What is quasicrystal? I have it in mind that quasicrystal is the crystal with 5-fold symmetry, from the course of crystallography. It is well know that according to translational symmetry, only 2, 3, 4 and 6 –fold symmetry can be exist. For 5-fold symmetry, it is impossible to cover a floor simply using the pentagon with the same length of sides! So what is the structure of quasicrystals and how do they form?


I would like first to show how the 5-fold symmetry ‘full fill the floor’ in Fig. 1[1]. It is clearly that the crystal has regular arrangement, but it does not have translational symmetry, which means it can not be repeated by simply translating along certain directions. In the Fig. 1a, atoms actually form into different shapes of rhombus, and pentagons appeared in certain positions which are inconsistent with translational symmetry. Those rhombus arrange into icosahedras (2 pentagons, one in the front side and another on the back size), and construct quasicrystals.

Fig .1

Fig. 1 5-fold symmetry


Most of the quasicrystals (NOT all) are metastable phases. The first 5-fold symmetry was discovered by Shechtman in 1984[2] in Al-Mn alloy. Two main methods, rapid cooling and chemical vapor deposition, are used to achieve quasicrystals. It is difficult to control the cooling rate to get quasicrystals, as low cooling rate induced crystals while high cooling rate introduce amorphous phases. I remembered now when I prepared diamond through hot-filament CVD in CSU for my master’s degree, I have achieved 5-fold symmetry crystal grains!!

Why in CVD process diamond quasicrystals can be achieved? If I am correct, it should be caused by the phase transformation from the amorphous graphite. Comparing with amorphous, quasicrystal state is more stable and thus the amorphous graphite formed in HFCVD system tends to transfer into diamond quaicrystals. However, this metastable phase also tend to transfer into diamond crystal to reduce its total energy. Thus, any conditions (temperature, pressure, gas ratio……) varied in HFCVD system will cause certain phase transformations, and certain phase (diamond crystal, quaicrystal, or amorphous graphite) will obtained.


When we talking about quaicrystals, some basic scientific background should also mentioned. This kind of symmetry is inconsistent with lattice translations, and was first discovered by Shechtman in 1984[2]. It was developed with the electronic microscopy. In China, Kexing Guo found the 5-fold symmetry in 1985, and contributed a lot to this field.



[2] D. Shechtman, I. Blech, D. Gratias and J. W. Cahn. Metallic phase with long-range orientational order and no translational symmetry. Physical Review letters 53(20), 1984: 1951-1953