Crystal structure of bismuth-containing NdFe₃(BO₃)₄ in the temperature range 20-500 K

Neodymium iron borate NdFe₃(BO₃)₄ is an intensively studied multiferroic with high electric polarization values controlled by a magnetic field. It is characterized by a large quadratic magnetoelectric effect, rigidity in the base plane and a rather strong piezoelectric effect. In this work, the atomic structure of (Nd_0.91Bi_0.09)Fe₃(BO₃)₄ was studied by single-crystal X-ray diffraction in the temperature range 20-500 K (space group R32, Z = 3). The Bi atoms found in the composition partially substitute the Nd atoms in the 3a position; they entered the structure due to the growth conditions in the presence of Bi₂Mo₃O₁₂. It was shown that in the temperature range 20-500 K there is no structural phase transition R32→P3₁21, which occurs in rare-earth iron borates (RE = Eu-Er, Y) with an effective rare-earth cation radius smaller than that of Nd. The temperature dependence of the unit-cell c parameter reveals a slight increase on cooling below 90 K, which is similar to the results obtained previously for iron borates of Gd, Y and Ho. The atomic distances (Nd,Bi)-O, (Nd,Bi)-B, (Nd,Bi)-Fe, Fe-O, Fe-B and Fe-Fe in the iron chains and between chains decrease steadily with decreasing temperature from 500 to 90 K, whereas the B1(3b)-O distance does not change and the average B2(9e)-O distance increases slightly. There is a uniform decrease in the atomic displacement parameters with decreasing temperature, with a more pronounced decrease for the Nd(3a) and O2(9e) atoms. The O2(9e) atoms are characterized by the maximum atomic displacement parameters and the most elongated atomic displacement ellipsoids. The characteristic Debye and Einstein temperatures, and the static component in the atomic displacements were determined for cations using multi-temperature diffraction data. It was shown that the Nd cations have the weakest bonds with the surrounding atoms and the B cations have the strongest.