The effects of the size of nanocrystalline materials on their thermodynamic and mechanical properties
© Yu and Zhan; licensee Springer. 2014
Received: 24 May 2014
Accepted: 9 September 2014
Published: 21 September 2014
This work has considered the intrinsic influence of bond energy on the macroscopic, thermodynamic, and mechanical properties of crystalline materials. A general criterion is proposed to evaluate the properties of nanocrystalline materials. The interrelation between the thermodynamic and mechanical properties of nanomaterials is presented and the relationship between the variation of these properties and the size of the nanomaterials is explained. The results of our work agree well with thermodynamics, molecular dynamics simulations, and experimental results. This method is of significance in investigating the size effects of nanomaterials and provides a new approach for studying their thermodynamic and mechanical properties.
Nanocrystalline materials exhibit novel physical and chemical properties which are different from the bulk behavior [1–5]. There are a great many theoretical and experimental investigations showing the size-dependent properties of nanomaterials. The typical trend is that the values of the thermodynamic and mechanical parameters fall with decreasing size of nanoparticles and nanostructure. These parameters include melting entropy and melting point [6–15], Debye temperature [10, 16, 17], cohesive energy [6, 18–23], diffusion activation energy [24, 25], amplitude of the thermal vibration [26, 27], thermal expansion coefficient [28–30], specific heat [31, 32], Young’s modulus [33–36], and mass density [37, 38]. All these behaviors are generally explained as a result of the high surface-to-volume ratio of nanomaterials. The proportion of atoms at the surface is no longer negligible and they possess higher energies than atoms in the interior of the particle. Over many decades, a huge volume of data has been established by experiments. However, the mechanism of the size effect is not clear because of the variation of these experimental results. Some excellent models have been developed using classical thermodynamics and modern molecular dynamics. However, most of them focus on only one or two parameters and give different explanations. As a result, there is no common understanding of the mechanism of size effects on nanomaterials. In particular, the question of whether it is possible to correlate the variation of the properties of nanomaterials has rarely received attention.
It is well known that the macroscopic thermodynamic and mechanical properties of crystalline materials are intrinsically determined by the binding energy. Therefore, the change of binding energy is the key to explaining the variation of the thermodynamic and mechanical properties of nanomaterials. In this paper, we present a model based on bond energy. By investigating the energy variation of a nanoparticle, an intrinsic interrelation between the thermodynamic and mechanical properties is achieved, revealing the effects of the size of nanocrystalline materials.
The values of the atomic packing factor ( η) for different crystal structures
Body-centered cubic (bcc)
Face-centered cubic (fcc)
Close-packed hexagonal (hcp)
Diamond structure (bct)
where W0 is defined as W0 = N ⋅ σ ⋅ 4 ⋅ π ⋅ r02, referring to the overall bond energy or the standard cohesive energy of the spherical particle in the perfect crystal.
where ΔE and E0 are the variational and standard cohesive energy of the nanomaterial, respectively. ΔG and G0 are the variational and standard Gibbs free energy, respectively, for a given value of Δ.
where, ΔX and X0 are the variational and standard thermodynamic and mechanical parameters, as determined by the bond energy, respectively.
In summary, we have demonstrated the intrinsic interrelations between the thermodynamic and mechanical properties of nanomaterials using our bond energy model and previous results to characterize aspects of the size effects on nanocrystalline materials. Equation 9 not only presents a new model to better describe the thermodynamic and mechanical properties of nanomaterials, but also provides a new approach to obtain these parameters from others without requiring the formulation and proof of new models. In other words, most of the thermodynamic and mechanical properties of nanomaterials can be predicted by using either experimental data or results of a theoretical analysis. In this way, all factors, such as shape, crystal structure, defects and fabrication processes of nanomaterials, which must be considered when predicting the physical parameters of nanomaterials, can be obtained from experimental data. This is a significant advancement in the investigation and application of nanomaterials.
This work was financially supported by the Natural Science Foundation of China (no. 51165016).
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