Dynamic crystals: First show of time periodicity in crystal structures and nano-materials

Dynamic crystals: First show of time periodicity in crystal structures and nano-materials | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Dynamic crystals: First show of time periodicity in crystal structures and nano-materials Feng Gao, Shengfa Li, Mou Zhang, Hang Li, Qingyi Lu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8230826/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The principle of time-translational symmetry is the cornerstone of the law of energy conservation. Crystals have three dimensional ordered lattices, and it is inconceivable to imagine that they have time periodicity. Herein, while constructing nanohelices, we discovered a completely unprecedented time periodicity on a new kind of nanohelix grown through a distinctive directional competition twisting mechanism. Its crystal structure spontaneously varies with time and then returns to the original structure (termed Time-structure). Moreover, by a long-term impact strategy, we discovered an unimaginable but very obvious time-dependent change in morphology. The material spontaneously changes from long nanohelices to small nanoparticles, then to short nanohelices, and finally back to its original morphology, long nanohelices (termed Time-material). The emergence of Time-structures and Time-materials undoubtedly has intrinsic underlying reasons. The directional competition mechanism makes the nanohelices misaligned along Z-axis, breaking the long-range order in this dimension. The resulting crystals do not have crystal characteristics in at least one dimension, different from crystals, quasicrystals and amorphous solids, indicating a new form of solid state, called Fractional-dimension crystals (FD-crystals). Their lattice rigidity has been broken, creating a unique transformability which is the key point for the realization of time periodicity. Furthermore, through repeated structural reorganization, even conventional crystals can be transformed into FD-crystals, thereby enabling time periodicity to emerge. This work is not only the first report on spontaneous time-periodicity of nanocrystals, but also the first introduction of time dimension in chemistry and materials science. It brings up a new field of non-equilibrium transformable crystals beyond current crystallographic theory, opens a door to various exquisite time-periodic processes, and makes the design, construction and application of time nanodevices possible. Time periodicity Dimensionally reduced long-range order Fractional-dimension crystals Time-structure Time-material Figures Figure 1 Figure 2 Figure 3 Figure 4 Full Text The principle of time-translational symmetry is an important law, under which the physical properties of the object measured at different times are the same in the absence of any external interference 1,2 . It is the cornerstone of the law of energy conservation and has long been thought unbreakable. Frank Wilczek, Nobel Prize winner in physics, by means of the space-periodic characteristic of crystals, proposed a concept of “time crystal” in 2012 to represent a state repeated periodically with time 3 . It emphasized a breaking of time-translational symmetry, and once proposed, it immediately caused a great shock in the scientific community 4,5 . In 2016, researchers from the University of California, Berkeley, described the manufacturing scheme of the “time crystal” for the first time 6 . The University of Maryland team lined up 10 ytterbium atoms, then flipped the spins of the ions with a laser and correlated these spins to form an “entangled” state, where the spins of the ions began to oscillate at twice the rate of the laser pulse 7 . The Harvard team introduced the defect by densely filling the diamond with nitrogen, flipped the spin of the diamond defect with microwave pulses, and found that the system repeated the change several times between microwave pulses 8 . In these experiments, the system requires an external excitation (laser or microwave pulses), and the spin direction of the atoms (ytterbium ions or diamond defects) changes regularly, and every certain period, the atoms return to their original state. The success of these experiments demonstrates the theoretical feasibility of “time crystals” and has attracted a large number of scientists to work intensively in related fields 9-18 . Although “time crystals” have very important application potential in quantum computing, precise measurement, and ultra-stable storage aspects, they are extremely difficult to obtain. The research mainly stays at the physical level, focusing on the repetitive changes of spin directions, ultra-low temperature atoms, or nonlinear cavities with time 19-29 . From the perspective of chemistry or material science, it would be significant undoubtedly if time dimension could be introduced into chemical reactions to construct a time periodic structure or produce a time periodic material. It could start from a kind of structure or material, and as time passed, it could go through a series of changes, and then spontaneously return to the original structure or material. However, given the crystal’s three-dimensional (3D) ordered lattices, the resulting rigidity, and the difficulty of the driving force spontaneously working and then spontaneously reversibly working, it's hard to even imagine its existence. A time periodic structure needs to continuously break the lattice and then recombine the lattice in a spontaneous way, and a time periodic material needs to spontaneously change from one morphology to many others and then change back to the original morphology. All these are completely unimaginable and have long been considered unachievable. So far, no related work has been reported. The crystal rigidity is closely related to its structure 30,31 . Two crystal intrinsic characteristics, long-range order and periodic arrangement, have been considered as unbreakable until the appearance of quasicrystals 32,33 . Quasicrystals have long-range order but no periodic arrangement, discovered by Danielle Shechtman 32 , who won the 2011 Nobel Prize in Chemistry for this work. An ideal quasicrystal is composed of two or more kinds of “primitive cells” repeated indefinitely in space, which can produce macroscopic symmetries that crystals do not allow, 5 axis of symmetry, for example 34,35 . The emergence of quasicrystals raises a question. Is the long-range order of crystals really so unshakable? Since a crystal has three spatial dimensions, is it possible to make one or two dimensions lose long-range order? The in-depth study might open a door to a field that we have never thought about, and bring up kinds of novel ideas and dramatic changes. While constructing and regulating nanohelices, we discovered a directional competition twisting mechanism and a new kind of nanohelix of tri-cobalt salicylate hydroxide hexahydrate has been successfully synthesized 36 . Through targeted adjustment of molecular interactions, a completely unprecedented time periodicity has been realized on these nanohelices. At room temperature and pressure, their crystal structure, including lattice parameters, crystallinity and spatial order degree, varies spontaneously with time and then returns to the original structure after a certain time. The whole structure transformation process takes place in ethanol without any external interference. It indicates a brand-new structure, not only transformable but also exhibiting time periodicity, termed Time-structure . Moreover, with a long-term impact strategy, these long nanohelices spontaneously undergo an unimaginable but very obvious time-dependent change in morphology. With external conditions unchanged, they break into small nanoparticles, then grow up, and finally grow back to the long nanohelices. The length varies by up to a hundred times, switching back and forth between tens of micrometers and hundreds of nanometers. It indicates an incredible dynamic material with time periodicity, which has never been seen before, termed Time-material . The emergence of Time-structures and Time-materials necessarily has its intrinsic factors. The twisting mechanism of competition between molecular interactions in different directions is quite different from the previous reports. It leads to the misalignment along Z-axis, breaking the long-range order in this dimension. The crystal rigidity decreases and the resulting nanohelices surprisingly display a very special flexibility, which is the key point for the realization of time periodicity. Such crystals do not have crystal characteristics in all dimensions, thus called Fractional-dimension crystals (FD-crystals) . They belong to a new form of solid state, different from crystals, quasicrystals and amorphous solids. Furthermore, based on the analysis of the structure characteristics of FD-crystals and the differences between nanorods and nanohelices, we designed a repeated structural transformation procedure, and successfully realized the transformation from conventional crystals to FD-crystals. On this basis, time periodicity can emerge from conventional crystals. This work not only reveals a new form of solid state, FD-crystals, overturning the conventional crystal concept, but also demonstrates a brand-new strategy for transformable crystals based on the synergistic effect between molecular configuration and interaction. The time dimension has been successfully introduced into the field of chemistry and materials science for the first time, directly showing that time translational symmetry is no longer an insurmountable red line. The achievement of the time periodic internal structure and external morphology brings up a previously unimaginable time-dependent field, making the design, construction and application of time nanodevices possible. 1 Fractional-dimension crystals (FD-crystals) Our work was based on a novel kind of nanohelix we reported earlier 36 . It was synthesized under ethanol-thermal conditions, and could be transformed into nanowires at higher temperatures. Given the rarity of the transformation between nanowires and nanohelices, further structural analysis and studies are highly warranted. During the investigation of nanohelix growth control, we found a strange phenomenon that their diffraction peaks in XRD patterns shifted with reaction conditions. For example, the d spacing of the strongest diffraction peak changed from 13.0 Å to 10.7 Å, which seems to imply an unfixed crystal lattice. Crystals have long-range order and periodic arrangement. The strictly ordered lattice in 3D space results in a unique structural rigidity. Does the above unfixed lattice structure mean that the long-range order and periodic arrangement of these nanohelieces have been broken somehow? To answer this question, we carefully investigated the crystal structure of the nanohelices and compared it with that of conventional nanorods. Nanorods were synthesized under a KOH alkaline solution at room temperature. SEM images (Figure 1a,b) show that the product consists of straight short rods with lengths usually less than a micrometer. XRD pattern (Figure 1c) confirms that all diffraction peaks are consistent with the result reported in the literature 37 (JCPDS Card No 39-1743), proving the successful synthesis of tri-cobalt salicylate hydroxide hexahydrate. Nanohelices were synthesized under 80°C ethanol-thermal conditions for at least 60 minutes, typically 4 hours. Higher reaction temperature and longer reaction time than those for nanorods indicate that the reaction in ethanol is much slower than that in an alkaline solution. SEM images (Figure 1d,e) show that the product consists of long nanohelices with lengths up to tens of micrometers. XRD pattern (Figure 1f) shows that compared with those of nanorods, all the diffraction peaks of the nanohelices shift proportionally to higher angles (indicating lower d spacing). That is, the lattice parameters of the nanohelices are significantly smaller; for example, the d spacing of the strongest peak decreases from 13.0 Å to 10.7 Å. The d spacings of other peaks are also reduced by the same proportion. At the same time, their diffraction peaks are significantly narrower, as indicated by their smaller half-peak width, suggesting a more orderly arrangement / better crystallinity in the corresponding crystal planes. In addition, the number of diffraction peaks is significantly reduced. It indicates that the long-range order of some crystal planes decreases, which makes the corresponding diffraction peaks fail to appear. Through indexing, we found that all diffraction peaks of the nanohelices were from (hk0) planes. Namely, the crystal planes corresponding to these diffraction peaks are associated solely with the ordered lattice points on XY-plane, such as (110), (300), etc. No diffraction peaks arise from crystal planes associated with Z-axis, such as (211), (321), etc. These results indicate that for these nanohelices, the long-range order is well maintained on XY-plane but disappears along Z-axis. According to our previous research 36 , theoretical calculations revealed that tri-cobalt salicylate hydroxide hexahydrate has a triangular molecular configuration, and the nanohelices are formed via a directional competition twisting mechanism, that is, the competition between the π-π stacking on XY-plane and the condensation along Z-axis. For the reaction in KOH solution, the condensation occurs immediately at room temperature due to the catalytic effect of the alkaline solution, resulting in the formation of a long chain along Z-axis. Then the six long chains approach each other through face-to-face π-π stacking (F-stacking), forming a hexagonal prism structure 36,38,39 , which leads to the formation of rod-like products. The growth schematic diagram of a nanorod is shown in Figure 1g. However, the condensation in ethanol is very slow, and to make it occur, more than 30 minutes 80° ethanol-thermal reaction is necessary. The π-π stacking on XY-plane takes precedence. Losing the constraint of the rigid chain along Z-axis, a tilting occurs between adjacent benzene rings to achieve a stronger edge-face π-π stacking (T-stacking) 36,40 . The following condensation along Z-axis forms a long chain with a little bit twisting, finally resulting in the formation of nanohelices 36 . The growth schematic diagram of a nanohelix is shown in Figure 1h. Based on this competition twisting mechanism, the specialty of the crystal lattice of the nanohelices, including smaller d spacing, higher order on XY-plane, and lower order along Z-axis, can be easily understood. Due to the slow condensation along Z-axis in ethanol and the strong T-stacking on XY-plane, the distance between benzene rings on XY-plane decreases, which is reflected in a decrease of d spacing. The strongest peak in XRD pattern changes from 13.0 Å to 10.7 Å and the others also vary proportionally. At the same time, the strong molecular interactions on XY-plane lead to a more orderly arrangement of the corresponding crystal planes, resulting in a smaller half-peak width and higher crystallinity on XY-plane. In the subsequent condensation along Z-axis, the tightly bound hexagonal structure on XY-plane has to twist a little to match another one. It not only leads to the formation of helical structure twisted along Z-axis, but also simultaneously breaks the long-range order along Z-axis, making the diffraction peaks associated with crystal planes along Z-axis disappear. Besides changing from 3D spatial order to 2D spatial order, the disappearance of long-range order along Z-axis also results in the decrease of the crystal rigidity. These nanohelices have a special kind of flexibility along Z-axis which conventional crystals do not have. Our previous experimental results confirm this suggestion, in which nanohelices can be straightened into nanowires at higher temperature 36 . It directly proves the rigidity missing and the structure variability along Z-axis. This kind of transformable crystal coming from the missing of long-range order in some dimension is quite difficult to understand by current crystallographic theory, representing a new form of solid state. Specifically, the crystalline intrinsic characteristics, long-range order and periodic arrangement, just can be found in only two dimensions (2D, on XY-plane) in a 3D structure. In the other dimension (along Z-axis), they disappear. These crystals have dimensionally reduced long-range order, which challenges the conventional definition of a crystal. If conventional crystals (i.e., those with a 3D morphology and 3D long-range order in space) are designated as “3D long-range order/3D morphology crystals,” then our crystals, which possess a 3D morphology but long-range order in only two dimensions, can be correspondingly designated as“2D long-range order/3D morphology crystals.” This type of structure may be referred to as a fractional-dimensional crystal (FD-crystal). The dimension lacking long-range order is termed the disordered dimension. FD-crystals are different from crystals, quasi-crystals and amorphous solids. Their appearance selectively breaks the overall rigidity of crystals, opens up a completely unexpected door to dynamic crystals and may brings a lot of unique and exquisite reversible transformations. Time-periodic process is a good application of FD-crystals. 2 Time-structures Time periodicity is contradictory to crystal rigid lattices, even though the concept of “time crystal” has been proposed. It uses crystal periodic arrangement in space to express a state with periodicity in time, such as the periodic change of spin directions with time. According to crystallographic theory, it is hard to imagine a crystal with time-periodicity. Based on the flexibility of FD-crystal and the distinctive twisting mechanism of these nanohelices, we found that when the crystal rigidity disappeared, the lattice could change within a certain range with reaction conditions. For example, even for the nanohelices with small lattice, the d spacing of the strongest XRD peak is not fixed at 10.7 Å and can vary, sometimes reaching as low as 9.5 Å (Figure 2a,b). More importantly, by targetedly adjusting molecular interactions, we surprisingly discovered that these nanohelices spontaneously underwent an unprecedented lattice change in ethanol at room temperature and pressure. Two controlled experiments were carried out simultaneously. One sample consisted of nanohelices exhibiting the strongest peak at 9.9 Å (Nanohelix I), and the other consisted of nanohelices exhibiting the strongest peak at 10.7 Å (Nanohelix II). Both of them were placed in ethanol, separately. A sample was taken every 2 days. From day 0 to day 10, a total of 6 samples were collected for Nanohelix I, labeled as Helix I-0d, Helix I-2d, Helix I-4d, Helix I-6d, Helix I-8d and Helix I-10d, respectively. Nanohelix II underwent the same treatment and the six collected samples were labeled as Helix II-0d, Helix II-2d, Helix II-4d, Helix II-6d, Helix II-8d, and Helix II-10d. Figure 2a shows the d spacing change rule of the strongest peak in XRD patterns of the nanohelices with time. The orange line represents the transformation process of Helix-I, and the XRD patterns at several critical stages are shown in Figure 2b. The blue line represents that of Helix-II, and the XRD patterns at several critical stages are shown in Figure 2c. From Helix I-0d to Helix I-10d, the d spacing of the strongest peak changes from 9.9 Å through 10.7 Å, 10.1 Å, 12.6 Å and 9.9 Å to 12.9 Å. Two cycles varying from small lattice to large lattice are observed in this case. From Helix II-0d to Helix II-10d, the d spacing of the strongest peak goes from 10.7 Å through 9.9 Å, 10.6 Å, 12.7 Å and 9.9 Å to 12.8 Å. There are also two cycles from small lattice to large lattice. Despite differing d-spacings for their strongest peaks, a phenomenon likely arising from the dynamic nature of the crystals, both Helix I-0d and Helix II-0d exhibit their own spontaneous time-periodicity, regardless of whether the original d-spacing is 9.9 Å or 10.7 Å. In such a cycle, some intermediate states, such as the state with the strongest peak of 10.1 Å and the state with both small and large lattices, can also be found. It demonstrates that the oscillations among small lattices and the transformations between small and large lattices all occur. After the lattice parameters change by ~20% and the half-peak width increases several-fold, the crystal structure not only does not break, but also returns to the original structure. During the whole process, no external force has changed. This time periodic structure (termed Time-structure), no matter in terms of lattice parameter or crystallinity, is completely unprecedented. It is the first manifestation of time dimension in chemistry, defying the current understanding of crystalline structure and opening a new field of time-dependent transformations. Why can a crystal spontaneously return to its initial structure after several structural changes? The formation of FD-crystals is no doubt the key point, which breaks the crystal rigidity and makes crystals transformable. Besides, there should be several stable stages with similar energies that can be captured and transformed between them. For tri-cobalt salicylate hydroxide hexahydrate nanohelices, there are two kinds of π-π stackings, F-stacking and T-stacking. The system has several stages, small lattice controlled by T-stacking, large lattice controlled by F-stacking, as well as various states with both T-stacking and F-stacking in different proportions, which can be confirmed by the d spacing of the strongest peak in XRD patterns (Figure 2). T-stacking is a little stronger than F-stacking 40 , but the difference between the two is not much and the transformation between them can occur under suitable conditions. The triangular molecular configuration and the resulting hexagonal geometric structure provide the structural foundation for the reversible transformation between T-stacking and F-stacking. Thus, the FD-crystal can be transformed to its initial structure. Figure 2d simply illustrates the structural change between T-stacking and F-stacking, highlighting the key stages involved. The schematic diagram of the time periodic transformation in structure is shown in Figure 2e. 3 Transformation from conventional crystals to FD-crystals Do FD-crystals have to exist in helical structures? Can time periodicity be seen in non-helical crystals? Is it possible to transform conventional crystals into FD-crystals? By analyzing the characteristics of FD-crystals and the microstructures of these nanohelices, we believe that time periodicity can emerge from conventional non-helical structures as long as a suitable method for targeted regulation of molecular interactions is developed. The tri-cobalt salicylate hydroxide hexahydrate nanorods were synthesized under alkaline conditions. Their XRD pattern (Figure 1c) is consistent with the JCPDS card (No 39-1743) and exhibits numerous diffraction peaks originating from crystal planes associated with the Z-axis. It indicates that these nanorods are conventional crystals, not FD-crystals, quite different from the long nanohelices. We designed a repeated structural transformation procedure and soaked these nanorods in ethanol for a much longer time. A sample was collected every few days. Figure 3a shows the d spacing change rule of the strongest peak in XRD patterns of the nanorods with time. XRD patterns at several critical stages of the transformation process are shown in Figure 3b and c. It can be seen that the diffraction peaks experience a large decrease in intensity on the 5th day, and then recover. After this cycle is repeated several times, the d spacing of the strongest peak becomes 10.7 Å on the 21st day. Its half-peak width decreases obviously, and the number of diffraction peaks drops sharply. All these indicate the formation of FD-crystals. It means that conventional crystals can be transformed into FD-crystals after they are almost destroyed and then reorganized several times. As a matter of course, such FD-crystals also can display time periodicity under suitable conditions. The schematic diagram of the transformation from conventional crystals to FD-crystals, and then to Time-structures is shown in Figure 3d. However, though both the FD-crystals transformed from the conventional crystals (nanorods) and the as-synthesized FD-crystals (nanohelices) are a kind of dynamic crystal, constantly changing with time, it is worth noting that the former are not exactly the same as the the latter. Compared with the former, the latter is more sensitive to reaction conditions and has more intermediate states. It means that the transformability of FD-crystals is not fixed, but adjustable, depending much on the constructing strategy and conditions. 4 Time-Materials The spontaneous periodic transformation of crystal lattice with time belongs to the time periodicity of internal structure at micro level, which is hard to imagine. The external morphology spontaneously changes to other morphology and then changes back to the original morphology, which is more unthinkable and belongs to the time periodicity at the macroscopic material level. Based on the dynamic characteristic of FD-crystal, we designed a long-term impact strategy to decrease the crystal rigidity. After the repeated structural transformation between small lattice and large lattice, we found a very obvious process of spontaneous time periodic changes in morphology, which is difficult to understand according to current knowledge. Figure 4a-t shows the morphology sketches, SEM images and XRD patterns of the long nanohelices soaked in ethanol for 0, 30, 45, 60, and 75 days, respectively. With the extension of time, these long nanohelices change to nanoparticles, then to short nanohelices, and finally back to long nanohelices. The initial long nanohelices have small lattices with high crystallinity, but the nanoparticles are at low crystallinity. Different from them, the short nanohelices have large lattices with moderate crystallinity. When the morphology changes back to long nanohelices, the crystal structure also returns to the initial small lattice with high crystallinity. As time passes, these long nanohelices first decrease sharply in crystallinity and break into nanoparticles, then reorganize into large lattices and regrow into short nanohelices, and finally transform into small lattice and continuously grow into long nanohelices. The changes of morphology are accompanied by the transformations of structure, suggesting that the time periodicity of external morphology is closely related to the time periodicity of internal structure. The latter is the internal root of the former, and the former is the macro manifestation of the latter. It should be noted that, due to the dynamic nature of the crystals, the time period reported represents a captured cycle and is not necessarily the fundamental period. In the whole process, all changes, no matter breaking or regrowing, occur along Z-axis. It is another direct evidence for the transformable FD-crystals with a disordered dimension of Z-axis. The length changes by up to 100 times, switching from tens of micrometers to hundreds of nanometers. The schematic diagram of the time periodicity in morphology is shown in Figure 4u. Conclusions In summary, through a distinctive competition twisting mechanism, we discovered a new kind of nanohelix, which lacks long-range order in one dimension but retains it in the other dimensions. The lattice rigidity has been decreased obviously and a very special transformability shows up. It is different from the existing crystals, quasicrystals, and amorphous solids, not only representing a new form of solid state, FD-crystals, but also pointing out a new research direction for non-equilibrium dynamic crystals. On the basis of FD-crystals, through targeted adjustment of molecular interactions, we discovered an unprecedented time periodicity in crystal lattices, from small lattices with high crystallinity, to lattices with low crystallinity, to large lattices with moderate crystallinity, and then back to small lattices with high crystallinity. This process does not obey the time translation symmetry principle and is quite difficult to understand with current crystallographic theory, indicating a special time periodic structure, Time-structure. Moreover, we found that the transformable degree and rate of FD-crystals are adjustable, and so is the time-periodic process. Through repeated structural reorganization, even conventional crystals can be transformed into FD-crystals, which successfully makes time periodicity show again. This is the first introduction of time-dimension in chemistry and provides a molecular level regulation strategy for various exquisite dynamic structures and time periodic processes. On the basis of Time-structure, through a long-term impact strategy, we discovered an unimaginable time periodicity in macro morphology. The long nanohelices change to small nanoparticles, then to short nanohelices, and finally back to the initial long nanohelices. The whole process occurs spontaneously with length variation up to 100 times, indicating an obvious time-periodic material, Time-material. It goes beyond the current knowledge and demonstrates that time translational symmetry principle is no longer an insurmountable red line. This is the first application of the time dimension in materials science and brings up a brand-new concept for material design and growth. 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Gao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYBAC9gYg8YGBDcQ2IE4LzwEGBsYZJGth5oGwidXCv/jhY9sdfIkN7M3bJBhq7hChReKZsXHuGbbEBp5jZRIMx54R1mIvccBMOrcNqEUix0yCseEwMbYc/yZtCdIi/4ZYLfw9ZtKMYFt4iLaFp9iwt43NuI0nrdgi4RhRthzf+OBn2zHZfvbDG298qCFCC4NEAog8BonMBCI0MDDwHwCRNUSpHQWjYBSMghEKAFICNDqavaj8AAAAAElFTkSuQmCC","orcid":"","institution":"Nanjing University","correspondingAuthor":true,"prefix":"","firstName":"Feng","middleName":"","lastName":"Gao","suffix":""},{"id":552303482,"identity":"24e9db96-66c9-446a-aa5f-d29a8f27a261","order_by":1,"name":"Shengfa Li","email":"","orcid":"","institution":"Nanjing University","correspondingAuthor":false,"prefix":"","firstName":"Shengfa","middleName":"","lastName":"Li","suffix":""},{"id":552303483,"identity":"3fb4af8d-9ea7-4ac9-b7c6-eec7a8b1be4b","order_by":2,"name":"Mou Zhang","email":"","orcid":"","institution":"Nanjing 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09:14:49","extension":"html","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":84714,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8230826/v1/03b70c88003b608bb0b0321e.html"},{"id":97230469,"identity":"e51c3c16-37e3-44b3-9f23-86eaea7b7fa7","added_by":"auto","created_at":"2025-12-02 09:14:49","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":480371,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCharacterization and growth schematic diagrams of nanorods and nanohelices:\u003c/strong\u003e SEM images (a,b) and XRD pattern (c) of the nanorods synthesized under a KOH alkaline solution at room temperature; SEM images (d,e) and XRD pattern (f) of the nanohelices synthesized under 80°C ethanol-thermal conditions for 4 hours; Growth schematic diagrams of a nanorod (g) and a nanohelix (h).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8230826/v1/6c41271621ba8a9941e814a2.png"},{"id":97230470,"identity":"c354d494-b9a3-42f4-bccb-bfdcf4ad951f","added_by":"auto","created_at":"2025-12-02 09:14:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":347166,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTime periodicity in the crystal structure of nanohelices:\u003c/strong\u003e(a) d spacing change rule of the strongest peak in XRD patterns of the nanohelices with time; XRD patterns of Helix I (b) and Helix II (c) at several key time points during the transformation process; Schematic diagrams of the structural change between T-stacking and F-stacking (d) and the time periodic transformation in structure (e).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8230826/v1/a95c29bd03cdf9eac5ce2dac.png"},{"id":97251114,"identity":"d6b70f90-54f3-4390-8c01-765ca2c3f200","added_by":"auto","created_at":"2025-12-02 13:16:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":529727,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTime periodicity in the crystal structure of nanorods:\u003c/strong\u003e(a) d spacing change rule of the strongest peak in XRD patterns of the nanorods with time; (b,c) XRD patterns at several key time points during the transformation process; (d) Schematic diagram of the transformation from conventional crystals to FD-crystals, and then to Time-structures.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8230826/v1/66137574079d709ef7c65190.png"},{"id":97230472,"identity":"d929ad2c-3ed8-4a9d-b4ad-6b70337704b6","added_by":"auto","created_at":"2025-12-02 09:14:49","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":743483,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTime periodicity of external morphology:\u003c/strong\u003e Morphology sketches, SEM images and XRD patterns of the long nanohelices soaked in ethanol for 0 day (a-d), 30 days (e-h), 45 days (i-l), 60 days (m-p), and 75 days (q-t); (u) Schematic diagram of the time periodic transformation in morphology.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8230826/v1/cf435e97f0d36e3dbc2ed83e.png"},{"id":97252592,"identity":"1d8aaff2-6893-42ab-8d78-6213d8fe3431","added_by":"auto","created_at":"2025-12-02 13:22:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2466354,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8230826/v1/caee08f4-a859-471b-8ca3-0dbeb0858a1b.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eDynamic crystals: First show of time periodicity in crystal structures and nano-materials\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"\u003cp\u003eThe principle of time-translational symmetry is an important law, under which the physical properties of the object measured at different times are the same in the absence of any external interference\u003csup\u003e1,2\u003c/sup\u003e. It is the cornerstone of the law of energy conservation and has long been thought unbreakable.\u003c/p\u003e\n\u003cp\u003eFrank Wilczek, Nobel Prize winner in physics, by means of the space-periodic characteristic of crystals, proposed a concept of \u0026ldquo;time crystal\u0026rdquo; in 2012 to represent a state repeated periodically with time\u003csup\u003e3\u003c/sup\u003e. It emphasized a breaking of time-translational symmetry, and once proposed, it immediately caused a great shock in the scientific community\u003csup\u003e4,5\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIn 2016, researchers from the University of California, Berkeley, described the manufacturing scheme of the \u0026ldquo;time crystal\u0026rdquo; for the first time\u003csup\u003e6\u003c/sup\u003e. The University of Maryland team lined up 10 ytterbium atoms, then flipped the spins of the ions with a laser and correlated these spins to form an \u0026ldquo;entangled\u0026rdquo; state, where the spins of the ions began to oscillate at twice the rate of the laser pulse\u003csup\u003e7\u003c/sup\u003e. The Harvard team introduced the defect by densely filling the diamond with nitrogen, flipped the spin of the diamond defect with microwave pulses, and found that the system repeated the change several times between microwave pulses\u003csup\u003e8\u003c/sup\u003e. In these experiments, the system requires an external excitation (laser or microwave pulses), and the spin direction of the atoms (ytterbium ions or diamond defects) changes regularly, and every certain period, the atoms return to their original state. The success of these experiments demonstrates the theoretical feasibility of \u0026ldquo;time crystals\u0026rdquo; and has attracted a large number of scientists to work intensively in related fields\u003csup\u003e9-18\u003c/sup\u003e. Although \u0026ldquo;time crystals\u0026rdquo; have very important application potential in quantum computing, precise measurement, and ultra-stable storage aspects, they are extremely difficult to obtain. The research mainly stays at the physical level, focusing on the repetitive changes of spin directions, ultra-low temperature atoms, or nonlinear cavities with time\u003csup\u003e19-29\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFrom the perspective of chemistry or material science, it would be significant undoubtedly if time dimension could be introduced into chemical reactions to construct a time periodic structure or produce a time periodic material. It could start from a kind of structure or material, and as time passed, it could go through a series of changes, and then spontaneously return to the original structure or material. However, given the crystal\u0026rsquo;s three-dimensional (3D) ordered lattices, the resulting rigidity, and the difficulty of the driving force spontaneously working and then spontaneously reversibly working, it\u0026apos;s hard to even imagine its existence. A time periodic structure needs to continuously break the lattice and then recombine the lattice in a spontaneous way, and a time periodic material needs to spontaneously change from one morphology to many others and then change back to the original morphology. All these are completely unimaginable and have long been considered unachievable. So far, no related work has been reported. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe crystal rigidity is closely related to its structure\u003csup\u003e30,31\u003c/sup\u003e. Two crystal intrinsic characteristics, long-range order and periodic arrangement, have been considered as unbreakable until the appearance of quasicrystals\u003csup\u003e32,33\u003c/sup\u003e. Quasicrystals have long-range order but no periodic arrangement, discovered by Danielle Shechtman\u003csup\u003e32\u003c/sup\u003e, who won the 2011 Nobel Prize in Chemistry for this work. An ideal quasicrystal is composed of two or more kinds of \u0026ldquo;primitive cells\u0026rdquo; repeated indefinitely in space, which can produce macroscopic symmetries that crystals do not allow, 5 axis of symmetry, for example\u003csup\u003e34,35\u003c/sup\u003e. The emergence of quasicrystals raises a question. Is the long-range order of crystals really so unshakable? Since a crystal has three spatial dimensions, is it possible to make one or two dimensions lose long-range order? The in-depth study might open a door to a field that we have never thought about, and bring up kinds of novel ideas and dramatic changes.\u003c/p\u003e\n\u003cp\u003eWhile constructing and regulating nanohelices, we discovered a directional competition twisting mechanism and a new kind of nanohelix of tri-cobalt salicylate hydroxide hexahydrate has been successfully synthesized\u003csup\u003e36\u003c/sup\u003e. Through targeted adjustment of molecular interactions, a completely unprecedented time periodicity has been realized on these nanohelices. At room temperature and pressure, their crystal structure, including lattice parameters, crystallinity and spatial order degree, varies spontaneously with time and then returns to the original structure after a certain time. The whole structure transformation process takes place in ethanol without any external interference. It indicates a brand-new structure, not only transformable but also exhibiting time periodicity, termed \u003cstrong\u003eTime-structure\u003c/strong\u003e. Moreover, with a long-term impact strategy, these long nanohelices spontaneously undergo an unimaginable but very obvious time-dependent change in morphology. With external conditions unchanged, they break into small nanoparticles, then grow up, and finally grow back to the long nanohelices. The length varies by up to a hundred times, switching back and forth between tens of micrometers and hundreds of nanometers. It indicates an incredible dynamic material with time periodicity, which has never been seen before, termed \u003cstrong\u003eTime-material\u003c/strong\u003e. The emergence of Time-structures and Time-materials necessarily has its intrinsic factors. The twisting mechanism of competition between molecular interactions in different directions is quite different from the previous reports. It leads to the misalignment along Z-axis, breaking the long-range order in this dimension. The crystal rigidity decreases and the resulting nanohelices surprisingly display a very special flexibility, which is the key point for the realization of time periodicity. Such crystals do not have crystal characteristics in all dimensions, thus called \u003cstrong\u003eFractional-dimension crystals (FD-crystals)\u003c/strong\u003e. They belong to a new form of solid state, different from crystals, quasicrystals and amorphous solids. Furthermore, based on the analysis of the structure characteristics of FD-crystals and the differences between nanorods and nanohelices, we designed a repeated structural transformation procedure, and successfully realized the transformation from conventional crystals to FD-crystals. On this basis, time periodicity can emerge from conventional crystals. This work not only reveals a new form of solid state, FD-crystals, overturning the conventional crystal concept, but also demonstrates a brand-new strategy for transformable crystals based on the synergistic effect between molecular configuration and interaction. The time dimension has been successfully introduced into the field of chemistry and materials science for the first time, directly showing that time translational symmetry is no longer an insurmountable red line. The achievement of the time periodic internal structure and external morphology brings up a previously unimaginable time-dependent field, making the design, construction and application of time nanodevices possible.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e1 Fractional-dimension crystals (FD-crystals)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eOur work was based on a novel kind of nanohelix we reported earlier\u003csup\u003e36\u003c/sup\u003e. It was synthesized under ethanol-thermal conditions, and could be transformed into nanowires at higher temperatures. Given the rarity of the transformation between nanowires and nanohelices, further structural analysis and studies are highly warranted.\u003c/p\u003e\n\u003cp\u003eDuring the investigation of nanohelix growth control, we found a strange phenomenon that their diffraction peaks in XRD patterns shifted with reaction conditions. For example, the d spacing of the strongest diffraction peak changed from 13.0 \u0026Aring; to 10.7 \u0026Aring;, which seems to imply an unfixed crystal lattice.\u003c/p\u003e\n\u003cp\u003eCrystals have long-range order and periodic arrangement. The strictly ordered lattice in 3D space results in a unique structural rigidity. Does the above unfixed lattice structure mean that the long-range order and periodic arrangement of these nanohelieces have been broken somehow? To answer this question, we carefully investigated the crystal structure of the nanohelices and compared it with that of conventional nanorods.\u003c/p\u003e\n\u003cp\u003eNanorods were synthesized under a KOH alkaline solution at room temperature. SEM images (Figure 1a,b) show that the product consists of straight short rods with lengths usually less than a micrometer. XRD pattern (Figure 1c) confirms that all diffraction peaks are consistent with the result reported in the literature\u003csup\u003e37\u003c/sup\u003e (JCPDS Card No 39-1743), proving the successful synthesis of tri-cobalt salicylate hydroxide hexahydrate.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNanohelices were synthesized under 80\u0026deg;C ethanol-thermal conditions for at least 60 minutes, typically 4 hours. Higher reaction temperature and longer reaction time than those for nanorods indicate that the reaction in ethanol is much slower than that in an alkaline solution. SEM images (Figure 1d,e) show that the product consists of long nanohelices with lengths up to tens of micrometers. XRD pattern (Figure 1f) shows that compared with those of nanorods, all the diffraction peaks of the nanohelices shift proportionally to higher angles (indicating lower d spacing). That is, the lattice parameters of the nanohelices are significantly smaller; for example, the d spacing of the strongest peak decreases from 13.0 \u0026Aring; to 10.7 \u0026Aring;. The d spacings of other peaks are also reduced by the same proportion. At the same time, their diffraction peaks are significantly narrower, as indicated by their smaller half-peak width, suggesting a more orderly arrangement / better crystallinity in the corresponding crystal planes.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn addition, the number of diffraction peaks is significantly reduced. It indicates that the long-range order of some crystal planes decreases, which makes the corresponding diffraction peaks fail to appear. Through indexing, we found that all diffraction peaks of the nanohelices were from (hk0) planes. Namely, the crystal planes corresponding to these diffraction peaks are associated solely with the ordered lattice points on XY-plane, such as (110), (300), etc. No diffraction peaks arise from crystal planes associated with Z-axis, such as (211), (321), etc. These results indicate that for these nanohelices, the long-range order is well maintained on XY-plane but disappears along Z-axis.\u003c/p\u003e\n\u003cp\u003eAccording to our previous research\u003csup\u003e36\u003c/sup\u003e, theoretical calculations revealed that tri-cobalt salicylate hydroxide hexahydrate has a triangular molecular configuration, and the nanohelices are formed via a directional competition twisting mechanism, that is, the competition between the \u0026pi;-\u0026pi; stacking on XY-plane and the condensation along Z-axis. For the reaction in KOH solution, the condensation occurs immediately at room temperature due to the catalytic effect of the alkaline solution, resulting in the formation of a long chain along Z-axis. Then the six long chains approach each other through face-to-face \u0026pi;-\u0026pi; stacking (F-stacking), forming a hexagonal prism structure\u003csup\u003e36,38,39\u003c/sup\u003e, which leads to the formation of rod-like products. The growth schematic diagram of a nanorod is shown in Figure 1g.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHowever, the condensation in ethanol is very slow, and to make it occur, more than 30 minutes 80\u0026deg; ethanol-thermal reaction is necessary. The \u0026pi;-\u0026pi; stacking on XY-plane takes precedence. Losing the constraint of the rigid chain along Z-axis, a tilting occurs between adjacent benzene rings to achieve a stronger edge-face \u0026pi;-\u0026pi; stacking (T-stacking)\u003csup\u003e36,40\u003c/sup\u003e. The following condensation along Z-axis forms a long chain with a little bit twisting, finally resulting in the formation of nanohelices\u003csup\u003e36\u003c/sup\u003e. The growth schematic diagram of a nanohelix is shown in Figure 1h.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBased on this competition twisting mechanism, the specialty of the crystal lattice of the nanohelices, including smaller d spacing, higher order on XY-plane, and lower order along Z-axis, can be easily understood. Due to the slow condensation along Z-axis in ethanol and the strong T-stacking on XY-plane, the distance between benzene rings on XY-plane decreases, which is reflected in a decrease of d spacing. The strongest peak in XRD pattern changes from 13.0 \u0026Aring; to 10.7 \u0026Aring; and the others also vary proportionally. At the same time, the strong molecular interactions on XY-plane lead to a more orderly arrangement of the corresponding crystal planes, resulting in a smaller half-peak width and higher crystallinity on XY-plane. In the subsequent condensation along Z-axis, the tightly bound hexagonal structure on XY-plane has to twist a little to match another one. It not only leads to the formation of helical structure twisted along Z-axis, but also simultaneously breaks the long-range order along Z-axis, making the diffraction peaks associated with crystal planes along Z-axis disappear.\u003c/p\u003e\n\u003cp\u003eBesides changing from 3D spatial order to 2D spatial order, the disappearance of long-range order along Z-axis also results in the decrease of the crystal rigidity. These nanohelices have a special kind of flexibility along Z-axis which conventional crystals do not have. Our previous experimental results confirm this suggestion, in which nanohelices can be straightened into nanowires at higher temperature\u003csup\u003e36\u003c/sup\u003e. It directly proves the rigidity missing and the structure variability along Z-axis.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis kind of transformable crystal coming from the missing of long-range order in some dimension is quite difficult to understand by current crystallographic theory, representing a new form of solid state. Specifically, the crystalline intrinsic characteristics, long-range order and periodic arrangement, just can be found in only two dimensions (2D, on XY-plane) in a 3D structure. In the other dimension (along Z-axis), they disappear. These crystals have dimensionally reduced long-range order, which challenges the conventional definition of a crystal. If conventional crystals (i.e., those with a 3D morphology and 3D long-range order in space) are designated as\u0026nbsp;\u0026ldquo;3D long-range order/3D morphology crystals,\u0026rdquo;\u0026nbsp;then our crystals, which possess a 3D morphology but long-range order in only two dimensions, can be correspondingly designated as\u0026ldquo;2D long-range order/3D morphology crystals.\u0026rdquo; This type of structure may be referred to as a fractional-dimensional crystal (FD-crystal). The dimension lacking long-range order is termed the disordered dimension. FD-crystals are different from crystals, quasi-crystals and amorphous solids. Their appearance selectively breaks the overall rigidity of crystals, opens up a completely unexpected door to dynamic crystals and may brings a lot of unique and exquisite reversible transformations. Time-periodic process is a good application of FD-crystals. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2 Time-structures\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTime periodicity is contradictory to crystal rigid lattices, even though the concept of \u0026ldquo;time crystal\u0026rdquo; has been proposed. It uses crystal periodic arrangement in space to express a state with periodicity in time, such as the periodic change of spin directions with time. According to crystallographic theory, it is hard to imagine a crystal with time-periodicity.\u003c/p\u003e\n\u003cp\u003eBased on the flexibility of FD-crystal and the distinctive twisting mechanism of these nanohelices, we found that when the crystal rigidity disappeared, the lattice could change within a certain range with reaction conditions. For example, even for the nanohelices with small lattice, the d spacing of the strongest XRD peak is not fixed at 10.7 \u0026Aring; and can vary, sometimes reaching as low as 9.5 \u0026Aring; (Figure 2a,b). More importantly, by targetedly adjusting molecular interactions, we surprisingly discovered that these nanohelices spontaneously underwent an unprecedented lattice change in ethanol at room temperature and pressure.\u003c/p\u003e\n\u003cp\u003eTwo controlled experiments were carried out simultaneously. One sample consisted of nanohelices exhibiting the strongest peak at 9.9 \u0026Aring; (Nanohelix I), and the other consisted of nanohelices exhibiting the strongest peak at 10.7 \u0026Aring; (Nanohelix II). Both of them were placed in ethanol, separately. A sample was taken every 2 days. From day 0 to day 10, a total of 6 samples were collected for Nanohelix I, labeled as Helix I-0d, Helix I-2d, Helix I-4d, Helix I-6d, Helix I-8d and Helix I-10d, respectively. Nanohelix II underwent the same treatment and the six collected samples were labeled as Helix II-0d, Helix II-2d, Helix II-4d, Helix II-6d, Helix II-8d, and Helix II-10d.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 2a shows the d spacing change rule of the strongest peak in XRD patterns of the nanohelices with time. The orange line represents the transformation process of Helix-I, and the XRD patterns at several critical stages are shown in Figure 2b. The blue line represents that of Helix-II, and the XRD patterns at several critical stages are shown in Figure 2c. From Helix I-0d to Helix I-10d, the d spacing of the strongest peak changes from 9.9 \u0026Aring; through 10.7 \u0026Aring;, 10.1 \u0026Aring;, 12.6 \u0026Aring; and 9.9 \u0026Aring; to 12.9 \u0026Aring;. Two cycles varying from small lattice to large lattice are observed in this case. From Helix II-0d to Helix II-10d, the d spacing of the strongest peak goes from 10.7 \u0026Aring; through 9.9 \u0026Aring;, 10.6 \u0026Aring;, 12.7 \u0026Aring; and 9.9 \u0026Aring; to 12.8 \u0026Aring;. There are also two cycles from small lattice to large lattice.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDespite differing d-spacings for their strongest peaks, a phenomenon likely arising from the dynamic nature of the crystals, both Helix I-0d and Helix II-0d exhibit their own spontaneous time-periodicity, regardless of whether the original d-spacing is 9.9 \u0026Aring; or 10.7 \u0026Aring;. In such a cycle, some intermediate states, such as the state with the strongest peak of 10.1 \u0026Aring; and the state with both small and large lattices, can also be found. It demonstrates that the oscillations among small lattices and the transformations between small and large lattices all occur. After the lattice parameters change by ~20% and the half-peak width increases several-fold, the crystal structure not only does not break, but also returns to the original structure. During the whole process, no external force has changed. This time periodic structure (termed Time-structure), no matter in terms of lattice parameter or crystallinity, is completely unprecedented. It is the first manifestation of time dimension in chemistry, defying the current understanding of crystalline structure and opening a new field of time-dependent transformations.\u003c/p\u003e\n\u003cp\u003eWhy can a crystal spontaneously return to its initial structure after several structural changes? The formation of FD-crystals is no doubt the key point, which breaks the crystal rigidity and makes crystals transformable. Besides, there should be several stable stages with similar energies that can be captured and transformed between them. For tri-cobalt salicylate hydroxide hexahydrate nanohelices, there are two kinds of \u0026pi;-\u0026pi; stackings, F-stacking and T-stacking. The system has several stages, small lattice controlled by T-stacking, large lattice controlled by F-stacking, as well as various states with both T-stacking and F-stacking in different proportions, which can be confirmed by the d spacing of the strongest peak in XRD patterns (Figure 2). T-stacking is a little stronger than F-stacking\u003csup\u003e40\u003c/sup\u003e, but the difference between the two is not much and the transformation between them can occur under suitable conditions. The triangular molecular configuration and the resulting hexagonal geometric structure provide the structural foundation for the reversible transformation between T-stacking and F-stacking. Thus, the FD-crystal can be transformed to its initial structure. Figure 2d simply illustrates the structural change between T-stacking and F-stacking, highlighting the key stages involved. The schematic diagram of the time periodic transformation in structure is shown in Figure 2e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3 Transformation from conventional crystals to FD-crystals\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDo FD-crystals have to exist in helical structures? Can time periodicity be seen in non-helical crystals? Is it possible to transform conventional crystals into FD-crystals? By analyzing the characteristics of FD-crystals and the microstructures of these nanohelices, we believe that time periodicity can emerge from conventional non-helical structures as long as a suitable method for targeted regulation of molecular interactions is developed.\u003c/p\u003e\n\u003cp\u003eThe tri-cobalt salicylate hydroxide hexahydrate nanorods were synthesized under alkaline conditions. Their XRD pattern (Figure 1c) is consistent with the JCPDS card (No 39-1743) and exhibits numerous diffraction peaks originating from crystal planes associated with the Z-axis. It indicates that these nanorods are conventional crystals, not FD-crystals, quite different from the long nanohelices. We designed a repeated structural transformation procedure and soaked these nanorods in ethanol for a much longer time. A sample was collected every few days.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 3a shows the d spacing change rule of the strongest peak in XRD patterns of the nanorods with time. XRD patterns at several critical stages of the transformation process are shown in Figure 3b and c. It can be seen that the diffraction peaks experience a large decrease in intensity on the 5th day, and then recover. After this cycle is repeated several times, the d spacing of the strongest peak becomes 10.7 \u0026Aring; on the 21st day. Its half-peak width decreases obviously, and the number of diffraction peaks drops sharply. All these indicate the formation of FD-crystals. It means that conventional crystals can be transformed into FD-crystals after they are almost destroyed and then reorganized several times. As a matter of course, such FD-crystals also can display time periodicity under suitable conditions. The schematic diagram of the transformation from conventional crystals to FD-crystals, and then to Time-structures is shown in Figure 3d.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHowever, though both the FD-crystals transformed from the conventional crystals (nanorods) and the as-synthesized FD-crystals (nanohelices) are a kind of dynamic crystal, constantly changing with time, it is worth noting that the former are not exactly the same as the the latter. Compared with the former, the latter is more sensitive to reaction conditions and has more intermediate states. It means that the transformability of FD-crystals is not fixed, but adjustable, depending much on the constructing strategy and conditions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4 Time-Materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe spontaneous periodic transformation of crystal lattice with time belongs to the time periodicity of internal structure at micro level, which is hard to imagine. The external morphology spontaneously changes to other morphology and then changes back to the original morphology, which is more unthinkable and belongs to the time periodicity at the macroscopic material level. Based on the dynamic characteristic of FD-crystal, we designed a long-term impact strategy to decrease the crystal rigidity. After the repeated structural transformation between small lattice and large lattice, we found a very obvious process of spontaneous time periodic changes in morphology, which is difficult to understand according to current knowledge. Figure 4a-t shows the morphology sketches, SEM images and XRD patterns of the long nanohelices soaked in ethanol for 0, 30, 45, 60, and 75 days, respectively. With the extension of time, these long nanohelices change to nanoparticles, then to short nanohelices, and finally back to long nanohelices.\u003c/p\u003e\n\u003cp\u003eThe initial long nanohelices have small lattices with high crystallinity, but the nanoparticles are at low crystallinity. Different from them, the short nanohelices have large lattices with moderate crystallinity. When the morphology changes back to long nanohelices, the crystal structure also returns to the initial small lattice with high crystallinity. As time passes, these long nanohelices first decrease sharply in crystallinity and break into nanoparticles, then reorganize into large lattices and regrow into short nanohelices, and finally transform into small lattice and continuously grow into long nanohelices. The changes of morphology are accompanied by the transformations of structure, suggesting that the time periodicity of external morphology is closely related to the time periodicity of internal structure. The latter is the internal root of the former, and the former is the macro manifestation of the latter. It should be noted that, due to the dynamic nature of the crystals, the time period reported represents a captured cycle and is not necessarily the fundamental period.\u003c/p\u003e\n\u003cp\u003eIn the whole process, all changes, no matter breaking or regrowing, occur along Z-axis. It is another direct evidence for the transformable FD-crystals with a disordered dimension of Z-axis. The length changes by up to 100 times, switching from tens of micrometers to hundreds of nanometers. The schematic diagram of the time periodicity in morphology is shown in Figure 4u.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn summary, through a distinctive competition twisting mechanism, we discovered a new kind of nanohelix, which lacks long-range order in one dimension but retains it in the other dimensions. The lattice rigidity has been decreased obviously and a very special transformability shows up. It is different from the existing crystals, quasicrystals, and amorphous solids, not only representing a new form of solid state, FD-crystals, but also pointing out a new research direction for non-equilibrium dynamic crystals.\u003c/p\u003e\u003cp\u003eOn the basis of FD-crystals, through targeted adjustment of molecular interactions, we discovered an unprecedented time periodicity in crystal lattices, from small lattices with high crystallinity, to lattices with low crystallinity, to large lattices with moderate crystallinity, and then back to small lattices with high crystallinity. This process does not obey the time translation symmetry principle and is quite difficult to understand with current crystallographic theory, indicating a special time periodic structure, Time-structure. Moreover, we found that the transformable degree and rate of FD-crystals are adjustable, and so is the time-periodic process. Through repeated structural reorganization, even conventional crystals can be transformed into FD-crystals, which successfully makes time periodicity show again. This is the first introduction of time-dimension in chemistry and provides a molecular level regulation strategy for various exquisite dynamic structures and time periodic processes.\u003c/p\u003e\u003cp\u003eOn the basis of Time-structure, through a long-term impact strategy, we discovered an unimaginable time periodicity in macro morphology. The long nanohelices change to small nanoparticles, then to short nanohelices, and finally back to the initial long nanohelices. The whole process occurs spontaneously with length variation up to 100 times, indicating an obvious time-periodic material, Time-material. It goes beyond the current knowledge and demonstrates that time translational symmetry principle is no longer an insurmountable red line. This is the first application of the time dimension in materials science and brings up a brand-new concept for material design and growth. The achievement of the long-standing and constantly changed time periodic structure/material makes the exploration and development of time-sensitive nanodevices possible.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u0026nbsp;\u003c/strong\u003eF. G. and Q. L. guided the entire project. F. G. and Q. L. carried out the data analyses and co-wrote the manuscript. F. G. performed most of the experiments. S. L., M. Z. and H. L. performed some synthesis experiments and XRD, SEM characterizations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Financial Interests:\u0026nbsp;\u003c/strong\u003eThe authors declare no competing financial interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eGoldstein, H., Poole, C. \u0026amp; Safko, J. 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Soc.\u003c/em\u003e\u003cstrong\u003e118\u003c/strong\u003e, 11217-11224 (1996).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Nanjing University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Time periodicity, Dimensionally reduced long-range order, Fractional-dimension crystals, Time-structure, Time-material","lastPublishedDoi":"10.21203/rs.3.rs-8230826/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8230826/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe principle of time-translational symmetry is the cornerstone of the law of energy conservation. Crystals have three dimensional ordered lattices, and it is inconceivable to imagine that they have time periodicity. Herein, while constructing nanohelices, we discovered a completely unprecedented time periodicity on a new kind of nanohelix grown through a distinctive directional competition twisting mechanism. Its crystal structure spontaneously varies with time and then returns to the original structure (termed Time-structure). Moreover, by a long-term impact strategy, we discovered an unimaginable but very obvious time-dependent change in morphology. The material spontaneously changes from long nanohelices to small nanoparticles, then to short nanohelices, and finally back to its original morphology, long nanohelices (termed Time-material). The emergence of Time-structures and Time-materials undoubtedly has intrinsic underlying reasons. The directional competition mechanism makes the nanohelices misaligned along Z-axis, breaking the long-range order in this dimension. The resulting crystals do not have crystal characteristics in at least one dimension, different from crystals, quasicrystals and amorphous solids, indicating a new form of solid state, called Fractional-dimension crystals (FD-crystals). Their lattice rigidity has been broken, creating a unique transformability which is the key point for the realization of time periodicity. Furthermore, through repeated structural reorganization, even conventional crystals can be transformed into FD-crystals, thereby enabling time periodicity to emerge. This work is not only the first report on spontaneous time-periodicity of nanocrystals, but also the first introduction of time dimension in chemistry and materials science. It brings up a new field of non-equilibrium transformable crystals beyond current crystallographic theory, opens a door to various exquisite time-periodic processes, and makes the design, construction and application of time nanodevices possible.\u003c/p\u003e","manuscriptTitle":"Dynamic crystals: First show of time periodicity in crystal structures and nano-materials","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-02 09:14:45","doi":"10.21203/rs.3.rs-8230826/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d5a84b66-145e-4a26-8d90-9f75fe4b8ae1","owner":[],"postedDate":"December 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-02T09:14:45+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-02 09:14:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8230826","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8230826","identity":"rs-8230826","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}