Electronic Supplementary Information (ESI)
First-principles study of Sc1-xTixF3 (x ≤ 0.375 ):
negative thermal expansion, phase transition and
compressibility
Lei Wang, Cong Wang*, Ying Sun, Sihao Deng, Kewen Shi, Huiqing Lu, Pengwei
Hu, and Xiaoyun Zhang
Center for Condensed Matter and Materials Physics, Department of Physics, Beihang
University, Beijing, 100191, China
Calculation details
The supercell method is often used to model the structure of doped systems.
Doping concentration varies with increasing dopant atoms. The ordering of dopant
atoms leads to the various doping configurations and hence could more or less affect
the computational results. Normally, large supercell can better describe the doped
systems. While, the larger supercell, the more complex doping configurations. In our
work, combining with the calculation accuracy and efficiency, we choose a 2×2×2
supercell to model the structure of Sc1-xTixF3 (see Fig. S1). All the configurations at
each doping concentration (x = 0.125, 0.25, 0.375) are taken into consideration.
When one Sc atom is substituted by Ti atom, there are four possible doping
locations which are marked with I, II, III, and IV (I. body center; II. vertex; III. face
center; IV. edge). It is found that the energies of these four doping configurations are
almost same (see Fig. S2). The I doping configuration is selected as the research
object for Sc0.875Ti0.125F3.
Two Ti atoms replace the Sc atoms, forming seven possible doping configurations.
The doping positions include that: a. one body-centered atom + one vertex atom; b.
one body-centered atom + one face-centered atom; c. one body-centered atom + one
edge atom; d. one vertex atom + one face-centered atom; e. one vertex atom + one
edge atom; f. two face-centered atoms; g. two edge atoms. We find that the
energetically favorable ground states are the b and e configurations whose energies
are equal to each other (see Fig. S3). In this article, the research of Sc0.75Ti0.25F3
focuses on the b doping configuration.
Three Sc atoms are substituted by Ti atoms, there will be eight possible doping
positions, which are denoted as: 1. one body-centered atom + one vertex atom + one
edge atom; 2. one body-centered atom + one vertex atom + one face-centered atom; 3.
one body-centered atom + two face-centered atoms; 4. one body-centered atom + two
edge atoms; 5. one vertex atom + two face-centered atoms; 6. one vertex atom + two
edge atoms; 7. three face-centered atoms; 8. three edge atoms. Among all of the
considered configurations, the fifth one (one vertex atom + two face-centered atoms)
exhibits the lowest energy and hence is chosen as the ground state configuration for
Sc0.625Ti0.375F3. (see Fig. S4).
Figure S1: (Color online) a 2×2×2 supercell of cubic ScF3.
Figure S2: (Color online) Total energies as a function of volume for various doping
configurations in Sc0.875Ti0.125F3.
Figure S3: (Color online) Total energies as a function of volume for various doping
configurations in Sc0.75Ti0.25F3.
Figure S4: (Color online) Total energies as a function of volume for various doping
configurations in Sc0.625Ti0.375F3.