scholarly journals Simulation of crystal growth in multicomponent metastable alloys

2020 ◽  
Vol 62 (12) ◽  
pp. 943-949
Author(s):  
M. V. Dudorov ◽  
V. E. Roshchin
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Diffusion Processes ◽  
Mutual Influence ◽  
Crystallization Front ◽  
Metastable Phase ◽  
Phase Interface ◽  
Primary Crystallization ◽  
High Rate ◽  
Silicon Concentration

A method for predicting the regularities of crystal growth from metastable melts has been developed. The process of crystal growth from a multicomponent melt is described by the methods of nonequilibrium thermodynamics, taking into account the mutual influence of thermal and diffusion processes. The application of a new variational approach to the constructed system of equations made it possible to obtain expressions of the crystal growth rate from a multicomponent melt convenient for practical calculations. The obtained technique allowed us to analyze the features of crystal growth at high rate of crystallization front, which leads to “impurity capture” effect – deviation from equilibrium conditions at the phase interface. The developed mathematical model makes it possible to calculate the growth rate of new phase particles and to estimate the effect of metastable effects on deviation of the components’ concentration at surface of the growing crystal from equilibrium values. Thus, using the obtained method, a “metastable” phase diagram of the system under study can be constructed. The developed approach is applied to the calculation of growth of α-Fe(Si) nanocrystals during annealing of amorphous alloy Fe73,5 Cu1 Nb3 Si13,5B9. The calculation results were compared with the results of the experiment on the alloy primary crystallization. It is shown that the concentration of Fe at the surface of the growing crystal does not significantly deviate from the equilibrium values. On the other hand, silicon atoms are captured by the crystallization front, silicon concentration at the surface of the growing nanocrystal deviates significantly from equilibrium values. The calculation has shown that after the initial crystallization of the amorphous phase, occurring at a temperature of 400 – 450 °C, the deviation of silicon concentration from equilibrium value is about 2 %, while this equilibrium value is about 13.3 %.

Thermodynamic Regularities of Nuclei Growth during Crystallization of Metastable Alloys

2020 ◽  
Vol 299 ◽  
pp. 436-441
Author(s):  
Maxim V. Dudorov ◽  
Alexander D. Drozin ◽  
Victor P. Chernobrovin
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
High Speed ◽  
Local Equilibrium ◽  
Phase Interface ◽  
Chemical Methods ◽  
Physico Chemical ◽  
Interfacial Surface ◽  
Metastable Alloys ◽  
Metastable Effects

The process of crystal growth in a metastable multicomponent melt has a high speed of the solidification front, which captures atoms of some other components. As a result of such a growth, at the surface of the growing crystal the effect of “impurity capture” is observed, and the concentrations of components significantly deviate from the local equilibrium. Under such conditions, the conventional physico-chemical methods for description of processes at the interfacial surface become inapplicable. Therefore, a new variational approach was applied for an integrated description of diffusion and thermal processes at the phase interface. The growth rate of crystal nucleus in a metastable melt was obtained, using the methods of non-equilibrium thermodynamics. The developed approach allows estimation of the degree of metastable effects influence on a crystal growth rate.

Features of the Use of Equilibrium State Diagrams for Description of Crystal Growth from Metastable Melts

2020 ◽  
Vol 299 ◽  
pp. 622-627
Author(s):  
Maxim V. Dudorov ◽  
Alexander D. Drozin ◽  
B.G. Plastinin
Keyword(s):  
Growth Rate ◽  
Crystal Surface ◽  
Crystallization Front ◽  
Local Equilibrium ◽  
Product Formation ◽  
Metal Alloys ◽  
High Rate ◽  
Crystal Nucleus ◽  
State Diagrams ◽  
Equilibrium Effect

The crystallization of metastable metal alloys is characterized by a high rate of the crystallization front, which leads to the effect of "impurity capture" and deviation from the local equilibrium near the surface of the growing crystal. To calculate the growth rate of the crystalline nuclei, a method was developed for prediction of deviation of the components’ concentration near the crystal surface from the equilibrium values. A crystal nucleus was considered to be growing from the initial multicomponent phase, due to interphase transition of the components through its surface. It became possible to distinguish the equilibrium and non-equilibrium effect of the nucleus growth rate by decomposing the molar rate of the product formation near equilibrium, as a function of the molar concentration of the components in the Taylor series and limiting with the linear members. The practical calculations were carried out for the crystallization of the amorphous alloy Fe73,5Cu1Nb3Si13,5B9 of the FINEMET type. The local deviations were investigated for the silicon concentration from the equilibrium values at the surface of the growing crystal.

TEMPERATURE DEPENDENCE OF THE CRYSTAL GROWTH RATE IN POLAR GLACIERS

1987 ◽  
Vol 48 (C1) ◽  
pp. C1-661-C1-662 ◽  
Author(s):  
J. R. PETIT ◽  
P. DUVAL ◽  
C. LORIUS
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Temperature Dependence ◽  
Crystal Growth Rate

Comparison of copper sulphate pentahydrate growth rates determined by different methods

1990 ◽  
Vol 55 (7) ◽  
pp. 1691-1707 ◽  
Author(s):  
Miloslav Karel ◽  
Jiří Hostomský ◽  
Jaroslav Nývlt ◽  
Axel König
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Fluidized Bed ◽  
Growth Rates ◽  
Copper Sulphate ◽  
Crystal Growth Rate ◽  
Effect Of Temperature ◽  
Rotating Disc ◽  
Shape Factors ◽  
Data Treatment

Crystal growth rates of copper sulphate pentahydrate (CuSO4.5 H2O) determined by different authors and methods are compared. The methods included in this comparison are: (i) Measurement on a fixed crystal suspended in a streaming solution, (ii) measurement on a rotating disc, (iii) measurement in a fluidized bed, (iv) measurement in an agitated suspension. The comparison involves critical estimation of the supersaturation used in measurements, of shape factors used for data treatment and a correction for the effect of temperature. Conclusions are drawn for the choice of values to be specified when data of crystal growth rate measurements are published.

Optical resolution of N-formylphenylalanine succeeds by crystal growth rate differences of diastereomeric salts

2007 ◽  
Vol 18 (2) ◽  
pp. 260-264 ◽  
Author(s):  
Laura Bereczki ◽  
Emese Pálovics ◽  
Petra Bombicz ◽  
György Pokol ◽  
Elemér Fogassy ◽  
...  
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Optical Resolution ◽  
Crystal Growth Rate ◽  
Diastereomeric Salts

Crystal-growth kinetics of protein single crystals along capillary tubes in the gel-acupuncture technique

1999 ◽  
Vol 55 (2) ◽  
pp. 577-580 ◽  
Author(s):  
Abel Moreno ◽  
Manuel Soriano-García
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Capillary Tube ◽  
Crystal Growth Rate ◽  
Equilibrium Studies ◽  
Acta Cryst ◽  
Average Growth ◽  
X Ray Crystallography ◽  
Growing Cell ◽  
Kinetics Of

In attempts to obtain protein crystals of a sufficient size for structural studies, lack of knowledge of the physicochemical properties of protein solutions and of their crystal-growth behaviour lead to a bottleneck for drug design as well as for X-ray crystallography. Most formal investigations on crystal-growth phenomena have been focused on equilibrium studies, where the protein is soluble, and on the kinetics of crystal growth, which is related to both nucleation and crystal-growth phenomena. The aim of this work is to measure the crystal-growth rate along a capillary tube used as a growing cell. These experiments were carried out using the gel-acupuncture technique [García-Ruiz et al. (1993). Mater. Res. Bull. 28, 541–546; García-Ruiz & Moreno (1994). Acta Cryst. D50, 484–490; García-Ruiz & Moreno (1997). J. Cryst. Growth, 178, 393–401]. Crystal-growth investigations took place using lysozyme and thaumatin I as standard proteins. The maximum average growth rate obtained in the lower part of the capillary tube was about 35 Å s−1 and the minimum average growing rate in the upper part of the capillary tube was about 8 Å s−1. The crystal-growth rate as a function of the supersaturation was experimentally estimated at a constant height along the capillary tube.

Phase separation in undercooled molten Pd80Si20: Part I

1999 ◽  
Vol 14 (9) ◽  
pp. 3653-3662 ◽  
Author(s):  
K. L. Lee ◽  
H. W. Kui
Keyword(s):  
Growth Rate ◽  
Phase Separation ◽  
Crystal Growth ◽  
Grain Refinement ◽  
Crystallization Temperature ◽  
Sharp Decrease ◽  
Nucleation And Growth ◽  
Crystal Growth Rate ◽  
Large Undercooling ◽  
Kinetic Crystallization

Three different kinds of morphology are found in undercooled Pd80Si20, and they dominate at different undercooling regimens ΔT, defined as ΔT = T1 – Tk, where T1 is the liquidus of Pd80Si20 and Tk is the kinetic crystallization temperature. In the small undercooling regimen, i.e., for ΔT ≤ 190 K, the microstructures are typically dendritic precipitation with a eutecticlike background. In the intermediate undercooling regimen, i.e., for 190 ≤ ΔT ≤ 220 K, spherical morphologies, which arise from nucleation and growth, are identified. In addition, Pd particles are found throughout an entire undercooled specimen. In the large undercooling regimen, i.e., for ΔT ≥ 220 K, a connected structure composed of two subnetworks is found. A sharp decrease in the dimension of the microstructures occurs from the intermediate to the large undercooling regimen. Although the crystalline phases in the intermediate and the large undercooling regimens are the same, the crystal growth rate is too slow to bring about the occurrence of grain refinement. Combining the morphologies observed in the three undercooling regimens and their crystallization behaviors, we conclude that phase separation takes place in undercooled molten Pd80Si20.

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