Chemical Thermodynamics Research Articles

Chemical thermodynamics of biomass, cellulose, and cellulose derivatives: A review

This article provides a review of the research on the chemical thermodynamics and thermochemistry of biomass, cellulose, and its derivatives such as ethers, esters, and oxycelluloses. For diverse biomass types, gross and net heating values were studied. It has been established that these energetical characteristics of biomass can be calculated using a superposition of the energetical characteristics of the main components of biomass such as cellulose, hemicelluloses, lignin, lipids, proteins, etc. The pelletization of biomass improves its fuel performance. It was shown that, if the ultimate goal is to generate the maximum amount of thermal energy, then it is more profitable to directly burn the initial biomass in the form of pellets than to burn the amount of solid or liquid biofuel that can be extracted from this biomass. After the cellulose study, the direct and exact thermochemical method for determining the crystallinity degree of this biopolymer was proposed. In addition, the standard combustion and formation enthalpies of various cellulose samples were studied. As a result, the thermodynamic characteristics of four crystalline allomorphs of cellulose, CI, CII, CIII, and CIV, were obtained and their thermodynamic stability was evaluated. The thermochemistry of enzymatic hydrolysis of cellulose was studied. In addition. The thermodynamical characteristics of various cellulose derivatives were determined, and the thermochemistry of the reactions of cellulose alkalization, etherification, esterification, and oxidation was studied.

The oxide films formed under the low oxygen pressure in a particular system containing competing chromium and aluminium

AbstractIn this paper, pre‐oxidation treatment was carried out at 950 °C under oxygen pressure of 10−16 atm for nickel‐10 % chromium‐x % aluminium‐1 % silicon‐0.5 % yttrium(x=0 wt.–%, 1 wt.–%, 3 wt.–%, 5 wt.–%) alloys. Morphology and structure of oxide layers on the alloys after pre‐oxidation were analyzed by scanning electron microscopy and electron discharge spectroscopy. The results showed that a chromium oxide film was formed on the surface of the alloy without aluminium addition, while the oxide layer on the surface of the alloy with aluminium addition gradually transformed into M2O3 (M=aluminium and chromium) oxide film. The oxidation behavior was analyzed by means of chemical thermodynamics, and it was seen that because the interaction coefficient,εijof aluminium and chromium is a positive value, the increase of aluminium addition will strengthen the interaction and increase the diffusion coefficient,Diof aluminium and chromium. The diffusion of chromium and aluminium in each other therefore promotes their interaction, which is beneficial to the formation of the outer oxide film. Thus, with the increase of aluminium addition, the thickness of the outer oxide film gradually increased, and the aluminium content in M2O3 (M=aluminium and chromium) increased significantly, and with 5 % aluminium added, the aluminium oxide of the outer oxide film became the main body.

Biosynthetic fuels: A marriage of renewable resources and chemical thermodynamics

Terpenes represent a highly diverse group of natural products with wide applications. Terpenoid structures can be derived from different renewable sources and utilized as fuels. Application as fuels requires hydrogenation of the double bonds in the respective molecules to ensure clean combustion. This hydrogenation can be performed either directly with elemental hydrogen or indirectly via transfer hydrogenation with a Liquid Organic Hydrogen Carrier. In this study, the thermochemical fundamentals of these reaction has been evaluated. For this task, for a first time a combination of experimental thermochemistry and quantum-chemical molecular modelling has been applied. The results show the hydrogenation of the respective structures is thermodynamically highly favourable. Correspondingly, dehydrogenation would be comparatively unfavorable. Yet, for a fuel no dehydrogenation is required. As an alternative to conventional hydrogenation, transfer hydrogenation, which is often subject to partial conversions due to limitations by the reaction equilibrium, can be realized with a high degree of conversion. While the entropy of reaction for hydrogen transfer from cyclohexyl-structures to terpene structures is close to zero, the enthalpy of reaction is highly negative. This leads to a Gibbs energy of reaction which is clearly negative and ensures a large thermodynamic driving force for the reaction. As a consequence, downstream processing, which is usually very demanding for transfer hydrogenations, is comparatively easy. These finding underline the great potential of these bio-derived substances for conversion into sustainable fuels.

Introducing process simulation as an alternative to laboratory session in undergraduate chemical engineering thermodynamics course: A case study from Sunway University Malaysia

This study demonstrates the successful integration of process simulation using CHEMCAD into Sunway University's Chemical Engineering Thermodynamics curriculum, replacing the traditional lab sessions. This approach has two main benefits, i.e., it provides early exposure to process simulation software, bridging theory and practice, and it supports new chemical engineering programs where labs may not be fully operational. Aligned with Sunway University's commitment to innovative educational approaches, the impact of this integration on the students’ learning experiences is evident through feedback collected from a comprehensive survey conducted with a group of seven students enrolled in Chemical Engineering Thermodynamics in April 2023. The survey's three sections gathered the students’ perceptions, enjoyed aspects, challenges faced, and suggestions. Findings highlight the students’ positive views on the integration, enhancing comprehension of thermodynamics concepts and real-world applications. They also recognized the value of hands-on simulation experience for essential process simulation skills. The students appreciated the practical relevance in highlighting thermodynamics’ real-world importance. Challenges related to software access and technical issues were addressed, with planned improvements. The students expressed interest in deeper learning, including complex simulations, graphical representation use, and external resource access. While many found the integration effective, suggestions for more hands-on engagement and research resource access were noted.

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models.

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

The Formalism of Chemical Thermodynamics Applied to an Oscillatory Multistep Chemical System

The thermodynamic optimization of a process focuses on consumption, production, and efficient use of energy. The unsteady-state nature of batch reactor processing requires describing the set of processes’ dynamic behavior for energy optimization. This work aims to apply the formalism of chemical thermodynamics to a multistep chemical system in a batch reactor, aiming for a dynamic description of its evolution to the equilibrium state. As the system of study, we selected a mathematical model called the Oregonator, derived from the mechanism of the oscillating Belousov-Zhabotinsky reaction. In the methodology, we used the reaction quotient to evaluate the Gibbs function, the thermodynamic affinity, and the entropy generation as a function of the reaction extent. The results show that the overall reaction fulfills the thermodynamic fundamentals of chemical equilibrium, despite having a non-stoichiometric coefficient. However, the multistep coupled reaction system does not allow verifying compliance with the thermodynamic foundations of chemical equilibrium. We conclude that it is necessary to improve thermodynamic formalism to describe multistep chemical processes as a function of a global reaction extent variable. In this scenario, the entropy production rate emerges as a promising quantity.

Study on the inhibition mechanism of ammonium dihydrogen phosphate on the pyrolysis gas flame of red pine wood

Ammonium phosphate-based fire extinguishers are widely used in forest fires due to their low cost and effectiveness against solid combustibles. However, the mechanism by which ammonium phosphate interacts with pyrolysis gas flames is not well understood, and there is a lack of precise experimental validation and correction of the chemical kinetics models regarding the suppression mechanism. Therefore, this study utilized NH4H2PO4 powder as a fire extinguishing agent and constructed a PLIF experimental system suitable for NH4H2PO4/red pine pyrolysis gas/air interactions. Through experiments, the changes in the concentration of OH radicals with different amounts of extinguishing agent at various equivalence ratios were measured. By employing Chemkin software, the study comprehensively analyzed the kinetic regulation mechanism of NH4H2PO4 on red pine pyrolysis gas flames from aspects such as chemical inhibition, sensitivity of elementary reactions, chemical reaction pathways, and chemical thermodynamics. The study revealed the characteristics and mechanisms of NH4H2PO4 powder inhibition, identifying R1092, R1098, R1116, and R1120 as the primary elementary reactions suppressing flame combustion. The mutual inhibition cycles formed among these reactions were found to be the main reasons for the suppression of H and OH radicals in the flame. Moreover, PO2 was identified as the primary phosphorus-containing fire extinguishing agent responsible for extinguishing the flame.

Ultra-thin FeCoNi-LDH hollow nanoflower as solid-phase microextraction coating for targeted capture of six pesticides by electrostatic adsorption

Pesticides are common pollutants that cause detriment to the ecological environmental safety and health of human due to their toxicity, volatility and bioaccumulation. In this work, an ultra-thin polymetallic layered double hydroxide (FeCoNi-LDH) with hollow nanoflower structure composite was synthesized using ZIF-67 as a self-sacrificial template, which was used as solid-phase microextraction (SPME) coating for the targeted capture pesticides, which could be combined with high-performance liquid chromatography (HPLC) to sensitive inspection pesticides in real water samples. Orthogonal experimental design (OAD) was applied to ensure the best SPME condition. Additionally, the adsorption properties were evaluated by chemical thermodynamics and kinetics. Under the optimized conditions, high adsorption capacity was obtained (117.0–21.5 mg g−1). A wide linear range (0.020–1000.0 μg L−1), low detection limit (0.008–0.172 μg L−1) and excellent reproducibility were obtained under the established method. This research provided a new strategy for designing hollow materials with multiple cations for the adsorption of anion or organic pollutants.

MODEL FOR FLAMMABLE LIMITS CALCULATION OF SEVERAL HYDROCARBON FUELS MIXTURES

A model for calculating the flammable limits of two or more gaseous combustibles mixtures is proposed. It based on the equilibrium chemical thermodynamics (without involving the chemical kinetics) and a generalized model of chemical equilibrium. The flammability limits of single combustibles are assumed to be known. The model takes into account the possibility of the formation of condensed carbon in fuel-rich combustible mixtures. Using the proposed model, the concentration limits of ignition for a number of multifuel mixtures containing H2, C2H2, CH4, C6H12 and CO were calculated. The calculation results coincide well with similar results obtained using the well-known empirical formulas of Le Chatelier. The proposed model can be considered as a theoretical justification for these formulas.

Chemical kinetics and thermodynamics of PPO activity, colour changes and microbial degradation during blanching of the sugarcane billets.

Sugarcane juice, which has a short shelf life, is a popular thirst-quenching and rejuvenating beverage worldwide. The limited shelf life is a result of changes in polyphenol oxidase (PPO) activity, total plate count (TPC) and color attributes (L*, a* and b*-values). We hypothesized that chemical kinetics and thermodynamics of blanched sugarcane cane juice causing alterations in PPO, TPC, and L, a* and b*-values will address the challenges of sugarcane juice preservation. Sugarcane billets were blanched at variable time-temperature combinations in the range 0-20 min and 70-90 °C. Reaction rates increased with increasing temperature; PPO activity, TPC and colour followed first-order kinetics. PPO activity had an activation energy (Ea) of 81 kJ mol-1. The half life (t½) dropped from 16.5 to 3.47 min and decimal reduction time (D-values) dropped from 54.83 to 11.52 min. Thus reactions were temperature-sensitive. Thermodynamic studies indicated an endothermic (positive enthalpy values, ΔH > 0; 78.10 kJ mol-1) and reversible process (negative entropy values ΔS < 0; -0.044 kJmol-1 K-1). Michaeli-Menten constant (Km) and maximum velocity (Vmax) of PPO activity were determined by adding variable lemon juice concentrations in sugarcane juice. As the Km values increased (from 5.53 to 15.81 mm) and Vmax values decreased (from 666.67 to 384.61 UmL-1), a Lineweaver-Burk plot suggested decreased PPO affinity of sugarcane juice. The results of the present study indicate that studies on chemical kinetics and thermodynamics (PPO, TPC and L, a* and b*-values) of blanched sugarcane cane juice shall mitigate challenges of sugarcane juice preservation. © 2024 Society of Chemical Industry.

Modeling phase or chemical reaction equilibrium with an equation of state, an unrealistic modeling

The traditional chemical thermodynamics considered the chemical potential then fugacity of a component in a single-phase, open system is just the one of the component in a co-existing phase of an equilibrium, multi-component, multi-phase system or in an equilibrium, chemical reaction system and the fugacity can be calculated with the equation of state of the single-phase, open system. Therefore, the most common method to model phase or chemical reaction equilibrium is with an equation of state. Obviously, modeling phase or chemical reaction equilibrium with an equation of state requires to the single-phase, open system is equivalent to the co-existing phase or the equilibrium, chemical reaction system. However, there are significant differences in the thermodynamics properties between the single-phase, open system and the co-existing phase or the equilibrium, chemical reaction system. Therefore, the chemical potential then fugacity of a component in the single-phase, open system is impossible the one of the component in the co-existing phase or in the equilibrium, chemical reaction system. That is, the calculated fugacity of a component in a single-phase, open system with the equation of state of the single-phase, open system is impossibly the fugacity of the component in a co-existing phase of an equilibrium, multi-component, multi-phase system or in an equilibrium, chemical reaction system. Therefore, it is unrealistic to model phase or chemical reaction equilibrium with an equation of state. For this, we establish the chemical potential differential formula of a component in a co-existing phase and in an equilibrium, chemical reaction system to calculate phase or chemical reaction equilibrium. The calculated values of solubility in molar concentration within the framework of the present theory equals exactly the measured values of solubility in molar concentration by the experiments.

Physicochemical Perspective of Biological Heterogeneity.

The vast majority of chemical processes that govern our lives occur within living cells. At the core of every life process, such as gene expression or metabolism, are chemical reactions that follow the fundamental laws of chemical kinetics and thermodynamics. Understanding these reactions and the factors that govern them is particularly important for the life sciences. The physicochemical environment inside cells, which can vary between cells and organisms, significantly impacts various biochemical reactions and increases the extent of population heterogeneity. This paper discusses using physical chemistry approaches for biological studies, including methods for studying reactions inside cells and monitoring their conditions. The potential for development in this field and possible new research areas are highlighted. By applying physical chemistry methodology to biochemistry in vivo, we may gain new insights into biology, potentially leading to new ways of controlling biochemical reactions.

Corrosion behaviors of Inconel 617 and Incoloy 800H in impure helium with different CO contents at high temperatures

The helium coolant of the very high-temperature gas-cooled reactor (VHTR) is expected to contain trace impurities, which will cause corrosion to superalloys at high temperatures. The high-temperature corrosion behaviors of Inconel 617 and Incoloy 800H were investigated in the impure helium with various CO levels. For Inconel 617, the microclimate reaction occurred at high temperatures, releasing large amounts of CO and destroying the oxide layer. The corrosion model was established according to the chemical thermodynamics theory, showing that the reaction temperature is related to the CO content. However, this corrosion behavior was not observed for Incoloy 800H. The corrosion difference between these alloys was analyzed in this study, indicating that the silicon oxide interlayer of Incoloy 800H may inhibit the microclimate reaction. Although the interlayer could attenuate the chemical destruction of the oxide layer, the adhesion may be reduced leading to thermal damage, which was proved by the experiment in this study. This research clarified the different corrosion mechanisms of these two alloys and provided guidance for the control scheme of CO content in the primary circuit of HTGR.

Entropy‐Driven Direct Air Electrofixation

AbstractAccording to the principles of chemical thermodynamics, the catalytic activation of small molecules (like N2 in air and CO2 in flue gas) generally exhibits a negative activity dependence on O2 owning to the competitive oxygen reduction reaction (ORR). Nevertheless, some catalysts can show positive activity dependence for N2 electrofixation, an important route to produce ammonia under ambient condition. Here we report that the positive activity dependence on O2 of (Ni0.20Co0.20Fe0.20Mn0.19Mo0.21)3S4 catalyst arises from high‐entropy mechanism. Through experimental and theoretical studies, we demonstrate that under the reaction condition in the mixed N2/O2, the adsorption of O2 on high‐entropy catalyst contributes to activating N2 molecules characteristic of elongated N≡N bond lengths. As comparison to the low‐ and medium‐entropy counterparts, high entropy can play the second role of attenuating competitive ORR by displaying a negative exponential entropy‐ORR activity relationship. Accordingly, benefiting from the O2, the system for direct air electrofixation has demonstrated an ammonia yield rate of 47.70 μg h−1 cm−2, which is even 1.5 times of pure N2 feedstock (31.92 μg h−1 cm−2), overtaking all previous reports for this reaction. We expect the present finding providing an additional dimension to high entropy that leverages systems beyond the constraint of traditional rules.

Entropy-Driven Direct Air Electrofixation.

According to the principles of chemical thermodynamics, the catalytic activation of small molecules (like N2 in air and CO2 in flue gas) generally exhibits a negative activity dependence on O2 owning to the competitive oxygen reduction reaction (ORR). Nevertheless, some catalysts can show positive activity dependence for N2 electrofixation, an important route to produce ammonia under ambient condition. Here we report that the positive activity dependence on O2 of (Ni0.20Co0.20Fe0.20Mn0.19Mo0.21)3S4 catalyst arises from high-entropy mechanism. Through experimental and theoretical studies, we demonstrate that under the reaction condition in the mixed N2/O2, the adsorption of O2 on high-entropy catalyst contributes to activating N2 molecules characteristic of elongated N≡N bond lengths. As comparison to the low- and medium-entropy counterparts, high entropy can play the second role of attenuating competitive ORR by displaying a negative exponential entropy-ORR activity relationship. Accordingly, benefiting from the O2, the system for direct air electrofixation has demonstrated an ammonia yield rate of 47.70 μg h-1 cm-2, which is even 1.5 times of pure N2 feedstock (31.92 μg h-1 cm-2), overtaking all previous reports for this reaction. We expect the present finding providing an additional dimension to high entropy that leverages systems beyond the constraint of traditional rules.

XXIV International Conference on Chemical Thermodynamics in Russia (RCCT-2024)

XXIV International Conference on Chemical Thermodynamics in Russia (RCCT-2024)

Computational-aided analysis of the pathway and mechanism of dichloroacetonitrile formation from phenylalanine upon chloramination

Dichloroacetonitrile (DCAN) is an emerging disinfection by-product (DBP) that is widespread in drinking water. However, the pathway for DCAN formation from aromatic amino acids remains unclear, leading to a lack of an understanding of its explicit fate during chloramination. In this study, we investigated the specific formation mechanism of DCAN during the chloramination of phenylalanine based on reaction kinetics and chemical thermodynamics. The reason for differences between aldehyde and decarboxylation pathways was explained, and kinetic parameters of the pathways were obtained through quantum chemistry calculations. The results showed that the reaction rate constant of the rate-limiting step of the aldehyde pathway with 1.9 × 10−11 s−1 was significantly higher than that of decarboxylation (3.6 × 10−16 s−1 M−1), suggesting that the aldehyde pathway is the main reaction pathway for DCAN formation during the chloramination of phenylalanine to produce DCAN. Subsequently, theoretical calculations were performed to elucidate the effect of pH on the formation mechanism, which aligned well with the experimental results. Dehydrohalogenation was found to be the rate-limiting step under acidic conditions with reaction rate constants higher than those of the rate-limiting step (expulsion of amines) under neutral conditions, increasing the rate of DCAN formation. This study highlights the differences in DCAN formation between the decarboxylation and aldehyde pathways during the chloramination of precursors at both molecular and kinetic levels, contributing to a comprehensive understanding of the reaction mechanisms by which aromatic free amino acids generate DCAN.

Ab Initio Conformational Analysis of 3,7-Diacetyl-3,7-Diazabicyclo[3.3.1]Nonanes

Introduction: The importance of the conformational behavior comprehension for proper prediction of properties for a certain compound or for a class of compounds is indisputable. For 3,7-diacylbispidines (3,7-diacyl-3,7-diazabicyclo[3.3.1]nonanes), only “double chair” (CC) conformers were prior found experimentally in the condensed phase, which differ only in the acyl groups relative orientation, “parallel,” pa or “antiparallel,” ap. However, 2 other conformer families, “boat-chair,” BC and “double twist,” TT, are known for other bicyclo[3.3.1]nonane derivatives. Features of these conformers would be useful for the accurate prediction of properties and activities of the compounds. Methods: Second-order perturbation theory ab initio techniques (MP2) in the triple-zeta correlation-consistent orbital basis set cc-pVTZ was employed to optimize the electronic energy for structures, to characterize the optimized structures as potential energy surface minima by energy hessian eigenvalue calculations and to calculate zero-point energy corrections for the minima using the “rigid rotor-harmonic oscillator” approximation to model the molecular ensemble thermodynamics. Additionally, the computational chemical thermodynamics benefits much from the concept of the molecular strain and its energy assessed successfully through the bond separation energy formalism. We combine both approaches in our investigation to find and consistently characterize the conformers previously unknown for the compounds under the studies. Results: Six possible conformers were found for the investigated 3,7-diacetyl-3,7-diazabicyclo[3.3.1]nonanes 1-4, formed by combining the skeletal conformation changes with the internal rotation of acyl substituents. The conformational behavior is quite similar for all investigated molecules. In all cases, the CC conformation is optimal for the bicyclic skeleton and ap orientation prevails over pa for 2 acetyl groups. This prevalence is 4-5 kcal mol−1 in CC and less than 1 kcal mol−1 in other skeletal forms, making rotation of 2 acyl groups in BC and TT almost independent. Concerning the skeletal conformations, the common energy sequence CC &lt; BC &lt; TT is found. While the relative BC energy is 6-7 kcal mol−1 over the optimal CC structure, TT forms are all strained by more than 12 kcal mol−1. Conclusions: For the first time, both BC and TT conformers of 3,7-diacetylbispidines were characterized by their strain and conformation energies together with known less strained CC forms. On the basis of our calculations, the relative energies of BC conformers are expected to be close to those of the CC acetyl amide bond rotamers found previously in experiment, therefore, their exclusion from the conformational behavior would look unjustified. On the contrary, TT conformers are found to be much more strained enough to be neglected in the conformational ensemble modeling.

Introduction to the modeling of complex chemical reaction equilibrium using gPROMS® and GAMS®

AbstractIn the present paper several aspects of the simulation of complex chemical equilibrium are discussed, using two research and educational software: gPROMS® and GAMS®. All computations are performed to boost the understanding of chemical engineering students, undergraduate, and graduate, of the complex concepts behind both thermo‐chemical processes and optimization techniques. Four case studies with varying levels of difficulty illustrate the proposed methodology and robustness of the modeling systems: Catalytic steam reforming of bio‐ethanol at high temperatures. Partial oxidation of naphthalene using either air or pure oxygen. Supercritical water gasification of Microalga Spirulina. Dry and mixed reforming of glucose.Our results indicate that the use of optimization tools offered bygPROMS® and GAMS®software are useful and efficient tools to calculate the chemical and phase equilibrium by minimizing the Gibbs energy, provided that adequate initial guesses are used. Furthermore, the computational time spent in the calculations was generally quite short. The obtained equilibrium compositions are benchmarked using the ubiquitous process simulators: ASPEN‐Plus® and/or ASPEN‐Hysys® as well as data available from the open literature. We obtained excellent agreement between our results and their counterpart obtained using ASPEN‐Plus®. In the last part of this manuscript, authors share their experience in supervising senior term projects on the subject. A questionnaire was used to collect qualitative and quantitative feedback from the nine students involved in the projects. Their responses to a questionnaire focused on the chemical engineering thermodynamics theory as well as software usage during their investigations. This questionnaire demonstrates that students can overcome mathematical complexity by either using mathematical software or equivalent modeling systems (e.g., Matlab®, Mathematica©, gPROMS®, and GAMS®).

Dislocations/Defects analysis in III-V nitrides - a cost effective MOCVD epitaxy solution

In present paper an innovative technique to reproduce the epitaxial growth results through lateral flow metal organic chemical vapor deposition (MOCVD) reactor process at atomistic scale is reported. It includes the equivalent MOCVD reactor geometry architecture of AIXTRON 200/4 RF-S horizontal flow reactor. The gas- and surface phase chemical reaction kinetics and thermodynamics are given due consideration in the present study without use of any continuum or fluid dynamics models. The optimum conditions are extracted by running design of experiments over TNL-EpiGrow simulator to achieve high crystalline quality aluminum nitride (AlN) films over Si (111) substrate. The impact of variation in precursor NH3 flow rates and carrier gas N2 pressure are used to predict the conditions to optimize the improved morphology and quality of the AlN films. The defects densities are characterized in terms of vacancies and dislocation densities. The roughness and lattice parameters are extracted. The growth rates obtained in present studies are compared against reported the similar experiments. The excellent agreement is observed between experimental and simulated results. The dislocation densities in grown samples are also found in good agreement with the similar experimental reported densities in each sample.