There is a fundamental difference between pressure-induced phase transformations (PTs) that occur during compression in diamond anvil cell (DAC) within hydrostatic medium and plastic strain-induced PTs occurring in DAC without hydrostatic medium or under high-pressure torsion in rotational DAC (RDAC) or Bridgman anvils.¹ Pressure-induced PTs occur by nucleation at pre-existing defects (e.g. dislocations) below the yield. Strain-induced PTs occur by nucleation at new defects generated during plastic flow. Strain-induced PTs require completely different thermodynamic and kinetic treatment and experimental characterization.^1,2 However, there is currently no quantitative experimental characterization of strain-induced PTs for any material. Here, we report the first in situ quantitative study of strain-induced α-ω PT in ultrapure Zr under compression in DAC and shear under fixed force in RDAC. Samples plastically deformed through cold rolling were studied.

In situ X-ray diffraction (XRD) measurements were performed at the 16-BM-D beamline at Advanced Photon Sources using X-rays of wavelength 0.3108 Å. At each load/shear condition, the sample was radially scanned over the entire culet with steps of 10 µm and 2D XRD images were recorded using a Perkin Elmer flat panel detector.  Radial distribution of lattice parameters of α and ω phases and their volume fractions, averaged over the sample thickness, were obtained using Rietveld refinement of XRD patterns. Pressure distribution was determined using lattice parameters of Zr phases and their equations of state. Distribution of the total pressure was obtained based on mixture theory. X-ray absorption measurement along the radius was used to determine the sample thickness (h) profile.

Under hydrostatic loading, α-ω PT started at 5.4 GPa. Without a pressure-transmitting medium, the pressure distribution exhibited no signature of PT. The maximum yield strength determined based on the pressure gradient and sample thickness is about 0.4 GPa for both phases. The minimum pressure for the strain-induced α-ω PT, 1.2 GPa, was the same at the center of a sample and at the periphery, after different compression or compression/torsion loadings. Thus, plastic straining reduced PT pressure by a factor of 4.5 in comparison with hydrostatic loading. Also, since there are no shears at the center of a sample and large plastic shears away from the center, the same minimum pressure means that the physics and mechanisms of strain-induced PTs are the same for compression in DAC and torsion in RDAC. The only difference is in the pressure p – accumulated plastic strain q path. An analytical kinetic equation dc/dq=f[p(q)] was determined using experimental parameters at the sample center, defining q as ln(h_o/h) with initial thickness h₀. All experimental points obtained in three compression and compression/torsion loadings with three different p-q paths are close to the analytical equation. PT to β-Zr within a steel gasket was not observed, even at maximum pressure of 13 GPa and total rotation of 200°. The obtained results represent the first in situ quantitative characterization of plastic strain-induced PT under high pressure in DAC and RDAC.

1. Levitas V. I. Phys. Rev. B 70, 184118 (2004)

2. Levitas V.I. J. Phys.: Cond. Mat. 30, 163001 (2018)