4.1 Conditions for twin formation combining impact experiments and simulations
The twins were formed even near the rear surfaces of the target samples where the shock pressures decayed below 2 GPa estimated by the iSALE (Fig. 11a, c), suggesting that the threshold pressure of the twin formation is close to 1.5–2 GPa. Murr et al. (2002b) reported the relation of the impact velocity and the depth of twin formation and estimated the threshold impact velocity for the twin formation to be 0.1 km/s (corresponding to 1 GPa) at room temperature, which is consistent with our observations.
We can estimate the thermal history of iron meteorites experienced during and after collision based on their shock textures. Our experiments revealed that the Neumann band is a signature of shock above 1.5–2 GPa, which can be formed by impacts below temperatures about 670 K. However, our result also showed that too high degrees of compression above 13 GPa cannot produce the twins possibly because of too high dislocation density in one grain. Therefore, the Neumann band can be used as a shock indicator between 1.5–2 GPa and around 13 GPa. The relations between the twin density and pressure are also presented as shown in Fig. 12b. We found that the twin density can be well fitted by a simple linear relation as a function of peak pressure. The phase boundary between bcc and hcp iron locates at around 13 GPa. Figures 11 and 12 also suggest saturation of the twin density due to large deformation. Although we observed the texture after pressure release, the recent in situ XRD measurements of the released stages from shocked iron using XFEL (Hwang et al. 2020) suggested the process occurred in the large deformation region of our recovered samples, i.e., the phase change occurred very quickly and even fcc phase could be formed due to expansion of the samples. These processes likely occurred in the highly deformed regions of our samples.
We found that the initial temperature does not largely affect the twin density at least up to 670 K, indicating that the production rate of twins is high enough to neglect the effects of annealing kinetics at least below 670 K. The present experiments combined with the numerical simulations revealed that the Neumann band was shocked by impacts with shock pressures from 1.5–2 GPa to around 13 GPa and temperatures at least up to 670 K.
4.2 Annealing and disappearance of twins
Our annealing experiment (Run 011H) revealed that twins disappeared easily in bcc iron by annealing and recrystallization at 1070 K below the bcc–fcc transition temperature only for ten minutes. This observation is consistent with experimental results of high-temperature annealing of iron meteorites conducted by Jain and Lipschutz (1968), Buchwald (1975), and Davidson (1940). These previous annealing experiments on iron meteorites indicated that the samples recrystallized at temperatures above 870 K, which is below the bcc–fcc phase transition boundary, after 0.5–3 h of annealing. Annealing experiments on heavily deformed iron, Fe–0.3 wt%Al, and Fe–0.3 wt%Si alloys also indicated that recrystallization started at temperatures above 770 K with a heating rate of 10 K/min and significant grain growth occurred at 1070 K (Tomita et al. 2017), which is also consistent with our observation of twin disappearance in the shocked iron sample.
Recrystallization including reduction of dislocation density has been studied extensively (Humphreys et al. 2017). The conventional analysis for recrystallization may be applied to reduce the twin density by recrystallization, and the decrease rate may be expressed by an empirical n-th order recrystallization kinetics expression, dρ/dt = −kρn, where k is the rate constant for recovery (Humphreys et al. 2017), and ρ is the twin density. Different values are proposed for n-values depending on the materials; n = 2 for the recovery of olivine (Farla et al. 2010) and LiF (Li 1962), n = 2 (Van Drunen and Saimoto 1971) or 3 (Prinz et al. 1982) for Cu, and n = 3 for Ni (Prinz et al. 1982). Therefore, we adopted n = 2 and 3 for decrease in twin density by annealing. By fitting our data by this equation, dρ/dt can be obtained with a parameter k = 3.084 × 10–8 for n = 2 and k = 4.316 × 10–13 for n = 3 at 1070 K for 10 min. Based on this equation, we can estimate the time dependency of the decrease in twin density for various durations from 1 min to 1 h at 1070 K as shown in Fig. 13a. Significant reduction of the twin density occurred by annealing at 1070 K as shown in this figure.
Decrease in twin density because of annealing and recrystallization at different temperatures may be estimated by the temperature dependence of the rate constant, k, which can be expressed by k = k0exp(− Ea/RT), where Ea is the activation energy for the process considered, k0 is a constant, R is the gas constant, and T is the temperature. Because we obtained k(1070 K), as mentioned, we can obtain a temperature-dependent rate constant k(T) if Ea is given. The activation energy for the recovery is expected to be close to the self-diffusion of the metals for Cu (Cottrell and Aytekin 1950), Fe (Michalak and Paxton 1961), and Zn (Van Drunen and Saimoto 1971). Experiments on recovery/recrystallization of steel suggest the activation energy, Ea, is around 250 kJ/mol, which is close to that of the iron self-diffusion (e.g., Watanabe and Karashima 1970; Glover and Stellars 1973). Therefore, the activation energy of 250 kJ/mol was adopted in the recrystallization of twins. Finally, we can estimate the temperature dependence of the disappearance of twins, as shown in Figure 13b. This figure indicates annealing and disappearance of twin occur above 700 K, which is consistent with annealing experiments on iron meteorites (Jain and Lipschutz 1968; Buchwald 1975). This is the reason why the shocked sample at 670 K was free from the annealing. In our impact experiment conducted at 1100 K (Run 012), we cannot observe twins in the iron target, as shown in Figure 7. The cooling rate after the impact at 1100 K is estimated to be 20 K/min as shown in Sect. 2.2. Therefore, the disappearance of twins at 1100 K impact (Run 012) annealed for 10 min during cooling to 900 K is consistent with the recrystallization rate of twin estimated here.
Our experiments showed that twins were formed by impacts at least up to 670 K, and it was not formed by high-temperature impacts above 1100 K. The annealing experiment and the analysis of the kinetics given in Fig. 13a and b revealed that the twin in iron disappeared easily by reheating and annealing at 1070 K.
The bcc–fcc transition temperature in iron is 1184 K, whereas the transition of kamacite with 5–7.5 mol% Ni occurs at 770–905 K (Reisener and Goldstein 2003). Therefore, the maximum temperature for survival of the Neumann band in kamacites might be as low as the temperature of the bcc–fcc equilibrium phase boundary. Although we used iron in this study, our result may provide insight into Neumann band formation in iron meteorites because kamacite can survive even at 1070 K metastably because of sluggish transition kinetics (Dunlop and Özdemir 2007) when it was reheated rapidly. Therefore, iron meteorites with Neumann bands were not heated to the temperatures above 1070 K after the Neumann band formation.