This is the author manuscript accepted for publication and has undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1111/jace.15071
DR. JEAN-MARIE LEBRUN (Orcid ID : 0000-0002-7347-2549) PROF. WALTRAUD M. KRIVEN (Orcid ID : 0000-0002-2230-1301) DR. RISHI RAJ (Orcid ID : 0000-0001-8556-9797)
Article type : Communication
Corresponding author mail id: [email protected]
In-situ Measurements of Lattice Expansion Related to Defect
Generation During Flash Sintering
J.-M. Lebrun1,4, C. S. Hellberg2, S. K. Jha1, W. Kriven3, A. Steveson3, K. C. Seymour3, N. Bernstein2, S. C. Erwin2, and R. Raj1
1
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA
2
Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375, USA
3Department of Materials Science and Engineering, University of Illinois, Urbana Champaign, IL 61801, USA 4
Saint-Gobain Innovative Materials - NRDC, 9 Goddard Road, Northboro, MA 01532, USA
April 2017
Submitted as a Communication to the Journal of the American Ceramic Society.
Abstract
We report results from in-situ measurements of lattice expansion during flash sintering of 3mol% yttria stabilized tetragonal zirconia taken at the Advanced Photon Source, Argonne National Laboratory. The expansion is anisotropic, with the relative expansion of the a-lattice constant exceeding that of the c-lattice constant. The
anisotropic expansion cannot be explained by thermal expansion and is consistent with predictions from ab-initio calculations based upon the generation of vacancy-interstitial pairs of zirconium and oxygen.
1. Introduction
The phenomenon of flash sintering [1], showed that modest electrical fields applied directly to the specimen could sinter ceramics in mere seconds at low furnace temperatures. This first work on 3 mol% yttria stabilized tetragonal zirconia (3YSZ) has since expanded to many different oxides, including semiconductors, ionic conductors, electronic conductors, and insulators. However, the mechanism of flash remains uncertain; in-situ experiments that probe changes in the atomic structure in real time can provide useful information in
unraveling the underlying science of this phenomenon.
In this communication, we introduce in-situ diffraction results, monitoring the lattice parameters of a 3YSZ sample while it is flash sintered. We also present density functional theory (DFT) calculations of the effects of the point defect density on the lattice constants of tetragonal ZrO
Author Manuscript
2.2. Experimental methods
The experiments were performed at beam line 33BM-C at APS. The experimental set up is shown in Fig. 1. A monochromatic X-ray beam travels through the specimen.
Rectangular bar-shaped specimens of 3YSZ (TZ-3YB, Tosoh USA, Grove City, OH) were pressed into rectangular bars with length of 5 mm and a cross section of 1.65 mm × 0.74 mm; they had a relative green density of 0.53. A thin sliver of platinum paste on one side serves as the standard for measuring the temperature by its thermal expansion. The diameter of the incident beam was 1 mm; thus it spanned nearly the full width of the specimen. The experiments were carried out at a furnace temperature of 800 oC. An electric field of 185±15 Vcm-1 was applied as a step function, with a current limit of 80 mA mm–2
An X-ray wavelength of 0.75 Å was chosen in order to have the lowest possible absorption in zirconia ( ). Local scans were recorded with a fixed Pilatus 100K 2D image plate detector (DECTRIS Ltd, Villigen Switzerland), spanning a 2θ range of 20.5 to 24.5
.
o
� =���(��
200) (1)
, which allowed to record diffraction peaks from (112) and (200) planes of tetragonal zirconia as well as the (200) diffraction peak of platinum. As a major difference with full scans, the local scans cover a limited span of the diffraction angle but can be completed quickly, typically in about 1 s plus another 0.4 s to transfer the data. The diffraction peaks were analyzed by fitting them to a pseudo-voigt equation [2] and then used to calculate the and lattice parameters of tetragonal zirconia as well as the lattice parameters of Pt by:
� = � ����2(�112)−1
2���2(�200)� −1 2�
(2)
In earlier work, we have reported in-situ diffraction results during flash of already dense specimens [3, 4]. Here, the experiments are performed on un-sintered specimens, as in ref. [5], were the emergence of a pseudo cubic phase was reported when the specimen is held under current control for several minutes. We show the changes in the "a" and "c" lattice parameters, within a period of 75 s, which is before the emergence of the cubic phase.
3. Experimental Results
The raw and fitted data of the (112) and (200) diffraction peaks of zirconia at several points during the flash are reported in Fig. 2(a). A shift of diffraction peaks towards lower angles signals lattice expansion. The changes in the & parameters through the entire flash experiment are shown in Fig. 2(b). These data are synchronized with the power density expended in the specimen (obtained from the product of voltage and current which were measured in real time). The onset of the flash is seen by the sudden rise in the power density, which reaches a peak when the power supply is switched to current control [6]. The height of this peak is equal to the product of the initially applied voltage and the current limit set at the power supply, that is 1600 mW mm–3. The sample sinters during this transient. Following the transient, the power density declines to an approximately steady value of 500 mW mm–3
The changes in the lattice parameters in Fig. 2(b) occur on two time scales. There is a sharp increase when the current rises quickly as the flash is instigated, and an equally sharp decline in the lattice parameters when the field is turned off. Then there are changes in the lattice parameter that occur over a longer time scale, over and above the thermal expansion, which are the main subject of this letter.
.
The sharp rise during the transient is caused by both, thermal expansion from Joule heating and an excess lattice expansion, which is linked to the persisting lattice expansion seen after the field is turned off as the specimen returns to the furnace temperature. The sharp decline when the power is turned off, which occurs on a time scale of about 5 seconds, is related to cooling. The excess lattice expansion, over and above the thermal expansion is attributed to the generation of point defects during the flash as confirmed by ab-initio simulations described below.
Further affirmation of the thermal expansion is obtained by the measurement of the specimen temperature using the platinum standard as described in refs. [3, 5]. The diffraction pattern in Fig. 3(a) show the movement of the Pt (200). The lattice expansion in Pt is
converted into temperature using the tabulated data for the thermal expansion of Pt [7]. As shown in Fig. 3(b), the specimen temperature rises to 1300 oC, 500 oC above the furnace temperature, just after the onset of the flash, when the power dissipation reaches its peak. During the quasi steady-state, established under current control, the specimen is at ~1200 oC.
As soon as the field is turned off the specimen temperature falls back to the furnace temperature. This temperature drop of ~400oC amounts to a lattice contraction of ~0.45%, given the coefficient of thermal expansion of 1.15 x 10–5oC–1 for zirconia. This value is consistent with the contraction in the lattice parameter seen in Fig. 2(b) when the power is switched off. The contraction in the parameter is somewhat less, 0.35 %; this difference is attributed to defect relaxations.
4. Ab-initio Calculations
The most intriguing result in Fig. 2(b) is the residual lattice expansion at the end of the flash experiment; it is ~0.05% for the parameter, and ~0.20% for the lattice parameter. We sought to understand this permanent excess lattice expansion in terms of the creation of vacancies and interstitials of oxygen and zirconium as Frenkel pairs. (Given the very fast nature of these events, it is reasonable to assume that the materials functioned as a closed system; therefore vacancies and interstitials would have been created in pairs.)
Ab-initio calculations were carried out to determine if vacancy interstitial pairs can indeed cause
lattice expansion.
The Vienna ab-initio Simulation Package (VASP) software was used for the density functional calculations [8] with the Perdew-Burke-Enzerhoff (PBE) generalized gradient approximation [9], a Projector-Augmented Wave (PAW) basis with a 900 eV plane-wave cutoff. The calculation of the elastic tensor used 6×6×4 Monkhorst-Pack k-points for the 6-atom cell. The Γ k-point was used for the super-cells, which contained 64 and 128 ZrO2
formula units in the tetragonal structure. Atomic positions were relaxed using the conjugate gradient algorithm until the residual forces were less than 0.2 meV Å–1. In order to prevent relaxation of the overall crystal structure to a lower energy structure (the computed ground state of ZrO2 is monoclinic, which has increased volume), the translation vectors of the
super-cells were fixed. Elastic tensors, computed for an ideal tetragonal ZrO2 structure, were
then used to estimate the strain resulting from the computed stress tensors. The stress tensors were calculated for super-cells containing oxygen vacancies and interstitials, and zirconium vacancies and interstitials, taken separately. The tensors were then summed to obtain the lattice expansion arising from oxygen and from zirconium Frenkel pairs. The oxygen defects
were charged ±2 and the Zr defects were charged ±4. Separate calculations of complete Frenkel pairs were performed as consistency checks: Similar expansions were observed.
The results from ab initio calculations for lattice expansion resulting from
disassociated vacancy-interstitial Frenkel pairs are given in Fig. 4(a). Oxygen Frenkels give an ansotropic expansion with a>c while Zr Frenkels give c>a. The lattice expansion associated with Zr Frenkels is about four times that for the O Frenkels. The computed formation energy of Zr Frenkels of approximately 8 eV is much larger than the
approximately 3 eV formation energy for O Frenkels. Thus O Frenkels should be generated in far greater densities than Zr Frenkels.
Strains resulting from different combinations of O and Zr defects, as given by the rule of mixtures, are given in Fig. 4(b). Three cases where the Zr are 1/2, 1/4, and 1/8 of the O Frenkels are presented. While these results are approximate, they do give an order of magnitude estimate of the concentration of defects and the relative concentrations of O and Zr. Apparently, the ratio of Zr to O Frenkel pairs varies from ~1/2 during the flash transient (i.e. while the sample sinters) to ~1/8 at the end of the flash. Comparison with the
measurements of residual lattice expansion suggest defect concentrations of 1-2 mol%.
4. Discussion
We attempt to compare the high values of defect concentrations reported just above, to the nominal defect concentrations that are expected to exist during conventional sintering. Since sintering requires mass transport it is controlled by the slowest diffusing species. In zirconia this species is Zr. Measurements of cation diffusion in zirconia are summarized in [10]. They show that while the pre-exponential can vary, the activation energies for diffusion are fairly consistent at ~5 eV. The activation energy is equal to the sum of the enthalpy of formation of Zr vacancies, and the activation barrier of cation jumps to neighboring
vacancies. The activation barrier for Zr vacancy diffusion calculated with the nudged-elastic-band method gives a value of ~2.8 eV. Therefore a reasonable value for the enthalpy of formation of Zr vacancies, , may be assumed to be given by �� = 2.2 eV . The molar
concentration of Zr vacancies is then given by ���=��� �−Δ��
���. At the nominal
conventional sintering temperature of 1450 oC, we obtain that ��� = 8.6 × 10−7− 2.8 ×
10−5. The defect concentration for Zr vacancies in flash sintering is estimated to be approximately 0.4 mol%, which is two to four orders of magnitude greater than in
conventional diffusional sintering. In an order of magnitude way this enhancement in defect concentration agrees with the sintering rate during flash being about three orders of
magnitude faster than in conventional sintering [11].
Lattice parameters in non-stoichiometric ceramics can change during reactions with the environment in an open system. For example, changes in oxygen pressure which can alter the defect concentration in ceria and zirconia has been shown to produce lattice expansion [12]. Contraction and expansion of electrode materials in batteries upon charging and discharging is well known [13]. However, the present experiments represent a closed system since the lattice parameter changes abruptly during the flash. If the lattice parameter were changing through interactions with the environment, then a gradient in expansion through the thickness of the sample would have caused the diffraction peaks to broaden since the incident beam traversed through the full thickness of the sample. In the same manner, temperature gradients within the sample would lead to broadening of the diffraction peak. Careful experiments to measure the peak broadening have shown that any temperature inhomogeneity is less than 10 o
Eventually, the anisotropic change in the lattice parameter of zirconia during the current hold is unique to the type of Frenkel defects created and their recombination kinetics. The product of the concentration of Frenkel defects and their probability of recombination gives the recombination rate. During the flash transient, the ratio of Zr to O Frenkels is roughly ½. However, Zr Frenkels have a higher binding energy and have therefore a higher probability of recombination than O. Even though created in slightly lower extent during the transient, Zr Frenkels can then be expected to recombine at a higher rate. This is confirmed by the decrease in the ratio of O to Zr Frenkels during the current hold, as measured by the larger relaxation of the ‘c’ lattice direction as compared to ‘a’.
C (the sensitivity of the measurement) during the flash experiments [4]. Some examples of the 3YSZ diffraction peaks are shown in Fig. 2(a) and show a sharp reduction of the peak width during the transient, which is related to sintering [14], the peak remaining sharp with a constant width thereafter, confirming that flash sintering occurs in a closed system configuration.
5. Conclusions
In summary, we have used in-situ synchrotron X-ray diffraction to measure the lattice constants of 3YSZ during flash sintering, and observed anisotropic lattice expansion that is inconsistent with simple thermal expansion due to Joule heating, and remains after the electric field is switched off. First principles DFT calculations show that O and Zr Frenkel pairs lead to anisotropic expansion consistent with the experimental observations if the defect concentrations are of order 1 mol%. These defect concentrations are three orders of
magnitude higher than thermally activated concentrations in conventional sintering,
consistent with the similar increase in sintering rate between conventional and flash sintering.
Acknowledgements
We are pleased to acknowledge assistance and discussion with Evguenia Karapetrova and Christian M. Schlepuetz, physicists at the beam line 33BMC at the Argonne Photon Source.
The work at the University of Colorado Boulder was supported by the Office of Naval Research under grant number N00014-15-1-2505.
Hellberg, Bernstein, and Erwin were supported by the Office of Naval Research under grant number N0001415WX01515. Computations were performed at the AFRL and ERDC DoD Major Shared Resource Centers.
Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357.
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Figure Captions
1. The set-up used for in-situ experiments at the synchrotron. The thin film of Pt on the surface serves as the standard for the measurement of specimen temperature. Note that the X-ray beam travels through the full thickness of the specimen.
2. (a) Diffraction pattern showing 3YSZ (112) and (200) peaks at five time points during the flash experiment, corresponding to points 1-5 in the right panel. (b) Power dissipation and the synchronized changes in the a and c lattice parameters of tetragonal zirconia during the full flash experiment. The onset of the flash is signaled by an abrupt rise in conductivity. The peak in power dissipation represents the power supply being switched from voltage to current control. The sample sinters during this short transient. Under current control the specimen establishes a steady state of flash.
3. Measurement of the specimen temperature from the Pt standard. (a) The shifts in the (200) peaks of Pt with power density. (b) The specimen temperature computed from the thermal expansion coefficient of Pt. The specimen temperature changes quickly in response to Joule heating and cooling. At first it rises from the furnace temperature (800 oC) up to 1300 oC at the power peak, then declines to 1200 o
4. (a) The increase in the
C during the steady state under current control. It falls back quickly to the base furnace temperature when the electrical power to the specimen is turned off.
and lattice parameters from the insertion of vacancy-interstitial pairs of oxygen and zirconium. The expansion is anisotropic, but in the opposite
sense for oxygen and zirconium. (b) Comparison with experimental lattice expansion which is also anisotropic. The oxygen Frenkel pairs are predicted to have much higher concentration than zirconium Frenkel pairs. Lattice constant shifts that remain at the end of the flash
experiment correspond to defect concentrations of 1 mol%.
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