Article | Open | Published:

First-Principles Studies on the Structural Stability of Spinel ZnCo2O4 as an Electrode Material for Lithium-ion Batteries

Scientific Reports volume 6, Article number: 36717 (2016) | Download Citation


Systematic first principles calculations were performed for ZnCo2O4 to clarify its structural and electronic properties, and particularly the structural stability as an electrode material for lithium-ion batteries. For samples with low Li concentration, e.g., LinZnCo2O4 with n < 1, Li atoms take the center of oxygen octahedra and may diffuse rapidly. Structure distortions and volume expansions can be observed in LinZnCo2O4 with n > 1 and amorphous structures eventually prevail. The AIMD simulations for Li9ZnCo2O4 suggest the formation of Li2O, Co3O4 and LiZn local compounds or alloys. In particular, the formation of Zn-Co aggregations and the losing of ZnO pairs are identified as the possible reasons that are responsible to the Li capacity fading in ZnCo2O4 anodes.


Lithium-ion batteries (LIBs) are now ubiquitous in portable electronics due to their high energy density, low weight and small volume. Intercalation of LIBs to more advanced battery systems has also been used in a verity of devices including electric vehicles1,2,3,4. Researchers are continually exploring new electrode materials to further enhance the Li capacity and safety of LIBs, and to reduce the cost. To this end, deep understanding of electrochemical processes during charge-discharge (delithiation-lithiation) cycle of LIBs is essential5,6. Transition metal oxides (TMOs), such as Fe3O4, CuO, NiO, and Co3O4, have been widely used as high-capacity anode materials for LIBs7,8,9,10,11. Among these, the cubic spinel Co3O4 has a high capacity of ~900 mAhg−1, with 100% capacity retention for up to 25 cycles12,13. Recently, extensive efforts have been made towards replacing Co in Co3O4 partially by eco-friendly and cheaper alternative metals, such as Ni14 and Zn15.

ZnCo2O4 (ZCO) spinel is a typical p-type transparent conducting oxide that combines high optical transparency and high electrical conductivity. It is promising for broad applications in solar cell, smart window and liquid crystal display16,17. With its high reversible Li capacity, long cycling life and environmental friendliness, ZCO is also an attractive material for the use in LIBs and supercapacitors18,19,20,21,22,23. Previous ex-site TEM24 and ex-site X-ray diffraction (XRD) studies25 have established that the electrochemical reactions of ZCO with Li during a charge-discharge cycle include several steps:

One may therefore expect a total capacity corresponding to ~8.33 mol of recyclable Li per mole of ZCO, with the formation of metal oxides and decomposition of Li2O18. However, the real capacity of ZCO-based LIBs decays quickly upon Li charge-discharge cycles. A few dozen studies have explored the possible causes of capacity degradation, and have identified several possible factors such as the large volume changes and subsequent mechanical instabilities in electrodes26,27,28,29, the formation of a solid electrolyte interphase (SEI)30, and the reduction of metal oxide to metal with the formation of Li2O23. No consensus has been reached yet and further fundamental studies are desired for the development of superb anode materials in LIBs. At the present stage, theoretical studies have been focused on the structure and electronic properties of ZCO31,32,33, and very few touched on structural transformation and stability during the electrochemical reaction process. According the reactions listed above, the charging and discharging processes involve local chemical reaction and structure destruction, a case that differs significantly from the classical lithiation/delithiation processes in the layered or olivine electrode materials. The appropriate descriptions on the entire electrochemical process of Li atoms in spinels are still challenging tasks for theoretical studies.

In this work, we study the structural and electronic properties of ZnCo2O4 by using first-principles calculations. The structural stability, Li diffusion, and the key electrochemical reaction steps of LinZnCo2O4 after lithium insertion are simulated and analyzed. We find that, the electronic characters of ZCO ground state, a nonmagnetic cubic spinel structure, are mainly dominated by alignment and hybridization between the Co-3d and O-2p orbitals. The structure of LinZnCo2O4 is stable for a small lithium capacity, e.g., n ≤ 1, and the energy barrier for Li atom diffusing from the center of one oxygen octahedron to its adjacent octahedron is about 0.4 eV. For cases with n > 1, the structure becomes locally disordered with a large volume expansion as large as 180%. The pair correlation functions of the final state of Li9ZnCo2O4 show the formation of ZnCo network, instead of ZnO, during the electrochemical reactions of ZCO with Li, which leads to a reduction of the reversible lithium capacity.

Results and Discussions

Structure and electronic properties of ZCO

Zinc oxide spinels may have different configurations, depending on the positions of Zn and Co atoms. If the tetrahedron sites (Td, tetrahedrally coordinated) in Co3O4 are only occupied by Zn2+, its structure is a cubic spinel, as shown in Fig. 1(a). When Zn3+ stay on the octahedral sites (Oh, octahedrally coordinated), and Co3+ and Co2+ occupy the octahedral and tetrahedron center, respectively, the structural deformation occurs to form a tetragonal spinel structure, as shown in Fig. 1(b). The phase transition between these two structures happens under certain temperature or pressure34,35. With the GGA+U functional, our energy calculations of the cubic and tetragonal spinels show that ZCO is a nonmagnetic (NFM) cubic spinel structure. The calculated lattice constant, 8.164 Å, and band gap, 2.22 eV, are in good agreement with the corresponding experimental values of 8.0946(2) Å (JCPDS card no. 23–1390) and 2.26 eV, respectively36. Note that the regular GGA method gives a similar lattice constant but a very small band gap of only 0.60 eV. The ground magnetic state of the tetragonal spinel is ferromagnetic and its energy is higher than that of the cubic spinel by about 2.30 eV, indicating that the phase transition between the two phases of ZCO is almost impossible under normal experimental conditions.

Figure 1
Figure 1

(a) The cubic spinel and (b) tetragonal spinel structures of ZnCo2O4. Grey, blue and red balls represent Zn, Co and O atoms, respectively. (c) The total (the black line with gray shadow) and projected density of states of Zn, Co and O atoms. (d) Band structure, with a red color indicating the contributions from the Co atom. The horizontal blue lines indicate the energy positions of the VBM and CBM.

The calculated total and projected density of states in Fig. 1(c) show that the O-2p orbitals have a weak hybridization with Co-3d states just below the Fermi level. Both Co-3d and O-2p orbitals determine the valance band maximum (VBM) of ZCO, whereas the conduction band minimum (CBM) is mainly dominated by the Co-3d states. The Zn atom is relatively inert in determining the band edges of ZCO, but it bridges the interactions between tetrahedrally coordinated Co-3d and O-2p electrons. These features can be clearly seen from the band structure in Fig. 1(d), where the red color indicates the contributions from the Co atom. We see that the ZCO spinel has an indirect band gap: the VBM is near the W point along the W-L direction and the CBM is located near the X point along the Γ-X direction. The VBM of ZCO is characterized by a very flat dispersion, which results in heavy holes with large effective masses and may lead to poor p-type conductivity.

Electrochemical properties of LinZnCo2O4

We may understand the structural stability and electrochemical properties of ZnCo2O4 upon lithiation process starting from one Li atom insertion in ZCO, i.e., Li0.125ZnCo2O4. Here we constructed three possible sites for the Li atom in the supercell shown in Fig. 2(a), denoted as A, B and C. For site A, the Li atom locates in the octahedral center surrounding by six oxygen atoms; Li stays in the lattice channel of the structure in site B, and it is in the “cage” consisting of four Co atoms and four O atoms in site C. All the three configurations are stable after structure relaxation, and the site A has the lowest energy. The energy difference between the site A and site C is as high as 2.67 eV. So the possibility of having Li on site C is negligible and the diffusion pathway of Li atom in ZCO should be along A −> B −> A. The relative energy and local structure for each step calculated by the nudged elastic band (NEB) method37,38 are shown in Fig. 2(b). Here we use a GGA method to avoid the energy disturbance caused by charge transition on the energy barrier39,40,41. We can see that the Li atom leaves the center of the oxygen octahedron for the transition state, i.e. the site B, and then moves to the adjacent octahedron. The calculated energy barrier of Li diffusion is about 0.4 eV as shown in Fig. 2(b), which should be easy to overcome under the normal experimental conditions.

Figure 2
Figure 2

(a) Three possible models of inserting one Li atom in the supercell denoted as A, B and C. (b) The energy barrier of one Li atom diffusing in a 2 × 2 × 2 ZCO supercell. The insets show the local structures at each step. The purple ball is the Li atom.

We then insert more Li atoms in the supercell to observe the structural stability of LinZnCo2O4 and the lithium capacity of ZCO. For each n, we searched different configurations, and those with the lowest energies are shown in Fig. 3(a–c) for n = 0.125, 0.25 and 1. Interestingly, we found that the second Li atom tends to stay in the center of the nearest neighbor oxygen octahedron, which is consistent with the diffusion channel of one Li atom we discussed above. For n ≤ 1, the structure of LinZnCo2O4 is stable until all octahedral “cages” in ZCO have been fully occupied, and the volume of LiZnCo2O4 expands by ~10% compared with that of ZnCo2O4. Note that the positions of Zn atom are not in the ideal lattice site already. So the nearest neighbor distance between Zn and Zn atoms shrinks from 3.3 Å to 2.4 Å. As n > 1, such as for n = 2 in Fig. 3(d), the atoms in LinZnCo2O4 are clearly not in the lattice sites of cubic spinel and the crystalline structure starts to distort.

Figure 3
Figure 3

The structures of LinZnCo2O4 with n = (a) 0.125, (b) 0.25, (c) 1 and (d) 2. The grey, blue, red and purple balls represent Zn, Co, O and Li atoms, respectively, and Li atoms are in the center of the blue octahedrons in (ac).

According to Eqs (1, 2, 3, 4, 5), one can expect a ratio of 9 mol of Li in a mole of ZCO. We thus examined Li9ZnCo2O4 for the high concentration case through AIMD studies. The initial and final structures are depicted in the upper and lower panels in Fig. 4(a). As expected, the structure of Li9ZnCo2O4 is disordered and its volume expands by ~180% compared with that of clean ZnCo2O4. The local chemical order in LinZnCo2O4 alloys can be directly characterized by the partial pair correlation functions (PCF, gAB), which is defined as the number of B-type atoms in the spherical shell ranging from r to (r + dr) around an A-type atom. Quantitatively, it is calculated by:where L is the lattice length of the 128-atom cubic unit cell, NA and NB are the numbers of A and B atoms, respectively, in the unit cell, and nAB is the average number of A-B pairs with a saparation r.

Figure 4
Figure 4

(a) The initial (upper panel) and final (lower panel) states of Li9ZnCo2O4 by using AIMD method. (b) The total and partial pair correlation functions of the Li9ZnCo2O4 final state. The left and right insets show the local atomic pairs with a band-length range of 1.65–2.25 Å (blue rectangle) and 2.25–2.80 Å (red rectangle), respectively.

The total pair correlation function of Li9ZnCo2O4, gtot(r), shows broad peaks in Fig. 4(b), indicating the amorphous feature of the final structure. The first peak of gtot(r) at ~2.0 Å primarily results from Li-O and Co-O pairs, indicating the formation of Li2O and Co3O4 local structures Some Li-O and Co-O pairs have a bond length range of 1.65–2.25 Å, as highlighted in the blue rectangle in Fig. 4(b). Another peak of gtot(r) at ~2.5 Å represents Zn-Zn, Zn-Co, Co-Co and Li-Zn pairs. Interestingly, we searched Zn- and Co- pairs within a bond length range of 2.25–2.80 Å in the red rectangle, and clearly saw the formation of Zn-Co network with some Li atoms connecting with Zn atoms, as depicted in the right inset in Fig. 4(b). On the contrary, we can rarely find the Zn-O pairs, indicating that more Zn atoms interact with Co atoms instead of O. Y. Sharma et al. have confirmed that Zn- and Co- nano-particles contribute to the stability and high lithium capacities of ZCO through both alloy formation and displacement reaction, namely LiZn ↔ Zn ↔ ZnO and Co ↔ CoO ↔ Co3O418. The lack of ZnO breaks the mutual beneficial matrices and makes the reversible Li capacity of ZCO to be smaller than 6.33 mol in real experiments according to the Eq. (3).

We also studied the changes of atomic pairs as a dependence of n value in LinZnCo2O4, as shown in Fig. 5, to observe the structure evolution upon lithiation process. With the addition of Li atoms, gLiO(r) increases but gZnO(r) and gCoO(r) decrease quickly. In particular, gZnO(r) is almost zero for n = 8 and 9, as shown in the lower panel in Fig. 5(a). The positions of the first peaks of gLiO(r), gCoO(r) and gZnO(r) are almost unchanged compared with the ideal ZCO, which illustrates the stability of these metal oxides. However for gZnZn(r), gZnCo(r), and gCoCo(r), the positions of their first peaks shown in Fig. 5(b) obviously change with the insertion of Li atoms and there are broad peaks at around 2.45 Å. In contrast with the decrease of gZnO(r), the number of Zn-Zn, Zn-Co and Co-Co pairs increases with the increasing Li composition. Therefore, one may expect Zn-Co aggregation in real samples after several rounds of lithiation/delithiation cycles, which might be responsible to the decrease of Li capacity. A stable Li capatity could occur in nanophase or porous ZnCo2O4 materials due to the inhibition of Zn-Co network and the flexibility of nanograins. More experiments are expected for the verification of our theoretical results.

Figure 5: The partial pair correlation functions of LinZnCo2O4 as a function of n.
Figure 5

In summary we performed systematic density functional studies on the structure, magnetic, and electronic properties of ZnCo2O4, as well as the lithium diffusion and structural stability upon lithiation process as an anode material of LIBs. It was shown that ZCO is a nonmagnetic cubic spinel structure with an indirect band gap of 2.22 eV by using GGA+U functional. Lithium atom in ZCO prefers to occupy the center of oxygen octahedron and the energy barrier of one Li atom diffusing to the adjacent octahedral center is about 0.4 eV. While the structure of LinZnCo2O4 is stable for small lithium capacity, it becomes locally disordered as Li: Zn >1 mol: 1 mol with a volume expansion of >180%. We further found the formation of Zn-Co network instead of ZnO alloy in the final structures of Li9ZnCo2O4 through AIMD calculations. So the structure destruction occurs in the lithiation process that makes the reversible lithium capacity fading during cycles. Our extensive calculations provide instructive information for understandings of experimental results and also give useful insights for the design and optimization of high rate electrode materials.


Spin-polarized density functional calculations were performed by using the Vienna Ab initio Simulation Package (VASP)42 along with the projector augmented wave (PAW) method43. The Perdew-Burke-Ernzerhof (PBE) formulation of the generalized-gradient approximation (GGA)44 was adopted to describe the exchange-correlation interaction among electrons, and a Hubbard U of 4 eV (GGA+U) was added for Co 3d orbitals45,46. Throughout this work, we used an energy cutoff of 500 eV for the plane wave expansion. The convergence of our results against the k-points sampling in the Brillouin zone was carefully examined for all cases, for example, an 11 × 11 × 11 Monkhorst-Pock k-point set for a primitive cell. The crystal constant and positions of the ions were fully relaxed until the final force on each atom is smaller than 0.01 eV/Å. Gaussian smearing method with a smearing width of 0.05 eV was used to accelerate the convergence. We used a 2 × 2 × 2 supercell (128 atoms) to study the structural stability of Li insertion in ZCO, as well as the diffusion channels and energy barrier of Li atoms.

We did Ab initio molecular dynamics (AIMD) calculations for the determination of the final structures and reaction products upon lithiation processes. The atomic spacing and positions were fully optimized in a cubic supercell and the annealing process was performed at 300 K for 5 ps in a canonical (NVT) ensemble with a time step of 3 fs. While only the Γ-point was used to sample the Brillouin-zone during the annealing process, 3 × 3 × 3 Monkhorst-Pack k-points were used for the geometry relaxation and electronic structure determination after the AIMD simulations.

Additional Information

How to cite this article: Liu, W. W. et al. First-Principles Studies on the Structural Stability of Spinel ZnCo2O4 as an Electrode Material for Lithium-ion Batteries. Sci. Rep. 6, 36717; doi: 10.1038/srep36717 (2016).

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

    Electrical energy storage and intercalation chemistry. Science 192, 1126–1127 (1976).

  2. 2.

    Energy storage beyond the horizon: Rechargeable lithium batteries. Solid State Ionics 179, 752–760 (2008).

  3. 3.

    & The Li-ion rechargeable battery: a perspective. Journal of the American Chemical Society 135, 1167–1176 (2013).

  4. 4.

    , & Electrical energy storage for transportation—approaching the limits of, and going beyond, lithium-ion batteries. Energy & Environmental Science 5, 7854–7863 (2012).

  5. 5.

    , , , & A review of advanced and practical lithium battery materials. Journal of Materials Chemistry 21, 9938–9954 (2011).

  6. 6.

    & Nanostructured silicon for high capacity lithium battery anodes. Energy & Environmental Science 4, 56–72 (2011).

  7. 7.

    , , , & High rate capabilities Fe3O4-based Cu nano-architectured electrodes for lithium-ion battery applications. Nature materials 5, 567–573 (2006).

  8. 8.

    et al. Facile synthesis of nanocrystalline-assembled bundle-like CuO nanostructure with high rate capacities and enhanced cycling stability as an anode material for lithium-ion batteries. Journal of Materials Chemistry 22, 11297–11302 (2012).

  9. 9.

    et al. NiO nanocone array electrode with high capacity and rate capability for Li-ion batteries. Journal of Materials Chemistry 21, 9988–9990 (2011).

  10. 10.

    , , & Beyond Intercalation‐Based Li‐Ion Batteries: The State of the Art and Challenges of Electrode Materials Reacting Through Conversion Reactions. Advanced Materials 22, 170–192 (2010).

  11. 11.

    et al. Virus-enabled synthesis and assembly of nanowires for lithium ion battery electrodes. Science 312, 885–888 (2006).

  12. 12.

    et al. Porous Co3O4 Nanotubes Derived From Co4(CO)12 Clusters on Carbon Nanotube Templates: A Highly Efficient Material For Li‐Battery Applications. Advanced Materials 19, 4505–4509 (2007).

  13. 13.

    , , , & Nano-sized transition-metal oxides as negative-electrode materials for lithium-ion batteries. Nature 407, 496–499 (2000).

  14. 14.

    , , & NiCo2O4 spinel: First report on a transition metal oxide for the negative electrode of sodium-ion batteries. Chemistry of Materials 14, 2847–2848 (2002).

  15. 15.

    , , & Synthesis and characterization of spinel type ZnCo2O4 as a novel anode material for lithium ion batteries. Journal of Materials Science 39, 1077–1079 (2004).

  16. 16.

    Transparent conducting oxide semiconductors for transparent electrodes. Semiconductor Science and Technology 20, S35 (2005).

  17. 17.

    Study of systematic trends in electronic and optical properties within ZnM2O4 (M = Co, Rh, Ir) family by FPLAPW method with PBE and TB-mBJ potentials. Optical Materials 45, 141–147 (2015).

  18. 18.

    , , & Nanophase ZnCo2O4 as a High Performance Anode Material for Li‐Ion Batteries. Advanced Functional Materials 17, 2855–2861 (2007).

  19. 19.

    & Linker-free 3D assembly of nanocrystals with tunable unit size for reversible lithium ion storage. Nanotechnology 22, 355401 (2011).

  20. 20.

    et al. Facile synthesis of uniform mesoporous ZnCo2O4 microspheres as a high-performance anode material for Li-ion batteries. Journal of Materials Chemistry A 1, 5596–5602 (2013).

  21. 21.

    , , , & A novel nanostructured spinel ZnCo2O4 electrode material: morphology conserved transformation from a hexagonal shaped nanodisk precursor and application in lithium ion batteries. Journal of Materials Chemistry 20, 4439–4444 (2010).

  22. 22.

    et al. Porous ZnCo2O4 nanowires synthesis via sacrificial templates: high-performance anode materials of Li-ion batteries. Inorganic chemistry 50, 3320–3324 (2011).

  23. 23.

    et al. Hierarchical three-dimensional ZnCo2O4 nanowire arrays/carbon cloth anodes for a novel class of high-performance flexible lithium-ion batteries. Nano letters 12, 3005–3011 (2012).

  24. 24.

    et al. Electrochemical study of nanometer Co3O4, Co, CoSb3 and Sb thin films toward lithium. Solid State Ionics 166, 295–305 (2004).

  25. 25.

    et al. A study on the charge–discharge mechanism of Co3O4 as an anode for the Li ion secondary battery. Electrochimica Acta 50, 3667–3673 (2005).

  26. 26.

    & Lithium Batteries: Science and Technology (Springer: US, , 2003).

  27. 27.

    & Key Factors Controlling the Reversibility of the Reaction of Lithium with SnO2 and Sn2BPO6 Glass. Journal of The Electrochemical Society 144, 2943–2948 (1997).

  28. 28.

    & Electrochemical lithiation of tin and tin-based intermetallics and composites. Electrochimica Acta 45, 31–50 (1999).

  29. 29.

    , , , & Nanostructured materials for advanced energy conversion and storage devices. Nature Materials 4, 366–377 (2005).

  30. 30.

    et al. Heteroepitaxial growth of ZnO nanosheet bands on ZnCo2O4 submicron rods toward high-performance Li ion battery electrodes. Nano Research 6, 348–355 (2013).

  31. 31.

    & Band gap anomalies of the ZnM2IIIO4 (MIII = Co, Rh, Ir) spinels. Physical Chemistry Chemical Physics 13, 9667–9675 (2011).

  32. 32.

    & P-type zinc oxide spinels: application to transparent conductors and spintronics. New Journal of Physics 16, 055011 (2014).

  33. 33.

    , , , & The origin of p-type conductivity in ZnM2O4 (M = Co, Rh, Ir) spinels. Physical Chemistry Chemical Physics 16, 2588–2596 (2014).

  34. 34.

    Phase transitions in crystals with the spinel structure. Journal of Physics and Chemistry of Solids 26, 1225–1232 (1965).

  35. 35.

    , , , & High-pressure phase transition and properties of spinel ZnMn2O4. Physical Review B 60, 12651 (1999).

  36. 36.

    , & ZnIr2O4, a p-type transparent oxide semiconductor in the class of spinel zinc-d6-transition metal oxide. Applied Physics Letters 90, 21903–21903 (2007).

  37. 37.

    & Classical and quantum dynamics in condensed phase simulations (World Scientific,1998).

  38. 38.

    & Quantum and thermal effects in H2 dissociative adsorption: evaluation of free energy barriers in multidimensional quantum systems. Physical Review Letters 72, 1124 (1994).

  39. 39.

    & Lithium diffusion in layered LixCoO2. Electrochemical and Solid-State Letters 3, 301–304 (2000).

  40. 40.

    , & Li conductivity in LixMPO4 (M = Mn, Fe, Co, Ni) olivine materials. Electrochemical and Solid-State Letters 7, A30–A32 (2004).

  41. 41.

    et al. Voltage, stability and diffusion barrier differences between sodium-ion and lithium-ion intercalation materials. Energy & Environmental Science 4, 3680–3688 (2011).

  42. 42.

    & Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 6, 15–50 (1996).

  43. 43.

    Projector augmented-wave method. Physical Review B 50, 17953 (1994).

  44. 44.

    , & Generalized gradient approximation made simple. Physical Review Letters 77, 3865 (1996).

  45. 45.

    , & First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method. Journal of Physics: Condensed Matter 9, 767 (1997).

  46. 46.

    , , , & Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+ U study. Physical Review B 57, 1505 (1998).

Download references


This work was supported by startup fund of China Thousand Young Talents, National Basic Research Program of China (973 program, No. 2013CB934700) and NSFC-Guangzhou Joint Fund for Super Computational Science and Application Research (second phase). The calculations were supported by Tianhe2-JK in Beijing Computational Science Research Center and supercomputers in National Supercomputer Center in Guangzhou.

Author information


  1. Beijing Computational Science Research Center, Beijing 100193, China

    • Wei-Wei Liu
    • , Woon-Ming Lau
    •  & Y. N. Zhang
  2. Chengdu Green Energy and Green Manufacturing Technology R&D Center, Chengdu, Sichuan, 610207, China

    • M. T. Jin
    •  & Y. N. Zhang
  3. Sichuan New Material Research Center, Mianyang, 621000, Sichuan, China

    • W. M. Shi
    •  & J. G. Deng
  4. Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang, 621900, Sichuan, China

    • W. M. Shi
    •  & J. G. Deng


  1. Search for Wei-Wei Liu in:

  2. Search for M. T. Jin in:

  3. Search for W. M. Shi in:

  4. Search for J. G. Deng in:

  5. Search for Woon-Ming Lau in:

  6. Search for Y. N. Zhang in:


Wei-Wei Liu, Woon-Ming Lau and Y.N. Zhang wrote the main manuscript text, Wei-Wei Liu and J.G. Deng prepared Figures 1, 2 and 3, and M.T. Jin and W.M. Shi prepared Figures 4 and 5. All authors reviewed the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Y. N. Zhang.

About this article

Publication history






By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.