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Empirical Formula of Lattice Constant and Tolerance Factors of A2BSbO7 (A3+ = Y, Dy, Gd, Bi; B3+ = Fe, Ga) Pyrochlore Solid Solution

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Abstract

In this work, we apply the concept of tolerance factors (t) to pyrochlore solid solution, particularly when the B-site contains two different ions with different masses (as well as charge states) in the formula unit \({A}_{2}^{3+}{B}^{3+}{B}^{{{\prime}}5+}{O}_{7}\) as in the present sample of A2BSbO7 (A3+ = Y, Dy, Gd, Bi; B3+ = Fe, Ga). We examine the previous tolerance factor and proposed a model of lattice constant (a) that depends only on the ionic radii RA, RB (= \(\frac{R\left(Fe\right)+R(Sb)}{2}\) or \(\frac{R\left(Ga\right)+R(Sb)}{2}\)) and RO. Then we proposed an empirical tolerance factor (t), that depends only on the \({R}_{A},{R}_{B}\,{\mathrm{ and }\,R}_{O}\) of the constituent atoms. We discuss the structural stability field and property features of mixed pyrochlore oxide compounds before measuring their structural data as for the case of perovskites.

Graphical abstract

In the present work, we have proposed the empirical formula of lattice constant of A2BSbO7 (A3+ = Y, Dy, Gd, Bi; B3+ = Fe, Ga) of formula unit \({A}_{2}^{3+}{B}^{3+}{B}^{{{\prime}}5+}{O}_{7}\) and hence find the tolerance factor, which predict the structural stability field and property features of mixed pyrochlore oxide compounds before measuring their structural data as for the case of perovskites. Caption: Errors (in %) between the calculated and experimental lattice constants. In the above figure, we shown that the errors (%) between the calculated and experimental lattice constants found from empirical lattice formula a = \(\frac{8}{\sqrt{3}}\left[1.4474357143\left({R}_{A}+{R}_{O}\right)-0.42931\frac{{\left({R}_{A}+{R}_{O}\right)}^{2}}{({R}_{B}+{R}_{O})}\right]\) and Rietveld analysis of powder diffraction data respectively. The error of predicting for the lattice constant by Brik and Srivastava (J Am Ceram Soc 95:1454–1460, 2012) is moderately higher than the error (≤ 0.523%) obtains by our model for mixed pyrochlore oxides.

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Data Availability

We previously synthesized few iron-antimonate pyrochlores A2BSbO7 (A3+ = Y, Dy, Gd, Bi; B3+ = Fe, Ga) by the solid-state reaction method. Then we characterized through powder X-ray diffraction and its Rietveld analysis, SEM-EDAX, FTIR and Fe57 M \(\ddot{o}\) ssbauer spectroscopy [19]. The ionic radius of RA, RB, Sb and O are publicly available in the database of ionic radius, as part of the record: Acta Cryst. A32 751–767 (1976). Remaining parts of the Raw and Rietveld analysis datasets can be accessed on request from Dr. Yatramoham Jana, corresponding author of our previous papers [19, 20, 24]. All calculations and figures were done by using the publicly available Microsoft Excel office 2019 and Origin Pro 8 respectively. This paper is intended to serve as a reference for calculating lattice constant and tolerance factor of mixed pyrochlore, particularly when the B-site contains two different ions having different mass (and also charge state) in the formula unit \({A}_{2}^{3+}{B}^{3+}{B}^{{{\prime}}5+}{O}_{7}\).

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Authors and Affiliations

  1. Department of Physics, Krishnath College, Berhampore, Murshidabad, W.B., India

    S. N. Saha

  2. Department of Physics, Berhampore Girls’ College, Berhampore, Murshidabad, W.B., India

    P. Halder

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  1. S. N. Saha
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Saha, S.N., Halder, P. Empirical Formula of Lattice Constant and Tolerance Factors of A2BSbO7 (A3+ = Y, Dy, Gd, Bi; B3+ = Fe, Ga) Pyrochlore Solid Solution. J Chem Crystallogr 52, 371–377 (2022). https://doi.org/10.1007/s10870-022-00934-4

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