The Scheil Equation

2020 ◽  
pp. 162-179
Author(s):  
Brian Cantor
Keyword(s):  
20Th Century ◽  
Thermal Conditions ◽  
Nucleation And Growth ◽  
Homogeneous Material ◽  
Max Planck ◽  
Two Phase ◽  
Scheil Equation ◽  
Material Type ◽  
Eutectic Materials ◽  
Spatial Redistribution

Many materials are manufactured by solidification, either as a final product by casting, or as an intermediate ingot or bar. The Scheil equation describes the partitioning that takes place during solidification and the resulting spatial redistribution of solute, which makes it difficult to maintain a homogeneous material composition, and which leads to unwanted concentrations of harmful impurities. This chapter explains nucleation and growth processes during solidification, the resulting dendritic, faceted, equiaxed and columnar structures depending on thermal conditions and material type, coupled solidification of two-phase eutectic materials, and typical casting methods and associated structures and defects. Very little is known about Erich Scheil, who worked at the Max Planck Institute in Stuttgart in the mid-20th century.

scholarly journals Nonlinear multiscale simulation of instabilities due to growth of an elastic film on a microstructured substrate

2020 ◽  
Vol 90 (11) ◽  
pp. 2397-2412
Author(s):  
Iman Valizadeh ◽  
Oliver Weeger
Keyword(s):  
Deformation Gradient ◽  
Multiscale Simulation ◽  
Numerical Results ◽  
Unit Cell ◽  
Homogeneous Material ◽  
Two Phase ◽  
Biological Phenomena ◽  
Elastic Film ◽  
Living Tissues ◽  
Analytical Approaches

Abstract The objective of this contribution is the numerical investigation of growth-induced instabilities of an elastic film on a microstructured soft substrate. A nonlinear multiscale simulation framework is developed based on the FE2 method, and numerical results are compared against simplified analytical approaches, which are also derived. Living tissues like brain, skin, and airways are often bilayered structures, consisting of a growing film on a substrate. Their modeling is of particular interest in understanding biological phenomena such as brain development and dysfunction. While in similar studies the substrate is assumed as a homogeneous material, this contribution considers the heterogeneity of the substrate and studies the effect of microstructure on the instabilities of a growing film. The computational approach is based on the mechanical modeling of finite deformation growth using a multiplicative decomposition of the deformation gradient into elastic and growth parts. Within the nonlinear, concurrent multiscale finite element framework, on the macroscale a nonlinear eigenvalue analysis is utilized to capture the occurrence of instabilities and corresponding folding patterns. The microstructure of the substrate is considered within the large deformation regime, and various unit cell topologies and parameters are studied to investigate the influence of the microstructure of the substrate on the macroscopic instabilities. Furthermore, an analytical approach is developed based on Airy’s stress function and Hashin–Shtrikman bounds. The wavelengths and critical growth factors from the analytical solution are compared with numerical results. In addition, the folding patterns are examined for two-phase microstructures and the influence of the parameters of the unit cell on the folding pattern is studied.

An experimental study of reflected liquefaction shock waves with near-critical downstream states in a test fluid of large molar heat capacity

1994 ◽  
Vol 277 ◽  
pp. 163-196 ◽  
Author(s):  
Seyfettin C. Gülen ◽  
Philip A. Thompson ◽  
Hung-Jai Cho
Keyword(s):  
Shock Wave ◽  
Heat Capacity ◽  
Phase Change ◽  
Molar Heat Capacity ◽  
Continuous Process ◽  
Nucleation And Growth ◽  
Test Fluid ◽  
Average Lifetime ◽  
Wave System ◽  
Two Phase

Near-critical states have been achieved downstream of a liquefaction shock wave, which is a shock reflected from the endwall of a shock tube. Photographs of the shocked test fluid (iso-octane) reveal a rich variety of phase-change phenomena. In addition to the existence of two-phase toroidal rings which have been previously reported, two-phase structures with a striking resemblance to dandelions and orange slices have been frequently observed. A model coupling the flow and nucleation dynamics is introduced to study the two-wave system of shock-induced condensation and the liquefaction shock wave in fluids of large molar heat capacity. In analogy to the one-dimensional Zeldovich–von Neumann–Döring (ZND) model of detonation waves, the leading part of the liquefaction shock wave is a gasdynamic pressure discontinuity (Δ ≈ 0.1 μm, τ ≈ 1 ns) which supersaturates the test fluid, and the phase transition takes place in the condensation relaxation zone (Δ ≈ 1–103 μm, τ ≈ 0.1–100 μs) via dropwise condensation. At weak to moderate shock strengths, the average lifetime of the metastable state, τ ∞ 1/J, is long such that the reaction zone is spatially decoupled from the forerunner shock wave, and J is the homogeneous nucleation rate. With increasing shock strength, a transition in the phase-change mechanism from nucleation and growth to spinodal decomposition is anticipated based on statistical mechanical arguments. In particular, within a complete liquefaction shock the metastable region is entirely bypassed, and the vapour decomposes inside the unstable region. This mechanism of unmixing in which nucleation and growth become one continuous process provides a consistent framework within which the observed irregularities can be explained.

Explosive crystallization phenomena in SOI structures

1989 ◽  
Vol 4 (6) ◽  
pp. 1473-1479 ◽  
Author(s):  
H. D. Geiler ◽  
M. Wagner ◽  
E. Glaser ◽  
G. Andrä ◽  
D. Wolff ◽  
...  
Keyword(s):  
Solid Phase ◽  
Amorphous Layer ◽  
Nucleation And Growth ◽  
Time Interval ◽  
Two Phase ◽  
Pulse Technique ◽  
Explosive Crystallization ◽  
Crystalline Nucleus ◽  
Phase Nucleation ◽  
Temperature Time

Using the double pulse technique with two synchronized lasers, we studied the conditions of ignition and evolution of explosive crystallization. The structure of the resulting crystallized layers is analyzed by TEM. Results of calculations are reported describing the development of the two phase fronts: amorphous/molten and molten/crystalline. It is shown that the system takes more than 500 ns to reach the steady state. The experimental results support the model of creating first a melt nucleus in the amorphous layer followed by the formation of the crystalline nucleus in the molten sphere. Competitive solid phase nucleation and growth in the amorphous layer limit the temperature-time interval of melt nucleation. Defined explosively crystallized areas in laterally structured SOI layers are presented.

scholarly journals Methodology for Thermal Behaviour Assessment of Homogeneous Façades in Heritage Buildings

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Enrique Gil ◽  
Carlos Lerma ◽  
Jose Vercher ◽  
Ángeles Mas
Keyword(s):  
Thermal Behaviour ◽  
Minimum Energy ◽  
Thermal Conditions ◽  
Homogeneous Material ◽  
Closed Chamber ◽  
Validation And Verification ◽  
Finite Element Software ◽  
Minimum Energy Consumption ◽  
Heritage Buildings ◽  
Comparison Of The Results

It is fundamental to study the thermal behaviour in all architectural constructions throughout their useful life, in order to detect early deterioration ensuring durability, in addition to achieving and maintaining the interior comfort with the minimum energy consumption possible. This research has developed a methodology to assess the thermal behaviour of façades in heritage buildings. This paper presents methodology validation and verification (V & V) through a laboratory experiment. Guidelines and conclusions are extracted with the employment of three techniques in this experiment (thermal sensors, thermal imaging camera, and 3D thermal simulation in finite element software). A small portion of a homogeneous façade has been reproduced with indoor and outdoor thermal conditions. A closed chamber was constructed with wood panels and thermal insulation, leaving only one face exposed to the outside conditions, with a heat source inside the chamber that induces a temperature gradient in the wall. With this methodology, it is possible to better understand the thermal behaviour of the façade and to detect possible damage with the calibration and comparison of the results obtained by the experimental and theoretical techniques. This methodology can be extrapolated to the analysis of the thermal behaviour of façades in heritage buildings, usually made up of homogeneous material.

Kinetics of Oxidation of Columbium And Other Refractory Metals★

CORROSION ◽  
1962 ◽  
Vol 18 (10) ◽  
pp. 382t-389t ◽  
Author(s):  
J. N. ONG ◽  
W. M. FASSELL
Keyword(s):  
Phase Boundary ◽  
Nucleation And Growth ◽  
Rate Equations ◽  
Order Complex ◽  
Two Phase ◽  
Kinetics Of Oxidation ◽  
Chain Reactions ◽  
First Order ◽  
Consecutive Reactions ◽  
Kinetics Of

Abstract The oxidation of tungsten and molybdenum occurs by two consecutive reactions, forming first a suboxide then the trioxide. Tantalum and columbium oxidize by four simultaneous reactions: solution of oxygen in the metal, nucleation and growth of a suboxide phase at the metal surface and two phase boundary processes giving rise to two different modifications of the pentoxide. By assuming that all reactions are first order complex chain reactions, rate equations are formulated giving the rate of oxidation as a function of pressure, temperature and time. Regression rate expressions for the metals tungsten, tantalum and columbium above 700 C are given as;; and, respectively. The rate is expressed in cm/hr, T is in degrees K and Po2 in atmospheres pressure of oxygen. 3.8.4, 2.1,1, 6.3.5, 6.3.16, 6.3.13

Theoretical Treatments of Two-Dimensional Two-Phase Flows of Steam and Comparison with Cascade Measurements

2005 ◽  
Vol 219 (12) ◽  
pp. 1335-1355 ◽  
Author(s):  
F Bakhtar ◽  
A J White ◽  
H Mashmoushy
Keyword(s):  
Numerical Methods ◽  
Nucleation And Growth ◽  
Nucleation Theory ◽  
Two Dimensional ◽  
Wet Steam ◽  
Calculation Methods ◽  
Two Phase ◽  
Droplet Nucleation ◽  
Condensing Flows ◽  
State Path

During the course of expansion of steam in turbines, the state path crosses the saturation line and hence subsequent turbine stages operate with wet steam. These stages have lower thermodynamic efficiencies than those operating in the superheated region, and currently the phenomena contributing to the increased losses are not fully understood. The development of the nucleation theory has opened the way for the study of condensing flows in turbines. As, with the advances in numerical methods, the equations describing droplet nucleation and growth rates can be combined with the field conservation equations and the set treated numerically, which allows the behaviour of complex nucleating and wet steam flows in turbines to be analysed. This paper outlines and reviews wet steam calculation methods and discusses comparisons between numerical and experimental results. For the most part, the comparisons presented are based on work of the authors and their co-workers, but some more recent calculations by other investigators are also included.

Study Of Nucleation And Growth Ev Al-Zn Alloys Using TEM

1993 ◽  
Vol 321 ◽  
Author(s):  
G. Sundar ◽  
E. A. Kenik ◽  
J. J. Hoyt ◽  
S. Spooner
Keyword(s):  
Completion Time ◽  
Nucleation And Growth ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Initial Value ◽  
Two Phase ◽  
Transmission Electron ◽  
Time Required ◽  
Zn Alloys

ABSTRACTNucleation and growth studies were conducted on Al-Zn alloys at several temperatures using transmission electron Microscopy (TEM) with an in-situ furnace. The value of the critical undercooling was established by noting the lowest temperature at which precipitates were no longer observed, following a quench into the two-phase metastable region. These results were compared with the Langer-Schwartz Model of nucleation and growth in which it is predicted that the half-completion time (i.e, the time required for the supersaturation to reach half its initial value) diverges for initial supersaturations which are higher than those predicted by the classical nucleation theory.

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