Directed Growth of Ferrite in Austenite and Kurdjumov-Sachs Orientation Relationship

2012 ◽  
Vol 715-716 ◽  
pp. 128-133
Author(s):  
Dong Nyung Lee ◽  
Heung Nam Han
Keyword(s):  
Growth Rate ◽  
Orientation Relationship ◽  
Strain Energy ◽  
Lattice Mismatch ◽  
Solid Phase ◽  
Metastable Phase ◽  
Maximum Growth ◽  
Growth Direction ◽  
Stable Phase ◽  
Directed Growth

The solid phase transformation of a metastable phase into a stable phase needs the activation energy. The energy is usually supplied in the form of thermal energy. When the nucleation takes place, the strain energy may develop in the metastable matrix and the stable nucleus. The strain energy can result from differences in density of the nucleus and matrix and the lattice mismatch between the nucleus and matrix. The stable-metastable interface region has the highest strain-energy density in the maximum Youngs modulus direction of the stable phase. Accordingly, the growth rate of the stable phase is the highest in its highest Youngs modulus directions. As the transformation temperature decreases, the strain energy contribution increases and the growth rate anisotropy is likely to increase. When austenite transforms into ferrite at low temperatures, the directed growth of ferrite is observed as forms of Widmanstätten ferrite plates and acicular ferrite plates. The maximum growth direction of ferrite is along the maximum Youngs modulus direction of ferrite, <111>α, and the broad interfaces are parallel to the maximum growth direction and formed so that they minimizes the shear strain energy in the interface layer. The directed growth results in the Kurdjumov-Sachs orientation relationship between austenite and ferrite, <111>α//<110>γand {110}α//{111}γ.

Orientation Relationships between Directionally Grown Precipitates and their Parent Phases in Steels

2012 ◽  
Vol 706-709 ◽  
pp. 61-68
Author(s):  
Dong Nyung Lee ◽  
Heung Nam Han
Keyword(s):  
Strain Energy ◽  
Lattice Mismatch ◽  
Solid Phase ◽  
Metastable Phase ◽  
Parent Phase ◽  
Maximum Growth ◽  
Interface Energy ◽  
Stable Phase ◽  
Orientation Relationships ◽  
Parent Austenite

There are four prominent orientation relationships (ORs) between directionally grown precipitates and their parent phases in steel. They are ORs between ferrite precipitate and parent austenite (the Kurdjumov and Sachs OR), between orthorhombic cementite precipitate and parent austenite (the Pitsch OR), between cementite precipitate and parent ferrite (the Bagaryatski OR) and between hexagonal molybdenum carbide precipitate and parent ferrite (the Dysonet al.OR). The directed precipitation occurs at low transformation temperatures. The ORs have been explained by the directed growth model. The solid phase transformation of a metastable phase into a stable phase needs the activation energy. The energy is usually supplied in the form of thermal energy. When the nucleation takes place, the strain energy may develop in the stable nucleus and the metastable matrix. The strain energy can result from a difference in density between the nucleus and matrix and the lattice mismatch along the nucleus:matrix interface. The fundamental concept of the model is that the maximum growth rate of precipitate is along the direction that generates the maximum strain energy and the interface energy is minimized. The four ORs are determined, based on the concept, such that the mismatch along the interface between the minimum shear modulus planes of precipitate and its parent phase that are parallel to the maximum Young’s modulus direction of the precipitate is minimized.

scholarly journals The kinetics of solvent-mediated phase transformations

1985 ◽  
Vol 398 (1815) ◽  
pp. 415-428 ◽  
Keyword(s):  
Copper Phthalocyanine ◽  
Solid Phase ◽  
Metastable Phase ◽  
Phase Changes ◽  
Growth Time ◽  
Stable Phase ◽  
Surface Areas ◽  
Mechanistic Insight ◽  
Time Required ◽  
Kinetics Of

A number of mineralogical and synthetic precipitates undergo solid to solid phase changes via a solution phase. A review of the literature reveals a lack of both experimental data and a framework for its interpretation. A model is developed, for the case of a polymorphic phase transformation, which involves the dissolution of the metastable phase and growth of nuclei of the stable phase. The concepts of dissolution and growth time scales have been introduced and it is shown that their sum is the time required for the disappearance of the metastable phase. Mechanistic insight is best obtained by measure­ment of the supersaturation profile rather than conversion data. It is shown that such profiles are dominated by the plateau supersaturation, which is the point at which dissolution and growth are balanced. Its value is determined by the relative surface areas of the phases and their kinetic constants. The model has been successfully used to simulate available kinetic data for the α → β polymorphic transformation in copper phthalocyanine.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

scholarly journals Stable and Metastable Phase Equilibria Involving the Cu6Sn5 Intermetallic

2021 ◽  
Author(s):  
A. Leineweber ◽  
M. Löffler ◽  
S. Martin
Keyword(s):  
Phase Equilibria ◽  
Electron Backscatter Diffraction ◽  
Metastable Phase ◽  
Stable Phase ◽  
X Ray Diffraction ◽  
X Ray ◽  
Heat Treated ◽  
Ordered Phases ◽  
Backscatter Diffraction ◽  
Kinetics Of

Abstract Cu6Sn5 intermetallic occurs in the form of differently ordered phases η, η′ and η′′. In solder joints, this intermetallic can undergo changes in composition and the state of order without or while interacting with excess Cu and excess Sn in the system, potentially giving rise to detrimental changes in the mechanical properties of the solder. In order to study such processes in fundamental detail and to get more detailed information about the metastable and stable phase equilibria, model alloys consisting of Cu3Sn + Cu6Sn5 as well as Cu6Sn5 + Sn-rich melt were heat treated. Powder x-ray diffraction and scanning electron microscopy supplemented by electron backscatter diffraction were used to investigate the structural and microstructural changes. It was shown that Sn-poor η can increase its Sn content by Cu3Sn precipitation at grain boundaries or by uptake of Sn from the Sn-rich melt. From the kinetics of the former process at 513 K and the grain size of the η phase, we obtained an interdiffusion coefficient in η of (3 ± 1) × 10−16 m2 s−1. Comparison of this value with literature data implies that this value reflects pure volume (inter)diffusion, while Cu6Sn5 growth at low temperature is typically strongly influenced by grain-boundary diffusion. These investigations also confirm that η′′ forming below a composition-dependent transus temperature gradually enriches in Sn content, confirming that Sn-poor η′′ is metastable against decomposition into Cu3Sn and more Sn-rich η or (at lower temperatures) η′. Graphic Abstract

Effect Of Phosphorus On Ge/Si(001) Island Formation

2002 ◽  
Vol 737 ◽  
Author(s):  
Theodore I. Kamins ◽  
Gilberto Medeiros-Ribeiro ◽  
Douglas A. A. Ohlberg ◽  
R. Stanley Williams
Keyword(s):  
Deposition Rate ◽  
Strain Energy ◽  
Competitive Adsorption ◽  
Lattice Mismatch ◽  
Three Dimensional ◽  
Deposition Process ◽  
Thin Layers ◽  
Island Size ◽  
Partial Pressures ◽  
Intermediate Size

ABSTRACTWhen Ge is deposited epitaxially on Si, the strain energy from the lattice mismatch causes the Ge in layers thicker than about four monolayers to form distinctive, three-dimensional islands. The shape of the islands is determined by the energies of the surface facets, facet edges, and interfaces. When phosphorus is added during the deposition, the surface energies change, modifying the island shapes and sizes, as well as the deposition process. When phosphine is introduced to the germane/hydrogen ambient during Ge deposition, the deposition rate decreases because of competitive adsorption. The steady-state deposition rate is not reached for thin layers. The deposited, doped layers contain three different island shapes, as do undoped layers; however, the island size for each shape is smaller for the doped layers than for the corresponding undoped layers. The intermediate-size islands are the most significant; the intermediate-size doped islands are of the same family as the undoped, multifaceted “dome” structures, but are considerably smaller. The largest doped islands appear to be related to the defective “superdomes” discussed for undoped islands. The distribution between the different island shapes depends on the phosphine partial pressure. At higher partial pressures, the smaller structures are absent. Phosphorus appears to act as a mild surfactant, suppressing small islands.

A note on growth curves of rabbit lines selected on growth rate or litter size

1993 ◽  
Vol 57 (2) ◽  
pp. 332-334 ◽  
Author(s):  
A. Blasco ◽  
E. Gómez
Keyword(s):  
Growth Rate ◽  
Litter Size ◽  
Growth Curves ◽  
Live Weight ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Standard Errors ◽  
Adult Weight ◽  
Weight Growth ◽  
Using Data

Two synthetic lines of rabbits were used in the experiment. Line V, selected on litter size, and line R, selected on growth rate. Ninety-six animals were randomly collected from 48 litters, taking a male and a female each time. Richards and Gompertz growth curves were fitted. Sexual dimorphism appeared in the line V but not in the R. Values for b and k were similar in all curves. Maximum growth rate took place in weeks 7 to 8. A break due to weaning could be observed in weeks 4 to 5. Although there is a remarkable similarity of the values of all the parameters using data from the first 20 weeks only, the higher standard errors on adult weight would make 30 weeks the preferable time to take data for live-weight growth curves.

Macrosegregation of Y2Ba1Cu1O5 particles in Y1Ba2Cu3O7−δ crystals grown by an undercooling method

1996 ◽  
Vol 11 (4) ◽  
pp. 795-803 ◽  
Author(s):  
A. Endo ◽  
H. S. Chauhan ◽  
T. Egi ◽  
Y. Shiohara
Keyword(s):  
Growth Rate ◽  
Flux Pinning ◽  
Faraday Effect ◽  
Growth Direction ◽  
Pinning Force ◽  
Garnet Film ◽  
Iron Garnet ◽  
Flux Pinning Force ◽  
Good Agreement ◽  
Iron Garnet Film

Macrosegregation of Y2Ba1Cu1O5 (Y211) particles was observed in Pt-added Y1Ba2Cu3O7−δ (Y123) crystals grown by an undercooling method. It was found that the macrosegregation of Y211 particles depended on the growth direction and the growth rate (R) as a function of undercooling (ΔT). The amount of Y211 particles in Y123 crystals grown at large R was larger than at small R. Also, the amount of Y211 in Y123 growing along the a-direction was larger than that along the c-direction. Further, it was noted that the smaller Y211 particles in size were distributed in Y123 grown at large R. These phenomena could be at least qualitatively explained by the prevalent trapping/pushing theory. In the direct observation of magnetic flux with the Faraday effect of iron garnet film, the flux pinning force was found to be in good agreement with the macrosegregation of Y211 particles.

Ecophenotypic plasticity in shell growth direction of asari clam Ruditapes philippinarum

2021 ◽  
pp. 1-6
Author(s):  
Takeshi Tomiyama
Keyword(s):  
Growth Rate ◽  
Shell Growth ◽  
Shell Height ◽  
Growth Direction ◽  
Ruditapes Philippinarum ◽  
Shell Morphology ◽  
Individual Growth ◽  
Shell Size ◽  
Internal Factors ◽  
Suitable Habitats

Abstract Asari clam (or Manila clam) Ruditapes philippinarum is an important bivalve for local fisheries. This species exhibits a large variation in shell morphology, and the shell roundness tends to be greater in more unsuitable habitats. To test whether the increments in shell size parameters (length, height and width) were affected solely by environmental conditions or by internal factors such as initial shell shapes or growth rate, a field caging experiment was conducted at two different sites of unsuitable and suitable habitats in Matsukawaura Lagoon, Japan, where shell shapes of wild clams were significantly different between the habitats. In the experiment, clams were released from the two sites to the same site or to the other site and were re-collected after 3, 6 and 12 months of caging. Caged clams originating from unsuitable habitats and released to suitable habitats showed a reduction in shell height relative to shell length, while clams from suitable habitats introduced to unsuitable habitats showed marked increases in both shell height and width. Generalized linear mixed models suggested that the increase in shell height was affected largely by the release habitat (environment) whereas the increase in shell width was affected largely by the individual growth rate. These results suggest that marginal growths in shell height and width respond differently to external and internal factors of clams, resulting in plasticity in their shell shapes according to the environments to which they are translocated.

Reassessment of Maximum Growth Rates for C3 and C4 Crops

1978 ◽  
Vol 14 (1) ◽  
pp. 1-5 ◽  
Author(s):  
J. L. Monteith
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Growing Season ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Crop Growth ◽  
Close Inspection ◽  
Similar Difference ◽  
Photosynthetic Efficiencies

SUMMARYFigures for maximum crop growth rates, reviewed by Gifford (1974), suggest that the productivity of C3 and C4 species is almost indistinguishable. However, close inspection of these figures at source and correspondence with several authors revealed a number of errors. When all unreliable figures were discarded, the maximum growth rate for C3 stands fell in the range 34–39 g m−2 d−1 compared with 50–54 g m−2 d−1 for C4 stands. Maximum growth rates averaged over the whole growing season showed a similar difference: 13 g m−2 d−1 for C3 and 22 g m−2 d−1 for C4. These figures correspond to photosynthetic efficiencies of approximately 1·4 and 2·0%.

scholarly journals Growth of GaN from elemental Gallium and Ammonia via Modified Sandwich Growth Technique

2004 ◽  
Vol 831 ◽  
Author(s):  
E. Berkman ◽  
R. Collazo ◽  
R. Schlesser ◽  
Z. Sitar
Keyword(s):  
Growth Rate ◽  
Gas Flow ◽  
Transport Model ◽  
Theoretical Calculations ◽  
Substrate Surface ◽  
Maximum Growth ◽  
Direct Reaction ◽  
Pure Nitrogen ◽  
Flow Rates ◽  
Reactor Pressure

ABSTRACTGallium nitride (GaN) films were grown on (0001) sapphire substrates at 1050°C by controlled evaporation of gallium (Ga) metal and reaction with ammonia (NH3) at a total reactor pressure of 800 Torr. Pure nitrogen (N2) was flowed directly above the molten Ga source to prevented direct reaction between the molten Ga and ammonia, which causes Ga spattering and GaN crust formation. At the same time, this substantially enhanced the Ga transport to the substrate. A simple mass-transport model based on total reactor pressure, gas flow rates and source temperature was developed and verified. The theoretical calculations and growth rate measurements at different ammonia flow rates and reactor pressures showed that the maximum growth rate was controlled by transport of both Ga species and reactive ammonia to the substrate surface.

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