What Can Be Inferred From the Results of Scheme a About the Relative Thermodynamic Stabilities

Natural Gas Conversion VI

E.G. Wilcox , ... G.W. Roberts , in Studies in Surface Scientific discipline and Catalysis, 2001

4 CONCLUSIONS

Thermodynamic calculations testify that the equilibrium for the straight synthesis of acetic acrid from methane and carbon dioxide is highly unfavorable. However, the DRIFTS studies show the formation of acetate over a 5%Pd/carbon catalyst exposed to CO ₂ and CH₄. The spectra show no prove of the formation of syngas or methyl formate, which are other possible reactions. Nosotros have demonstrated here, the feasibility of the direct synthesis of acetic acid from CO₂ and CH₄ over a solid catalyst. Further work to overcome the thermodynamic limitations of the reaction is underway.

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Metal dusting of ferritic Fe–Al–M–C (One thousand = Ti, 5, Nb, Ta) alloys in CO–H2–Water gas mixtures at 650 °C

A SCHNEIDER , J ZHANG , in Corrosion past Carbon and Nitrogen, 2007

10.3 Thermodynamic calculations

Thermodynamic calculations were performed using the software Thermo-Calc [ 24] with the SGTE SSOL database [25]. The κ-phase Fe₃AlC _X was introduced separately equally a line compound with an average fixed composition Fe₃AlC_0.565 according to Kumar and Raghavan [26]. In the calculations, the carbides, Laves phase and ferrite were considered to be possible components in the phase equilibria of the alloys. For the Ta-containing system information technology is non possible to perform the calculations, considering in that location is no thermodynamic clarification of TaC bachelor in the SSOL database. Graphite formation was not considered in the calculations.

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Single step synthesis of transition metal nanoparticles in aqueous phase for catalytic applications

Anand Kumar , ... Leo J.P. van den Broeke , in Proceedings of the 4th International Gas Processing Symposium, 2015

3 Results and Discussion

3.one Thermodynamic investigation:

Thermodynamic calculations were performed to investigate the possibility of synthesizing pure transition metal nanoparticles by using the SCS reagents. Anhydrous metal nitrates of Ni, Cu and Co were used as metal precursors and glycine was added in an appropriate ratio determined by the equation (1) with varying φ values to obtain metal and metallic-oxide distribution in individual metal-nitrate glycine systems. As seen in equation (ane), the reaction products are mainly gases except the metal oxide (or metallic, in some cases), and so the amount of gases produced were also monitored forth with the solid products and adiabatic combustion temperature.

Fig two shows the thermodynamically predicted adiabatic combustion temperature for the three metals investigated. In all the 3 cases an optimum value of φ (φ = one − one.25) is obtained giving maximum combustion temperature. For Ni and Co systems the maximum temperature was 1954°C and 1939°C respectively at φ = i. For Cu system the maximum temperature was 1922 at φ = 1.2 − 1.25. The maximum combustion temperature at φ = ane is expected from scheme (1) equally it gives the stoichiometric condition and optimum amount of fuel is present for consummate combustion of the reactants. For φ < 1, being a fuel lean case, part of free energy is utilized in decomposing the boosted metallic nitrate resulting in a lower temperature, and φ > i could upshot in an incomplete combustion every bit excess amount of reducing agent is nowadays in the system. The optimum combustion temperature for Cu system could be at a φ value slightly more than 1 as there are multiple oxidation states of Cu (Cu(0), Cu(I) or Cu(II)) which could consequence in extra enthalpy exchange during reduction from higher oxidation land to a lower one.

Figure 2. Adiabatic combustion temperature in metal-nitrate glycine systems

The amount of gases released during SCS process for three metals are shown in Fig 3. In each case, total gas phase products increase monotonically with φ, which is in agreement with equation (1). If the metal nitrate amount is kept abiding, increasing φ will result in an increased fuel content producing more than gases per unit solid subsequently combustion. At higher φ values single stage reduced metal is obtained as the just solid production (discussed after) in all the three cases. This could be the reason why equal corporeality of gases are obtained at high φ, as the maximum valency is same (equation (ane), 5 = 2) for all the 3 metals. The gases released during combustion contribute towards porosity of the synthesized materials, leading to high surface expanse. As discussed later in the experimental section, the microstructure of the SCS products displays high porosity attributable to these gases.

Effigy 3. Predicted total amount of gases released during SCS

So far, on the basis of above discussions it can be concluded that the amount of fuel content (proportional to φ) affects the combustion temperature and the gaseous products distribution resulting in an expected loftier porosity. As discussed in the following sections, the φ value also affects the nature (metal, metal – oxide or mixture) and the nanoparticle size of synthesized products.

The solid products distributions in SCS process for Ni, Cu and Co SCS systems are presented in Fig 4a, Fig 4b and Fig 4c respectively. In each instance, at low φ values, fully oxidized metals are obtained (NiO, CuO and CoO) which gradually reduce to zero valence metals with increasing φ values. Nickel and Cobalt display simply two oxidation states (Ni(0) and Ni(II); and Co(0) and Co(II)) and follow a similar reduction contour. Completely reduced Ni and Co phases can be obtained for φ ≥ i.25 and φ ≥ ane.v respectively. Copper on the other hand shows three different phases equally the φ value is inverse. For φ ≤ 0.5 pure Cu(II) is obtained, while for 1.2 ≥ φ ≥ 0.five   a mixture of Cu(0), Cu(I) and Cu(II) is obtained and college values of φ > one.2 produce single stage Cu(0). As predicted in other publications [five, 6] the SCS process appears to go along by producing metallic oxide first, and so subsequent reduction of metal oxide to pure metal in presence of higher fuel content.

Effigy 4. Predicted solid products distributions in SCS systems; (a) Ni-nitrate glycine, (b) Cu-nitrate glycine, and (c) Co-nitrate glycine

These thermodynamic calculations point the possibility of synthesizing pure transition metals (Ni, Cu and Co) in their reduced states by SCS method. Similar calculations can be performed for other metals (e.1000. Iron, Zn etc.) to investigate the feasibility of their synthesis using SCS method. Some synthesis experiments were carried out to verify the in a higher place predictions. The following sections present the experimental synthesis Ni every bit an example displaying the possibility of synthesizing transition metals using SCS process.

3.ii Experimental investigations for synthesizing transition metals using SCS method

The experimental synthesis of Ni metallic was carried out by using nickel nitrate and glycine precursors. The amounts of reactants were calculated based on the synthesis of 3g of final product post-obit the equation (1). These precursors were dissolved in 75ml of deionized water in a beaker of 400ml capacity to make a homogeneous solution which was heated over a hot plate until ignition temperature is reached, once ignited the combustion proceeds automatically without requiring further external heating.

A typical time temperature profile for SCS is shown in Fig 5. The contour was obtained by recording the temperature values with time for a Ni-nitrate glycine system (φ = 1.0). Every bit it can be seen, after evaporation of water at 100°C, the mixture temperature increases, until it reaches a point (T_ig), where the exothermic reaction starts. Thereafter the mixture temperature increases to a maximum value in a short flow of time, resulting in high heating charge per unit. Depending on the nature of the reaction system, the heating rate could be as high as few 1000 Kelvins per second [two, 11, xx]. After combustion, the temperature of the synthesized materials decreases rapidly equally shown in Fig 5. This fast cooling of products, to some extent, prevents the product sintering resulting in smaller particles and loftier area.

Figure 5. A typical time-temperature profile in SCS processes

As discussed in earlier sections, the gases released during SCS process will form channels while escaping the synthesis organization and thus produce highly porous microstructure, which is confirmed past the SEM shown in Fig 6. The value of φ is predictable to affect the pore size distribution and total pore book (not shown) of the synthesized nanoparticles equally it directly controls the amount of gases produced during SCS procedure. A number of experiments were carried out by varying the φ value to investigate the combustion temperature and the solid product phase experimentally, as summarized in Table ane. As φ is changed, combustion temperature as well changes and a temperature peak is obtained at an optimum φ. The combustion temperatures recorded in Table 1 are lower than the predicted values from thermodynamic calculations. This difference could be due to following factors:

Figure half-dozen. A typical microstructure of SCS products

Tabular array 1. The effect of fuel content on combustion temperature and the product stage

φ	Combustion Temperature	Production Phase
0	-	NiO
one	251	NiO/Ni
1.75	417	Ni
3.5	444	NiO/Ni
5.two	651	NiO/Ni
vii	512	NiO/Ni

•

The experimental atmospheric condition are not perfectly adiabatic, as they were performed in open air.

•

The thermodynamic calculations were based on anhydrous precursors and did not include the crystalline h2o as well as the water used for dissolving the precursors.

Tabular array 1 as well shows the nature of solid product obtained, which is based on the XRD results. XRD results for selected φ values are shown in Fig seven. At lower φ values NiO is obtained which gradually reduces to pure Ni at φ = 1.75. Increasing φ to higher values again starts to produce NiO, which could be due to re-oxidation of the Ni metals in open up air and in presence of large amount of fuel.

Figure seven. XRD patterns for Ni-nitrate glycine SCS systems at various ϕ values

The experimental combustion temperature and crystallite size (obtained from XRD for Ni and NiO peaks) for various φ values are plotted in Fig 8. As expected, the crystallite size for both Ni and NiO nanocrystals incrases with increment in temperature and gives an optimum φ value for getting largest crystallite size. Controlling the combustion temperature would help in controlling the crystallite size of the nanoparticles.

Figure eight. combustion temperature, crystallite size every bit a office of phi

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Energy Conversion

Ibrahim Dincer , Murat Due east. Demir , in Comprehensive Free energy Systems, 2018

4.7.ix.1.2 Results and discussion

Thermodynamic calculations of each system component are performed past using EES software. The values of temperature (One thousand), pressure (kPa), mass flow rate (kg/s), specific enthalpy (kJ/kg), specific entropy (kJ/kg Thou), and exergy (kJ/kg) are adamant for each state bespeak of the system as listed in Table 9.

Table nine. Thermodynamic data for all state points

Land No.	Stream	T (K)	P (kPa)	m (kg/s)	h (kJ/kg)	s (kJ/kg·K)	Ex (kW)
0	Air	298.2	100	–	104.viii	0.3669	–
0`	Water	298.two	100	–	298.iv	6.864	–
one	Air	298.2	100	41.99	298.4	6.862	0
2	Air	706.3	1410	41.99	720.half dozen	six.989	16,141
3	Combustion gases	1207	1410	42.54	1287	7.593	33,394
four	Combustion gases	753.6	100	42.54	771.six	seven.82	7986
5	Combustion gases	400	100	42.54	401.2	7.159	611.9
6	Water	334.2	800	5.397	256	0.8433	49.ii
7	Water	630	800	5.397	3176	7.431	5206
8	H2o	333.two	nineteen.93	5.397	2373	7.431	873.8
nine	Water	333.ii	nineteen.93	5.397	251.2	0.8312	42.half-dozen

Equally seen in Table 9 and Fig. 39, the highest exergy destruction rates are adamant in the combustion chamber and gas turbine. The summation of exergy destruction rates of two components has more than than fifty% of the total destruction rates in the system. It is because of the irreversibilities of these elements. Equally presented in Tabular array ix and Fig. 39, the exergy destruction charge per unit of the pump has the everyman share in the overall organisation (less than ane%). The principal reason for this state of affairs is that h2o enters the pump at low temperature and its temperature slightly increases inside the pump. Thus, even the pump has a poor exergy efficiency (see Fig. twoscore), along with the lowest exergy destruction charge per unit of the cycle. The compressor has the highest exergy efficiency by 91%. It has the highest efficiency as the heat losses through the surface of the compressor are neglected.

Fig. 39. Exergy destruction ratios in the arrangement.

Fig. 40. Exergy efficiencies of the system components.

The produced powers past the organization elements are comparatively illustrated in Fig. 41. As it is expected, the highest power is generated by the gas turbine with 21,937 kW and followed past the steam turbine with 3726 kW power production. The power generation by the steam turbine presents the recovered power by the implementation of the bottoming wheel.

Fig. 41. Generated power past organisation components.

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Development of sorbents used in dry out syngas purification

Makoto Kobayashi , in Dry Syngas Purification Processes for Coal Gasification Systems, 2021

four.2.1 Basic chemistry of halide removal sorbent

Thermodynamic calculation of the equilibrium for halogenation of brine metals and element of group i earth metals predicts their potential for reducing halide concentration in syngas [ 4]. The estimation suggests that sodium aluminate has more potential than sodium carbonate for reducing the concentration of hydrogen chloride in syngas. Sodium aluminate, NaAlO₂, is attributed to the double oxide of sodium and aluminum from its crystal structure, which is the cause of the lower equilibrium concentration of hydrogen chloride removal. The reaction scheme of sodium aluminate is rather elementary compared with that of zinc ferrite desulfurization sorbent. The reaction scheme of assimilation of hydrogen chloride with sodium aluminate tin can be expressed as in Eq. (4.13), for case. Regeneration of sodium-based halide sorbent is almost impossible due to the nature of sodium chloride (salt) produced during the absorption. The salt bond is quite strong, estimated as −787   kJ/mol by Born–Haber bike. The practical methodology to divide the ionic bond is electrolysis, which is an industrial process for the product of sodium hydroxide, NaOH, and chlorine, Cl₂, from the aqueous solution of NaCl. Consequently, online regeneration of the spent sodium aluminate sorbent is non established. Basic chemistry of sodium aluminate sorbent is limited to the absorption reaction, Eq. (4.thirteen), and the possible side reaction shown in Eq. (four.xiv). The latter reaction may occur in syngas at a lower temperature range equally well as in an ambient environment under the existence of atmospheric carbon dioxide.

(4.13) ${\text{NaAlO}}_2+\text{HCl}\rightleftarrows \text{NaCl}+\frac{\mathrm{i}}{\mathrm{ii}}{\text{Al}}_{\mathrm{two}}{\text{O}}_{\mathrm{iii}}+\frac{\mathrm{ane}}{2}{\text{H}}_{\mathrm{two}}\text{O}$

(four.14) $\mathrm{two}{\text{NaAlO}}_{\mathrm{two}}+{\text{CO}}_2\rightleftarrows {\text{Na}}_{\mathrm{ii}}{\text{CO}}_3+{\text{Al}}_2{\text{O}}_{\mathrm{iii}}$

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Catalytic reforming: a sustainable technology for hydrogen production

Carole Tanios , Madona Labaki , in Recent Advances in Renewable Energy Technologies, 2022

v.two.3 Thermodynamic study

Thermodynamic calculations testify that the principal dry reforming reaction [ Reaction (5.1a)] is not spontaneous at atmospheric force per unit area and a temperature below 633°C (ΔG>0) given its strongly endothermic grapheme. In improver, the C–H bail of the methyl hydride molecule is very stable with a high dissociation energy, of the club of 435   kJ/mol. Then, to achieve expert conversion of methane in the reforming reaction, high temperature is required in order to dissociate the C–H bond. On the other hand, at temperatures in a higher place 633°C, where the reforming reaction is spontaneous, other side reactions may take identify [Reactions (five.1d), (5.1e), (5.1f)], significantly affecting the targeted reaction [Reaction (5.1a)]. Fig. five.1 shows the variations of the equilibrium constants of the reactions involved as a function of temperature.

Figure five.one. Variation of the equilibrium constants as a role of the temperature of: (1.a) the dry reforming of methyl hydride, (1.b) the opposite water gas shift; (1.c) the methanation reaction; (1.d) the methane decomposition; (1.due east) the Boudouard reaction; (ane.f) the reverse of carbon gasification.

Due to its endothermic nature, the equilibrium constant of the dry reforming reaction increases considerably with the increase in temperature [bend (1.a)]. For moderately endothermic reactions, the equilibrium constants increment with temperature: the case of the methyl hydride decomposition reaction [curve (i.d)] and the reverse water gas shift (RWGS) [curve (1.b)]. On the other mitt, being exothermic, the methanation reaction [curve (i.c)], the Boudouard reaction [curve (1.e)], and the reverse reaction of carbon gasification [curve (ane.f)] are thermodynamically unfavorable at high temperatures. Thus proceeding at high temperatures (T≥750°C) makes it possible to increase the conversion equilibrium of the main reaction and consequently to favor it compared to the other side reactions (Zhang, Wang, & Dalai, 2007).

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Theoretical and Modeling Studies on Diamond Nucleation

Huimin Liu , David S. Dandy , in Diamond Chemical Vapor Degradation, 1995

ii.0 THEORETICAL STUDIES ON NUCLEATION THERMODYNAMICS

Diamond is a metastable phase under CVD conditions. The processes competing with diamond nucleation and growth are the nucleation and growth of graphite and/or amorphous carbon, as well as spontaneous graphitization of the diamond surface. The graphite nuclei may also contribute to creation of planar defects, which along with other defects, found the major obstacles to growth of single crystal diamond films. ^[22] The free-energy differences between these carbon phases are relatively minor, and then that kinetic factors, size effects, surface reconstruction, etc., during diamond nucleation may be more important than thermodynamic factors, and hence metastable diamond can be formed under kinetically controlled atmospheric condition. Searching such preferential conditions for diamond growth has taken decades of research. ^[21]

Thermodynamic calculations ^[372] demonstrate that the equilibrium pressure of carbon vapor over diamond is ∼2 times higher than over graphite in the temperature range of 1000–2000 Thousand. In the absence of other factors, graphite nucleation is more than probable than diamond. To explain the improbable nucleation and growth of diamond nether manifestly metastable atmospheric condition, Derjaguin and Fedoseev ^[372] considered chemical kinetics based on macroscopic concepts of classical nucleation theory, adsorption-desorption kinetics and equilibrium, likewise as surface mobility of the adsorbed carbon species, and revealed several key points:

1.

The presence of a diamond surface, for example, an epitaxial or diamond-seeded surface, increases the probability of diamond nucleation.

two.

There should exist a small range of conditions under which the nucleation rate of diamond is greater than that of graphite.

3.

Hydrogen dilution decreases the growth charge per unit of graphite more than diamond.

iv.

Atomic hydrogen etches graphite faster than diamond.

Thus, there exists a narrow range of conditions, such as pressure level (supersaturation), temperature, and composition equally well as substrate surface land (structure, roughness, etc.), nether which the nucleation and growth of diamond are meaning and graphite is etched. In this contest, graphite nucleation and growth will essentially cease or will be covered by diamond. ^[22]

To decide this potentially small range of conditions, Derjaguin and Fedoseev ^[372] derived the ratio of the nucleation rates of diamond to graphite on the (111) diamond surface as a function of supersaturation, given by

$\frac{I_D}{I_G}=\frac{\mathrm{0.viii}\mathrm{ten}}{x-1}exp\left[-\frac{\mathrm{0.ix}{({\phi }_D/\kappa T)}^2(1-\mathrm{0.half-dozen}x)}{\mathrm{ten}(\mathrm{ten}-\mathrm{i})}\right]$

with

$x\mathrm{=}\ln \mathrm{\left(}\frac{p}{p_{\mathrm{due\; east}\mathrm{G}}}\ln 2\mathrm{\right)}$

under the assumption of a two-dimensional nucleus. In these expressions, I is the nucleation rate, ten is the supersaturation, ϕ_D is the bond energy of the closest neighbors in diamond crystal, κ is the Boltzmann's constant, T is the temperature, p is the partial force per unit area of carbon-containing vapor, p_eG is the equilibrium pressure of the vapor over graphite, and the subscripts D and M denote diamond and graphite, respectively. The calculated results show that a maximum of I_D/I_G exists at × = two.7. Within a very narrow range around this value of x, the nucleation rate of diamond is high relative to that of graphite, but outside this small range, the nucleation charge per unit of diamond is shut to aught. Therefore, graphite nucleation volition generally predominate, and only within a small range of conditions volition diamond nucleation occur.

Information on diamond degradation rates equally a function of temperature ^{[xviii] [22]} show a maximum at virtually thou°C. Surface reconstruction and relaxation on the {111} diamond surfaces ^[22] may occur in the range of 900 to 1000°C. ^[373] Other phenomena and backdrop which critically depend on temperature in the aforementioned range (i.e., 900–yard°C) include ^[22] adsorption/desorption and migration of atomic hydrogen, etch pit orientation, coefficient of static friction with metals, and oxidation rate. For example, 2 peaks in hydrogen desorption rates are present at ∼900°C and 1000°C. ^[22] This temperature dependence of desorption conspicuously suggests the being of a disquisitional temperature in nucleation and growth processes of CVD diamond. This has been confirmed by contempo experimental and theoretical results. ^{[72] [346] [361] [362]}

It has been recognized that large hydrogen gas dilution, typically 98–99 vol.% H_ii, is the key to successful diamond growth under the metastable atmospheric condition. ^[22] Diminutive hydrogen plays an of import role in stabilizing diamond structure on the substrate surface relative to graphite: ^{[22] [196] [368] [374]}

1.

Every bit an adsorbent on the surface, diminutive H acts to maintain the bonding of the surface carbon atoms in sp ³ form, and the interchange of adsorbed H atoms with C atoms allows continuation of growth of the diamond construction;

2.

Atomic H helps to reduce the amount of graphitic or amorphous C deposited on the substrate surface by apace reacting with these phases only assuasive sp ³ bonded diamond component;

3.

The dangling bonds at the surface of diamond are energetically unstable, and the surface volition reconstruct to a graphite-like surface containing a mixture of single and double bonds to reduce the surface energies. A monolayer of reactive atomic H bonded to the dangling bonds will prevent the surface reconstruction and sp ² bond formation, and hence stabilizes the diamond construction relative to graphite.

Additionally, by bonding to the surface and capping dangling bonds at the surface, atomic H reduces the surface energies of diamond.

The role of atomic H in the nucleation processes of diamond is similar to that in the growth processes of diamond. It has been inferred that the influence of atomic H on diamond nucleation and growth is more important than the influence of temperature. ^[22]

The role of diverse substrates in stabilizing diamond relative to graphite was evaluated past Machlin ^[196] for weather condition under which graphite is thermodynamically stable relative to diamond in the majority. The theoretical calculations of entropy, bond, and bond angle strain reveal that many metal substrates that bail to carbon can stabilize the diamond phase even in the absence of diminutive hydrogen. This stability of the diamond structure relative to graphite is attributable to the large differences in the bond energies or strain energies betwixt diamond-substrate and graphite-substrate systems and so that the small difference in the complimentary-energy between diamond and graphite in the bulk (about 0.454 kcal mol⁻¹) is overwhelmed. The substrate surfaces, that are near effective in achieving the thermodynamic stabilization of metastable phases, are those that can produce an epitaxial fit in cantlet organization between the crystal planes of the metastable phases and the substrate surfaces. Therefore, substrate materials should be limited to those that can minimize the difference in atom configuration between the substrates and diamond crystals.

Pseudomorphic stabilization of diamond is possible on the following substrates: ^[196]

1.

Unreconstructed, clean diamond surfaces in ultra loftier vacuum (UHV) or exposed to atomic hydrogen.

2.

Reconstructed, clean diamond surfaces in UHV or exposed to atomic hydrogen higher up the temperature for surface reconstruction.

3.

Make clean surfaces of many metals in UHV or exposed to diminutive hydrogen.

4.

Clean liquid metals exposed to diminutive hydrogen when the average of the metallic-metal and carbon-carbon bond energies is less than the metal-carbon bail energies, and the metals do not bond strongly to hydrogen.

The influence of substrate materials on the relative nucleation rates of diamond to graphite was quantitatively determined by Kern ^[195] on the basis of classical nucleation theory. The crux of the theory is the formation of a nucleus of disquisitional size. The Gibbs costless-energy of the formation of a critical nucleus of spherical geometry, ΔOne thousand, is expressed as

$\mathrm{\Delta }G\mathrm{=}\frac{\mathrm{one}\mathrm{six}\pi {\mathit{\sigma }}^3}{3\mathrm{\Delta }{\mu }^{\mathrm{ii}}}$

where σ is the surface gratis-energy at the nucleus-vapor interface, and Δμ is the departure in volume free-energies betwixt the vapor and solid phase. Assuming that the temperature is high enough for the thermodynamic driving forces of the nucleation of diamond and graphite, from a supersaturated vapor to exist nearly equal, i.e., Δμ _D-Five ≈Δμ _{One thousand-5}, just not and then high that diamond, when formed, reverts to graphite, the ratio of the Gibbs gratuitous-energies of the nucleation of diamond to graphite reduces to

$\frac{\mathrm{\Delta }{G}_D}{\mathrm{\Delta }{G}_{\mathrm{1000}}}\mathrm{=}\mathrm{\left(}\frac{27\mathrm{.}7}{\mathrm{iv}8\mathrm{\cdot }{3}^{0\mathrm{.}5}}\mathrm{\right)}\mathrm{(}\frac{V_D}{V_G}{\mathrm{)}}^2\frac{\mathrm{(}{\sigma }_{\mathrm{one}1\mathrm{one}}{\mathrm{)}}^3}{{\sigma }_{000\mathrm{ane}}\mathrm{(}{\sigma }_{10\mathrm{one}0}{\mathrm{)}}^{\mathrm{ii}}}$

where 5 is the volume of an atom. The relative nucleation rates of diamond to graphite are and so governed past the surface energies. From the bond strength, lattice parameters and densities of diamond and graphite, the ratio is calculated to be ΔG_D/ΔG_G ≈ 16. However, on a substrate, this ratio must be modified past a cistron

$\frac{\mathrm{[}\mathit{1}\mathrm{-}{\beta }_{\mathrm{i}\mathrm{,}s}/\mathrm{(}\mathit{two}{\sigma }_i\mathrm{)}{\mathrm{]}}_D}{\mathrm{[}\mathit{1}\mathrm{-}{\beta }_{\mathrm{southward}}/\mathrm{(}\mathit{ii}{\sigma }_{\mathrm{i}}\mathrm{)}{\mathrm{]}}_{\mathrm{Grand}}}$

where σ _i is the surface energy of the deposit crystal face i, which comes into contact with the substrate, s, and β _{i,due south} is the adhesion free energy given past the Dupré relation

${\beta }_{i,s}={\sigma }_i+{\sigma }_s-{\sigma }_{i,s}$

where σ _i,s is the interface free energy between the deposit crystal face i and the substrate. On a clean, unreconstructed diamond substrate, for example, if the crystal plane of the diamond deposit is parallel and identical to that of the substrate, and then σ _i = σ _s and σ _i,s = 0, then that [1 – β _i,south/(2σ _i ) = 0]_D, while that of graphite is non-zero. Thus, diamond is expected to nucleate faster than graphite.

It should be noted, however, that nearly conditions of deposition from the vapor phase have been shown to be such that classical nucleation theory is not well-suited to describe the nucleation kinetics of diamond, since the critical nucleus size is on the club of a few atoms. ^[375] The small size of the critical nucleus makes information technology quite inappropriate to use the classical thermodynamic variables to draw the nucleation processes. Under such weather condition, the Gibbs free-energy of the formation of a critical nucleus cannot be expressed with the above formulation. The surface energy contribution may cause a reverse effect on the phase stability ^[22] and ΔG may be less than zero. ^[376] Hence, a nanometer-sized diamond nucleus may exist more stable at subatmospheric or atmospheric pressures than a graphite nucleus containing the same number of atoms. ^{[22] [377]} A quantitative adding ^[377] shows that surface energies are an important aspect in the stabilization of nanocrystalline diamond, and for surface bonds terminated with hydrogen atoms, diamond crystals smaller than ∼iii nm in diameter are energetically favored over polycyclic aromatics (the precursors to graphite). The case of ΔK < 0 has been referred to as a nonclassical nucleation process. In such a instance, the surface energy contribution to nucleation must be evaluated on the basis of a microscopic framework of a nucleus, ^[376] and atomistic theory ^[375] should be employed for studying the nucleation procedure.

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The Use of Phase Studies in the Development of Whiskers and Whisker-Reinforced Ceramics

ALEKSANDER J. PYZIK , ALAN K. HART , in Phase Diagrams in Advanced Ceramics, 1995

1. THERMAL STABILITY OF THE Al₂O₃–SiC SYSTEM

Thermodynamic calculations conducted by Homeny et al. [ 44 ] predicted that no reactions would have identify between Al_iiO₃ and SiC even at very loftier temperatures with the only melting phase being Al_twoO₃. The alumina melts at 2015°C, which is above the processing temperature required to densify this material. The presence of SiO₂ and C, nonetheless, changes this equilibrium. The SiO₂ from the SiC surface reacts with Al_twoO₃ to class mullite (3Al₂O_three 2SiO_two), and carbon reacts with Al₂O_three to form Al₄C₃.

The stability of these phases is governed by the total pressure level of gases produced during the reaction. If the force per unit area at the Al_twoO₃–SiC interface exceeds the ambient pressure level, the interface can exist considered as chemically unstable. According to Misra [ fourscore ] the carbon–mullite interfaces become unstable above 1567°C (1840 Thousand), whereas the SiC–mullite interfaces go unstable above 1867°C (2140 K) (Fig. 18). In composites having SiC whiskers with a carbon-rich surface (loftier C/SiO_two ratio), all SiO₂ would be converted to SiC in a higher place 1567°C. At these conditions the Al₂O₃–SiC–C interface is stable until an Al_iiO_three–Al_fourC₃ eutectic forms at 1947°C. The solubility of SiC in the Al₂O₃–Al₄C₃ cook is non known. Yet, the sintering experiments suggest that SiC must be soluble in Al₂O_iii–Al₄C₃ melt because densification occurs past a solution-reprecipitation mechanism. In Al₂O₃–SiC composites with oxidized and/or carbon-free whiskers (depression C/SiO₂ ratio), all free carbon would be converted to SiC in a higher place 1567°C. Under these conditions, SiO_ii reacts with Al₂O₃ to form mullite. Alumina saturated mullite melts above 1827°C [ 1 ] forming an aluminosilicate melt. At this temperature, SiC, Al₂O₃, and molten mullite are still chemically stable. At 1867°C, the SiC/mullite becomes unstable, resulting in the formation of the liquid silicon. Although the solubility of SiC in aluminosilicate melt is doubtful [ fourscore ], the solubility in molten Si reaches about viii mole % at 1867°C. The modification of interfacial bonding between Al₂O₃ and SiC can, therefore, exist expected above 1827°C; and dissolution of SiC whiskers tin take place above 1867°C. Both changes reduce the backdrop of Al₂O₃/SiC whisker composites.

FIG. 18. Total pressure of gases corresponding to the SiC–Si–mullite and SiC–C–mullite equilibria equally a function of temperature.

Subsequently Misra [ eighty ]. Reproduced with permission of the American Ceramic Social club, Westerville.

The critical temperature above which the modification of the Al₂O_iii–SiC interface occurs is frequently even lower than 1827°C because pure SiC whiskers and pure Al₂O₃ powders are not unremarkably used. Typically SiC contains residual amounts of Fe, Co, Si, or Ni, which are used as catalysts in the whisker production. Alumina contains small amounts of sintering additives, such as CaO and MgO. SiO₂–Al_iiO₃–CaO and SiO₂–Al_twoO_three–MgO form depression-temperature eutectics, which alter the interfacial bonding. The presence of sintering additives can also change the crystallization products formed during cooling or during loftier-temperature employ. Powell–Dogan and Heuer [ 95 , 96 ] studied the crystallization characteristics of an Al₂O₃ ceramic containing MgO and CaO. They showed that the crystallization of high-magnesia grain-purlieus spectacles resulted in the formation of orthoenstatite ((Al)MgSiO₃), α–cordierite (Mg₂Al₄Si₅O₁₈), forsterite (Mg₂SiO_four), sapphirine (Mg₄Al₁₀Si₂O₂₃), and spinel (MgAl₂O_iv). The crystallization of high-calcia glasses produced equally circuitous phases consisting of anorthite (CaAl_twoSi₂O₈), gehlenite (Ca_twoAl_iiSi₃O₇), a solid solution of grossularite (Ca₃Al_iiSi₃O₁₂) and pyrope (Mg₃Al₂Si₃O₁₂), calcium hexaluminate (CaAl₁₂O_nineteen), and spinel.

The different fabrication routes result in Al_twoO_three powders and SiC whiskers with different surface characteristics. The interfacial chemic compositions vary depending on the combination of whiskers and Al₂O₃. This causes the formation of a liquid phase and the chemical reactions at the Al_twoO₃–SiC interface to occur at different processing temperatures. Therefore, conditions selected to achieve full density also have a critical influence on interfaces and on material mechanical properties. Some combinations of Al₂O₃ and SiC work better than others, merely all require individual optimization of processing conditions.

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Application of Hot Gas Turboexpanders

Heinz P. Bloch , Claire Soares , in Turboexpanders and Process Applications, 2001

Determining Susceptibility of Ni₃S_two Germination Using a Stability Diagram

Using thermodynamic calculations, a competent manufacturer can predict the susceptibility of the formation of Ni ₃Due south₂ from whatsoever gas assay. This is accomplished past determining the oxygen and sulfur partial pressures present in the gas assay. Using a computer program, the gas analysis is programmed to summate the equilibrium concentration of formation. This information is and then used to calculate the partial pressure of oxygen and sulfur of the detail gas. By plotting this information on the nickel/NiO/Ni₃Due south₂ stability diagram, the susceptibility for the formation of Ni₃S_ii can exist assessed. Figure 4-119 shows a stability diagram with gas assay plots of A and B. Gas analysis A corresponds to a gas that has a more oxidizing status under a certain pressure and temperature. In this condition, the Waspaloy cloth will favor the formation of the protective oxides NiO/Cr₂O_iii rather than the Ni₃S_ii. Even so, with gas analysis B the gas is in a more reducing-type condition and will tend to form the corrosive Ni₃Due south_ii scale in preference to the protective oxides. This aspect is extremely important since preformed oxide scales in blade/disc pressure lands could be damaged or removed and would not preferentially reform nether this gas condition. Consequently, the sulfur in the gas is more probable to react with Waspaloy to grade Ni_iiiSouthward₂, which could have detrimental effects on its material property. It is of import to understand that this method does not precisely predict which style the reaction volition go; it mainly indicates a country or form that would most likely occur. If there is a change in temperature, the sulfide/oxide stability diagrams must be adjusted.

Figure 4-119. Stability diagram with region B indicating the more corrosive condition.

The importance of being able to predict the event of a specific gas assay on the formation of the corrosive calibration is essential in the prevention of blade failures. Again, competent manufacturers take successfully developed a means of achieving this through the application of modern computer programs. However, the gas analysis provided must be every bit accurate equally possible if the program and calculations performed are to accept any existent value.

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Production of biofuels via biomass reforming

G. Van Rossum , Due south.R.A. Kersten , in Handbook of Biofuels Production, 2011

20.3 Chemical thermodynamics

The thermodynamic calculations are done with a Gibbs free free energy minimization model ¹³ using the predictive Soave-Redlich-Kwong Equation of state to summate the required fugacity coefficients. ¹⁴ In the thermodynamic calculations the not-gasified function of the feedstock remains as solid carbon. Biomass is taken as C₆H₁₀O_iv in these calculations. As mentioned before, a thermodynamic assay gives expert insight in the possible product yields, because most reforming catalysts are actually designed to obtain chemical equilibrium.

Figure 20.two shows the carbon decomposition boundaries for several steam over carbon rations (South/C   =   1, ii, iii) against the groundwork of the phase diagram of water. Operating points located in a higher place the carbon boundary lines give thermodynamic coke, while points below do not. Obviously, the absence of thermodynamic coke does non requite much information about kinetic coke. On the other paw, if thermodynamics predicts coke, there is bound to be coke in practise. In Figure 20.two, the operating regimes for steam reforming and reforming in hot compressed h2o are also depicted.

twenty.2. Thermodynamic carbon deposition boundaries for S/C   =   1, 2 and 3. Biomass   =   C_sixH_tenO_iv.

From thermodynamic point of view, steam reforming of biomass can exist done without coke formation already for South/C   =   1 at temperatures in a higher place ~   700   °C. Reforming below 700   °C, thus including pre-reforming toward marsh gas, is certainly costless of thermodynamic coke for S/C   >   2. Reforming in hot compressed h2o will produce thermodynamic coke for concentrated feedstock solutions of l   wt% organics or more (S/C   =   one, ~ 57   wt% organics). In a higher place 450   °C feeds of up to twoscore   wt% organics (S/C   =   2, ~   40   wt% organics) can be handled. For the whole hot compressed region it holds that feeds beneath xxx   wt% (~ Southward/C   =   3), organics do non produce thermodynamic coke. Dry reforming of biomass (reaction equation[twenty.2]) always produces thermodynamic coke. To avoid coke germination, dry out reforming should exist combined with steam reforming.

The carbon distribution of the product gas and the hydrogen yield are depicted in Effigy 20.3 for relevant atmospheric condition for steam reforming and reforming in hot compressed water. The carbon distribution is given as fraction of the total carbon content of the gas and the hydrogen yield is given as fraction of the maximal amount of hydrogen that can be produced according to:

xx.three. Carbon distribution and hydrogen yield of the product gas for relevant steam reforming and reforming in hot compressed water conditions equally predicted by thermodynamics. Biomass   =   C₆H₁₀O₄. For thirty   bar and S/C   =   3 also the lines for methyl hydride steam reforming are given (dotted lines).

[20.8] ${\mathrm{C}}_{\mathrm{vi}}{\mathrm{H}}_{\mathrm{x}}{\mathrm{O}}_4+8{\mathrm{H}}_{\mathrm{ii}}\mathrm{O}\to 6{\mathrm{CO}}_2+13{\mathrm{H}}_{\mathrm{two}}$

The information for reforming in hot compressed water are given for 250   bar, temperatures between 250   °C and 700   °C and 10   wt% and twenty   wt% organics. More full-bodied feeds turned out to be very susceptible to coking in practice; more than diluted feeds suffer from a also depression energetic efficiency. Steam reforming is evaluated betwixt 500   °C and 1000   °C, 1   bar and 30   bar for S/C   =   1 to 12.

For reforming in hot compressed h2o it can be seen that thermodynamics dictate a CH₄/CO_two-rich gas below 400   °C while gas mixtures containing CH₄, CO₂, and H_two are obtained at higher temperatures. H₂/CO₂ gas can be only accomplished thermodynamically at high temperature (>   600   °C) and for unrealistic low reactant concentrations (<   2   wt%). There are some attempts reported ^{6 , 15} to subtract catalytically the methane formation charge per unit via C–O bail cleavage and hydrogenation by poisoning while maintaining the high rates of C–C bail cleavage and shift for hydrogen production. Gas produced past reforming in hot compressed water typically has a (very) low CO content considering of the high h2o concentration in combination water-gas-shift activity.

At 30   bar, steam pre-reforming (~   500   °C) creates according to thermodynamics CH₄ and CO₂, while at 1   bar already quite some hydrogen is produced. Complete methane conversion is obtained at moderate S/C (2–3) for 1   bar at 700   °C and for 30   bar 900   °C is required. The H₂/CO and CO/CO₂ ratio can be easily manipulated with the steam over carbon ratio. For typical CH₄ steam reforming conditions (Due south/C   =   3, 30   bar) the gas yields are also presented in Figure 20.3. The differences betwixt CH_four and biomass can be explained past the fact that biomass contains 'internal' h2o in its molecular structure: C₆H₁₀O_four  =   C₆H_ii(H₂O)₄.

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