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4D Visualization of Transitional Structures in Phase Transformations by Electron Diffraction

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Science  02 Nov 2007:
Vol. 318, Issue 5851, pp. 788-792
DOI: 10.1126/science.1147724

Abstract

Complex systems in condensed phases involve a multidimensional energy landscape, and knowledge of transitional structures and separation of time scales for atomic movements is critical to understanding their dynamical behavior. Here, we report, using four-dimensional (4D) femtosecond electron diffraction, the visualization of transitional structures from the initial monoclinic to the final tetragonal phase in crystalline vanadium dioxide; the change was initiated by a near-infrared excitation. By revealing the spatiotemporal behavior from all observed Bragg diffractions in 3D, the femtosecond primary vanadium–vanadium bond dilation, the displacements of atoms in picoseconds, and the sound wave shear motion on hundreds of picoseconds were resolved, elucidating the nature of the structural pathways and the nonconcerted mechanism of the transformation.

When transformations of matter involve many atoms, as in complex molecular structures or in condensed phases, understanding their dynamical behavior requires the determination of actual transitional structures with spatial and temporal resolution of the atoms and their motions. In general, such transformations involve an energy landscape described by transition states and transient intermediates (1), and only when the time scale of observation is appropriate can such species be studied (2). For direct probing, the radiation or particle used must also have a wavelength on the scale of atomic distances, as demonstrated in the studies of melting and lattice dynamics by ultrafast x-ray absorption (3) and diffraction (47) and electron diffraction (810). In our laboratory, ultrafast electron microscopy (UEM) and ultrafast diffraction (11) have been the methods of choice for studies of molecular and phase transitions (1216).

In the condensed phase, the use of the energy landscape concept has recently been theoretically addressed (17, 18) for transformations involving two thermodynamically stable configurations, as in solid-solid transitions. There are two classes of descriptions: those that invoke first the motion of the atoms in the unit cell and then the lattice organization and those that deal with the total rearrangement of the lattice including the displacement of unit-cell atoms. The time scales and nature of structures dictate the validity of the theoretical approach and what approximations are appropriate for the separation of different types of nuclear motions. As with chemical reactions, the concept of concerted (or concurrent) versus consecutive nuclear motions (1, 2) becomes central to understanding the elementary steps of the mechanism.

Here, we report on the nature of transitional structures during a symmetry-raising process, from initial monoclinic (insulator) to final tetragonal (metal), observed with atomic-scale spatial and temporal resolution. The study is performed on single crystals of vanadium dioxide, whose phase transition exhibits a well-defined hysteresis between two thermodynamically stable structures. In order to map pathways of motion, all observed Bragg diffractions of different planes and zone axes were examined on the femtosecond to nanosecond time scale. The three-dimensional (3D) sampling and long-range order studied make possible the separation of different nuclear motions, which are mirrored in the temporal change of the structure factor for various indices. Because the transformation takes place in a strongly correlated system, the dependence on excitation fluence is evident in a threshold behavior, and we studied such dependence at short and long times to elucidate the nonequilibrium transition from local atomic motions to shear at sound wave (and carrier) velocity.

At equilibrium, the phase transition in vanadium dioxide has been studied by examining the change of heat capacity with temperature (1921). Such studies identify the transition as first order with a hysteresis. Seminal contributions using optical reflection and x-ray methods have indicated the ultrafast nature of the transition (2226). The transition can be induced nonthermally on the ultrashort time scale, with the required excitation a variable characteristic dependent on the morphology of the specific sample. Real-space imaging (and diffraction) was achieved with UEM for nanoscale structures (14, 15). We investigated high-quality single crystals of vanadium oxide, invoked ultrafast electron crystallography with a tilted geometry (11, 27, 28), and used the 3D reciprocal space of atoms involved (20 Bragg spots).

The initial and final crystal structures of vanadium dioxide are depicted in Fig. 1A: in the monoclinic phase the vanadium atoms arrange into pairs, but in the tetragonal phase (referred to as rutile) all V–V distances are equal and the symmetry is tetragonal (21). The structure and long-range order of our vanadium dioxide single crystals were confirmed by static x-ray diffraction, and one of three crystals was cut and polished to have a surface that is not naturally grown. For these crystals, the characteristic hysteresis near 340 K was observed, with a width of 5.6 K. In Fig. 1, B to E, the static electron diffraction patterns, obtained at an incidence angle of ∼5° and at room temperature (monoclinic phase), are shown for different surface normal directions, , and electron directions (zone axis), Math. All spots were identified as monoclinic vanadium dioxide; transmission-like patterns originate from surface structures (12), and the single-crystal order is evident in the well-indexed diffraction patterns.

Fig. 1.

Crystal structures of vanadium dioxide phases and observed Bragg diffraction. (A) Crystal structure of the monoclinic, low-temperature phase (left) and the rutile, high-temperature phase (right). Vanadium atoms are depicted in red and oxygen atoms in a lighter color. Because of a symmetry-breaking pairing of vanadium atoms (violet lines), the axis definitions change. Monoclinic coordinates and axes are used in the paper. (B to E) Typical diffraction patterns observed by ultrafast electron crystallography for different crystal surfaces and different zone axes; is the surface normal direction and Embedded Image is the electron direction (zone axis). All Bragg spots can be identified as the monoclinic structure (yellow labels).

With such rich diffraction, 16 of the Bragg spots were intense enough for time-resolved investigations. The change was initiated by using near-infrared (800 nm) pulses, and, after a variable delay time, structural dynamics were followed by diffracting the electron packets. The optical excitation fluence was up to 14 mJ/cm2, enough to drive the phase transition with a single pulse. Within the experimental repetition period of 1 ms, the crystal held at room temperature fully recovers to the initial monoclinic phase. This recovery was confirmed by observing no change in the diffraction patterns whether recorded at negative delay time (an effective 1-ms delay) or without the excitation. The observed changes by fs excitation, therefore, reveal the nonequilibrium dynamics without contributions from static heating.

We checked for possible effects of surface potential change or charge trapping on the diffraction during the transition from insulator to metal phase; no such effects were found, as evidenced from our observation of a steady position and intensity of the direct nondiffracted electron beam for scans at all time delays. At 5° incidence, the electrons diffract from a material thickness of about 10 nm; we do not observe rods in the diffraction patterns but instead well-defined Bragg spots, suggesting that at least 10 interatomic layers in the surface-normal direction are contributing to the interferences (28). A rough estimate of the mean free path of a 30-keV electron gives a penetration depth (∼5 nm) that is about 20 times larger than the interplanar separation. Because of the small angle of incidence, the probed area on the surface is ∼2 mm by 0.2 mm, giving a group velocity mismatch of ∼20 ps between the optical excitation and the electron pulses. In order to overcome such mismatch and reach fs resolution, the optical pulse was tilted to achieve temporal synchrony with the electron packet on the entire probed crystal surface (27). A fs transient, however, includes convolution from any residual spread and the involved duration of optical and electron pulses, as discussed below.

The observed temporal change of intensity of one class of Bragg spots, for example, the (606) spot, is shown in Fig. 2A. With time steps of 250 fs, a notable decrease in intensity is observed. In order to record such a transient, the number of electrons in one pulse was reduced to ∼500, which is below the space-charge limit (11, 13), and in this limit of low flux the electron pulse width was measured (322 ± 128 fs) in situ at a streaking speed of 140 ± 2 fs per pixel (29). Given the optical pulse width of 120 fs, the cross-correlation was used in the analysis of the transient, thus obtaining a time constant, τ1, of 307 fs. The error bar at each delay time is a result of 18 single measurements. For all of the Bragg spots studied (Fig. 1), we observed two types of behavior (Fig. 2B): a fs decay in intensity (blue) similar to the (606) spot and, remarkably, a decay lacking such fast dynamics but exhibiting an intensity decrease with a time constant, τ2, of 9.2 ps (red); the Miller indices (hkl) of the two classes of spots are listed in the figure caption. We note that no shift in position or change in width was measurable at early times. The absence of a spot shift (12) shows that no substantial lattice expansion is taking place on the ultrashort time scale; the absence of a clear width change also indicates that no measurable disorder is introduced on this time scale. These observations exclude thermal expansion or lattice inhomogeneity (strain) in this time range (28).

Fig. 2.

Ultrafast, fs and ps, diffraction dynamics of the structural phase transition. (A) Intensity change of the (606) Bragg spot with time. A decay with a time constant τ1 of 307 fs was obtained on the total time scale of ±3 ps (40); note the change in intensity of diffraction in the 250-fs steps. (B) Intensity change of (606) (blue) and (091) (red) spots with time. For all investigated Bragg spots, two different types of dynamics were observed: a femtosecond decay similar to the blue trace was measured for (806), (826), (Embedded Image), (846), (Embedded Image), (606), (714), (Embedded Image), (10 2 4), and (Embedded Image); a decay with a time constant τ2 of 9.2 ps, similar to the red trace, was measured for (091), (084), and (Embedded Image), on the total time scale of 40 ps. The temporal range values (Δt1 and Δt2) over which the decay is pronounced are 760 fs and 15 ps (40). This difference indicates a stepwise mechanism for atomic motions.

All Bragg spots that show the fs behavior involve nonzero values of (hkl), whereas those displaying the slower ps behavior have a zero component of h. Accordingly, the observed fs and ps intensity changes of Bragg spots are associated with motion of atoms within the unit cell by destructive interferences, and these changes are determined by the structure factor monitored in the intensity of scattered electrons for a given direction and zone axis. Specifically, the intensity I of a Bragg spot (hkl), which is proportional to the square of the structure factor F(hkl), is determined by the position (xyz) of atom j within the unit cell (Eq. 1) Math(1) Math where fj is the atomic scattering factor. The monoclinic phase has a lower symmetry than that of the rutile phase, and the symmetry-raising processes cause a large change in Bragg diffraction, even when small-amplitude atomic motions are involved, as shown below.

The observed two types of dynamics indicate stepwise atomic motions along different directions. Figure 3A depicts the initial and final vanadium positions in the two phases. From the inner product in Eq. 1, it is evident that an atomic movement along a certain direction can only affect such Bragg spots that have nonzero contributions in the corresponding Miller indices. It is thus concluded that the initial fs motion is along the a axis, which is the direction of the V–V bond in the monoclinic structure. On the other hand, the ps structural transformation projects along the c and b axes (Fig. 3A). If the fs motion had large components along b or c, it would show up in the dynamics of all investigated spots, contrary to observations.

Fig. 3.

(A) Atomic movements and the calculated structure factors. (Top left) Initial (purple) and final (blue) positions of the vanadium atoms. The monoclinic unit cell is depicted as dotted purple lines, and the rutile unit cell as a blue dotted box. (Top right) The direct motion of the vanadium atoms from the initial (purple) to the final (blue) position, mostly along the c axis, is depicted. (Bottom left) Structure factor and expected intensity change for the listed Bragg spots for a displacement of the vanadium atoms along the chemical bond, as depicted in the top left image. (Bottom right) Structure factor and intensity change for a displacement of the vanadium atoms along the direct path, as depicted in the top right image. The V–V displacements shown are for delocalized excitation of the lattice. (B) Transitional structures during the ultrafast phase transformation. (Top) The experimental data, here the (606) spot (blue), reflects the stepwise atomic motion within the unit cell and, on larger length scales, of shear motion. (Inset) The difference in static x-ray patterns between monoclinic (low temperature) and rutile (high temperature) vanadium dioxide suggests macroscopic shear (angular) displacement. (Bottom) Shown are frames at the corresponding times (ti, t1, t2, and tf) of structural changes.

To quantify selective intensity changes, we calculated for the observed Bragg diffraction the structure factor and intensity changes of the monoclinic phase when the atoms undergo small atomic displacements. Two possible pathways for atomic movement were considered. In Fig. 3A, we display the consequence of V–V bond weakening (or dilation) motion on the values of |F|2; all spots with h ≠ 0 show a decrease in intensity, and for those with h = 0 the intensity remains unchanged, as observed experimentally. In contrast, when considering direct movement leading to the transition from the monoclinic to the rutile phase, most spots show an increase and some a decrease in |F|2 values, a behavior that was not observed experimentally on the ultrafast time scale.

The initiating excitation at 1.55 eV primarily involves the d band, which arises from bonding of the vanadium pairs (30, 31). From a chemical perspective, the excitation is to an antibonding state, which instantly results in a repulsive force on the atoms, and they separate along the bond direction. In sequence and on a slower time scale, the unit cell transforms toward the configuration of the rutile phase. Therefore, the observed stepwise atomic motions show that the phase transition proceeds by a nondirect pathway on the multidimensional potential energy surface and not by a direct structural conversion.

Several points are worth mentioning. First, these resolved structures are for transient species, en route to the stable rutile structure, and involve a landscape with distinct coordinates. In Fig. 3B, the overall temporal behavior up to 1.2 ns and structural snapshots are shown. Second, optical reflectivity and diffraction from polycrystalline samples provide an average over all orientations and will give rise to composite transient behavior. Cavalleri et al. (22) have shown that x-ray diffraction around the (011) spot region (32) of a crystal is dominated by ∼12-ps change, with a relatively small faster component (≤500 fs). Given our results, we concluded that dominance of the fs dynamics can emerge if the relevant direction of diffraction is monitored and that the ps component is due to the transversal motion. Lastly, for the first step, comparison with the ∼100-fs time constant from optical reflectivity (23, 25) and ∼500 fs from the x-ray study (22) is not straightforward, because the former approach is more sensitive to the electronic changes of the material whereas the latter one integrates the structural changes over the x-ray probing length of micrometers. Future experiments may reveal the vibrational time scale of ∼170 fs of the equilibrium structure or a somewhat longer time due to a potential-driven motion in the excited state (28).

The transient behavior on the longer, sub-nanosecond time scale reveals another dimension of structural dynamics. As shown in Fig. 3B, after the initial insulator-metal transition after a delay, there is a continued temporal change of intensity that levels off at ∼300 ps. Given the optical penetration depth (1/α) of ∼100 nm (20) and the thermal diffusion coefficient of 0.02 cm2/s (20), we conclude that heat conduction away from the probed layer must be slower than 1 ns and cannot explain the observed ∼100-ps dynamics. However, because the speed of sound in the material is v ≈ 4000 m/s (33), shear, which is necessary for the formation of rutile vanadium dioxide (34) and may involve dislocations (35), will occur in ∼100 ps for a length scale of hundreds of nanometers (36). This shear motion is further supported by other observations. First, although the Bragg spots exhibit the same early fs-ps behavior, they show intensity increase or decrease at the sub-ns scale for different zone axes, consistent with shear interferences (37). Second, when we obtained x-ray diffraction of the crystal at different temperatures (Fig. 3B, inset) as it passed through the phase transition, nearly all Bragg spots were observed to move angularly, indicating rotation of the principle axes. Further evidence comes from the fluence dependence and its threshold behavior.

Figure 4 shows the fluence dependence of diffraction change, for example, for the (606) Bragg spot, at two time points, t = 10 ps and t = 1 ns. The intensity change displays (almost) a linear dependence with a threshold at 6 ± 1 mJ/cm2. The threshold, which translates to ∼0.05 photon per vanadium atom (38), indicates the minimum fluence required for switching into the new phase in this crystalline material and as such defines a level of connectivity among the different sites involved (15). For the spots that exhibit the fs dynamics, we noted that the threshold for the sub-ns component is either the same or higher than that of the fs component, suggesting that the shear is associated with the initial atomic motions.

Fig. 4.

Dependence of the fs dynamics and the large-scale shear displacement on excitation fluence. The magnitude of the initial intensity decrease (violet) and the amplitude of the long-time change (green) are plotted for different excitation fluences. A common threshold region is observed. (Inset) Transients of the (606) Bragg spot for two different excitation fluences. The magnitudes of change were measured at 10 ps and 1 ns.

From Eq. 1, the calculated V–V displacement (Fig. 3A) reaches 0.02 Å for ∼0.1 photon per vanadium for delocalized excitation of the lattice. However, vanadium dioxide is a strongly correlated system, and this value could be as high as 0.2 Å for localized V–V pairs. We note that the total energy deposited at threshold (∼ 0.4 ± 0.1 J/mm3) matches well with the total heat required (0.38 J/mm3) for thermally inducing the phase transition, including the latent heat (20). This observation suggests that the phase transition is critically dependent on the total number of carriers, thermal and optical (26), and that the described transitional structures may be reached similarly but with different rates, as shown, for example, in surface femtochemistry (39). Lastly, we have repeated these experiments at different temperatures; at 110 K, the fluence threshold shifts to a higher value compared with that at 300 K, which further supports the above-mentioned stepwise mechanism.

The ability to decipher the nature of the atomic motions during a structural phase transition is demonstrated by the results reported here. For vanadium dioxide crystals, the elementary steps follow a nonconcerted mechanism with a sequence of transitional structures, first involving local displacements on the fs and ps time scale followed by long-range shear rearrangements on the sub-ns time scale and at the speed of sound. The V–V bond dilation is the initial step of the insulator-to-metal transformation, providing a dynamical molecular picture. The coincidence of the thermal and photoinduced transition thresholds at different temperatures suggests the common pathway mechanism for the transition. With 4D atomic-scale spatial and temporal resolutions, we expect, by using this table-top approach, many future extensions in the studies of designed nanoscale materials and biological systems (11).

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