Figure 1 shows a unit cell of barium titanate Ba Ti Figure 1 Unit cell of barium
ID: 565676 • Letter: F
Question
Figure 1 shows a unit cell of barium titanate Ba Ti Figure 1 Unit cell of barium titanate a. How many Ba, Ti and O ions are there in the unit cell? Explain how you arrived at your answers. (5 marks) b. The formula of barium titanate is BaTIOs. How many formula units are there in the unit cell? (2 marks) c. What is the coordination number and geometry around the titanium ion? (2 marks) . (3 marks) 401 pm. What is the distance between the centre of a titanium ion and he unit cell of BaTiO3 has length a the centre of an oxygen ion? ii. The ionic radius of T-is 60.5 pm. The ionic radius of O2-is given in the Data Book. From the ionic radii of Tit and O2- calculate the distance apart these ions would be if they were hard spheres and just touched. ili. How might your answers to () and (i) relate to the ferroelectric property of BaTiOs?Explanation / Answer
The formula is BaTiO3
No of Ba atoms at corners - 8; contribution- 1/8
Total no of Ba = 8*1/8 = 1
no of Ti atoms -1 present in center of unit cell; toatal ccontribution is 1
No of Oxygen atoms per unitcell - 6; they are face centered so contribution- 1/2
Total no of O = 6*1/2 = 3
So the final structure of unit cell is BaTiO3.
2.
In one unitcell there is only one molecular formula i.e. BaTaO3 is there.
3.
The following formulas show how the sphere (atom) radius, r, is related to the unit cell edge length, a = (root)8r
a = 401 pm; r +?
r = a/(root)8 = 401/2.82 = 141.7 pm
4. O2- size = 120 pm
Ti4 size is 60.5 ppm
r
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