Matrix Description of Some Thermodynamic Properties of Multicomponent Alloys in Explicit Form

2007 ◽  
Vol 268 ◽  
pp. 51-58
Author(s):  
L.I. Erokhin
Keyword(s):  
Thermodynamic Properties ◽  
Explicit Form ◽  
Short Range ◽  
Binary Systems ◽  
Chemical Potential ◽  
Diffusion Processes ◽  
Diffusion Theory ◽  
Multicomponent Systems ◽  
Multicomponent Alloys ◽  
Practical Applications

A matrix method for description of some thermodynamic properties in multicomponent alloys in explicit form has been proposed. It has been found that the method for determining thermodynamic properties from the cross-section data allows to find the contribution of short-range ordering into the thermodynamic state of an imperfect alloy. Diffusion processes in alloys are formed both from purely kinetic migrations of particles and from the system's thermodynamic properties. A consequence of this fact is that the diffusion coefficients D in all systems except for perfect solid solutions include to factors being D = Lg , the second one is the thermodynamic factor directly related to the system's chemical potential. However direct experimental separation of these factors can easily be performed in binary systems only while in triple systems in is highly difficult let alone multicomponent systems. Experimental evaluation of the factors in multicomponent systems from short-range order's parameters [1] would allow to establish a relation between the system's thermodynamic properties which is highly important for further progress in multicomponent diffusion theory and for practical applications.

The Representation of Thermodynamic Properties in Multicomponent Alloys

1982 ◽  
Vol 19 ◽  
Author(s):  
I. Ansara
Keyword(s):  
Thermodynamic Properties ◽  
Binary Systems ◽  
Theoretical Models ◽  
Higher Order ◽  
Interaction Parameters ◽  
Experimental Measurements ◽  
Multicomponent Systems ◽  
Multicomponent Alloys ◽  
Summation Methods ◽  
Different Types

ABSTRACTIn addition to theoretical models which have been developped to interpret the interactions in metallic systems, polynomials of different types have been used to represent the thermodynamic properties of solution phases. Ternary and higher order systems have been described by adding the properties of the limiting binary systems, using various summation methods ; interaction parameters specific to the multicomponent systems can be derived from sufficiently precise experimental measurements.

Effect of Diffusion Induced Driving Forces on Interdiffusion - Stress Development/Relaxation and Kinetics of Diffusion Processes

2011 ◽  
Vol 309-310 ◽  
pp. 113-120 ◽  
Author(s):  
Dezső L. Beke ◽  
Z. Erdélyi ◽  
B. Parditka
Keyword(s):  
Steady State ◽  
Binary Systems ◽  
Chemical Potential ◽  
Diffusion Processes ◽  
Driving Forces ◽  
Complex Form ◽  
General Description ◽  
Parabolic Kinetics ◽  
Induced Field ◽  
Single Field

General description of the interplay between the Kirkendall shift (as a special way of relaxation) and diffusion induced driving forces in diffusion intermixing of binary systems is given. It is shown that, if the Kirkendall shift is negligible, a steady state Nernts-Planck regime is established with diffusion coefficient close to the slower diffusivity, independently of the type of the diffusion induced field and also independently whether this is a single field or a combination of different fields (e.g. stress field and extra chemical potential of non-equilibrium vacancies). Deviations from parabolic kinetics are expected only before or after this steady state stage. Using the results of our previous paper, on development and relaxation of diffusion induced stresses, it is illustrated that the setting of time of the Nernst-Planck regime is very short: intermixing on the scale of few tenths of nanometer is enough to reach it. It is also illustrated that this stage is realized even in the case of asymmetric interdiffusion (in one side of the diffusion zone the diffusion is orders of magnitude higher than in the other), when the stress distribution has a more complex form (having a sharp peak at the interface). Surprisingly the steady state is longer than it would be expected from the relaxation time of Newtonian flow: This is so because the composition profile is not static but changes fast in the timescale of the stress relaxation, and thus the stress re-develops continuously.

Calculation of phase diagrams and thermodynamic properties of 14 additive and reciprocal ternary systems containing Li2CO3, Na2CO3, K2CO3, Li2SO4, Na2SO4, K2SO4, LiOH, NaOH, and KOH

1984 ◽  
Vol 62 (3) ◽  
pp. 457-474 ◽  
Author(s):  
A. D. Pelton ◽  
C. W. Bale ◽  
P. L. Lin
Keyword(s):  
Phase Diagram ◽  
Thermodynamic Properties ◽  
Molten Salt ◽  
Phase Diagrams ◽  
Binary Systems ◽  
Ternary Phase ◽  
Ternary Phase Diagram ◽  
Ternary Systems ◽  
Maximum Error ◽  
Critical Assessment

Phase diagrams and thermodynamic properties of five additive molten salt ternary systems and nine reciprocal molten salt ternary systems containing the ions Li+, Na+, [Formula: see text], OH− are calculated from the thermodynamic properties of their binary subsystems which were obtained previously by a critical assessment of the thermodynamic data and the phase diagrams in these binary systems. Thermodynamic properties of ternary liquid phases are estimated from the binary properties by means of the Conformal Ionic Solution Theory. The ternary phase diagrams are then calculated from these thermodynamic properties by means of computer programs designed for the purpose. It is found that a ternary phase diagram can generally be calculated in this way with a maximum error about twice that of the maximum error in the binary phase diagrams upon which the calculations are based. If, in addition, some reliable ternary phase diagram measurements are available, these can be used to obtain small ternary correction terms. In this way, ternary phase diagram measurements can be smoothed and the isotherms drawn in a thermodynamically correct way. The thermodynamic approach permits experimental data to be critically assessed in the light of thermodynamic principles and accepted solution models. A critical assessment of error limits on all the calculated ternary diagrams is made, and suggestions as to which composition regions merit further experimental study are given.

Collective influence maximization for multiple competing products with an awareness-to-influence model

2021 ◽  
Vol 14 (7) ◽  
pp. 1124-1136
Author(s):  
Dimitris Tsaras ◽  
George Trimponias ◽  
Lefteris Ntaflos ◽  
Dimitris Papadias
Keyword(s):  
Diffusion Processes ◽  
Influence Maximization ◽  
Second Phase ◽  
Social Graph ◽  
Practical Applications ◽  
Influence Model ◽  
Best Response ◽  
The Social ◽  
Game Theoretic ◽  
Collective Influence

Influence maximization (IM) is a fundamental task in social network analysis. Typically, IM aims at selecting a set of seeds for the network that influences the maximum number of individuals. Motivated by practical applications, in this paper we focus on an IM variant, where the owner of multiple competing products wishes to select seeds for each product so that the collective influence across all products is maximized. To capture the competing diffusion processes, we introduce an Awareness-to-Influence (AtI) model. In the first phase, awareness about each product propagates in the social graph unhindered by other competing products. In the second phase, a user adopts the most preferred product among those encountered in the awareness phase. To compute the seed sets, we propose GCW, a game-theoretic framework that views the various products as agents, which compete for influence in the social graph and selfishly select their individual strategy. We show that AtI exhibits monotonicity and submodularity; importantly, GCW is a monotone utility game. This allows us to develop an efficient best-response algorithm, with quality guarantees on the collective utility. Our experimental results suggest that our methods are effective, efficient, and scale well to large social networks.

Transient responses of sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative

2018 ◽  
Vol 22 (8) ◽  
pp. 2505-2543 ◽  
Author(s):  
Tianhu He ◽  
Yan Li
Keyword(s):  
Time Delay ◽  
Sandwich Structure ◽  
Chemical Potential ◽  
Diffusion Theory ◽  
Kernel Functions ◽  
Characteristic Parameters ◽  
Material Characteristic ◽  
Transient Responses ◽  
Thermoelastic Diffusion ◽  
With Memory

The present work is devoted to investigating the transient responses of a sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative. Both the left and the right bounding surfaces are subjected to a thermal shock and a chemical potential shock simultaneously. It is assumed that the values of thermal contact resistance and diffusional contact impedance at the interface are zero with ideal adhesion. The coupled governing equations containing time delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The influences of the material characteristic parameters at the interface on the structural responses are emphatically discussed, and the non-dimensional temperature, chemical potential, displacement, stress as well as concentration at different values of time delay factors and kernel functions are obtained and illustrated graphically. The results show that: the changes of the time delay factors, kernel functions, and material characteristic parameters have the varying degrees of influences on the considered variables. Based on the above conclusions, the sandwich structure working under the thermoelastic diffusion coupling condition can be designed reasonably.

scholarly journals On the macroscopic limit of Brownian particles with local interaction

2020 ◽  
Vol 20 (06) ◽  
pp. 2040007
Author(s):  
Franco Flandoli ◽  
Marta Leocata ◽  
Cristiano Ricci
Keyword(s):  
Explicit Form ◽  
Diffusion Processes ◽  
Particle System ◽  
Local Interaction ◽  
Nonlinear Pde ◽  
Rigorous Results ◽  
Precise Form ◽  
Interacting Particle ◽  
Brownian Particles ◽  
Main Ideas

An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. This paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical informations on the precise form of the nonlinearity which are new with respect to the literature and coherent with the few known informations.

Thermodynamic Calculation of Phase Equilibria in the Mn-RE (RE=Nd, Gd, Dy) Binary Systems

2017 ◽  
Vol 898 ◽  
pp. 1036-1041
Author(s):  
M.H. Rong ◽  
S.D. Lin ◽  
Jiang Wang ◽  
H.Y. Zhou ◽  
G.H. Rao
Keyword(s):  
Magnetic Properties ◽  
Thermodynamic Properties ◽  
Phase Equilibria ◽  
Thermodynamic Calculation ◽  
Binary Systems ◽  
Ternary Systems ◽  
Experimental Information ◽  
Calphad Method ◽  
Self Consistent ◽  
Ternary Intermetallic Compounds

Ternary intermetallic compounds with rare earth elements and transition metals in the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems show interesting magnetic properties. As key sub-binary systems of the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems, the information of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems are indispensable to explore the RE-Mn-X (X=Si, Ge, Sn etc.) alloys with better magnetic properties. In this work, the experimental data of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems in the published literature were reviewed. Based on the available experimental information, thermodynamic calculation of phase equilibria of the Mn-RE (RE=Nd, Gd, Dy) binary systems was performed using the CALPHAD method. As a result, further experimental investigation and thermodynamic optimization would be still necessary in order to develop the self-consistent and compatible thermodynamic database of the RE-Mn-based alloy systems.

Study of dynamic and thermodynamic properties of zinc-blend and wurtzite cadmium sulfide (CdS) using density functional theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Teshome Gerbaba Edossa ◽  
Menberu Mengasha Woldemariam
Keyword(s):  
Density Functional Theory ◽  
Thermodynamic Properties ◽  
Density Functional ◽  
Chemical Potential ◽  
Phonon Dispersion ◽  
Dynamic Properties ◽  
Dielectric Constants ◽  
High Symmetry ◽  
Functional Theory ◽  
Zinc Blend

Abstract The dynamic and thermodynamic properties of wurtzite (wz) and zinc-blend (zb) CdS are investigated within the density functional theory using different approximation methods such as LDA, PBE, and DFT+U. Hellmann–Feynman approach is implemented for the relaxation of atomic position for both phases. To guarantee the accuracy of calculation, the convergence test of total energy with respect to energy cutoff and k-point sampling is performed. The dynamic properties such as phonon dispersion, phonon density of state, frequency along with high symmetry points, static and dynamic polarizability, and dielectric constants are calculated. The obtained values are compared with previous theoretical results. DFT + U approximation gives a good result that is consistent with the available theory. Moreover, the vibrational energy, vibrational free energy, entropy, electron chemical potential, and constant-volume specific heat are obtained within LDA, PBE, and DFT + U approximations.

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