesis of novel reaction product.

Statistical thermodynamic approach to molten Fe–Cr–P

Statistical thermodynamic analysis was applied to the available phosphorus solubility data set for molten Fe1 –yCryPx given as functions of Cr composition y, temperature T and phosphorus activity a(P) under the assumption that the solubility limit x of P in the molten Fe1-yCry was 0.50 irrespective of y. The evaluated values of the energy parameter representing the extent of stability of P atoms in the molten Fe1– yCryPx showed an apparently realistic variation pattern with y for the level of y up to 0.465. Further, it was demonstrated by an interpolating estimation using the obtained statistical thermodynamic parameter values at two known levels of y that a(P) vs. x relationships for arbitrary y at specified T could be derived with acceptable accuracy

Thermal decomposition of δ-MoN and ε-Fe2N synthesized under concentrated solar radiation in NH3 gas stream

ABSTRACT: Decomposition temperatures of δ-MoN and ε-Fe2N synthesized with flowing NH3 gas under concentrated solar radiation heating were evaluated by Differential Scanning Calorimetry (DSC) in Argon (Ar) gas environment. The measured decomposition temperature of δ-MoN and ε-Fe2N were dependent on the solar synthesis conditions, particularly either NH3 or N2 gas flow rate at temperature. Sample containing δ-MoN showed two exothermic peaks around 680 and 900 ◦C, attributed to the reactions of δ-phase into γ-single-phase and (γ+β)-two-phase Mo2N, respectively, attributed to the dissociation reaction of δ-phase into γ-single phase and the dissociation reaction of γ-phase into metallic M saturated with N, respectively. Decomposition of ε-Fe2N took place into γ’-Fe4N in two steps occurring at 606 and 660 ◦C, respectively. When N2 instead of ammonia (NH3) gas was used, complete dissociation of γ’-Fe4N into Fe took place at around 610 ◦C. Full decomposition of γ’-Fe4N into metallic α-Fe(N) was corroborated by X-ray diffraction (XRD) analysis.info:eu-repo/semantics/publishedVersio

Synthesis of FeTi hydrogen storage material via ball milling: effect of milling energy and atmosphere.

Attempts were made earlier to synthesize and activate the FeTi intermetallic during ball milling (BM), for H2 storage using sodium boron tetra-hydride (NaBH4) additive as a process controlling agent. Simple reactive milling starting from Fe and Ti powders resulted in heavy agglomeration of powders, due to the self sustaining nature of the reaction following an incubation period. When NaBH4 was used as the process control agent to avoid agglomeration, this resulted in the production of titanium hydride besides FeTi, and as a consequence unfavorable irreversibility in the subsequent hydrogen charging/discharging cycles [1,2,12]. The present work reports on modifications introduced in the synthesis process by changing two processing parameters, namely the milling energy and atmosphere compositio

Effects of NaBH4 additions on hydrogen absorption by nanostuctured FeTi powders

Hydrogen is nowadays considered as one of the most promising fuels for the future transportation market, since it is highly energetic and its combustion products are non-toxic. There are however some inherent problems related to its handling and storage that makes its implementation difficult in the energy market [1]. One way of storing hydrogen is in form of intermetallic hydrides. Some intermetallics can store large amounts of hydrogen in their interstitial sites and, in some cases, reversible equilibrium absorption/desorption cycles might be realized near ambient temperature and normal pressure. FeTi is an intermetallic compound that is being widely studied for hydrogen storage purposes. This system has one of the highest volumetric storage capacities and can be produced at low cost [2,3]. However, the FeTi alloy prepared through conventional metallurgical process requires activation treatments at elevated temperature. It has been shown previously that the nanostructured FeTi can be activated at room temperature with the mechanical alloying of pure metallic constituents, Fe and Ti, with NaBH4 [4]. In this work nanostructured FeTi based powders were produced by mechanical alloying, and the effects of adding different amounts of NaBH4 on the hydrogen absorption capacity and on the agglomeration of the powders were studied. The effect of handling powders in a glovebox with oxygen free atmosphere or in atmospheric ambient condition was also examined. Several parameters of the as-milled powders were controlled. Among the characterization performed are phase identification and crystallite size determinations by X-ray diffraction, micro hardness measurements, scanning electron microscopy and absorption isotherms determinations