Thermochemistry of Nanosintering: Improving Nanostructure Control

by Professor Ricardo H. R. Castro

Nanostructured materials already play important roles in our everyday lives. From sun blockers to anti-scratching paintings, nanomaterials are revolutionizing how we see materials, improving their performances, and broadening the horizons of applications. To fully understand the origin of their unique properties and better utilize them, it is important to realize that nanomaterials are different from bulk materials not just because they are smaller, but because the small sizes significantly affect their properties, creating novel and different responses to the environment. The size effects can be seen as different colors, tastes, electrical responses, catalytic activities, etc.

Most of this nano-related behavior can be attributed to the fact that a large fraction of the volume of the material is within the "interface region", that is, a few nanometers or less from the interface itself (as shown in Figure 1)^1,2. Thus, nanomaterials' properties can be considered a consequence of, and will be strongly influenced by, their interface features, such as composition³, structure⁴, stress^5,6 and, fundamentally, energetics^1,7-10.

Figure 1. Calculus of the fraction of atoms on the surface (within 0.5 nm of the surface) for a general nanoparticle.

The energetics will rule the stability of a nanomaterial and how its structure spontaneously grows or responds to a heat treatment. That is, in any system, micro or nano, the total energy has at least two important contributions: the bulk energy and the interface energy. The bulk energy is mainly determined by the crystalline structure and composition of the core of the material. This energy can be predicted by using regular phase diagrams, with which you can study phase stability of micro and macro samples.

The interface energy is proportional to the interface area. By definition, interfaces are unstable as they represent the work needed to create a unit area by breaking or stretching a material. Logically, the higher the area, the higher the energy of a system. Hence, systems with high interface areas, such as nanomaterials, tend to collapse by coarsening, sintering or coalescence to decrease the total free energy.

Though this may sound like a bad thing, the tendency of the system to sinter can be smartly exploited to create controlled nanostructures, offering an alternative to the time consuming and expensive methodologies to create nanostructures based on hard templates and complex nanolithography. This thermodynamic control of nanostructure is based on a manipulation of the interface energetics, which may force the system to grow only in a desired direction and to stop grow to retain certain structure.

Controlling Thermodynamics of Nanostructure

Sintering is commonly considered a heat ignited process which driving force is the surface energy and curvature potentials. However, a new type of interface is created when necks start to form during sintering. This is generally called grain boundary (or solid-solid interface) and is shown both schematically and in a real micrograph in Figure 2.

Figure 2. ZrO2 nanoparticles partially sintered showing grain boundary formation.

The grain boundaries typically have different energies than the surfaces (solid-vapor interfaces), such that, when the system is transforming surface into grain boundary during sintering, there is an energy 'cost' which is dependent on the balance between surface energy and grain boundary energy. This balance will define the evolution of the nanostructure and can be controlled to provide desirable products.

For instance, MgO and ZnO have significantly different surface and grain boundary energies¹¹. A significantly different nanostructure evolution upon heating is observed in these samples, as shown in Figure 3. Note that though the starting nanoparticles are similar in size and shape, the ZnO samples coarse significantly more than the MgO powders. There are certainly many kinetic concepts to explain this behavior, but the difference in the ratio between the surface and the grain boundary energy plays an additional significant role here. Because the grain boundary energy of MgO is relatively high with relation to its surface energy, there is a relatively high energy cost in creating a neck. So, the neck formation stops when the energy 'gained' by the system due to the surface elimination is comparable to the 'needed' energy to form the boundary. As the surface to grain boundary energy ratio in ZnO is significantly higher, this energy barrier is not as present, and grain boundary is more freely formed. This suggests that the absolute energies are not of prime importance, but the relative energies would be governing nanosintering.

Figure 3. Sintering experiments showing the behavior of MgO, ZnO, and doped MgO under heat treatment. Though kinetics plays a major role, nanoenergetics is proven to be way to improve nanosintering. (γS is surface energy and γGB is grain boundary energy)

The effect of the energy ratio on the nanostructure evolution is clearly seen when doping MgO samples with CaO. As this dopant is observed to change the interface energies without significantly changing the kinetics, one can somehow isolate the energetic effects from kinetics. Observing the microstructure of doped MgO after sintering and comparing to MgO and ZnO, there are much more similarities with ZnO microstructure, consistently with the energetics trend.

A logical application of this approach would be in the improvement of sintering itself. One of the main challenges in ceramic sintering industries is to obtain dense parts with controlled shrinkage and controlled grain sizes. This control is currently only done on a kinetic basis, by using dopants to control densification mechanisms. The thermodynamic approach can help to identify how dopants affect densification driving forces, providing a tool to further optimize the industrial composition design of nanoceramics.

Another application would be to induce particular shapes and long range ordering of nanoparticles as a consequence of interface energy minimizing. This can be driven by changing the energetics of selected planes to force certain preferential growth. The idea lies on the fact that the surface energies are not unique on a particle, meaning that, because of the crystal structure, different crystal facets are present at the surface of a particle. Each of those facets has a different energy, and could be independently controlled. Since the higher energy surfaces grow faster, a fine control of those energies by using specific atmospheres, liquid phases, or dopants can promote the growth of different morphologies, such as star-like and nanowires¹²(Figure 4).

Figure 4. Faceted nanoparticles with exposed planes of different interface energies can rearrange or grow to distinct shapes and rearrange spontaneously.

Measuring Interface Energies

The measurement of interface energies is not a simple task at all, and therefore limited data is available in the literature to be exploited in the nano-control strategy discussed here. Thermochemistry has been proposed as a very powerful technique to determine accurate interface energies for nanoceramics^13,14. Briefly, the idea of these calorimetric measurements is to evaluate the heat released during the dissolution of samples with similar shapes, but different interface areas (Figure 5).

Figure 5. (Left) Typical result of surface energy measurements using DS. The surface gives an excess energy that is proportional to the surface area and measured as a difference in the enthalpy of DS. (Right) Setup for the measurement of enthalpy of drop solution (DS). Solvent is kept at 702 °C and sample is dropped from room temperature to be dissolved. A thermochemical cycle accounts for the reactions during dissolution.

As the excess energy is directly proportional to the interface areas, a good characterization of the samples will provide absolute values for the interface energies. This technique can be used to virtually any crystalline material, as the only requirement is a relatively high interface area to make it measurable.

The perspectives are that this technique will be able to provide lots of data to improve the control of nanostructure on a thermodynamics basis. This may be a breakthrough in the nanotechnology, but is still in the beginning of its potentials. We may dream however on being capable of tuning the interface energies of nanomaterials such that they can assemble themselves spontaneously the way we want them to, promoting macro organized shapes, with mesopores for catalysis applications, controlled contacts for battery cathodes, aligned channels for molecular filtering, etc. Well, perhaps this dream is not that far away of becoming true.

References

1. Navrotsky, A., Thermochemistry of nanomaterials, in Reviews in Mineralogy and Geochemistry: Nanoparticles and the Environment, Banfield, J.F. and Navrotsky, A., Editors. 2001, Mineralogical Society of America and the Geochemical Society: Washington. p. 73-103.
2. Cao, G., Nanostructures and Nanomaterials: Synthesis, Properties, and Applications. 1st ed. 2004, Danvers: Imperial College Press. 433.
3. Castro, R.H.R., Ushakov, S.V., Gengembre, L., Gouvea, D., and Navrotsky, A., Surface energy and thermodynamic stability of gamma-alumina: Effect of dopants and water. Chemistry of Materials, 2006. 18: p. 1867-1872.
4. Zhao, Z.J., Meza, J.C., and Van Hove, M., Using pattern search methods for surface structure determination of nanomaterials. Journal of Physics-Condensed Matter, 2006. 18(39): p. 8693-8706.
5. Yun, G. and Park, H.S., A multiscale, finite deformation formulation for surface stress effects on the coupled thermomechanical behavior of nanomaterials. Computer Methods in Applied Mechanics and Engineering, 2008. 197(41-42): p. 3337-3350.
6. Castro, R.H.R., Marcos, P.J.B., Lorriaux, A., Steil, M.C., Gengembre, L., Roussel, P., and Gouvea, D., Interface Excess and Polymorphic Stability of Nanosized Zirconia-Magnesia. Chemistry of Materials, 2008. 20: p. 3505-3511.
7. Navrotsky, A., Energetics of nanomaterials: The competition between polymorphism and surface energy. Abstracts of Papers of the American Chemical Society, 2003. 225: p. U939-U939.
8. Hill, T.L., Perspective: Nanothermodynamics. Nano Letters, 2001. 1(3): p. 111-112.
9. Hill, T.L., Extension of nanothermodynamics to include a one-dimensional surface excess. Nano Letters, 2001. 1(3): p. 159-160.
10. Rusanov, A.I., Nanothermodynamics. Russian Journal of Physical Chemistry, 2003. 77(10): p. 1558-1563.
11. Castro, R.H.R., Torres, R.B., Pereira, G.J., and Gouvea, D., Interface Energy Measurement of MgO and ZnO: Understanding the Thermodynamic Stability of Nanoparticles. Chemistry of Materials, 2010. 22(8): p. 2502-2509.
12. Zhang, P., Xu, F., Navrotsky, A., Lee, J.S., Kim, S., and Liu, J., Surface enthalpies of nanophase ZnO with different morphologies. Chemistry of Materials, 2007. 19: p. 5687-5693.
13. McHale, J.M., Auroux, A., Perrotta, A.J., and Navrotsky, A., Surface energies and thermodynamic phase stability in nanocrystalline aluminas. Science, 1997. 277(5327): p. 788-791.
14. Costa, G.C.C., Ushakov, S.V., Castro, R.H.R., Navrotsky, A., and Muccillo, R., Calorimetric Measurement of Surface and Interface Enthalpies of Yttria-Stabilized Zirconia (YSZ). Chemistry of Materials, 2010. 22(9): p. 2937-2945.

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