Comment on “Cleaved surface ofi-AlPdMnquasicrystals: Influence of the local temperature elevation at the crack tip on the fracture surface roughness”

Abstract

Quasicrystals are intermetallic compounds with long-range quasiperiodic translational order, composed of atomic clusters, which can be interpreted as basic geometric building blocks. It is a persistent discussion whether these clusters also represent physical entities. Cleavage planes of fractured icosahedral AlPdMn as well as sputtered surfaces annealed up to about 900 K are rough with clusterlike protrusions. Fivefold surfaces annealed at higher temperatures exhibit flat terraces. Thus, obviously, the clusters cannot be termed supermolecules. However, experiments and numerical simulations indicate that fracture is influenced by the clusters. Thus, they determine physical properties. In a recent paper, Ponson et al. ͓Phys. Rev. B 74, 184205 ͑2006͔͒ investigated experimental fracture surfaces of AlPdMn and questioned the signature of the clusters. In this comment, we study the self-affinity of cleavage planes obtained by molecular-dynamics simulations. We conclude that the findings of Ponson et al. are not excluding a physical role of the clusters in quasicrystals.One method to analyze the roughness of fracture surfaces is to calculate the height-height correlation functions. These reveal scaling properties ͑see Ref. 1 for a review paper͒ with a "universal" roughness exponent of about 0.8 for a wide range of materials. However, up to now, no theoretical model is able to satisfactorily capture this self-affinity. Thus, it is hard to interpret microscopic properties of the investigated structures starting from the scaling behavior. It might even not be possible to distinguish a fractured from a sputtered surface, as the roughness exponents of both surfaces can lie in the same range. 2,3 Although the scaling behavior of fracture surfaces seems to be universal, the range of length scales in which it is valid may strongly vary for different materials. It has been argued that the corresponding cut-off length is related to the size of the process zone R c . 4 Inside this region, linear elastic predictions do not fit the real deformation field. Such a nonlinear and dissipative zone always exists, as atomic bonds break at the crack tip. The behavior on and below this scale determines whether, how, and where a crack travels. R c should therefore be related to the microstructure. In the following, we investigate the role and interpretation of for fracture surfaces of icosahedral quasicrystals. The roughness of i-AlPdMn fracture surfaces was analyzed in a recent paper by Ponson et al. 5 They found scaling properties which resemble those of various disordered materials. The height-height correlation function reveals a selfaffine behavior from the atomic scale up to Ϸ 2 nm. The corresponding Hurst exponent H is found to be about 0.72 ͑see Fig. 2 of Ref. 5͒. The authors pointed out that the selfaffine region includes the radius of the clusters r c Ϸ 0.5 nm, which are inherent in the structure. It is stated that the morphology of the fracture surfaces therefore does not reflect the cluster distribution. Thus, the influence of th...

Charge Balance Controls the (100) Surface Structure of the Ba8Au5.25Ge40.75 Clathrate

“…Focusing on the surface structure, a fundamental question relates to the interplay between the three-dimensional bulk structure described previously and the two-dimensional surface. While this question has been investigated for other types of complex intermetallic compounds like quasicrystals and their approximants, ,− surface studies of metal-based clathrate compounds have remained untouched. Several scenarios may occur, ranging from the preservation of the cluster substructure at the surface to surface reconstruction for covalently bonded materials .…”

Crack front propagation by kink formation

“…Hence, in general, fracture surfaces are not explicitely those of lowest energy or lowest roughness. Furthermore, due to the dynamic process, the crack tip heatens up and acoustic waves are emitted from the crack line as atomic bonds break [5,20,21].…”

“…Bending of the crack front is not restricted to the atomic level. In more complex systems like quasicrystals, containing clusters [5,20,21,[23][24][25] or inclusions, the crack front tends to avoid the obstacles and is deviating from a straight line on a larger scale.…”

Reply to “Comment on ‘Cleaved surface ofi-AlPdMnquasicrystals: Influence of the local temperature elevation at the crack tip on the fracture surface roughness’ ”

“…This second regime is fully understood using linear elastic fracture mechanics extended to heterogeneous media [9][10][11] and is reminiscent of a brittle failure. In their Comment, 12 Rösch and Trebin claim that the observed scaling behavior of QC fracture surfaces is compatible with a crack propagation between the clusters, and so, this observation is not in contradiction with a physical role of the clusters during failure processes. At first, the damage mechanisms-nucleation and behavior of dislocationssuggested by the scaling behavior of QC surfaces is discussed.…”