Multiphase transformation and ostwald's rule of stages during crystallization of a metal phosphate

ARTICLES
PUBLISHED ONLINE: 23 NOVEMBER 2008 DOI: 10.1038/NPHYS1148
Multiphase transformation and Ostwald's rule of
stages during crystallization of a metal phosphate
Sung-Yoon Chung1,2*, Young-Min Kim3, Jin-Gyu Kim3 and Youn-Joong Kim3
Although the classical picture of crystallization depicts a simple and immediate transformation from an amorphous to
a crystalline phase, it has been argued that, in selected systems, intermediate metastable phases exist before a stable
state is finally reached. However, most experimental observations have been limited to colloids and proteins, for which the
crystallization kinetics are fairly slow and the size is comparatively large. Here, we demonstrate for the first time in an inorganic
compound at an atomic scale that an amorphous phase transforms into a stable crystalline state via intermediate crystalline
phases, thus directly proving Ostwald's rule of stages. Through in situ high-resolution electron microscopy in real time at a
high temperature, we show the presence of metastable transient phases at an atomic scale during the crystallization of an
olivine-type metal phosphate. These results suggest a new description for the kinetic pathway of crystallization in complex
The final shapes and sizes of crystals, factors that govern Taking amorphous LiFePO4 as a multi-component model their resulting physical properties, are critically influenced compound in this study, we revealed the existence of intermediate by the kinetic pathway of the phase transformation during metastable crystalline states during crystallization. For direct crystallization from amorphous phases and melts. Accordingly, atomic-level observations, we used in situ high-resolution electron a number of studies have been conducted on transition kinetics microscopy (HREM) at a high temperature. Recent progress and thermodynamics in a variety of systems. A traditional in HREM has led to enhanced resolution for rapid and clear model for the early stage of crystallization can be described by imaging even at elevated temperatures. Thus, it enables observation two distinct processes: nucleation for the formation of stable of structural variations in real time in a variety of nanoscale atomic (or molecular) clusters and subsequent growth of the nuclei.
materials. HREM image processingbased on two- In contrast to this conventional description for crystallization, dimensional electron crystallography was also used to determine a system in an unstable state does not necessarily transform the atomic arrays of intermediates phases, showing the different directly into the most thermodynamically stable state, thus implying crystallographic characteristics between each phase.
the existence of metastable intermediate states, as empirically A series of in situ HREM images was acquired during the described by Ostwald in 1897 and dubbed the rule of stages.
crystallization of amorphous LiFePO4 at 450 ◦C. shows the In his conjecture, Ostwald stated that an unstable system could initial series of images between 40 and 44 min of heating. As shown transform into another transient state, the formation of which is for the earlier stage in another series of images (Supplementary attained by the smallest loss of free energy before finally reaching a Information, Fig. S1), the nuclei, which can be distinguished stable state. Therefore, the recognition of such intermediate states through their level of contrast in the images, initially form in would provide new insight into transformation kinetics during the matrix and subsequently grow as nanocrystals over time.
crystallization and be the first crucial step towards ultimate control Coalescence of nanocrystals can also be seen in of overall crystallization behaviour.
includes fast Fourier transforms (FFTs) corresponding to the Since the notable work by ten Wolde and Frenkel showing the nanocrystal denoted by the arrow in Although the crystal presence of an intermediate dense fluid during the crystallization structure of the nanocrystal does not change, the appearance of of globular proteins, many simulations and predictions have been diffraction spots with a high-order index in the FFT of offered in attempts to shed light on possible intermediate states together with the clearer development of the lattice fringe indicates during the early stage of crystallization, largely in organic proteins, that the crystallinity of the nanocrystal improves with heating time.
colloidsand Lennard-Jones fluids. With the exception However, lattice defects, which seem to be stacking faults, are also of several experimental attempts in such selective systems, observed in the crystal, as clearly shown in the Fourier-filtered however, no atomic-scale evolutions during crystallization in image for the region outlined by a green rectangle in inorganic compounds—which would provide direct evidence for The thermodynamically stable crystalline form of LiFePO4 is the Ostwald rule—have been observed. Compared with organic known to be an olivine structure with cation ordering (Li at proteins and colloidal crystals with comparatively large units, most the M 1 octahedral site and Fe at the M 2 octahedral site)in inorganic compounds have ångström-scale lattice parameters in the Pnma space group (no. 62 (ref. Here, the diffraction the unit cell. Furthermore, their crystallization usually occurs at pattern shown in the FFTs of cannot be derived from high temperatures. Owing to such limitations, a direct experimental the ordered olivine structure. Therefore, this result demonstrates observation in real time of the transformation kinetics is difficult in that the nanocrystal shown in is in a metastable transient most inorganic systems.
crystalline state, thus implying further transitions to the stable 1Department of Materials Science and Engineering, Inha University, Incheon 402-751, Korea, 2Nalphates LLC, Wilmington, Delaware 19801, USA, 3KoreaBasic Science Institute, Daejeon 305-333, Korea. *e-mail: [email protected].
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NATURE PHYSICS DOI:10.1038/NPHYS1148
b 42 min 0 s
c 42 min 30 s
d 43 min 30 s
Figure 1 First series of in situ HREM images and corresponding FFTs
during the crystallization of LiFePO4 at 450 ◦C. a–d, Images taken at 30 s
intervals. FFTs of a nanocrystal that nucleated from the matrix (denoted by an arrow in a) show the same pattern, indicating an identical crystal
structure. The presence of lattice defects, which appear to be stacking
faults, can be distinguished in the Fourier-filtered image in d for the region
outlined by the green square.
phase. reveals multiple phase transformations and theexistence of resultant intermediate crystalline states of LiFePO4before an ordered stable olivine structure is finally achieved duringcrystallization. The nanocrystal shown in (red), which hasa crystallographic structure identical to that shown in sequentially transforms into other phases with a different crystal structure over the course of a few minutes, as represented in different colours (yellow in and blue in The changein diffraction patterns in each FFT and the different high-resolutionlattice fringes of each structure also confirm the crystal-to-crystaltransformations. The final phase (green) shown in wasidentified as ordered olivine-type LiFePO4 in the [122] projection based on a simulated electron diffraction pattern, which is shown be identical to the FFT, along with the reflection indices. The magnified HREM image (green) and the simulated [122]-projection image (black and white) are confirmed to be in good agreement with During real-time HREM, we observed two distinct transition behaviours when the metastable intermediate crystalline phases Atomic displacement transformed into the next phase. First, it was found that the phasesshown in make a fairly rapid transition, showing no Surface nucleation and growth nucleation inside the nanocrystal for the next new crystalline state.
Such a martensitic-type massive transformation can be achieved byfast atomic displacement at an ångström scale if the phases before Figure 2 Second series of in situ HREM images and corresponding FFTs
and after the transformation do not differ considerably from each of a LiFePO4 nanocrystal at 450 ◦C. a–d, Both the HREM images and the
other. As mentioned in a recent review, the precise determination related FFTs demonstrate that the crystal structures differ from each other.
of the atomic structure in nanoscale materials remains challenging.
For clear discrimination, the images and the FFTs are presented in different Although there is currently no robust method to fully identify the colours (red, yellow and blue for the intermediate crystalline states). The intermediate states shown in we were able to demonstrate final state (green) shown in d was identified as an ordered olivine structure
their crystallographic relationship based on the HREM images.
in the [122] projection. The inset in d shows a magnified image of the
HREM images, which are constructed by transmitted and diffracted region outlined by the square. A simulated HREM image in black and white electron beams, afford crystallographic phase information along is also superimposed to confirm the ordered olivine structure. The image with the amplitude information of the diffracted electrons.
simulation was carried out under conditions of t = 40 Å (specimen Therefore, the resulting two-dimensional atomic potentials (or thickness) and 1f = −60 Å (defocus length). An electron diffraction atomic arrangement) can be determined accurately by electron pattern simulated under a dynamical condition is also presented with the crystallography via HREM image processing.
spot indices in d.
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NATURE PHYSICS DOI:10.1038/NPHYS1148
shows the projected potential contours reconstructed, using CRISP, from the HREM images in Eachinset also shows the black-and-white potential informationextracted from the images. On the basis of these image-processingresults, the plausible atomic arrays of Fe and P for each intermediatecrystalline phase can be estimated, although it is difficult todetermine the exact positions of Li and O owing to their lowatomic numbers. Red and yellow spheres superimposed on the contours denote Fe and P atoms, respectively. From the potentialcontour maps, we can easily see that the linear connectivity betweenFe and P in has been changed to a zigzag geometry in implying the ångström-scale displacement of atoms duringthe transformation. Given the atomic potentials, correspondingplane groups (or two-dimensional space groups) and the resultantsymmetry elements shown in can be identified for these metastable phases: a p1m1 plane group (no. 3) for and a p1g 1 plane group (no. 4) for Symbols and diagrams showingeach symmetry element in the unit cell for all 17 plane groupsare summarized in Supplementary Information, Table S1 and Fig. S2.
The change of the atomic configuration into a p1g 1 plane group,which contains glide planes instead of mirror planes parallel tothe a axis (Supplementary Information, Fig. S2), directly indicatesthat the phases shown in differ crystallographically fromeach other. The plane groups and the parameters of each unit celloutlined by a white rectangle in the contour maps for the phases are summarized in the table in In addition to the displacive transformation shown in another distinguishable transition behaviour was observed duringthe in situ analysis. This behaviour is characterized by nucleationfor a new crystalline phase and its subsequent growth, as generallyobserved in phase-transition phenomena. shows a seriesof real-time HREM images taken at intervals of 30 s for a heatingtime between 45 min and 48 min In contrast to the transitions shown in the formation of new crystallinestates inside the nanocrystal can be observed, as denoted by the arrows in However, compared with the lattice image shownin and the new crystalline phases nucleated in the Lattice parameters (Å) nanocrystal shown in do not seem to be the ordered olivine structure that should finally form. This again confirms the occurrence of multiple phase transformation and the resultingpresence of intermediate crystalline states.
Another noteworthy feature of is that the new crystalline phases seem to nucleate at the surface of the nanocrystal, as indicated by the arrows in More detailed lattice fringesbetween the surface and the interior bulk are compared in Figure 3 Atomic potential contour maps calculated by crystallographic
A magnified lattice image for the surface region, outlined by a image processing. a,b, The HREM images (left) shown in Fig. 2b,c were
green square, and its FFT directly show that the surface region processed to obtain the potential information. Each inset shows the has transformed into a stable olivine phase, consistent with potential information extracted from the images. Plausible atomic arrays the simulated HREM image and the FFT shown in In for Fe (red spheres) and P (yellow spheres) are indicated on each map, contrast, the bulk region, outlined by a blue square, remains in suggesting possible connectivity between the oxygen (grey spheres) an intermediate crystalline state, as can be seen in the magnified octahedra and tetrahedra on the left. Crystallographic information for the HREM image in Subsequent growth of the stable phase intermediate phases is listed in the table.
into the interior with time is observable in the magnified HREMimage in finally resulting in an ordered olivine structure in result verifies that the transition behaviours observed in this study the [122] projection for the entire crystallographic configuration of are not unique to a specific crystallite, but instead prevail in most the nanocrystal.
crystals during the crystallization process. Although the FFTs of the Multiple transformations such as this could also be observed in initial intermediate phases (red) in and show different other regions of the amorphous sample. shows another patterns from each other (see the comparison in Supplementary series of in situ HREM images and their FFTs, further ensuring Information, Fig. S3a), the rapid transition to the other states based the presence of the intermediate transient crystalline states. In on the atomic displacement was consistently similar between the particular, when the FFTs in are compared with those shown in it can be recognized that each intermediate The final intermediate crystalline state (blue, was also phase in is compatible with the metastable phases in confirmed to transform into the stable olivine structure (green, (For a direct and straightforward comparison, see Supplementary through surface nucleation and growth, the behaviour of Information, Fig. S3. The a and b axes of the FFTs presented in which is analogous to that shown in A detailed series of both and are aligned in the same directions.) This HREM images is presented in Supplementary Information, Fig. S4.
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NATURE PHYSICS DOI:10.1038/NPHYS1148
Figure 4 Third series of in situ HREM images of a LiFePO4 nanocrystal at 450 ◦C. a–f, Images taken at 30 s intervals. In contrast to Fig. 2a–c, this series
of images shows the transformation with the observable nucleation and subsequent growth of new phases inside the nanocrystal, as indicated by the
arrows in c and e. The magnified HREM images shown in e demonstrate that the interior bulk (blue square) remains in a metastable transient state,
compared with the stable surface region (green square). The enlargement shown in f and its FFT confirm that the nanocrystal finally transforms by growth
of a phase with an olivine structure.
A simulated electron diffraction pattern of LiFePO4 in the [010] the antisite defects in LiFePO4 with temperature, it is anticipated zone direction is compared with the FFT in Although the that the final stable crystals shown in and would have relative intensities of the reflection spots are different, the good considerable cation intermixing between the M 1 and M 2 sites due agreement between the FFT and the simulated pattern reveals to the much lower heating temperature and insufficient time to that the nanocrystal (green) is of the olivine structure in the complete the ordering.
[010] projection.
The present findings, which represent the first direct evidence at Because the ionic radii of Li+ (0.76 Å) and Fe2+ (0.78 Å) in an atomic level of multiple transitions via intermediate metastable a coordination octahedron of anions are similar to each other, crystalline phases in an inorganic compound, suggest a plausible it is not likely that the two different cations are distributed in a pathway for the crystallization of LiFePO4, as schematically completely ordered manner onto octahedral interstitial sites of the represented in The overall driving force for the crystallization intermediate phases. In addition, on the basis of a recent study of to the finally stable ordered olivine structure is denoted by 1G. The NATURE PHYSICS VOL 5 JANUARY 2009 www.nature.com/naturephysics
NATURE PHYSICS DOI:10.1038/NPHYS1148
39 min 30 s
44 min 30 s
48 min 30 s
Figure 5 Extra series of in situ HREM images of another LiFePO4 nanocrystal at 450 ◦C. a–d, HREM images and corresponding FFTs presented in
different colours to discriminate the different crystal structures consistently, as shown in Fig. 2. The FFT of the final state (green) shown in d represents a
pattern that is identical to the simulated electron diffraction pattern of LiFePO4 in the [010] projection, confirming that the final state is of the olivine
structure. The simulation was carried under a dynamical condition. Plus signs in the simulated pattern denote nearly invisible spots with low intensity.
between nanocrystals, suggesting local variations, as compared in Supplementary Information, Fig. S3a.
The observations in this study are based on HREM, which is usually carried out in comparatively thin regions of a sample for better electron transparency under electron irradiation. Thus, in reality, not all of the nanocrystals are predicted to show precisely identical transition rates and activation energies from a statistical standpoint. In addition, quantitative energy variations have notbeen provided by which to judge how stable each intermediatephase becomes after transformation in terms of the relative energy stability. In this respect, statistical investigations accompaniedby quantitative simulations can be suggested to make further Structure (or reaction time) progress in understanding the multiple phase transformationduring crystallization.
Figure 6 Schematic diagram showing the transition pathway during the
crystallization of LiFePO
4. 1G indicates the total driving force for
crystallization from an amorphous to a finally stable olivine-type crystal. A, Sample preparation. An amorphous LiFePO4 powder sample was prepared
B and C represent metastable intermediate states with a local energy using high-purity lithium carbonate (Li2CO3, 99.99%, Aldrich), iron(ii)oxalate dihydrate (Fe( minimum, and each 1G∗ denotes the activation energy that should be 2 O, 99.99%, Aldrich) and ammonium dihydrogenphosphate (NH4H2PO4, 99.999%, Aldrich). A small amount (2 mol%) overcome for the transition to the next phase.
of potassium carbonate (K2CO3, 99.995%, Aldrich) was also added as a flux forready formation of an amorphous phase at a low temperature. A stoichiometric structure having the lowest energy barrier to transition crystallizes powder mixture of the three starting materials with the additive was ball-milled inacetone for 24 h with zirconia milling media. After drying, the slurry was calcined first, before transforming to another structure with the next lower at 350 ◦C for 5 h in a stream of high-purity Ar (99.999%) at 400 s.c.c.m. The energy state. Consistent with the Ostwald rule, the activation calcined powder sample was confirmed to be amorphous by transmission electron energy 1G∗ for the first transition to A is expected to be the microscopy (TEM) before in situ analysis.
lowest among the other activation energies, showing a sequence of In situ HREM and crystallographic image processing. A transmission electron
G∗ < 1G∗ < 1G∗ < 1G∗. When the energy barrier is sufficiently microscope (JEM-ARM 1300S, JEOL Ltd) was used along with a hot-stage heating low, it can be easily overcome by thermal fluctuation, leading to a holder (Gatan) for atomic-scale in situ observation at a high temperature. Images fast transition via atomic displacement, as demonstrated in were recorded using a CCD (charge-coupled device) camera (2,048 × 2,048 pixels, and However, as a large activation is required, for example, SPUS1000 HV-IF, Gatan Inc.) mounted in the post-column high-voltage Gatan in the case of 1G∗, a displacive transformation is no longer imaging filter. After heating at a rate of 10 ◦C min−1 to 450 ◦C, the samples were stabilized for 20 min without electron irradiation to prevent drifting during the likely to occur. Therefore, as shown in the formation of observation. A two-dimensional Difference Filter (HREM Research Inc.) was used energetically more stable nuclei that have overcome the energy to eliminate the background noise of the HREM images taken during the in situ barrier along with their subsequent growth are favourable for experiment and thereby to obtain clearer FFTs along with accurate crystallographic further transition. It is also noted that the first intermediate information. For image processing based on the electron crystallography with crystalline phase from an amorphous solid is readily achieved by the lattice fringe images and their FFTs, CRISP (Calidris Inc.) was used to determinethe projected atomic potentials and estimate the plausible positions of Fe and P.
smallest reduction of energy along with the lowest energy barrier.
During the data analysis, an optimal plane group for each image was determined, Consequently, the initial transient phase corresponding to A in and thus the values of the difference of the amplitude of symmetry-related may not always be of the same crystallographic structure reflections (Rsym) and the mean phase error (ϕRes) are as low as possible.
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NATURE PHYSICS DOI:10.1038/NPHYS1148
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