ARTICLE pubs.acs.org/JPCA
Kinetics of the Wurtzite-to-Rock-Salt Phase Transformation in ZnO at High Pressure Vladimir L. Solozhenko,*,† Oleksandr O. Kurakevych,†,‡ Petr S. Sokolov,† and Andrey N. Baranov§ †
LSPMCNRS, Universite Paris Nord, 93430 Villetaneuse, France IMPMC and CMCP, Universite P&M Curie, 75015 Paris, France § Chemistry Department, Moscow State University, 119991 Moscow, Russia ‡
ABSTRACT: Kinetics of the wurtzite-to-rock-salt transformation in ZnO has been studied in the 57 GPa pressure range at temperatures below the activation of diffusion processes. The detailed analysis of non-isothermal experimental data using the general evolution equation describing the kinetics of direct phase transformations in solids allowed us to study the kinetic particularities of both nucleation and growth of the rock-salt phase in parent wurtzite ZnO. The main rate-limiting processes are thermally activated nucleation (EN = 383 kJ mol1 at 6.9 GPa) and thermally nonactivated (most probably quasimartensitic) growth (kG = 0.833 min1 at 6.9 GPa). The high impact of thermal deactivation of nucleation places has been evidenced in the case of slow heating, which indirectly indicates that the rsZnO nucleation places are mainly produced by pressure-induced stresses in the parent phase.
’ INTRODUCTION Zinc oxide belongs to the family of wide-bandgap semiconductors with strong ionic character of chemical bonds. At ambient conditions ZnO has a wurtzite structure (P63mc) that transforms into a rock-salt one (Fm3m) at high pressures.1 At 300 K the wurzite-to-rock-salt phase transformation shows a substantial hysteresis (∼9 GPa on compression and ∼2 GPa on decompression), while at temperatures of about 1000 K the transformation pressure decreases down to 5.2 GPa, and hysteresis tends to zero.2 The recovery of high-pressure rs-ZnO phase at ambient conditions is possible either in the nanostructured form3,4 or from the stabilization matrix of the rock-salt structure (MgO5 or NaCl6). It seems that the possibility to recover this phase is due to some changes in nucleation mechanism rather than thermodynamic (bulk or surface) stabilization. However, no detailed kinetic studies of this phenomenon have been performed so far. The kinetics of phase change is of great importance for understanding the processes underlying both the microstructure development7 and formation of new phases.79 The recent advances in high-pressure X-ray diffraction instrumentation at synchrotron sources have created the possibility to investigate in situ the transformation kinetics under high pressure.10 At the same time, only a very limited number of such studies has been performed,1013 while the main features of highpressure transformations have been studied mainly in the quenching experiments. In the present work, the kinetics of phase transformation of wurzite ZnO into rock-salt modification has been studied in the 57 GPa pressure range at temperatures up to 1000 K. ’ MATERIALS AND METHODS As starting materials we have used w-ZnO powders of various grain size (from 40 μm down to 9 nm), i.e., commercial microcrystalline ZnO (325 mesh, 99.99%, Alfa Aesar) for kinetic r 2011 American Chemical Society
studies and nanopowders of uniform grain-size distribution synthesized by chemical routes described elsewhere5 for studies of microstructural evolution. The in situ kinetic experiments were carried out using MAX80 multianvil X-ray system with anvils of tungsten carbide. The diffraction measurements were performed in an energy-dispersive mode at F2.1 beamline, HASYLAB-DESY. The experimental setup has been described earlier.14 The primary polychromatic synchrotron beam was collimated down to 60 μm (height) by 100 μm (width) and was perpendicular to the vertical axis of the sample chamber. The diffracted beam was collected in the vertical plane using an intrinsic Ge solid-state detector and a Canberra multichannel analyzer. A radioactive 241Am-source provided X-ray fluorescence KR and Kβ lines from Rb, Mo, Ag, Ba, and Tb targets for energy calibration of the detector. The diffraction angle θ = 5.956(6)° was calculated from the X-ray diffraction pattern of NaCl taken at ambient conditions. The temperature of the high-pressure cell was controlled by a Eurotherm PID regulator within (2 K. The sample temperature was measured by a Pt 10% RhPt thermocouple with its junction 300 μm below the sample region under study. The correction for the pressure effect on a thermocouple electromotive force was made using the data of Getting and Kennedy15 extrapolated to 7 GPa. Sample pressure at different temperatures was determined from the d002 value of hBN (P3 = 0.98) using its thermoelastic equation of state.16 Diffraction patterns were collected in the “autosequence” mode at a linear heating with rates of 10, 5, and 2 K/min; collection time was 30 s for each pattern. The conversion degree of the wurtzite-to-rock-salt transformation has been estimated by Rietveld analysis using PowderCell 2.4 program.17 The correction of the Received: February 16, 2011 Revised: March 30, 2011 Published: April 13, 2011 4354
dx.doi.org/10.1021/jp201544f | J. Phys. Chem. A 2011, 115, 4354–4358
The Journal of Physical Chemistry A
ARTICLE
collected powder X-ray diffraction patterns in regard to the highpressure cell absorption, the spectral distribution of the brilliance of the synchrotron radiation source, and the energy dependence of the quantum efficiency of the Ge detector has been performed using the integral intensities of diffraction lines of pristine microcrystalline w-ZnO phase. Studies of microstructural evolution during the phase transformation at 7.7 GPa and temperatures up to 1650 K have been performed in quenching experiments using a toroid-type highpressure apparatus.18 Phase composition and microstructure of the recovered samples have been studied by X-ray powder diffraction using MZIII Seifert (Cu KR radiation) and G3000 TEXT Inel (Cu KR1 radiation) diffractometers. The PowderCell 2.4 program17 has been used for Rietveld analysis of the diffraction patterns.
’ KINETIC ANALYSIS Usually considering the nucleation complicates the kinetic description of transformation at both isothermal and nonisothermal conditions, because at the initial stage of the transformation the nucleation is a dominant process and the growth is negligible, while the experimentally observed amount of a new phase is mainly attributed to the particle growth. At high pressure the situation is additionally complicated by the experimental difficulties of obtaining the sufficient number of high-precision kinetic data, which require nontrivial methods for solving the inverse kinetic problem.11 That is why the use of the general evolution equation, which takes into account both nucleation and growth independently, is of utmost importance for nonisothermal kinetic studies. The experimental kinetic curves have been fitted to the classical evolution equation proposed in the original paper of Avrami,19 which includes the multitude of experimentally observed nucleationgrowth regimes as particular cases. The extended conversion degree Rex (the value calculated under the assumption of infinite particle growth, without geometrical restrictions due to the presence of neighbor growing particles) is therefore Z t Z t ð kG ðTðτÞÞ dτÞr Rex ¼ 0
Z
θ
expð
θ
kN ðTðζÞÞ dζÞN0 ðTðθÞÞkN ðTðθÞÞ dθ
ð1Þ
0 ((E )/(R T))
((E )/(R T))
where kN(T) = ezN N 3 and kG(T) = ezG G 3 are the kinetic constants of nucleation and growth (EN and EG are the activation energies of nucleation and growth, respectively, while zN and zG are logarithms of corresponding pre-exponential factors), T(t) is a timetemperature profile of the heating, r is the order of particle growth, and N0(T) is a number of available nucleation places (germs). The Rex value as a function of the true conversion degree (R in mole fraction) can be estimated using the generalized Avrami relationship20 that allows taking into account the possible noncompleteness of transformation Rex ¼
1 lnð1 ηRÞ η
ð2Þ
where η is a ratio of the volume occupied by a new phase at the end of transformation to the volume accessible for growth.20 The fitting of experimental data to eq 1 has been performed using the MATLAB software. The discrepancy functional (the root-mean-square deviation of experimental conversion degree
Figure 1. X-ray diffraction patterns of starting w-ZnO powders and samples recovered after high-pressure experiments at 7.7 GPa and 800 K. w-ZnO nanopowder with grain size of 9 nm (a) passes directly into nanostructured rock-salt phase that can be recovered (b) (the transformation is accompanied by the grain size increase up to 36 nm), while the use of microcrystalline w-ZnO powder (c) leads to the recovery of w-ZnO nanopowder (d).
from the calculated one) has been minimized using the simplex method. The uniqueness and stability of solution of the inverse kinetic problem have been tested by multiple minimization procedures from various sets of starting parameters. The number and diversity of initial data were sufficient to exclude the possibility of mutual compensation of fitting parameters.
’ RESULTS AND DISCUSSION Temperature Dependence of Kinetic Constants. The w-ZnO-to-rs-ZnO transformation in the pressure range under study (57 GPa) starts at temperatures of about 550 K, i.e., much below the intensification of diffusion processes (Tamman temperature for ZnO is ∼1200 K21). This fact allows one to conclude that the kinetics of this transformation is mainly determined by the nucleation and kinetic quasi-martensitic growth (opposite to diffusion-determined growth at higher temperatures). This suggestion agrees well with the fact that below 1200 K w-ZnO with grain size
