The IV-VI narrow band gap semiconductor GeTe undergoes a ferroelectric phase transition at about 600 K. At this transition the high temperature paraelectric cubic NaCl type phase undergoes a structural phase transition to the rhombohedral ferroelectric phase. In the high temperature phase all Ge-Te distances of the GeTe6 octahedra are equal whereas in the low temperature phase there exist two sets of Ge-Te distances: short and long. The phase transition was previously assumed to be a displacive type phase transition in which the short and long Ge-Te bond distances of the rhomboheral phase gradually approach each other with increasing temperature and become equal in the cubic phase. Recent EXAFS and PDF investigation of total scattering X-ray data suggest that the phase transition is order-disorder type. According to these investigations nothing at all happens to the short and long bond distances, they remain unequal in both phases in the local scale. Please note that the above two techniques probe the local structure. The phase transition does not occur at all in the local scale or the short-sighted local probe is in fact totally bind to probe the phase transition. The soft mode of the phase transition enters into the energy windows of the local probes and the local probe records soft mode dynamics as a static snap-shot because it does not analyze the energy. Can we then trust this local probe picture?
A short but incomplete answer would be as following:
To obtain a ferroelectric order, one needs positive and negative electric charges and off-centered ions. In GeTe there is a small difference between the electronegativities of Ge and Te, namely Te is more electronegative and Ge has a lower electronegativity, therefore a small part of 3% is ionic in nature and 97% of the bond is of covalent nature. Due to Ge off-centering, Ge-Te distances are divided into three short distances of 0.284 nm and three long distances (0.316 nm). The lattice constant of the rhombohedral structure GeTe is 0.4299 nm [1].
The Curie temperature can be calculated from long distances (0.316 nm) and ion Te2- Ge2+ radii as [2, 3, 4]:
TC=(pi*h2/2kB)*(1/(sqrt(MGe*MTe)*(3.16 Å-2.07 Å-0.87 Å)2))=643 K,
2.07 Å and 0.87 Å are radii of Te2- and Ge2+ taken from [5].
References:
[1] D. Dangić, A. R. Murphy, É. D. Murray, S. Fahy, and I. Savić Phys. Rev. B 97, 224106 (2018).
[2] S. Mushkolaj arXiv:0810.4265 (2008).
[3] S. Mushkolaj J. Mod. Phys. 5, 12, 1124-1138, (2014).
[4] S. Mushkolaj arXiv:0810.4088 (2008).
[5] R. D. Shannon Acta Cryst. A32, 751 (1978).
An additional solution is (Te-(Te-Ge))-electron collision along long distances (0.316 nm):
TC=(pi*h2/4kB)*(1/(sqrt(me*sqrt(MTesqrt(MGe*MTe)))*(3.16 Å)2))=609 K.
me, MTe and MGe are electron mass, and atomic masses of Ge and Te.
A rather recent article in the PNAS seems to be of interest, stating that the transition "is a major obstacle", see Zihang Liu et al., PNAS, May 22, 2018, 115 (21), 5332-5337 (www.pnas.org/content/115/21/5332). There are quite a few references to related articles on that transition in GeTe.
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