Papers by Keyword: Thermodynamic Factor

Abstract: The self-or tracer diffusivity of one component in a binary alloy is often required when there is knowledge of the other component’s self-or tracer diffusivity and the interdiffusivity (and the thermodynamic factor). In the present paper, this problem is addressed for the random alloy model by applying three possible approximations having different levels of accuracy: Darken (low level of accuracy), Manning (medium level of accuracy) and Moleko, Allnatt and Allnatt (MAA) (high level of accuracy). There are unexpectedly large differences between the results of these approximations that sometimes are reflected in the high sensitivity of the vacancy-wind factor to the level of approximation. Generally, for the application of Manning and the MAA approximations, it is found that there is a difference in the number of self-diffusivity roots depending on whether the tracer diffusivity is available for the faster diffuser or for the slower diffuser and depending on how close the composition is to the forbidden (according to Manning’s description) region. Provided that the interdiffusion coefficient (divided by the thermodynamic factor) is greater than the available self-diffusion coefficient multiplied by its complementary composition, the application of the Darken approximation always results in one self-diffusivity root.

Abstract: The role of the thermodynamic factor in determining the magnitude of Ficks diffusion constant, DH, for H in metals and alloys is discussed using mainly Pd and its fcc alloys as examples because data are available for some of these systems over a wide range of H contents. Procedures are given for obtaining DH*, the concentration-independent diffusion constant, from DH under permeation conditions where the H concentration varies through the membrane; which is the common situation for H₂ purification membranes where p_upstream >> p_downstream. The role of the thermodynamic factor in H diffusion through multi-layer membranes will also be discussed.

Abstract: The impact of thermodynamic factors on deviation from linearity of diffusion path in the ternary system Cu-Fe-Ni is analyzed. For that the slope function of the diffusion path for the diffusion couples 65Ni30Cu5Fe –29.5Ni16.5Cu54Fe, 49.5Ni50.5Fe – 51Ni49Cu and 84Cu16Ni – 50Ni50Fe, annealed at 1000°C for 196h, were calculated by an approximate equation using only thermodynamic data. Results of the calculation were compared with the values of the slope function obtained directly from experimental data. It is shown that despite of the fact that the tracer diffusion coefficients of the components in the system Cu-Fe-Ni are not equal the coincidence between the calculated and experimental values of the slope function is remarkable. This allows us to conclude that at least in this case the deviation of the diffusion path from linearity depends mainly on the thermodynamic properties of the system.

Abstract: 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.

Abstract: We present diffusion measurements in metallic melts measured by capillary techniques and results of molecular dynamic simulations. The investigated systems are the binary alloy AlNi20 and the multicomponent bulk glass-forming alloy Pd43Cu27Ni10P20. The temperature range of interest reached from the glassy state to the equilibrium melt. In the glassy as well as in the deeply supercooled state, below the critical temperature Tc of the mode-coupling, theory (MCT), diffusion is a highly collective atomic hopping process. Both investigated systems show around Tc a change in the diffusion mechanism. Above the liquidus temperature, diffusion in Pd43Cu27Ni10P20 is a collective process whereas in AlNi20 the atoms diffuse probably by uncorrelated binary collisions. The influence of thermodynamic forces on diffusion in the liquid state of AlNi20 can be described by the Darken equation with an additional temperature independent correction factor (“Manning”- factor).

Abstract: Description of diffusion paths is one of the most interesting and topical problems in experimental investigations of interdiffusion in multicomponent systems and, particularly, in ternary systems. The relationship between effective interdiffusion coefficients and diffusion paths in ternary systems has been discussed earlier but the specific influence of the mobility and thermodynamic properties of components on the characteristics of the diffusion path is still unclear. In this paper an attempt is made to clarify the separate influences of mobility and thermodynamics on the behavior of diffusion paths in ternary systems and the corresponding correlation is found. It is shown that in most cases the deviation of the diffusion path from linearity (an ideal system) is related to the deviation of the thermodynamic properties from the ideal. The results obtained are analyzed on the basis of thermodynamic data for the ternary system Cu-Fe-Ni.

Abstract: We have investigated interdiffusion in iron-aluminium alloys using single-phase interdiffusion couples of FexAl1−x–FeyAl1−y for three combinations of x and y for Al contents between 18 and 49.5 at. % Al. Experimental diffusion profiles were obtained from electron-microprobe analysis of the diffusion zone. Interdiffusion coefficients were deduced via the Sauer-Freise method taking into account volume changes. A temperature interval between 997 and 1447 K was covered in our experiments. Thermodynamic factors were obtained from two theoretical models and judged by an analysis of the Kirkendall effect in the diffusion couples. The Darken-Manning equation was used to deduce self-diffusion coefficients of aluminium from the present interdiffusion coefficients, the thermodynamic factors, the vacancy-wind factors, and the iron tracer diffusivities obtained recently at the M¨unster laboratory. The results show that Al diffusion is always slightly faster than Fe diffusion. The difference never exceeds a factor of three. This small difference indicates that Fe and Al diffusion in B2 ordered iron-aluminides are closely coupled.