Formation Criteria Of Ternary Quasicrystals And Their Applications In The Al-Ni-Fe And Ti-Zr-Ni Systems

Quasicrystals (QCs) are Hume-Rothery phases stabilized by interactions between Fermi surfaces and Brillouin zone boundaries. It is known that quasicrystals and their approximants are located near straight lines with constant e/a ratios in ternary phase diagrams. This is the e/a-constant criterion for the formation of QCs. The present investigation aims at revealing quantitative criteria that can help locate the compositions of stable ternary quasicrystals.We first focus on the e/a-constant feature of ternary quasicrystalline phase diagrams. We found that QCs are grouped into three kinds according to their e/a ratios, i.e. the Mackay-type stable QCs containing small amounts of transition metals (TM), with e/a ratios close to 1.86, the Frank-Kasper-type QCs containing no transition metals, with e/a ratios close to 2.10, and the Frank-Kasper-type QCs consisting entirely of transition metals, with e/a ratios close to 1.20. We further notice that a ternary QC, its related binary QC, and the third elements are located along a straight line in a given ternary phase diagram, termed e/a-variant line. This line indicates that the ternary QC and the binary one are inter-related by common building blocks. Therefore, the ideal composition of a ternary QC is at the crossing point of the e/a-constant and the e/a-variant lines.In phase diagrams, binary approximants of the ternary TM-contained Mackay-type QCs are located at peritectoid points, which coincide with the extreme points of the e/a-constant line. At the same time, the composition of some binary QCs can be calculated using the icosahedral-glass close-packed model.The appropriate third element in favor of the formation of a stable QC must meet the following conditions: first, it can change the e/a value to the ideal one (1.86), second, the atomic size should be close to that of the smaller element in the binary QCs. For the TM-free Frank-Kasper-type QCs, the e/a-constant line can directly be obtained with the ideal e/a ratio, and its e/a-variant line can be considered as an atomic-size-constant line which is defined by the 1/1 Frank-Kasper-type approximants.The above phase diagram features of quasicrystalline alloy systems can be regarded as empirical formation criteria to optimize QCs' compositions and to search for new QCs.These criteria have been applied to the Al-Ni-Fe system, where there are ambiguities over the exact compositions of the stable ternary QCs. Two alloys Aly2.5Fei4.sNiia and AlviFe5Ni24 were prepared and their structures were analyzed. The former alloy mainly consists of two phases: the hexagonal AlsFeNi and decagonal quasicrystal D phase. The latter alloy contains three phases, hexagonal Al3Ni2, orthorhombic AlsNi, and decagonal quasicrystal D'. The two decagonal phases with different measured compositions, D-Alva.eFei^Nin.g andin(Abstract)D'-A170.5FeioNii9.5, correspond respectively to the AlFe-based and the AINi-based decagonal phases. They are located at the cross points of e/a-constant and e/a-variant lines, as expected.According to these empirical rules, a wide quasicrystal-forming composition zone, (TixZr10o-x)ioo-yNiy( 43.75