Solutions to multiphase diffusion in binary metal interstitial systems

Abstract

General analytical expressions for multiphase diffusion under nonsteady-state conditions, which treats the special degenerative case of steady-state diffusion, are developed. The validity of these solutions is examined by application to multiphase layer growth in the Zr-0 and Fe-N systems. The analytical solutions examined include closed-form error function solutions and steady-state approximations to the solutions developed by Wagner. The solutions are general and can accommodate solubility ranges in all phase layers as well as terminal solubilities in the end member phases of the diffusion couple. In diffusion couples where the end member phases have finite, terminal solubilities and where these terminal phases have diffusivities greater than in the intermediate phases (which is common in many metal-interstitial phases), closed-form error function solutions are particularly useful in determining chemical diffusivities from simple intermediate phase layer growth measurements.

Titanium Nitriding by Microwave Atmospheric Pressure Plasma: Towards Single Crystal Synthesis

“…The activation energy of nitrogen in TiN deduced from these measurements is close to 217 ± 4 kJ · mol −1 up to 1 630 K. This value is in agreement with those proposed in ref 21, 22. as shown in Table 1 but not with the value proposed by Metin and Inal 19. Above 1 630 K, the slope decreases, indicating a slowdown of the weight gain kinetics.…”

“…Diffusion of nitrogen in titanium at high temperature was studied by several authors 19–22. Reliable sets of data (i.e., values of the diffusion coefficient that are similar) were produced in a rather large range of temperature (see Table 1).…”

Rapid Nitriding of Titanium Alloy with Fine Grains at Room Temperature

“…The nitrided layer on the surface treated using the developed room‐temperature process was thicker than that formed by conventional nitriding at 1173 K at a comparable treatment time (Figure 3b). [ 15 ]…”

“…The nitride layer formed by the developed method was thicker than that of the layer formed by conventional nitriding at 1173 K at a comparable treatment time. [ 15 ] The formation rate of the nitrided layer, d t eq /d√ t , in conventional nitriding at 1173 K had a constant value of 0.19 µm s −1/2 , [ 15 ] whereas d t eq /d√ t in the developed method depended on the treatment time. The developed process can achieve rapid nitriding of a Ti alloy within a short period at room temperature because of the transfer and mechanical alloying of CP Ti particles with a nitrided phase.…”

Surface hardening of Ti alloys by gas-phase nitridation: Kinetic control of the nitrogen surface activity

“…We assume (1) a laterally infinite Ti plate with a thickness of 2 h, (2) that the nitrogen molecules impinge on the surface with a homogeneous current density given by Eq. nitrogen diffusion in Ti cited earlier, [22] the diffusion equation [4] can be solved under these boundary conditions to yield the solution [23] [5] Again assuming the concentrationindependent diffusion coefficient and the parameters for [20] indicating the equilibrium dissociation pressure p of nitrogen for Cr-bearing nitrides over a wide range of temperatures.…”