That's not what the article says. The alloy is harder. Not the same thing as stronger.
I did not miss the point. I am a working chemist with experience in inorganic solid state materials.You are correct that less crystalline materials can be "tougher" and less prone to fracture; this has been known in materials chemistry for decades. But your comment is irrelevant to this paper. They found that the ß-AuTi3 component of the material is responsible for its high hardness and do not comment on its toughness. Studies of the material surface and bulk composition show that this crystalline material represents the bulk of the compound.
Really this is very well known material science, not new physics. The unexpected hardness is really due to the improved chemical bonding environment in the ßAuTi3 crystalline phase providing greater than expected improvement.
I'll also mention this due to some earlier discussion in the thread: the new material has a much lower melting point than pure titanium despite high hardness.
It really is good work and will certainly be useful, but there is no way that this is "new physics for space technology". More like "New materials for bioimplant technology".
On another note, please familiarize yourself with quasicrystals. They really do mirror "penrose tilings" but are not related to this paper and I think you would find them quite interesting. Unfortuantely, most quasicrystalline materials have worse materials properties than existing substances and have not found much of a niche in applied work.
My interest is in the group theory (mathematics) of the bond structure as a quantum mechanical version of a "ring oscillator". So-called "dynamic stability".
Single crystals are by definition extremely pure and homogeneous samples. The paper measures the properties of ß-Ti3Au, a crystalline material, and used microtribology, XRD, and computational tools to probe its properties. By definition, materials measurements of single crystals do not depend on experimental factors like preparation method. Two single crystals of a compound will have identical properties, so long as they share the same crystal structure, regardless of how you got them.
Hardness is an intrinsic property of covalent crystalline materials, as laid out in reference 23 of the paper under discussion, arising from the net strength of the covalent bonds between atoms in a crystal lattice.
From a physical standpoint, a single crystal is an infinitely repeating spacial tiling of a defined unit cell.
In the paper, there is a lot of talk about valence electron density.
I think you are misunderstanding this term. It is just the total number of valence shell electrons per volume; when considered in combination with the band gap one can estimate the strength of the chemical bonds in a covalent crystal and, with some assumptions and approximation, an estimate of the hardness.
This work has nothing to do with defect density, higher-dimensional symmetry as found in quasicrystals, or "transitory valence states" (do you mean transition states?). Also I would say that the new physics you see in "valence grouping" has another name: century old types of chemical bonds, analyzed through a century old technique (x-ray crystallography).
QuoteMy interest is in the group theory (mathematics) of the bond structure as a quantum mechanical version of a "ring oscillator". So-called "dynamic stability".Can you elaborate on this?