The CN is 2, as each O is at the edge of a TiO6 octahedron. Therefore, each O is shared by 2 Ti, hence CN = 2. Ba is not coordinated with O, but is present for compensating the negative charge of the TiO6 octahedron.

Alain

 CN is 3 .Each O is shared by one Ti

BaTiO3 represents the perowskite struture type.

The coordination number in crystaline solids is always a chameleon. The question may be answered in serveral ways, depending on how you define "coordination".

Just regarding the coordination by Ti(4+), the coordination number of the oxide ions is 2. Each oxide ion has two Ti(4+) in linear Ti-O-Ti coordination. This answer is surely reasonable.

But you may give another answer. In perowskite, both the Ba(2+) and the O(2-) together form a cubic closest packing of spheres. This just means that the coordination of each O(2-) ion is 12 in cuboctahedral form, it is 8 other O(2-) ions and 4 Ba(2+) ions. Ti(4+) is embedded in this packing in octahedral holes, in just that holes, formed by six oxide ions. For an individual O(2-) ion the overall coordination is thus 14, it is 8 other O(2-) ions, 4 Ba(2+) ions and two Ti(4+) ions.

Both answers are correct. But would you like a third answer? You may say, answer 2 is silly, because here anion-anion-coordination is taken into consideration. But are are you allowed to neglect the Ba(2+) - O(2-) cation-anion interactions? Surely not. So you may come to answer number three: each O(2-) is surrounded by two Ti(4+) and by four Ba(2+) forming an octahedron giving coordination number 6.

As you can see, many answers for a superficially simple question. We come back to the beginning point: what is the "coordination number"? Set up a definition and you can choose the suitable answer.

Mr. Mahmood,

In term associated with CN or coordination environment, or interaction of a central chromophore ion, usually metal ion with neighbouring disposed atoms/ions, affecting the electronic states of the central one, the crystallographic files [Refs 1 and 2] (attachment) have shown TiO6 unit (almost perfect Oh), BaO12 unit (polyhedron) in hexagonal P63/mcm, tetragonal P4/mmm and cubic Pm-3m crystal structures as well as BaO10 unit in tetragonal P4mm structure.

In terms of coordination chemistry if we have described "O" as central chromophore or this atom, which electronic states are perturbed under influence of mentioned above neighbouring atoms/ions, than in P4/mmm, P4mm and Pm-3m structures you have OTi2Ba4 - unit in a trans-disposition in classical from a coordination chemistry point of view "term" for Oh, while in P63/mcm structure you have two non-equivalent Os, having following coordination environment: OTi2Ba4O'8 and OTi2Ba4O'7. Because of you have O...O' 2.835 and O...O' 2.774 A interactions between so-called central "O" in your case and corresponding 8O and 7O-atoms in those polyhedron "chromophores" again speaking in classical term. In other words you have "CN" = 6 (for tetragonal and cubic structures) and "CN" = 14 and 13 (hexagonal structure). There are real moderate - to - weak interactions in the crystals between the charged species, despite the fact that you have not covalent Ba-O, but those interactions affect electronic states of both Ba/O centers.

You could pay attention to our papers [Refs. 3 and 4], where we have correlated crystallographic with mass-spectrometric data of organic ionic species [Refs. 3 and 4]. In gas - phase those salts have yielded to NH4+ adducts, where have described the effect of coordination environment around N-center on thermodynamic stability and electronic states of non-metal atoms/ions of two possible [M+H...(NH3)]+ or [M...(NH4)]+ structures of those adducts stabilized under ESI-MS experiments.

You could follow also discussion: "How can I use NBO/NPA analysis to determine intra-molecular hydrogen bond strength?" (https://www.researchgate.net/post/How_can_I_use_NBO_NPA_analysis_to_determine_intramolecular_hydrogen_bond_strength) on organics, too, but associated with coordination environment around N-center and it effect on macroscopic properties of the systems.

Please bear in mind, that I have not checked occupancy of ions of structures in Refs 1 and 2, so that the shown values (attachment) are if it is 100 %. If however you have half- or other % occupancy, that those values should be corrected accordingly. Even you can obtain a non-stoichometric balance of "chromophores", meaning OxTiyBazO'k.

Please bear in mind as well as describing labelled schemes in the attachment, that coordination environment (or CN) is not equivalent to the operation of symmetry determining the crystallographic position of the atoms within the frame of the crystal, meaning that O1...O1 is not interaction of O1 with itself or disordered O.

[Ref. 3] Ivanova B., Spiteller M. (2013) Factors stabilizing the gas-phase ionic species of crystals of organic salts - Experimental and theoretical study, Journal of Molecular Structure, 1036, 226-234

[Ref. 4] Ivanova, B.; Spiteller, M. (2014) Simultaneous quantitation of naturally occurring insecticides, acaricides, and piscicides in rapeseed oil by UV-MALDI mass spectrometry, Journal of Food Measurement & Characterization, 8, 15-28

@Johannes Beck 

thank you very much.

I agree with you " The coordination number in crystalline solids is always a chameleon. " 

@Bojidarka B. Ivanova

thank you very much Dr.Ivanova 

As you know that BaTiO3 and the other peroviskite [ ABX3 ] have many phase transition with temperature Rhombohedral - Orthorhombic - Tetragonal - Cubic - Hexagonal .

Taking into consideration:

1- The Coordination Number ( CN ) is very important factor to determine the ion radii . http://www.geo.arizona.edu/xtal/geos596a/ACB25_925.pdf 

http://abulafia.mt.ic.ac.uk/shannon/radius.php 

2- Goldschmidt Tolerance Factor ( GTF ) is an important factor to estimate the crystal structure . also many researchers think that the phase transition of peroviskite family is related to the change in the value of GTF.  https://en.wikipedia.org/wiki/Goldschmidt_tolerance_factor

3- As a result of 1 & 2  . Any change  in the value of CN leads to increase or decrease the Value of GTF which lead to phase transition {  rhombohedral - orthorhombic - tetragonal - cubic - Hexagonal .} . 

4- The CN in crystaline solids is always a chameleon

5- So 1,2&3 lead to think that CN play an Important factor in the phase transition of perovikite . 

I think rather than being deceived by "Coordination number" and different ways to justify different answers, there is a requirement to write/refer the complete and unambiguous information on this.