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Experimental observation of carousel-like phason flips in the decagonal quasicrystal Al60Cr20Fe10Si10

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aState Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, People's Republic of China, bLPICM, CNRS, Ecole polytechnique, Institut Polytechnique de Paris, Palaiseau, France, cBeijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China, dShenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, People's Republic of China, and eDepartment of Materials, ETH Zurich, 8093 Zurich, Switzerland
*Correspondence e-mail: hezhanbing@ustb.edu.cn

Edited by U. Grimm, The Open University, United Kingdom (Received 2 March 2021; accepted 22 July 2021; online 13 August 2021)

Quasicrystals have special crystal structures with long-range order, but without translational symmetry. Unexpectedly, carousel-like successive flippings of groups of atoms inside the ∼2 nm decagonal structural subunits of the decagonal quasicrystal Al60Cr20Fe10Si10 were directly observed using in situ high-temperature high-resolution transmission electron microscopy imaging. The observed directionally successive phason flips occur mainly clockwise and occasionally anticlockwise. The origin of these directional phason flips is analyzed and discussed.

1. Introduction

Quasicrystals show long-range order, but without translational symmetry (Shechtman et al., 1984[Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. (1984). Phys. Rev. Lett. 53, 1951-1953.]; Levine & Steinhardt, 1984[Levine, D. & Steinhardt, P. J. (1984). Phys. Rev. Lett. 53, 2477-2480.]). Generally, two or more unit tiles are utilized to describe the crystal structures of quasicrystals, where the tiles have to abide by strict matching rules in the case of perfect quasiperiodic tilings. However, local phasonic disorder has been widely found experimentally (Levine & Steinhardt, 1986[Levine, D. & Steinhardt, P. J. (1986). Phys. Rev. B, 34, 596-616.]; de Boissieu, 2012[Boissieu, M. de (2012). Chem. Soc. Rev. 41, 6778-6786.]). Quenched phasons are generally reflected by shifts and broadenings of diffraction spots in the diffraction patterns or by jagged atomic rows in high-resolution transmission electron microscopy (HRTEM) images (Levine & Steinhardt, 1986[Cao, K., Skowron, S. T., Biskupek, J., Stoppiello, C. T., Leist, C., Besley, E., Khlobystov, A. N. & Kaiser, U. (2020). Sci. Adv. 6, eaay5849.]). Recently, we found a quasicrystal-related mosaic with aperiodically distributed unit tiles inlayed in the lattice of translationally periodic structural blocks, where the origin of this distinctive feature was also ascribed to phasonic disorder (He et al., 2020[He, Z., Shen, Y., Ma, H., Sun, J., Ma, X., Li, H. & Steurer, W. (2020). Acta Cryst. A76, 137-144.]). The actions of phason flips were experimentally observed indirectly by neutron scattering (Coddens et al., 1991[Coddens, G., Bellissent, R., Calvayrac, Y. & Ambroise, J. P. (1991). Europhys. Lett. 16, 271-276.]; Lyonnard et al., 1996[Lyonnard, S., Coddens, G., Calvayrac, Y. & Gratias, D. (1996). Phys. Rev. B, 53, 3150-3160.]; Coddens & Steurer, 1999[Coddens, G. & Steurer, W. (1999). Phys. Rev. B, 60, 270-276.]), Mössbauer spectroscopy (Coddens et al., 1995[Coddens, G., Lyonnard, S., Sepiol, B. & Calvayrac, Y. (1995). J. Phys. I Fr. 5, 771-776.]) and NMR (Dolinšek et al., 1998[Dolin˘sek, J., Ambrosini, B., Vonlanthen, P., Gavilano, J. L., Chernikov, M. A. & Ott, H. R. (1998). Phys. Rev. Lett. 81, 3671-3674.], 1999[Dolinšek, J., Apih, T., Simsič, M. & Dubois, J. M. (1999). Phys. Rev. Lett. 82, 572-575.]). Importantly, Edagawa et al. carried out the first direct observations of phason flips in an Al–Cu–Co decagonal quasicrystal (DQC) using in situ high-temperature HRTEM (Edagawa et al., 2000[Edagawa, K., Suzuki, K. & Takeuchi, S. (2000). Phys. Rev. Lett. 85, 1674-1677.], 2002[Edagawa, K., Suzuki, K. & Takeuchi, S. (2002). J. Alloys Compd. 342, 271-277.]), where the phason flips were corresponding to the rearrangements of the unit tiles by a few atomic jumps. They observed thermally induced go-and-return transitions between A and B positions in the Al–Cu–Co DQC (Edagawa et al., 2000[Edagawa, K., Suzuki, K. & Takeuchi, S. (2000). Phys. Rev. Lett. 85, 1674-1677.]). Trebin et al. related the observability of phason flips in HRTEM experiments, which are on the timescale of seconds to minutes, to the atomic flip rate, which is of the order of picoseconds (Trebin & Lipp, 2017[Trebin, H. R. & Lipp, H. (2017). J. Phys. Conf. Ser. 809, 012019.]). The growth of decagonal quasicrystals was also found to be related to phason-flip-related error-and-repair processes instead of following strict local growth rules (Nagao et al., 2015[Nagao, K., Inuzuka, T., Nishimoto, K. & Edagawa, K. (2015). Phys. Rev. Lett. 115, 075501.]). In addition, successive phason flips involving more than two positions were also observed in the Al–Cu–Co DQC (Edagawa et al., 2002[Edagawa, K., Suzuki, K. & Takeuchi, S. (2002). J. Alloys Compd. 342, 271-277.]). However, these successive phason flips were generally considered as random actions because the occupied positions of flipping atoms in the tiling were random and no obvious rules were obeyed. Besides, thermally induced atomic fluctuations or atomic jumps were observed in other systems, where the routes of atomic jumps are also random (Cao et al., 2020[Cao, K., Skowron, S. T., Biskupek, J., Stoppiello, C. T., Leist, C., Besley, E., Khlobystov, A. N. & Kaiser, U. (2020). Sci. Adv. 6, eaay5849.]). These facts raise the question of the possibility of regular correlated dynamical flips of atoms or clusters.

In this article, we report peculiar thermally fluctuating phasons in decagonal Al60Cr20Fe10Si10, where a carousel-like successive flipping of atoms is observed directly using in situ high-temperature HRTEM. We found that the successive clockwise or occasionally anticlockwise phason flips of atoms are located on a 0.77 nm decagon inside the ∼2 nm decagons. This is the first time, as far as we know, that a carousel of successive phason flips could be observed. The origin of this novel kind of phason flips is analyzed and discussed in the following.

2. Experimental details

2.1. Preparation of the quasicrystals

Approximately 1 kg of the master alloy with a nominal composition Al60Cr20Fe10Si10 was first prepared by melting the high-purity elements in an induction furnace under an argon atmosphere. The molten alloy was then poured into a graphite crucible in the furnace to form an ingot. Some fragments of the obtained ingot were heated at 1100°C for 7 days in an evacuated quartz tube, and then cooled in the furnace by switching off the power.

2.2. Characterizations

The atomic resolution structural investigations were performed with a JEM-ARM200F microscope equipped with a cold field emission gun, Cs-probe corrector and Cs-image corrector. In situ HRTEM observations were carried out in a Thermo Fisher Titan environmental transmission electron microscope equipped with an image aberration corrector and operated at 300 kV. The crushed alloys were diluted in ethanol and dispersed with ultrasonic treatment. The solution was then dripped onto a Protochips Fusion in situ heating chip, which was then mounted on a double-tilt Protochips Fusion TEM heating holder. The heating history of the sample is shown in supplementary Fig. 1[link] in the supporting information. We focused the electron beam somewhat on the sample to benefit the evolution of atomic revolutions. Owing to the electron irradiation at elevated temperatures, the thickness of the observed sample was reduced and the profile of the samples also changed compared with that at room temperature. HRTEM images at 800°C were taken at a magnification of 3.8 × 105 and recorded by a Gatan US1000 CCD camera, using Gatan video recording software, with a frame rate of 1 frame per second.

[Figure 1]
Figure 1
Basic structural information for decagonal Al60Cr20Fe10Si10 viewed along the tenfold zone axis. (a) Selected-area electron diffraction pattern of the DQC taken at 800°C. The diffraction pattern exhibits obvious tenfold symmetry, as shown by the yellow circles. (b) HRTEM image of the DQC observed at 800°C. (c) The fast Fourier transform of (b), which also exhibits the features of the DQC. (d), (e) Enlarged HRTEM images of the DQC at 800°C with the structural blocks depicted by polygons (e), and with the ∼2 nm D clusters emphasized (the same color indicates the same type of D cluster). (f), (g) Atomic resolution HAADF-STEM images of the DQC with the structural blocks depicted as polygons (f), and with the ∼2 nm D clusters emphasized in (g). The same color indicates the same type of D cluster. (h), (i) Enlarged images of two typical D clusters: D2H+B in (h) and D3H+BT in (i).

3. Results and discussion

Fig. 1[link](a) shows a selected-area electron diffraction pattern (EDP) of decagonal Al60Cr20Fe10Si10 at 800°C, where the diffraction spots are arranged tenfold symmetrically (for example, those marked by circles), characteristic for DQCs. Fig. 1[link](b) presents a typical HRTEM image viewed along the tenfold axis of the DQC at 800°C; the features of the DQC are reproduced by the corresponding fast Fourier transform in Fig. 1[link](c), where the marked spots correspond to those marked in Fig. 1[link](a). An enlarged HRTEM image from the thin area of Fig. 1[link](b), overlaid with a proper tiling, is shown in Fig. 1[link](d). Its unit tiles mostly correspond to stars (S), boats (B), hexagons (H), bowties (BT) and, occasionally, to decagons (D) with almost perfect tenfold symmetry. Note that the combination of B, H and BT tiles may further form decagons with a diameter of ∼2 nm, as can be seen in Fig. 1[link](e). These kinds of D clusters can be classified in two types: one consists of two H tiles and one B tile (highlighted in purple), the other of three H tiles and one BT tile (highlighted in yellow). For clarity, these two typical D clusters are denoted as D2H+1B and D3H+1BT, respectively. For comparison, the structural features of decagonal Al60Cr20Fe10Si10 at room temperature (RT) are also shown in the atomic resolution high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image in Figs. 1[link](f) and (g). Enlarged images of the two typical D clusters, D2H+1B and D3H+1BT, are depicted in Figs. 1[link](h) and (i). There, the vertices of the unit tiles are occupied by smaller decagonal atomic clusters with a diameter of ∼0.47 nm. The different imaging conditions of HRTEM and HAADF-STEM do not allow a direct comparison of atomic arrangements at high and at low temperature. However, the unit tiles are the same at both temperatures, implying that the vertices of the structural tiles in Fig. 1[link](d) and (e) represent the positions of columnar atomic clusters. We note that the D clusters with broken tenfold symmetry in decagonal Al60Cr20Fe10Si10 consist of the unit tiles H, B or BT, which was also shown previously (Ma et al., 2018[Ma, H. K., He, Z. B., Hou, L. G. & Steurer, W. (2018). J. Alloys Compd. 765, 753-756.], 2020[Ma, H. K., You, L. & He, Z. B. (2020). Mater. Charact. 166, 110424.]). Therefore, the change of the structural units inside a ∼2 nm D cluster will be a rearrangement among the H, B or BT tiles.

Thermally induced atomic phason flips with directionally successive transitions, discovered using in situ high temperature HRTEM, are shown in Figs. 2[link]–4[link][link] (see also the video in the supporting information). The phason flips are confined to the decagon with a diameter of 0.77 nm within the larger ∼2 nm D clusters. Interestingly, these special atomic phason flips occur mainly in the clockwise direction, which was not expected. We take three highlighted D clusters, designated as D1, D2 and D3 in Fig. 2[link](a), as examples to demonstrate the directionally successive transitions of thermally induced atomic phason flips.

[Figure 2]
Figure 2
Successive clockwise propagation of atomic phason flips inside the D1 cluster at 800°C. (a)–(f) HRTEM images of the DQC taken at different times. Three ∼2 nm D clusters are marked, but we focus on the changes of the D1 cluster, as highlighted by the white outline. (g) Geometric schematic of the structural changes of D1 as time goes on. In the first row, the numbers 1, 2, …, 10 correspond to positions of possible atomic columns inside the first ∼2 nm D cluster, located on a smaller circle with a diameter of 0.77 nm. The positions occupied by atomic columns are indicated by green spots. In the middle and bottom rows, the changes of the atomic positions on the 0.77 nm D cluster are summarized. The occupied positions are indicated by solid spots and marked by numbers. The hopping of atomic columns is marked by arrows in the middle row. (h) Summary of continuous clockwise flips of atoms inside the D1 cluster.
[Figure 3]
Figure 3
Successive clockwise propagation of atomic phason flips inside the D2 cluster at 800°C. (a)–(d) HRTEM images of the DQC taken at different times. Three ∼2 nm D clusters are marked, but we focus on the changes of the D2 cluster, as highlighted by the white outline. (e) Geometric schematic of the structural change of D2 as time goes on. As in Fig. 2[link], the numbers 1, 2, …, 10 mark possible atomic column positions in a smaller circle with a diameter of 0.77 nm. The positions occupied by atoms are indicated by green spots. In the middle and bottom rows, the changes of atomic positions on the 0.77 nm circle are summarized. The occupied positions are indicated by solid spots and marked by numbers. The atom movements are marked by arrows in the middle row. (f) Summary of two groups of continuous clockwise flips of atoms in the D2 cluster. The arrows indicate the direction of dynamical processes and the colors of the arrows represent different groups. In the table at the bottom-right corner `P' means the position occupied by atoms on the 0.77 nm circle inside the ∼2 nm D cluster, and `T' means time.
[Figure 4]
Figure 4
Successive clockwise propagation of atomic phason flips inside the D3 cluster at 800°C. (a)–(d) HRTEM images of the DQC taken at different times. Three ∼2 nm D clusters are marked, but we focus on the changes of the D3 cluster, as highlighted by the white outline. (e) Geometric schematic of the structural changes of D3 as time goes on (same presentation as in Figs. 2[link] and 3[link]). (f) This time, contrary to the cases in Figs. 2[link] and 3[link], hopping is observed in both clockwise and anticlockwise directions.

Firstly, we focus on the change of D1 in Figs. 2[link](a)–(f), where the time is measured from the moment corresponding to Fig. 2[link](a) with the elapsed times of 0, 1, 2, 3, 4 and 5 s, respectively. We note that the directionally successive transitions occur inside D1, as schematically summarized in the first row of Fig. 2[link](g). We use the same color to denote the H tiles with the same orientation. The vertices of the subtiles inside the ∼2 nm D cluster could be some out of ten spots on the 0.77 nm circle, as marked as 1, 2, …, 10 in the first ∼2 nm D cluster in the first row of Fig. 2[link](g). Which unit tiles form where depends on which of the ten marked positions in the first D cluster in Fig. 2[link](g) are occupied. However, a motif made by two occupied positions with an interval of one empty position on the 0.77 nm D cluster is geometrically forbidden because it would result in geometric conflict for the generation of the observed structural tiles of the DQC (see supplementary Fig. 2 in the supporting information).

As seen clearly from the first row of Fig. 2[link](g), the changes are limited to the inner spots of the ∼2 nm D1 cluster, and not to the ten spots at the periphery of the 2 nm D1 cluster. The detailed processes of directionally dynamical phasons are analyzed in the lower part of Fig. 2[link](g), where the changeable positions are indicated with the corresponding numbers. Starting from the first circle in the bottom row of Fig. 2[link](g) [corresponding to the inner circle with a diameter of 0.77 nm in the D1 cluster in Fig. 2[link](c)], the occupied positions 2, 5, 8 and 9 at 2 s are flipped to the positions of 2, 3, 6 and 9 at 3 s, and then to 3, 4, 7 and 10 at 5 s. It is evident that the position 5 at 2 s continuously flips to the next position, 6, at 3 s and then to 7 at 5 s, forming a continuous clockwise motion [as summarized in Fig. 2[link](h)]. After these flips took place, the atoms on the 0.77 nm decagon inside the D1 cluster are mainly located on the positions 3, 4, 7, 10, occasionally flipping to the neighboring positions (not shown here).

Such a carousel of successive atomic jumps is also found in the D2 cluster, but it occurred at a different time compared to that in the D1 cluster, as seen in Fig. 3[link]. Note that the measured times in Fig. 3[link] are based on the frames in Fig. 2[link](a). There are two groups of directionally successive flipping of atoms in the clockwise direction, and each group involves four changeable positions. Interestingly, both groups proceed synchronously: they start at the positions 2 and 9 at 71 s, and then continuously hop to the following positions at 72 s, 73 s and 74 s, respectively, as analyzed in Fig. 3[link](e) as well as summarized in Fig. 3[link](f) and in the table at the bottom-right corner of Fig. 3[link], where the two groups of continuous flips are indicated by arrows with different colors. However, no successive flipping of atoms is observed in the nearby D1 cluster during this time.

In addition to the clockwise successive flipping of atoms, anticlockwise successive phason flipping is also occasionally observed, as seen in the D3 tile in Fig. 4[link]. There are three groups of directionally successive atomic jumps in the D3 tile, as summarized in Fig. 4[link](f), where two of them are clockwise and one is anticlockwise.

We now analyze the anticlockwise dynamical flipping from position 10 to 9 and finally to 8 in the D3 tile. When the atoms at position 3 at 28 s flip to the position 2 at 29 s, the atoms at position 10 at 28 s have to flip to the position 9 at 29 s to maintain a physically reasonable geometric configuration, namely to retain two, rather than one, empty interval positions between two occupied positions (as discussed above). Meanwhile, the atoms at position 10 cannot flip to position 1 because it would generate a structural block not found in Al–Cr–Fe–Si DQCs (see supplementary Fig. 2 in the supporting information). In the next step, the atoms at position 2 at 29 s flip back to position 3 at 30 s, performing a generally observed go-and-return transition (Edagawa et al., 2000[Edagawa, K., Suzuki, K. & Takeuchi, S. (2000). Phys. Rev. Lett. 85, 1674-1677.], 2002[Edagawa, K., Suzuki, K. & Takeuchi, S. (2002). J. Alloys Compd. 342, 271-277.]). The atoms at position 9 at 29 s remain there at 30 s. In the next step, the atoms at position 3 at 30 s flip to position 4 at 31 s, forming a clockwise successive phason flipping from position 2 to 3, and finally to position 4. Meanwhile, another group of clockwise successive phason flips from position 4 to 7 proceeds simultaneously. When the atoms at position 6 at 30 s flip to the position 7 at 31 s, the atoms at position 9 at 30 s flip to the position 8 at 31 s to maintain a physically reasonable geometric configuration, namely to eliminate the forbidden configuration with one interval position between two occupied positions on the 0.77 nm D cluster. Consequently, anti­clockwise successive phason flipping from position 10 to 9 and finally to 8 takes place, accompanying two groups of successive flipping of atoms in the clockwise direction, as summarized in Fig. 4[link](f) and the table on the right-hand side of Fig. 4[link](f). Apart from the requirement for a reasonable geometric configuration, we think the directional phason flips of atoms may also be affected by the magnetic field of the objective lens of transmission electron microscope. Atomic clusters can be thought of as charged particles to some extent when they are excited by an electron beam. When atoms are negatively charged, they spin in the same direction as electrons, and when they are positively charged, they spin in the opposite direction, which may result in the clockwise or counter-clockwise direction of phason flips observed in this study.

4. Conclusions

We observed experimentally a carousel of successive flipping of thermally fluctuating phasons in decagonal Al60Cr20Fe10Si10 by using in situ high-temperature HRTEM imaging. The atomic positions of directionally successive phason flipping were located on the small decagons with a diameter of 0.77 nm, inside larger ∼2 nm decagons. Successive phason flipping took place mainly clockwise and only occasionally anticlockwise. We found that this special kind of phason flipping is closely related to the geometric constraints of reasonable structural blocks in DQCs. The directional phason flips of atomic clusters may also be affected by the magnetic field of the objective lens of transmission electron microscope. However, the underlying mechanisms need to be explored theoretically as well in the future.

5. Data availability

The data that support the findings of this study are available from the corresponding author upon request.

Supporting information


Acknowledgements

We thank Mr Xinan Yang of the Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, for assistance in recording the HAADF-STEM images. ZH thanks Professor Marek Mihalkovič of the Institute of Physics, Slovak Academy of Sciences, Slovakia, for helpful discussions. The authors contributed to this work as follows: ZH conceived the research; ZH and J-LM performed the experiments; ZH, WS and J-LM wrote the manuscript; and ZH, J-LM, HM, YW, HL, TZ, XM and WS analyzed the data, discussed the results and drew the conclusions. The authors declare no competing interests.

Funding information

This work was supported by the National Natural Science Foundation of China (51871015 and 51471024) and a scholarship from the China Scholarship Council. It was partly supported by the French National Research Agency (ANR) through the TEMPOS Equipex (ANR-10-EQPX-50), pole NanoMAX.

References

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