Solid state phase transformation kinetics in Zr-base alloys

Abstract

We present a kinetic model for solid state phase transformation ($$\alpha \rightleftharpoons \beta$$ α ⇌ β ) of common zirconium alloys used as fuel cladding material in light water reactors. The model computes the relative amounts of $$\beta$$ β or $$\alpha$$ α phase fraction as a function of time or temperature in the alloys. The model accounts for the influence of excess oxygen (due to oxidation) and hydrogen concentration (due to hydrogen pickup) on phase transformation kinetics. Two variants of the model denoted by A and B are presented. Model A is suitable for simulation of laboratory experiments in which the heating/cooling rate is constant and is prescribed. Model B is more generic. We compare the results of our model computations, for both A and B variants, with accessible experimental data reported in the literature covering heating/cooling rates of up to 100 K/s. The results of our comparison are satisfactory, especially for model A. Our model B is intended for implementation in fuel rod behavior computer programs, applicable to a reactor accident situation, in which the Zr-based fuel cladding may go through $$\alpha \rightleftharpoons \beta$$ α ⇌ β phase transformation.

Kinetically Controlled Structural Transitions in Layered Halide-Based Perovskites: An Approach to Modulate Spin Splitting

“…The normalized enthalpy curves are shown in Supporting Figure 6. A notable shift in the first endothermic peak toward the lower-temperature zone with decreasing heating rate confirms the kinetic nature of the underlying phase transition . Moreover, with decreasing heating rate, the area of the first peak decreases until it tends to merge into the baseline, whereas the area of the second peak increases and becomes prominent, nominally consistent with the form of the single endothermal peak obtained at a lower ramping rate (∼0.08 K/s) from conventional DSC.…”

“…Upon cooling the (S-2-MeBA) 2 PbI 4 crystal from 343 to 173 K at various ramp rates (from 10 to 1000 K/s), no exothermic peak associated with a phase transition is observed and correspondingly no endothermic peak is observed during the subsequent heating cycle (heating rates from 10 to 1000 K/s; Supporting Figure 5). We ascribe the disappearance of the phase transition peaks to the fast cooling rates, which kinetically shift the phase transition to temperatures below 173 K and beyond the temperature range of the instrument. , An isothermal structural relaxation experiment was then performed to quantify the timescales associated with the phase transition (see details in the Methods section). For this study, the crystal was rapidly cooled and held at 173 K (near the structural transition temperature shown in Figure ) for different durations (from 0.1 to 600 s) to facilitate relaxation to the LT phase, prior to reheating.…”

“…We ascribe the disappearance of the phase transition peaks to the fast cooling rates, which kinetically shift the phase transition to temperatures below 173 K and beyond the temperature range of the instrument. 48,49 An isothermal structural relaxation experiment was then performed to quantify the timescales associated with the phase transition (see details in the Methods section). For this study, the crystal was rapidly cooled and held at 173 K (near the structural transition temperature shown in Figure 1) for different durations (from 0.1 to 600 s) to facilitate relaxation to the LT phase, prior to reheating.…”

The Mechanism of Joint Reduction of MoO3 and CuO by Combined Mg/C Reducer at High Heating Rates

“…HSTS studies are suitable for the solid-solid and solid-liquid intercollisions that are unquestionably the most abundant among nature's phase transformations [19,20]. It has already proved its ability to find out transformations and transitions in alloys, ceramic and composite materials.…”

The Mechanism of Joint Reduction of MoO3 and CuO by Combined Mg/C Reducer at High Heating Rates

“…Without underestimating other transformations, one may note that among nature's phase transformations the solid-solid and solid-liquid intercollisions are unquestionably the most abundant [11,12]. They perceive transformations and transitions in alloys and minerals, synthesis of ceramic and composite materials of wide variety.…”