| With the objective of understanding quasicrystalline powder solid lubrication effect, compositions and properties of Al-based quasicrystals (QCs) were investigated by using the cluster-plus-glue-atom model. The correlation between chemical composition, atomic structure and mechanical properties was explored, which would provide a theoretical basis for the design and development of practical quasicrystalline materials. Atomic structures of crystalline phases are generally described in terms of crystallography, i.e. atomic coordinates in unit cell scheme. We have developed the cluster-plus-glue-atom model to describe different kinds of structures, including QCs, metallic glasses and crystalline phases, from the view point of the nearest neighbor coordination polyhedra. In this model, any structure is represented by a strongly bonded1st-neighbor coordination polyhedron (i.e. cluster) part and a weakly-bonded2nd-neighbor part (i.e. the glue atoms), or expressed in the cluster formula [cluster](glue atom)x. Recently, a cluster-resonance structural model has been developed, which is a combination of the cluster-plus-glue-atom model and Haussler’s global resonance model. It is interesting to note that the total number of valence electrons per unit cluster formula is proved to be a constant value of about24, thus the cluster formulas here can be regarded as the "molecular" formulas, mimicking the molecular formulas for common chemical substances. In this contribution, compositions of Al-based binary metastable and ternary stable quasicrystals are interpreted within the framework of the cluster-plus-glue-atom model, and the valence electron concentration factor was considered to understand the stabilization mechanism of quasicrystals. A quantitative description of the structure-property relationships of quasicrystals was also given based on the cluster-plus-glue-atom model. The following four aspects are addressed in the present work.(1) Icosahedral clusters have long been identified as the prevalent atomic motif of QCs. With the assumption that the principal icosahedral short-range-order would be inherited from crystalline approximants, the highly close-packed icosahedron, along with the most isolated feature, was selected to construct cluster formulas of binary Al-TM(TM=Cr, Mn, Fe, Co, Ni, Ru, Rh, Pd, Re) QCs, i.e.[isolated icosahedron](gule)0.1. Icosahedral Al-TM binary QCs can be formulated by [isolated icosahedron], while while decagonal quasicrystals are expressed by icosahedron plus one TM atom, or [isolated icosahedron]TMi. Ternary quasicrystals are deciphered by the same formulas as the corresponding binary sub-systems, with a partial substitution on the shell sites of the principal icosahedra by third elements. Despite of the fact that Al-based QCs are constructed by different cluster formulas, the number of valence electrons accommodated in these unit cluster formula e/u all share the same value, approximately equal to24, which implies that the cluster formulas are both chemical and electronic structural units.(2) Although hardness has been widely accepted as an essential parameter of materials, it remains far from being completely understood because the measurements involve elastic, plastic, and even crack processes. A novel atomic-level hardness model is established by considering the rupture of the weakest bonds within the framework of the cluster-plus-glue-atom model. Taking quasicrystals as an example, we proposed that hardness of brittle materials corresponds to the breakage of the weakest bonds per unit volume. By introducing the volume of each cluster formula expressed as Z/ρa, Z being the number of atoms in unit cluster formula and ρa the atomic density (number of atoms per unit volume), we obtain H=nεw/(Z/ρa), n being the number of the ruptured weakest bonds per unit cluster formula and εw the bond enthalpy. With the conjecture that cluster formulas may serve as rigid "obstacles" during hardness tests, the breakage of the weakest inter-cluster bonds occurs around the crack tip during crack propagation. Note that this expression implies a crucial role of the weakest bonds in determining the hardness of QCs among various types of bonds, which can be recognized as the "Cask Effect". The hardness of ternary Al-based quasicrystals was assessed through the empirical atomic density pa, the average bond enthalpy of the weakest bonds εaw and a fitted number of the ruptured inter-cluster bonds n (about20). Typically, there is a good agreement between the measured hardness values and theoretical hardness values of8.4～9.3GPa, providing a robust check of the validity of the cluster-plus-glue-atom model.(3) The present work extends this cluster-based model to the assessment of the Young’s modulus E of QCs. By analogy to a series-parallel combination of harmonic springs, the elastic behaviour of QCs is pictured as rigid clusters connected through the inter-cluster ’springs’with force constant ks-s. Note that the elastic strain is mainly born by the weak inter-cluster springs, E could be expressed by where τ=(1+(?))/2is the golden ratio, r1is the radius of the cluster, N is the number of the inter-cluster bonds. Since all the Al-based QCs addressed in this work have the Mackay-type local structure, the total number of the bonds belonging to the central icosahedron (N=36) is adopted. The shell sites of the icosahedral clusters in Al-based QCs are mainly occupied by Al atom, with atomic fractions of7.5/12～11/12, respectively. For simplicity, we take the force constant ks-s of the inter-clusters bonds in Al-based QCs as the radial force constant kAl-Al in metal Al, i.e. ks-s=kAl-Al=21.232N/m. Here the ideal r1values exactly corresponding to e/u=24are adopted. The calculated E values are approximately within a narrow range of175～183GPa, which agree in general with the experimental data. As a preliminary attempt, the Young’s moduli of Mg-based and Fe-based bulk metallic glasses are also calculated with the aid of this inter-cluster spring scheme.(4) Although the Al-TM ternary QCs were constructed by different unit cluster formulas, they have almost identical Hy and E, with average values of8.9GPa and179GPa, respectively, and consequently Hy/E approaches0.05. It is interesting to note that this ratio coincides well with those for typical metallic glasses (Hy/E≈0.05) and covalent compounds (Hv/E≈0.06). Since both the hardness and Young’s moduli of Al-based QCs have been calculated by using the same cluster-plus-glue-atom model, we will explore their intrinsic relationship here. Preliminary results indicate that the hardness to Young’s modulus ratio may be viewed as a manifestation of the density and the nature of the weakest bonds in brittle materials. |
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