Thermodynamic Stability of Low‐k Amorphous SiOCH Dielectric Films

Si–O–C‐based amorphous or nanostructured materials are now relatively common and of interest for numerous electronic, optical, thermal, mechanical, nuclear, and biomedical applications. Using plasma‐enhanced chemical vapor deposition (PECVD), hydrogen atoms are incorporated into the system to form SiOCH dielectric films with very low dielectric constants (k). While these low‐k dielectrics exhibit chemical stability as deposited, they tend to lose hydrogen and carbon (as labile organic groups) and convert to SiO₂ during thermal annealing and other fabrication processes. Therefore, knowledge of their thermodynamic properties is essential for understanding the conditions under which they can be stable. High‐temperature oxidative drop solution calorimetry measurement in molten sodium molybdate solvent at 800°C showed that these materials possess negative formation enthalpies from their crystalline constituents (SiC, SiO₂, C, Si) and H₂. The formation enthalpies at room temperature become less exothermic with increasing carbon content and more exothermic with increasing hydrogen content. Fourier transform infrared spectroscopy (FTIR) spectroscopy examined the structure from a microscopic perspective. Different from polymer‐derived ceramics with similar composition, these low‐k dielectrics are mainly comprised of Si–O(C)–Si networks, and the primary configuration of carbon is methyl groups. The thermodynamic data, together with the structural analysis suggest that the conversion of sp² carbon in the matrix to surface organic functional groups by incorporating hydrogen increases thermodynamic stability. However, the energetic stabilization by hydrogen incorporation is not enough to offset the large entropy gain upon hydrogen release, so hydrogen loss during processing at higher temperatures must be managed by kinetic rather than thermodynamic strategies.     

White Si–O–C Ceramic: Structure and Thermodynamic Stability

While pyrolysis of a polysiloxane precursor in argon typically produces a black amorphous Si–O–C ceramic containing “free” carbon (sp² carbon), pyrolyzing the same precursor in hydrogen leads to a white amorphous ceramic with a negligible amount of sp² carbon and a considerable hydrogen content. ²⁹Si magic‐angle‐spinning nuclear magnetic resonance (MAS NMR) spectroscopy confirms the existence of very similar bonding environments of Si atoms in the Si–O–C network for both samples. In addition, ¹H NMR spectroscopic measurements on both samples reveal that the hydrogen atoms are bonded mainly to carbon. For the thermodynamic analysis, the enthalpies of formation with respect to the most stable components (SiO₂, SiC, C) of the black‐and‐white Si–O–C samples obtained after the pyrolysis at 1100°C are determined using high‐temperature oxidative drop‐solution calorimetry in a molten oxide solvent. The white ceramic is 6 kJ/g‐atom more stable in enthalpy than the black one. Although the role of hydrogen in the thermodynamic stability of the white sample remains ambiguous, the thermodynamic findings and structural analysis suggest that the existence of sp²‐bonded carbon in the amorphous network of polymer derived Si–O–C ceramics does not provide additional thermodynamic stability to the ceramic.     

Role of Interface(s) for the Growth of Ultra‐Thin Amorphous Oxides on Al–Si Alloys: A Thermodynamic Analysis

This study presents a thermodynamic analysis to predict the type of initial, amorphous oxide overgrowth (i.e., am‐Al₂O₃ or am‐SiO₂) on bare Al–Si alloy substrates. This analysis have taken into account the energies associated with both its interfaces (interface between the Al–Si alloy substrate and the thin oxide film and interface between the thin oxide film and vacuum) along with the bulk Gibbs free energy of oxide formation. This developed analysis is then applied for various parameters, such as, Si alloying element content at the substrate/oxide interface, the growth temperature, the oxide film thickness (up to 1 nm), and various low‐index crystallographic surfaces of the substrate. It is found that am‐SiO₂ overgrowth is thermodynamically preferred for a combination of lower oxide film thickness, lower growth temperature, and lower Si alloying content at the alloy/oxide interface. This is because of the overcompensation of the lower energies of both the interfaces over the bulk Gibbs free energy. Furthermore, it is found that for all cases, am‐Al₂O₃ forms a more stable interface with Al–Si alloy than am‐SiO_2.     

On the Thermodynamic Stability of Amorphous Intergranular Films in Covalent Materials

The thermodynamic origin, structure, and stability of the thin amorphous films commonly found in grain boundaries in covalent ceramics are investigated by molecular-dynamics simulation. To focus on the purely thermodynamic aspects, any kinetic effects associated with impurity-controlled interface chemistry are excluded by investigating pure silicon (described by the Stillinger–Weber three-body potential). For this single-component covalent model material, we demonstrate that all high-energy boundaries exhibit a universal amorphous structure, with a width of }0.25 nm, whereas low-energy boundaries are crystalline and much sharper. We also demonstrate that introduction of an amorphous film into a crystalline interface lowers the excess energy to a level similar to the energy of two bulk crystalamorphous interfaces. The competition between a narrow crystalline boundary structure and a wider amorphous boundary structure is shown to be governed by the relative excess energies of the atoms in the grain boundaries and in the bulk amorphous phase. These observations suggest that, in principle, amorphous grain-boundary films do not require impurities for their stabilization and that, as first proposed by Clarke, an equilibrium grain-boundary phase of uniform thickness can be the result of purely thermodynamic rather than kinetic factors.     

Phase Stability in Calcia‐Doped Zirconia Nanocrystals

Calcia‐doped zirconia exhibits all of the polymorphism seen in the yttria‐doped zirconia ceramics, but can be produced at lowered costs and in greater abundance due to the accessibility of Calcium precursors in comparison to Yttrium. Although with great challenges, there exists an opportunity to replace yttria with calcia in applications such as ionic conductors where phase stability is critical. There is a dearth of surface characterization to enable design and prediction of the polymorphism in nanoparticulate calcia–zirconia. With recent advances in water adsorption microcalorimetry, one can accurately probe surface energies of the four zirconia polymorphs: monoclinic, tetragonal, cubic, and amorphous. The surface energies can then be coupled with bulk enthalpies extracted from oxide melt drop solution calorimetry to create a nanocrystalline phase stability diagram similar to its bulk counterpart. We report here the surface and bulk thermodynamic data on polymorphs of calcia–zirconia with composition ranging from 0 to 20 mol% calcia and use it to build a nanophase diagram for this system. The effect of the humidity in the phase stability diagram trends is also addressed and demonstrated to minimize the effect of the surface energies in the overall polymorphism trends.     

Energetics and Structure of Polymer‐Derived Si–(B–)O–C Glasses: Effect of the Boron Content and Pyrolysis Temperature

The structure and properties of polymer‐derived Si–(B–)O–C glasses have been shown to be significantly influenced by the boron content and pyrolysis temperature. This work determined the impact of these two parameters on the thermodynamic stability of these glasses. High‐temperature oxide melt solution calorimetry was performed on a series of amorphous samples, with varying boron contents (0–7.7 at.%), obtained by pyrolysis of precursors made by a sol–gel technique. Thermodynamic analysis of the calorimetric results demonstrated that at a constant pyrolysis temperature, adding boron makes the materials energetically less stable. While the B‐containing glasses pyrolyzed at 1000°C were energetically less stable than the competitive crystalline components, increasing the pyrolysis temperature to 1200°C led to their enthalpic stability. ²⁹Si and ¹¹B MAS nuclear magnetic resonance (NMR) spectroscopy measurements on selected samples confirmed a decrease in the concentrations of mixed Si‐centered SO_iC_4?i and B‐centered BO_jC_3?j bonds at the expense of formation of SiO₄ and B(OSi)₃ species (indicating a tendency toward phase separation) when the boron content and pyrolysis temperature increased. In light of the findings from calorimetry and NMR spectroscopy, we propose a structure–energetic relationship in Si–(B–)O–C glasses.     

Transformation of microstructure and phase of disodium guanosine 5′-monophosphate: Thermodynamic perspectives

Microstructure and phase transformation of disodium guanosine 5′-monophosphate (5′-GMPNa₂) are extremely important for controlling the process and understanding the mechanism of crystallization. In this work, the thermodynamic properties of polymorphous 5′-GMPNa₂ especially the solubility were studied, the solubility results show that 5′-GMPNa₂ is more soluble in ethanol–water (E–W) than in isopropanol–water (I–W). The amorphous form of 5′-GMPNa₂ is more soluble than the crystalline form at the same mole fraction and temperature. Meanwhile, the crystalline forms and morphologies of the residual solids were characterized by PXRD and SEM. The results indicate that solid forms of 5′-GMPNa₂ transformed spontaneously from amorphous to crystalline when the ethanol proportion is ≥ 20%. In addition, increasing the pH facilitates the dissolution of 5′-GMPNa₂ and helps to maintain the crystalline form. The associated Gibbs free energy values were calculated to verify the trend of transformation from amorphous to crystalline 5′-GMPNa₂. These results should help to guide the industrial crystallization process and to obtain the crystalline form of 5′-GMPNa₂.     

Enthalpies and entropies of transfer of rubidium chloride from water to aqueous N,N-dimethylformamide solutions

Enthalpies of solution of rubidium chloride are measured in mixtures of water and N,N-dimethylformamide at 25°C by means of a calorimeter of the constant temperature-environment type. The standard enthalpies of solution appear to be nearly proportional to the solvent composition. Combination of the present results with Gibbs free energies of transfer given in the literature yield the entropies of transfer. The path of the Gibbs free energies of transfer from the mixtures to water is largely determined by the entropic contribution.     

Solvent‐induced crystal formation in polymers: Experimental studies and theoretical modeling of poly(vinyl alcohol) based on free‐volume concepts

A model has been developed to describe the simultaneous diffusion and solvent‐induced crystal formation in polymers based on the idea that crystal formation is governed by polymer chain mobility and a thermodynamic driving force. The polymer chain mobility is described based on solvent and polymer physical characteristics using the free‐volume theory of transport. The semicrystalline polymer‐solvent system is treated as a ternary system consisting of crystalline polymer, amorphous polymer, and solvent. The addition of solvent to the amorphous phase is assumed to increase the local free volume and facilitate movement of polymer chains, thereby enabling crystal formation. Diffusion of the solvent is assumed to occur solely in the amorphous polymer phase. The species continuity equations are formulated in volume‐averaged coordinates and give rise to a convective term due to the density change accompanying transformation of the amorphous polymer to the crystalline polymer. Accurate modeling of this problem requires that a moving boundary be considered. The model was tested using gravimetric sorption data for the poly(vinyl alcohol)‐water system. In the experimental studies, the water was initially absorbed and then a high percentage of it was expelled. The proposed model accurately describes this behavior. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45171.     

Excess enthalpy,volume, and gibbs free energy; and viscosity of acetonitrile-methylcellosolve mixtures

Molar excess enthalpies of mixing at 48.2°C, and molar excess volumes at 40°C were measured for acetonitrile-methyl cellosolve system using an isothermal phase change calorimeter and a glass dilatometer respectively. Molar excess Gibbs free energies were calculated from the isothermal vapour-liquid equilibrium data obtained in a circulation still at 70, 60 and 48.2°C. Complete isobaric vapour-liquid equilibrium data at 1 atm pressure are also reported. The kinematic viscosity of binary mixtures were measured at 40°C with an Ostwald viscometer. The VLE data are corrected for vapour phase nonideality, tested for thermodynamic consistency and correlated by Wilson equation. The viscosity data were correlated by McAllister and excess function models.     

Manipulating crystal growth and polymorphism by confinement in nanoscale crystallization chambers

The phase behaviors of crystalline solids embedded within nanoporous matrices have been studied for decades. Classic nucleation theory conjectures that phase stability is determined by the balance between an unfavorable surface free energy and a stabilizing volume free energy. The size constraint imposed by nanometer-scale pores during crystallization results in large ratios of surface area to volume, which are reflected in crystal properties. For example, melting points and enthalpies of fusion of nanoscale crystals can differ drastically from their bulk scale counterparts. Moreover, confinement within nanoscale pores can dramatically influence crystallization pathways and crystal polymorphism, particularly when the pore dimensions are comparable to the critical size of an emerging nucleus. At this tipping point, the surface and volume free energies are in delicate balance and polymorph stability rankings may differ from bulk. Recent investigations have demonstrated that confined crystallization can be used to screen for and control polymorphism. In the food, pharmaceutical, explosive, and dye technological sectors, this understanding and control over polymorphism is critical both for function and for regulatory compliance. This Account reviews recent studies of the polymorphic and thermotropic properties of crystalline materials embedded in the nanometer-scale pores of porous glass powders and porous block-polymer-derived plastic monoliths. The embedded nanocrystals exhibit an array of phase behaviors, including the selective formation of metastable amorphous and crystalline phases, thermodynamic stabilization of normally metastable phases, size-dependent polymorphism, formation of new polymorphs, and shifts of thermotropic relationships between polymorphs. Size confinement also permits the measurement of thermotropic properties that cannot be measured in bulk materials using conventional methods. Well-aligned cylindrical pores of the polymer monoliths also allow determination and manipulation of nanocrystal orientation. In these systems, the constraints imposed by the pore walls result in a competition between crystal nuclei that favors those with the fastest growth direction aligned with the pore axis. Collectively, the examples described in this Account provide substantial insight into crystallization at a size scale that is difficult to realize by other means. Moreover, the behaviors resulting from nanoscopic confinement are remarkably consistent for a wide range of compounds, suggesting a reliable approach to studying the phase behaviors of compounds at the nanoscale. Newly emerging classes of porous materials promise expanded explorations of crystal growth under confinement and new routes to controlling crystallization outcomes.     

Thermodynamic properties of DyNi intermetallic compounds

Electromotive force (EMF) measurements for various DyNi intermetallic compounds in two-phase coexisting states were carried out in the temperature range of 673-773 K in a molten LiCl-KCl-DyCl₃ (0.5 mol%) system. The activities and relative partial molar Gibbs free energies of Dy were obtained from the measured EMFs for various DyNi intermetallic compounds, DyNi₂, DyNi₃, Dy₂Ni₇, and DyNi₅. The relative partial molar entropies and enthalpies of Dy were also calculated from the temperature dependence of the EMFs. The activities and relative partial molar properties of Ni in the compounds were calculated from the activities of Dy by using Gibbs-Duhem equation. Finally, the standard Gibbs free energies of formation for the DyNi intermetallic compounds were estimated.     

Thermodynamics of hydrogen bonding in coal-derived liquids. Failure of the Bolles-Drago approach applied to mixtures

The validity of using the Bolles-Drago technique to calculate thermodynamic functions for the hydrogen bonding interactions of an acid with a pair of bases was tested by computer. Sets of ‘data’ were calculated for five cases having different enthalpies and free energies of association and these ‘data’ were used in the Bolles-Drago treatment to recalculate the thermodynamic perameters. If the enthalpies and free energies of association of the acid with the two bases are different, the Bolles-Drago treatment fails.     

Amorphous-to-crystalline transition of silicon-incorporated anodic ZrO2 and improved dielectric properties

Sputter-deposited zirconium and Zr-16 at.% Si alloy have been anodized to various voltages at several formation voltages in 0.1 mol dm⁻³ ammonium pentaborate electrolyte at 298 K for 900 s. The resultant anodic films have been characterized using X-ray diffraction, transmission electron microscopy, Rutherford backscattering spectroscopy, glow discharge optical emission spectroscopy, and electrochemical impedance spectroscopy. The anodic oxide films formed on Zr-16 at.% Si are amorphous up to 30 V, but the outer part of the anodic oxide films crystallizes at higher formation voltages. This is in contrast to the case of sputter-deposited zirconium, on which the crystalline anodic oxide films, composed mainly of monoclinic ZrO₂, are developed even at low formation voltages. The outer crystalline layer on the Zr-16 at.% Si consists of a high-temperature stable tetragonal phase of ZrO₂. Due to immobile nature of silicon species, silicon-free outermost layer is formed by simultaneous migrations of Zr⁴⁺ ions outwards and O²⁻ ions inwards. An intermediate crystalline oxide layer, in which silicon content is lower in comparison with that in the innermost layer, is developed at the boundary of the crystalline layer and amorphous layer. Capacitances of the anodic zirconium oxide are highly enhanced by incorporation of silicon due to reduced film thickness, even though the permittivity of anodic oxide decreases with silicon incorporation.     

Excess Gibbs free energy and excess enthalpy for mixtures of benzene and 1,1,2-trichlorotrifluoroethane

The rapid measurement of static vapour pressures of binary liquid mixtures as a function of composition by a new continuous-dilution apparatus is described. These measurements, together with the computed excess Gibbs free energies, are reported for mixtures of benzene and 1,1,2-trichlorotrifluoroethane at 283.30, 287.83, 293.21, 298.21, 303.06 and 308.15 K over the full composition range, and are compared with the results of Linford and Hildebrand. The excess enthalpies were measured directly at 303.15 K using a batch calorimeter. The equimolar excess enthalpy is + 754 J mol^?1, which is close to the value, + 727 J mol^?1, calculated from the temperature dependence of the computed equimolar excess Gibbs free energies.     

Biaxial orientation in LLDPE films: Comparison of infrared spectroscopy,X‐ray pole figures,and birefringence techniques

In this study, linear low‐density polyethylene films were produced using different processes (film blowing and biaxial orientation) and processing conditions. The orientation of the films was characterized in terms of their biaxial crystalline, amorphous, and global orientation factors using birefringence, tilted incidence polarized Fourier Transform Infrared Spectroscopy (FTIR), and X‐ray diffraction pole figures. Evaluation of a simplified FTIR procedure without the use of the tilted method for the determination of crystalline orientation factors proposed in the literature is also evaluated and assessed. The results indicate that FTIR overestimate the crystalline orientation factors, particularly for the crystalline a‐axis. Significant discrepancies are also observed for the b‐axis orientation, which may be due to an overlap of the amorphous phase contribution. Those differences are larger for films with low orientation, such as blown films. Amorphous phase orientation from FTIR depends on the band used and is not necessarily in agreement with that determined from the combination of X‐ray and birefringence. The simplified FTIR procedure is proven to be inadequate in the case of linear low‐density polyethylene blown films studied having a random lamellar crystalline morphology. POLYM. ENG. SCI. 46:1182–1189, 2006. © 2006 Society of Plastics Engineers.     

Thermodynamics of flat thin liquid films

The two main themes of this study aim to resolve conflicting results in the literature regarding the thermodynamics of flat (uniform thickness) thin liquid films. One of the themes concerns the augmented Young equation, which is a condition for mechanical equilibrium. Two different expressions for the augmented Young equation have appeared in the literature. It is shown that under certain assumptions, the two expressions can be made equivalent. The second main theme addresses thermodynamic functions describing systems with non‐pressure‐volume (non‐PV) work. In thin liquid films, the non‐PV work is the film tension work. Two different expressions that relate the film's Gibbs energy to its internal energy have appeared in the literature. This ambiguity is resolved by showing that only one of the Gibbs energies can be used to determine the equilibrium state via energy minimization. The analysis can be readily generalized to systems with other types of non‐PV work. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3104–3115, 2015     

Critical Evaluation and Thermodynamic Modeling of the MgO–MnO–Mn2O3–SiO2 System

A complete literature review, critical evaluation, and thermodynamic optimization of phase diagrams and thermodynamic properties of the MgO–MnO–Mn₂O₃–SiO₂ system at 1 atm pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model considering the short‐range ordering in molten oxide, and the Gibbs energies of solid solutions were described using the Compound Energy Formalism considering the crystal structure of each solid solution. A set of optimized model parameters of all phases was obtained which reproduces all available and reliable thermodynamic data and phase diagrams within experimental error limits from 25°C to above the liquidus temperatures over the entire range of composition under the oxygen partial pressures from metallic saturation to 1 atm. The database of the model parameters can be used along with software for the Gibbs energy minimization to calculate any phase diagram section and thermodynamic property within the present system.     

Oxidation behaviour of ceramic fibres from the Si–C–N–O system and related sub-systems

The oxidation of Si–C–N–O fibres has been investigated. The oxidation rates and the activation energies for the Si–C–O system are similar to those for crystalline SiC. The oxygen and the free carbon concentrations in the ceramics have a limited influence on the oxidation behaviour. As long as the formed silica scale is protective, oxidation kinetics are essentially controlled by the diffusion of oxygen through SiO₂. The parabolic rates in the Si–C–N–O and Si–N–O systems are lower and their activation energies higher than those for SiC. Their values strongly depend on the ratios of C and N bonds to Si and continuously vary from those for SiC (E_a=110−140kJ mol⁻¹) to Si₃N₄ (E_a=330–490 kJ mol⁻¹). The oxidation mechanism might be related to a complex diffusion/reaction regime via the formation of an intermediate silicon-oxynitride (like for Si₃N₄) or silicon-oxycarbonitride layer. The oxidation behaviour of such complex systems is not significantly influenced by the oxygen nor the free carbon contents. It might be governed by the C/Si and N/Si ratios, limiting the nitrogen concentration gradient of the silicon-oxy(carbo)nitride sub-layer and therefore affecting the diffusion/reaction rates.