PHENOMENOLOGICAL VIEW OF NUCLEATION AND GROWTH OF Si ON THE Si(111)-(7×7) SUPERLATTICE

2000 ◽  
Vol 07 (01n02) ◽  
pp. 61-66 ◽  
Author(s):  
YUKICHI SHIGETA
Keyword(s):  
Activation Energy ◽  
Free Energy ◽  
Surface Structure ◽  
Epitaxial Growth ◽  
Size Distribution ◽  
Nucleation And Growth ◽  
Island Growth ◽  
Rearrangement Process ◽  
Phenomenological Consideration ◽  
The Difference

The influence of surface structure on epitaxial growth, which has not been considered before in the crystal growth theory, is discussed for the case of epitaxial growth of Si on Si(111)-(7×7) substrate. Since the rearrangement of surface structure is essential for progressing the epitaxial growth, the activation energy for the rearrangement is considered into the free energy change in the nucleation and growth processes. From a phenomenological consideration, some features of island shape and size distribution, which had been observed, are clearly explained. The size distribution is discontinuous according to the size of the unit cell of the superlattice and the shape will be almost triangular. These features are caused by prevention of the lateral growth at the faulted half in the 7×7 structure. After the evaporation has been stopped, the detachment of atoms from corners of the triangular island starts and the island shows a rounded shape. The detachment after the deposition is also explained by the difference in the free energy changes between during and after deposition. It is suggested that the activation energy for the rearrangement process of the 7×7 structure with island growth is much higher than that for the formation process with thermal decay of the Si island.

scholarly journals Enzymatic Kinetic Issues and Controversies Surrounding Gibbs Free Energy of Activation and Arrhenius Activation Energy

2020 ◽  
pp. 1-13
Author(s):  
Ikechukwu I. Udema ◽  
Abraham Olalere Onigbinde
Keyword(s):  
Activation Energy ◽  
Free Energy ◽  
Equilibrium Constant ◽  
Gibbs Free Energy ◽  
Theoretical Research ◽  
Energy Of Activation ◽  
Arrhenius Activation Energy ◽  
Free Energy Of Activation ◽  
Different Temperatures ◽  
The Difference

Background: The equation of the difference between reverse and forward Gibbs free energy of activation (ΔΔGES#) reflects Michaelis-Menten constant (KM) in both directions; this may not be applicable to all enzymes even if the reverse reaction is speculatively Michaelian. Arrhenius activation energy, Ea and (Ea - ΔGES#)/RT) are considered = ΔGES# and KM respectively. The equations are considered unlikely. Objectives: The objectives of this research are: 1) To derive what is considered as an appropriate equation for the determination of the difference in ΔGES# between the reverse and forward directions, 2) calculate the difference between the reverse and total forward ΔGES#, and 3) show reasons why Ea ≠ ΔGES#  in all cases. Methods: A major theoretical research and experimentation using Bernfeld method. Results and Discussion: A dimensionless equilibrium constant KES is given. Expectedly, the rate constants were higher at higher temperatures and the free energy of activation with salt was < the Arrhenius activation energy, Ea; ΔΔGES#ranges between 67 - 68 kJ/mol. Conclusion: The equations for the calculation of the difference in free energy of activation (ΔΔGES#) between the forward and reverse directions and a dimensionless equilibrium constant for the formation of enzyme-substrate (ES) were derivable. The large positive value of the ΔΔGES# shows that the forward reaction is not substantially spontaneous; this is due perhaps, to the nature of substrate. The equality of Arrhenius activation energy (Ea) and ΔGES# may not be ruled out completely but it must not always be the case; the presence of additive like salt can increase the magnitude of Ea well above the values of the ΔGES#. A dimensionless equilibrium constant for the net yield of ES seems to be a better alternative than KM. The Ea unlike ΔGES#  requires at least two different temperatures for its calculation.

Exact Scaling Form for the Island Size Distribution in Submonolayer Epitaxial Growth

1996 ◽  
Vol 440 ◽  
Author(s):  
M. C. Bartelt ◽  
J. W. Evans
Keyword(s):  
Epitaxial Growth ◽  
Size Distribution ◽  
Nucleation And Growth ◽  
Complex Relationship ◽  
Island Size ◽  
The Relationship ◽  
Exact Scaling

AbstractThe exact scaling form is determined for the size distribution of islands created via irreversible nucleation and growth during submonolayer deposition. This form is controlled by a dependence on size of the propensity for islands to “capture” diffusing adatoms. This sizedependence is determined directly from simulations. It reflects a complex relationship between the size of an island, and the area of its cell in a tessellation of the surface based on the island locations. The relationship corresponds to a correlation between island size and separation.

Microscopic Interpretation of Arrhenius Parameters

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Activation Energy ◽  
Transition State ◽  
Transition State Theory ◽  
Average Energy ◽  
Zero Point ◽  
State Theory ◽  
Exponential Factor ◽  
Quantum Tunnelling ◽  
Microscopic Interpretation ◽  
The Difference

This chapter reviews the microscopic interpretation of the pre-exponential factor and the activation energy in rate constant expressions of the Arrhenius form. The pre-exponential factor of apparent unimolecular reactions is, roughly, expected to be of the order of a vibrational frequency, whereas the pre-exponential factor of bimolecular reactions, roughly, is related to the number of collisions per unit time and per unit volume. The activation energy of an elementary reaction can be interpreted as the average energy of the molecules that react minus the average energy of the reactants. Specializing to conventional transition-state theory, the activation energy is related to the classical barrier height of the potential energy surface plus the difference in zero-point energies and average internal energies between the activated complex and the reactants. When quantum tunnelling is included in transition-state theory, the activation energy is reduced, compared to the interpretation given in conventional transition-state theory.

Synthesis and characterization of a series of 1-methyl-4-[2-aryl-1-diazenyl]piperazines and a series of ethyl 4-[2-aryl-1-diazenyl]-1-piperazinecarboxylates

2004 ◽  
Vol 82 (8) ◽  
pp. 1294-1303 ◽  
Author(s):  
Vanessa Renée Little ◽  
Keith Vaughan
Keyword(s):  
Free Energy ◽  
Chemical Shifts ◽  
Linear Free Energy Relationship ◽  
Piperazine Ring ◽  
Linear Free Energy ◽  
In Series ◽  
Methylene Groups ◽  
Diazonium Coupling ◽  
The Difference

1-Methylpiperazine was coupled with a series of diazonium salts to afford the 1-methyl-4-[2-aryl-1-diazenyl]piperazines (2), a new series of triazenes, which have been characterized by 1H and 13C NMR spectroscopy, IR spectroscopy, and elemental analysis. Assignment of the chemical shifts to specific protons and carbons in the piperazine ring was facilitated by comparison with the chemical shifts in the model compounds piperazine and 1-methylpiperazine and by a HETCOR experiment with the p-tolyl derivative (2i). A DEPT experiment with 1-methylpiperazine (6) was necessary to distinguish the methyl and methylene groups in 6, and a HETCOR spectrum of 6 enabled the correlation of proton and carbon chemical shifts. Line broadening of the signals from the ring methylene protons is attributed to restricted rotation around the N2-N3 bond of the triazene moiety in 2. The second series of triazenes, the ethyl 4-[2-phenyl-1-diazenyl]-1-piperazinecarboxylates (3), have been prepared by similar diazonium coupling to ethyl 1-piperazinecarboxylate and were similarly characterized. The chemical shifts of the piperazine ring protons are much closer together in series 3 than in series 2, resulting in distortion of the multiplets for these methylenes. It was noticed that the difference between these chemical shifts in 3 exhibited a linear free energy relationship with the Hammett substituent constants for the substituents in the aryl ring. Key words: triazene, piperazine, diazonium coupling, NMR, HETCOR, linear free energy relationship.

scholarly journals Kinetics and thermodynamic properties related to the drying of 'Cabacinha' pepper fruits

2016 ◽  
Vol 20 (2) ◽  
pp. 174-180 ◽  
Author(s):  
Hellismar W. da Silva ◽  
Renato S. Rodovalho ◽  
Marya F. Velasco ◽  
Camila F. Silva ◽  
Luís S. R. Vale
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Free Energy ◽  
Thermodynamic Properties ◽  
Gibbs Free Energy ◽  
Removal Rate ◽  
Effective Diffusion ◽  
Drying Time ◽  
Three Samples ◽  
Different Temperatures

ABSTRACT The objective of this study was to determine and model the drying kinetics of 'Cabacinha' pepper fruits at different temperatures of the drying air, as well as obtain the thermodynamic properties involved in the drying process of the product. Drying was carried out under controlled conductions of temperature (60, 70, 80, 90 and 100 °C) using three samples of 130 g of fruit, which were weighed periodically until constant mass. The experimental data were adjusted to different mathematical models often used in the representation of fruit drying. Effective diffusion coefficients, calculated from the mathematical model of liquid diffusion, were used to obtain activation energy, enthalpy, entropy and Gibbs free energy. The Midilli model showed the best fit to the experimental data of drying of 'Cabacinha' pepper fruits. The increase in drying temperature promoted an increase in water removal rate, effective diffusion coefficient and Gibbs free energy, besides a reduction in fruit drying time and in the values of entropy and enthalpy. The activation energy for the drying of pepper fruits was 36.09 kJ mol-1.

Evolution of cluster size distribution in nucleation and growth processes

1991 ◽  
Vol 136 (3) ◽  
pp. 181-197 ◽  
Author(s):  
J. Bartels ◽  
U. Lembke ◽  
R. Pascova ◽  
J. Schmelzer ◽  
I. Gutzow
Keyword(s):  
Size Distribution ◽  
Cluster Size ◽  
Nucleation And Growth ◽  
Cluster Size Distribution ◽  
Growth Processes

Model for Epitaxial growth of Cobalt on CU(100)

1989 ◽  
Vol 160 ◽  
Author(s):  
Dimitri D. Vvedensky ◽  
Shaun Clarke
Keyword(s):  
Epitaxial Growth ◽  
Growth Kinetics ◽  
Solid Model ◽  
Free Energies ◽  
Diffusion Parameters ◽  
The Difference ◽  
Kinetics Of

AbstractThe epitaxial growth kinetics of Co on Cu(100) are investigated with a kinetic solid-on-solid model. Two effects are found to dominate the growth of this system reflecting the difference in surface free energies betweenthe two materials: the difference of diffusion parameters, and the inability of Co to wet Cu(100) at lower temperatures.

Epitaxial growth and surface structure of cuprous halide thin films

2000 ◽  
Vol 18 (2) ◽  
pp. 536-542 ◽  
Author(s):  
Tomoko Wake ◽  
Koichiro Saiki ◽  
Atsushi Koma
Keyword(s):  
Thin Films ◽  
Surface Structure ◽  
Epitaxial Growth

scholarly journals An experimental and theoretical investigation of diffusion in a two-phase alloy

1948 ◽  
Vol 192 (1031) ◽  
pp. 575-592 ◽  
Keyword(s):  
Free Energy ◽  
Single Phase ◽  
Phase State ◽  
Theoretical Treatment ◽  
Research Association ◽  
Essential Difference ◽  
Two Phase ◽  
Two Factors ◽  
Order Of Magnitude ◽  
The Difference

The present paper describes an investigation of diffusion in the solid state. Previous experimental work has been confined to the case in which the free energy of a mixture is a minimum for the single-phase state, and diffusion decreases local differences of concentration. This may be called ‘diffusion downhill’. However, it is possible for the free energy to be a minimum for the two-phase state; diffusion may then increase differences of concentration; and so may be called ‘diffusion uphill’. Becker (1937) has proposed a simple theoretical treatment of these two types of diffusion in a binary alloy. The present paper describes an experimental test of this theory, using the unusual properties of the alloy Cu 4 FeNi 3 . This alloy is single phase above 800° C and two-phase at lower temperatures, both the phases being face-centred cubic; the essential difference between the two phases is their content of copper. On dissociating from one phase into two the alloy develops a series of intermediate structures showing striking X-ray patterns which are very sensitive to changes of structure. It was found possible to utilize these results for a quantitative study of diffusion ‘uphill’ and ‘downhill’ in the alloy. The experimental results, which can be expressed very simply, are in fair agreement with conclusions drawn from Becker’s theory. It was found that Fick’s equation, dc / dt = D d2c / dx2 , can, within the limits of error, be applied in all cases, with the modification that c denotes the difference of the measured copper concentration from its equilibrium value. The theory postulates that D is the product of two factors, of which one is D 0f the coefficient of diffusion that would be measured if the alloy were an ideal solid solution. The theory is able to calculate D/D 0 , if only in first approximation, and the experiments confirm this calculation. It was found that in most cases the speed of diffusion—‘uphill’ or ‘downhill’—has the order of magnitude of D 0 . * Now with British Electrical Research Association.

Thermogravimetric Analysis of Glucose-Based and Fructose-Based Carbohydrates

2013 ◽  
Vol 805-806 ◽  
pp. 265-268 ◽  
Author(s):  
Fang Ming Cui ◽  
Xiao Yuan Zhang ◽  
Li Min Shang
Keyword(s):  
Activation Energy ◽  
Thermogravimetric Analysis ◽  
Kinetic Parameters ◽  
Degree Of Polymerization ◽  
Experiment Data ◽  
Pyrolysis Characteristics ◽  
The Difference ◽  
Kinetic Calculations

Thermogravimetric analysis (TGA) was employed to study the pyrolysis characteristics of four glucose-based and three fructose-based carbohydrates. Kinetic parameters were calculated based on the experiment data. The results indicated that the starting and maximal pyrolysis temperatures of the glucose-based carbohydrates were increased steadily as the rising of their degree of polymerization (DP). The fructose-based carbohydrates exhibited similar pyrolysis behaviors as the glucose-based carbohydrates, but the difference was smaller. Kinetic calculations revealed that the activation energy values of the glucose-based carbohydrates were higher than those of the fructose-based carbohydrates, indicating the glucose-based carbohydrates were more difficult to decompose than the fructose-based carbohydrates.

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