Although symmetry breaking is widely realized as one of the most powerful tools in modern scientific researches, it is unclear how symmetry breaking plays its role in nanocosm. Here, we show a correlation between spontaneous symmetry breaking and the formation of nanocrystals. In our experiments, some ZnO nanocrystals, including ZnO tetrapods, rod-based tetrapods, and aeroplane-like crystals, presented with specific structures and symmetries leading to an unexpected process of spontaneous symmetry breaking. According to the rule of spontaneous symmetry breaking, a hypothesis was proposed that the aeroplane-like nanocrystals might be resulted from the unequal development of the crystal twinnings. Subsequent work supported this hypothesis and proved the dramatic effect of spontaneous symmetry breaking. This work applies the rule of spontaneous symmetry breaking to the formation mechanisms for nanocrystals and highlights the causal contribution of spontaneous symmetry breaking to the intricate behaviors of the particles at nanoscale.

Symmetry breaking is recognized as one of the center concepts in contemporary physics for it is effective in acquiring simple and profound approaches in various systems. The rule of symmetry breaking is employed from the level of the universe as a whole to that of elementary particles,1 and it is even applied to other scientific branches, such as embryology and genetics.2,3 Yet its applicability and fertility in nanocosm are unclear. This paper shows how the rule of spontaneous symmetry breaking (SSB) discovers the formation of the aeroplane-like ZnO nanocrystals and indicates that the consideration of symmetry breaking is necessary to understand the formation mechanisms for some nanostructures.

Generally, SSB is defined as a process during which an initial state with higher symmetry transforms spontaneously to one of the multi-folded states with lower symmetry. In a qualifiedly homogeneous environment, nanocrystals tend to be as symmetrical as possible in their structures and morphologies for the extrinsic factors seldom break their intrinsic symmetries. For the symmetrical nanocrystals, some of them might grow up with all their equal locations developing equally, while some others might not for spontaneous symmetry breaking.

ZnO nanocrystals with different morphologies or structures have been widely investigated for they are relatively easy to be obtained via many methods,4 such as chemical vapor transport.4,5 Here, a series of ZnO nanocrystals were synthesized via thermal evaporation and their symmetries were focused on. In our experiments, Zn powders with analysis purity and grain size of 200 mesh were heated to the temperatures ranging from 860 °C to 900 °C, and they were oxidized completely in the air. The obtained white and fluffy powders were proved to be ZnO crystals with hcp structures (Fig. 1).

FIG. 1.

XRD pattern shows that the samples are ZnO crystals with hcp structure.

FIG. 1.

XRD pattern shows that the samples are ZnO crystals with hcp structure.

Close modal

Three morphologies of ZnO nanocrystals were often produced in these samples, and the transmission electron microscopy (TEM) demonstrated their structures: the tetrapods [Fig. 2(a)], the rod-based tetrapods [Fig. 2(b)], and the aeroplane-like crystals [Fig. 2(c)]. The selected area electron diffraction (SAED) patterns in the insets of Fig. 2(a) show that the legs in a tetrapod are extending along different c axes, respectively. The ZnO tetrapod with such a structure is accepted to be originated with a sphalerite nucleus first, then the tetrapod structure is resulted from the formation of wurtzite crystals protruding from the four plus {111} surfaces,6 and the angles between any two legs in a tetrapod are about 109.5°.7 Fig. 2(b) shows a rod-based tetrapod, which is composed of a rod, three sheets, and three wires extending from the ends of the three sheets. The insets in Fig. 2(b) demonstrate that the wires are extending along different c axes, and the grain boundaries exist between the wires and the sheets. The rod-based tetrapod is a 4-polycrystal, in which a rod and three uniformly distributed sheets have a common axis, while the other three single crystal wires with different orientations are connected to the ends of the three sheets via grain boundaries, respectively. The SAED pattern [in the inset of Fig. 2(c)] demonstrates that the aeroplane-like structure is a single crystal, which resembles a rod-based tetrapod without the three extending wires.

FIG. 2.

Three morphologies of ZnO nanocrystals: the tetrapod (a), the rod-based tetrapod (b), and the aeroplane-like crystal (c). Their models are colored differently according to their different orientations and structures. The scale bars in the TEM images are all 1 μm.

FIG. 2.

Three morphologies of ZnO nanocrystals: the tetrapod (a), the rod-based tetrapod (b), and the aeroplane-like crystal (c). Their models are colored differently according to their different orientations and structures. The scale bars in the TEM images are all 1 μm.

Close modal

These three structures are similar in their sizes and morphologies but not in their symmetries. The tetrapod [Fig. 2(a)] has four legs with the same structure and morphology, and it is as symmetrical as a regular tetrahedron with Td symmetry. The rod-based tetrapod and the aeroplane-like crystal are both D3 symmetrical for they both have a 3-fold rotational axis and 3 symmetrical planes. Here, D3 symmetry is a proper subgroup of Td symmetry. According to the rule of SSB, a possible method is that the ZnO structures with lower symmetries (D3) should be developed from the structures with higher symmetries (Td). So a hypothesis is proposed to explain the formation of these three kinds of ZnO nanocrystals (Fig. 3).

FIG. 3.

SSB assumes the development of the ZnO nanocrystals. The scale bars in the FESEM images are all 1 μm.

FIG. 3.

SSB assumes the development of the ZnO nanocrystals. The scale bars in the FESEM images are all 1 μm.

Close modal

As shown in the first step of Fig. 3, the tetrapod with Td symmetry can be taken as quadruplets for the four parts in the tetrapod are indistinguishable in their characteristics, such as orientations, morphologies, and structures.

During the development of the ZnO tetrapod, the sites between every two legs have the priority in being deposited for they have lower saturated vapor pressure and higher attachment energy.8 In an approximately homogeneous environment, the quadruplets in a tetrapod develop themselves equally, and they grow up to form a structure as shown in the second step in Fig. 3. Six sheets of twinning crystals, which are all divided into two equal parts by a twinning plane, are formed between any two legs.

With the development of these six sheets, the volume of the tetrapod increases, and the areas of the six twinning planes increase, too. These twinning planes can add interfacial energy to the tetrapod, and the interfacial energy can be a potential driving force to transform the twinning crystals to a single crystal with lower interface energy and higher stability. So the equal development of the four legs might give way to the unequal development, and this might lead to one leg's priority over the other three legs. As a result, the twinning crystal particle will recrystalline and a single crystal will be formed along the dominant leg's orientation. And the formed single crystal particle will be more stable than its precursor of the twinning crystal particle. The third step in Fig. 3 shows the critical transformation of SSB.

During this transformation, one leg in the tetrapod grows up preferentially by shearing the other three quadruplets' lattice, and the other three legs shrink themselves by rearranging their own lattice according to the dominant's orientation. On the boundaries between the prevailing one and the other three parts, the lattice shears continuously. Then the prevailing one advances its interfaces to the ends of the sheets, where three relatively small interfaces separate the dominant and the three wires. As the third step shown in Fig. 3, the prevailing quadruplet has occupied all the sheets of the losers, except three residual wires lying at the three ends of its domination. The structure at current step is composed of four parts, a prevailing quadruplet and three wires left by the three losers. The third step in Fig. 3 maps the crystal particle: a rod and three uniformly distributed sheets around the rod form a single crystal; three wires, which are extending along different c orientations and connecting to the ends of the three sheets via grain boundaries, are the other three parts.

Depositing and growing continue the development of the prevailing quadruplet, and the prevailing quadruplet expands itself and shears away the remnants till it transforms them all. As the forth step shown in Fig. 3, the final structure becomes an aeroplane-like single crystal. Thus, the prevailing crystal establishes its total supremacy over all the other three ones, with the other three quadruplets being disappeared completely.

This hypothesis is in good agreement with the proofs of field-emission scanning electron microscopy (FESEM) images (Fig. 3), but not in agreement with the previous conjecture on the formation mechanisms about these nanostructures.9 In recent years, the rod-based tetrapod is assumed to be formed from a rod, with an aeroplane-like structure as its intermediate (Fig. 4).9 Since this conjecture could not explain the formation of the three interfaces in the rod-based tetrapod, it has been quested before, and the above process dictated by SSB has been guessed in our previous work.10 Till now, neither of these two processes has been directly supported by empirical evidences.

FIG. 4.

The rod-based ZnO structure and the third growth model of tetrapod.

FIG. 4.

The rod-based ZnO structure and the third growth model of tetrapod.

Close modal

To test the hypothesis of SSB, an experiment was designed and performed. In this experiment, Zn powders with analytical purity were put in a porcelain boat, and a tube furnace was pre-heated to 890 °C with two ends opening to the air. Then the porcelain boat carrying Zn powders was inserted rapidly into the furnace. After 20 min, the porcelain boat was drawn out rapidly from the furnace and cooled down to the room temperature. The obtained samples were characterized via X-ray diffraction (XRD) and in-situ observed via FESTEM. XRD proves the samples are ZnO crystals with hcp structures. The in-situ features of these ZnO crystals (Fig. 5) show that the tetrapods, the rod-based tetrapods, and the aeroplane-like crystals are synthesized together, they are similar in sizes and morphologies, and their volumes are increasing according to such an order: the tetrapod, the rod-based tetrapod, and then the aeroplane-like structure.

FIG. 5.

ZnO nanocrystals with increasing volumes: the tetrapods (a), the rod-based tetrapods (b), and the aeroplane-like structures (c).

FIG. 5.

ZnO nanocrystals with increasing volumes: the tetrapods (a), the rod-based tetrapods (b), and the aeroplane-like structures (c).

Close modal

This in-situ feature proves that the aeroplane-like ZnO nanocrystal is originated from a growing tetrapod. Application of SSB predicts the development of a series of ZnO nanocrystals and derives an intrinsic habit of crystals from a formation mechanism of SSB. So, the aeroplane-like ZnO nanocrystals provide a significant link between the rule of SSB and the intricate behaviors of nanocrystals and declare that the nanocosm is not a no-go area for the rule of SSB anymore. Additionally, this attempt opens up a possibility for investigations on various nanotetrapods combined by IIB elements (Zn or Cd) and VIA elements (O, S, Se, or Te), such as ZnS,11 CdS,12 CdSe,13,14 and CdTe.15 

Y.Z., J.Z., B.Z., and L.Q. acknowledge NSFC (Nos. 51275508 and 51205383) for financial support.

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