scholarly journals Crystal Growth and Solute Trapping

1983 ◽  
Vol 23 ◽  
Author(s):  
Michael J. Aziz
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Laser Annealing ◽  
Solute Drag ◽  
Irreversible Processes ◽  
Maximum Speed ◽  
Growth Speed ◽  
Solute Trapping ◽  
Order Of Magnitude ◽  
Energy Dissipated

ABSTRACTA simple model for solute trapping during rapid solidification is presented in terms of a single unknown parameter, the interfacial diffusivity Di. A transition from equilibrium segregation to complete solute trapping occurs over roughly an order of magnitude in growth speed, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal. This diffusive speed is given by Di/λ, where λ is the interatomic spacing, and is typically of the order 10 meters per second. Comparison is made with experiment. The steady–state speed of a planar interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. A solute drag term and an intrinsic interfacial mobility term are included in the dissipation calculations. Steady–state solutions are presented for Bi–doped Si during pulsed laser annealing.

CRYSTAL GROWTH AND THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES

1959 ◽  
Vol 37 (6) ◽  
pp. 739-754 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Dendritic Growth ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Interface Morphology ◽  
Crystal Face ◽  
Thermodynamics Of Irreversible Processes ◽  
Alloy Crystal

The principle of minimum rate of entropy production is applied to steady-state transport processes in the neighborhood of an alloy crystal face growing into its melt. The procedure gives a satisfactory rationale of observed interface morphology. It is noted that segregation, which occurs in cellular or dendritic growth of alloys, is a direct manifestation of the system's attempt to minimize entropy production by conserving free energy. The general problems of growth of pure and impure single crystals from the melt and vapor are discussed.

scholarly journals The Role of Grain Boundary Diffusion in the Solute Drag Effect

Nanomaterials ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 2348
Author(s):  
R. K. Koju ◽  
Y. Mishin
Keyword(s):  
Free Energy ◽  
Solute Drag ◽  
Md Simulations ◽  
Lattice Diffusion ◽  
Solute Diffusion ◽  
Drag Effect ◽  
Solute Drag Effect ◽  
Order Of Magnitude ◽  
Thermodynamic Stabilization

Molecular dynamics (MD) simulations are applied to study solute drag by curvature-driven grain boundaries (GBs) in Cu–Ag solid solution. Although lattice diffusion is frozen on the MD timescale, the GB significantly accelerates the solute diffusion and alters the state of short-range order in lattice regions swept by its motion. The accelerated diffusion produces a nonuniform redistribution of the solute atoms in the form of GB clusters enhancing the solute drag by the Zener pinning mechanism. This finding points to an important role of lateral GB diffusion in the solute drag effect. A 1.5 at.%Ag alloying reduces the GB free energy by 10–20% while reducing the GB mobility coefficients by more than an order of magnitude. Given the greater impact of alloying on the GB mobility than on the capillary driving force, kinetic stabilization of nanomaterials against grain growth is likely to be more effective than thermodynamic stabilization aiming to reduce the GB free energy.

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.

scholarly journals Verification of Equation for Evaluating Dislocation Density during Steady-state Creep of Metals

2017 ◽  
Vol 6 (2) ◽  
pp. 20 ◽  
Author(s):  
Manabu Tamura
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Dislocation Density ◽  
Shear Modulus ◽  
Strain Rate ◽  
Gibbs Free Energy ◽  
Steady State Creep ◽  
Austenitic Steels ◽  
Exponential Factor ◽  
Delta G

Ninety-two sets of observed dislocation densities for crept specimens of 21 types of ferritic/martensitic and austenitic steels, Al, W, Mo, and Mg alloys, Cu, and Ti including germanium single crystals were collected to verify an equation for evaluating the dislocation density during steady-state creep proposed by Tamura and Abe (2015). The activation energy, Qex, activation volume, Vex, and Larson–Miller constant, Cex, were calculated from the creep data. Using these parameter constants, the strain rate, and the temperature dependence of the shear modulus, a correction term, Gamma, was back-calculated from the observed dislocation density for each material. Gamma is defined in the present paper as a function of the temperature dependences of both the shear modulus and pre-exponential factor of the strain rate. The values of Gamma range from −394 to 233  and average 2.1 KJmol-1, which is a value considerably lower than the average value of Qex (410.4 KJmol-1), and values of Gamma are mainly within the range from 0 to 50 KJmol-1. The change in Gibbs free energy, Delta G, for creep deformation is obtained using the calculated value of , and the empirical relation Delta G~Delta GD is found, where Delta GD is the change in Gibbs free energy for self-diffusion of the main componential element of each material. Experimental data confirm the validity of the evaluation equation for the dislocation density.

The A39G FF domain folds on a volcano-shaped free energy surface via separate pathways

2021 ◽  
Vol 118 (46) ◽  
pp. e2115113118
Author(s):  
Ved P. Tiwari ◽  
Yuki Toyama ◽  
Debajyoti De ◽  
Lewis E. Kay ◽  
Pramodh Vallurupalli
Keyword(s):  
Free Energy ◽  
Chemical Exchange ◽  
Exchange Process ◽  
Conformational Dynamics ◽  
Chemical Exchange Saturation Transfer ◽  
Folding Kinetics ◽  
Free Energy Surface ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Energy Surfaces

Conformational dynamics play critical roles in protein folding, misfolding, function, misfunction, and aggregation. While detecting and studying the different conformational states populated by protein molecules on their free energy surfaces (FESs) remain a challenge, NMR spectroscopy has emerged as an invaluable experimental tool to explore the FES of a protein, as conformational dynamics can be probed at atomic resolution over a wide range of timescales. Here, we use chemical exchange saturation transfer (CEST) to detect “invisible” minor states on the energy landscape of the A39G mutant FF domain that exhibited “two-state” folding kinetics in traditional experiments. Although CEST has mostly been limited to studies of processes with rates between ∼5 to 300 s−1 involving sparse states with populations as low as ∼1%, we show that the line broadening that is often associated with minor state dips in CEST profiles can be exploited to inform on additional conformers, with lifetimes an order of magnitude shorter and populations close to 10-fold smaller than what typically is characterized. Our analysis of CEST profiles that exploits the minor state linewidths of the 71-residue A39G FF domain establishes a folding mechanism that can be described in terms of a four-state exchange process between interconverting states spanning over two orders of magnitude in timescale from ∼100 to ∼15,000 μs. A similar folding scheme is established for the wild-type domain as well. The study shows that the folding of this small domain proceeds through a pair of sparse, partially structured intermediates via two discrete pathways on a volcano-shaped FES.

scholarly journals Geometry and Dynamics of a Surge-type Glacier

1977 ◽  
Vol 18 (79) ◽  
pp. 181-194 ◽  
Author(s):  
R. Bindschadler ◽  
W. D. Harrison ◽  
C. F. Raymond ◽  
R. Crosson
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Internal Stress ◽  
Ice Thickness ◽  
Surface Slope ◽  
Local Surface ◽  
Order Of Magnitude ◽  
Internal Deformation ◽  
Longitudinal Profiles ◽  
Similar Depth

AbstractMeasurement of geometry, motion, and mass balance from Variegated Glacier, Alaska portray conditions in this surge-type glacier close to the mid-point of its 20 year surge cycle. Comparison of longitudinal profiles of ice depth, surface slope, and surface speed indicate that the motion occurs largely by internal deformation assuming the ice deforms according to the experimental law of Glen. Surface speed is not noticeably affected by local surface slope on the scale of the ice thickness or smaller, but correlates well with slope determined on a longitudinal averaging scale about one order of magnitude larger than the ice depth. The rate of motion on Variegated Glacier agrees well with rates on non-surge type temperate glaciers which have similar depth and slope. Although the (low regime at the time of the measurements is apparently typical of temperate glaciers, a large discrepancy between the balance flux needed for steady state and the actual flux is indicative of a rapidly changing surface elevation profile and internal stress distribution.

Temperature dependence of oxygen diffusion and consumption in mammalian striated muscle

1993 ◽  
Vol 264 (6) ◽  
pp. H1825-H1830 ◽  
Author(s):  
T. B. Bentley ◽  
H. Meng ◽  
R. N. Pittman
Keyword(s):  
Diffusion Coefficient ◽  
Steady State ◽  
Oxygen Diffusion ◽  
Striated Muscle ◽  
Effect Of Temperature ◽  
Retractor Muscle ◽  
Oxygen Solubility ◽  
Order Of Magnitude

This study investigated the effect of temperature on the oxygen diffusion coefficient (DO2) of hamster retractor muscle from 11 to 37 degrees C. DO2 was measured using a non-steady-state technique, whereas muscle O2 consumption (VO2) was estimated after steady state was reached. DO2 was 0.84 +/- 0.04 x 10(-5) cm2/s at 11 degrees C and rose exponentially to 2.41 +/- 0.19 x 10(-5) cm2/s at 37 degrees C, producing a temperature coefficient for DO2 of 4.60%/degrees C for this temperature range. To measure DO2 directly at 37 degrees C, it was necessary to inhibit tissue VO2 with Amytal. The DO2 measurements made at 37 degrees C were significantly higher than previously reported values, which had been based on extrapolations from lower temperatures (6). Further analysis suggests a possible transition in the diffusion pathway between 23 and 30 degrees C, resulting in a DO2 higher than that previously expected. This larger DO2, together with a recently published value of oxygen solubility (alpha) (21), results in an in vitro Krogh's diffusion coefficient (KO2) that is 2.4 times larger than that previously reported (24) and therefore significantly reduces an order of magnitude discrepancy between in vitro and estimated in vivo KO2 values (24). Muscle VO2 was 0.35 ml O2.min-1.100 g-1 at 11 degrees C and increased with temperature, resulting in an activation energy of the rate-limiting reaction from the Arrhenius equation of -10.5 kcal/mol between 11 and 30 degrees C.

scholarly journals Dynamics of grain boundary premelting

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
M. Torabi Rad ◽  
G. Boussinot ◽  
M. Apel
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Grain Boundary ◽  
Liquid Layer ◽  
Phase Field Model ◽  
Melting Process ◽  
State Growth ◽  
Curvature Driven ◽  
Multi Phase ◽  
Solid Liquid Interface

AbstractThe mechanical strength of a polycrystalline material can be drastically weakened by a phenomenon known as grain boundary (GB) premelting that takes place, owing to the so-called disjoining potential, when the dry GB free energy $$\sigma _{gb}$$ σ gb exceeds twice the free energy of the solid–liquid interface $$\sigma _{sl}$$ σ sl . While previous studies of GB premelting are all limited to equilibrium conditions, we use a multi-phase field model to analyze premelting dynamics by simulating the steady-state growth of a liquid layer along a dry GB in an insulated channel and the evolution of a pre-melted polycrystalline microstructure. In both cases, our results reveal the crucial influence of the disjoining potential. A dry GB transforms into a pre-melted state for a grain-size-dependent temperature interval around $$T_m$$ T m , such that a critical overheating of the dry GBs over $$T_m$$ T m should be exceeded for the classical melting process to take place, the liquid layer to achieve a macroscopic width, and the disjoining potential to vanish. Our simulations suggest a steady-state velocity for this transformation proportional to $$\sigma _{gb} -2 \sigma _{sl}$$ σ gb - 2 σ sl . Concerning the poly-crystalline evolution, we find unusual grain morphologies and dynamics, deriving from the existence of a pre-melted polycrystalline equilibrium that we evidence. We are then able to identify the regime in which, due to the separation of the involved length scales, the dynamics corresponds to the same curvature-driven dynamics as for dry GBs, but with enhanced mobility.

High-Temperature Mechanical Behavior of B2 Type IrAl Doped With Ni

1996 ◽  
Vol 460 ◽  
Author(s):  
A. Chiba ◽  
T. Ono ◽  
X. G. Li ◽  
S. Takahashi
Keyword(s):  
Steady State ◽  
Mechanical Behavior ◽  
Constant Velocity ◽  
Single Phase ◽  
Elevated Temperatures ◽  
Constant Load ◽  
Secondary Creep ◽  
Compression Tests ◽  
Order Of Magnitude ◽  
Multi Phase

ABSTRACTConstant-velocity and constant-load compression tests have been conducted to examine the mechanical behavior of polycrystalline IrAl and Ir1-xNixAl at ambient and elevated temperatures. Although IrAl exhibits brittle fracture before or immediately after yielding below 1073K, steady-state deformation takes place at temperatures higher than 1273K. Ductility of Ir1-xNixAl is improved with increasing x. On the contrary, strength decreases with increasing x. IrAl exhibits the 0.2% flow stress of 1200MPa at 1073K and 350MPa at 1473K, about an order of magnitude higher than NiAl. Secondary creep of IrAl and Ir0.2Ni0.8Al(i.e., modified NiAl) exhibits class II and class I behavior respectively. Creep strength of binary IrAl and modified NiAl with Ir is about a magnitude of 4 higher than that of single-phase and multi-phase NiAl at a given applied stress.

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