The value of Z denotes the number of chemical formula units per unit cell. For example: The Z is 6 for R3c sapce group. I mean there are 6 chemical formula (e.g. BiFeO3) in a hexagonal unit cell (R3c) with a=b= 5.56 and c = 13.8 angstrom.  If we transform it in other crystal system, the Z value changes accordingly lattice parameters also change.

The value of Z denotes the number of chemical formula units per unit cell. For example: The Z is 6 for R3c sapce group. I mean there are 6 chemical formula (e.g. BiFeO3) in a hexagonal unit cell (R3c) with a=b= 5.56 and c = 13.8 angstrom.  If we transform it in other crystal system, the Z value changes accordingly lattice parameters also change.

Very interesting question. I never seen an equation relating Z and lattice parameters. As Dr Kumar signals  "The value of Z denotes the number of chemical formula units per unit cell" which can be an enter or fractional number.

Obviously, there is a direct relationship between Z and lattice parameter. For example, in the before mentioned case of a perovskite with R3c using hexagonal axis you would obtain a=b~5.5 A, c ~ 13.5 A and a Z = 6, but if you change to a rhombohedral axis then Z = 2 and a=b=c ~ 4 A!! (this is a tricky example, since this particular space group has 2 possible representations which is not a common thing). This is clear, you need more space to include more atoms, but sadly, as far I can remember now, there is no direct law between both.

If you know how the atomic species are ordered in your compound, you could have a rough approximation by the rigid spheres model. That is, you put an rigid sphere with the corresponding ionic radii on each atomic position until you fill your unit cell, but with the constrain that you have to obtain the most compact structure (that usually means that neighboring atoms are represented by touching spheres). In this way you could made a rough relationship between Z and lattice parameter.

I'm stressing the word 'rough' because this rigid spheres model is based on ionic radii of the atomic species and that would only be true for pure ionic compounds.

Hope this helps

The characteristic of a material changes as its lattice structure gets changed. Thus to describe crystallography at cell level, in turn,  behavioral part and has different formula. This is being provided by Z value

C3A (calcium aluminate) has formula unit Z=24 and lattice constant a= 15.259 A. I can not take lattice constant value of this directly. So, I thought there must be some relation between formula unit and lattice constants. As you may see in gamma-Al2O3 case, which is defect cubic spinel structure (space group Fd-3m and formula unit 8), with lattice parameter a= 7.924 A, but still we are using a= (7.924 / 2) A. Why should we divide it with 2 and what integer should I take to divide lattice constant of C3A depending upon formula unit?

I am a bit puzzled regarding the statement: "The Z is 6 for R3c space group." From my point of view this is the multiplicity of the general position, but Z can be a part of 6 (e.g. bcc iron where Z=2 wheras the number of general positions is 96) or a multiple of 6.  Other examples are subgroup relationships where the lattices keep constant but the symmetry is changing. This means Z keeps unchanged but the number of equivalent formular units increases.

With respect to the Z and the lattice parameter: Assuming a quite stable density for a phase it should be possible to predict the required volume, and considering a cubic symmetry it is even possible to predict a lattice parameter. However without any other knowledge it is impossible if you have only one number. In your example of spinel which is AB2O4 you compare two different phases with different formulars and different densities. There are numerous phases having the same formula unit=2 and all have (totally) different lattice parameters.

Relation between Z and cell parameters includes density and molar weight.

The number (Z) of formula units in a unit cell depends on the density and on the cell volume, hence the answer to the original question is Yes: there is a relationship between number formula units and cell parameters (in terms of cell volume) and it depends on the density (i.e. how closely packed the atoms are in the formula unit (bonds) and their atomic weights).

Hi Romano, how do you describe the lattice parameters of lets say a orthorhombic cell using Z? :-) As I mentioned, this is only possible for cubic phases where you only have one lattice parameter. Well, she has... Can you solve her specified problem (see 3 comments above yours)?

Please Note: I was talking about epitaxial gamma-Al2O3 film on Al substrate.

How did you measure the epitaxy? I am not an expert for this system but this means that and fcc packing of Al has an epitaxial growth with an "fcc" packing od O-atoms? sound at least unexpected to me.

" Is there any relation between formula unit (Z) and lattice parameters? "

Yes, Here's a direct illustration of NaCl which has Z = 4.

NaCl is a cubic (F m -3 m) with a = 562 pm and density = 2.19 g/cm^3

1.  volume =  a^3 = 1.775 x 10^-29 m^3

2.  mass= 1.775 x 10^-29 m^3 x 2.19 g/cm^3 x (100 cm/m)^3 = 3.88725 x 10^-22 g

3.  g to mol = 3.88725 x 10^-22 g x  (1 mol/58.44 g) = 6.6514 x 10^-24 mol

4.  formula unit = 6.6514 x 10^-24 mol x (6.022 x 10^23 formula unit/mol) = 4

In structures composed of single type molecules which has no symmetry, the asymmetric unit is usually a molecule, a "formula unit", or occasionally two or more molecules which differ from one another in orientation or conformation. When it has symmetry which conform to crystallography symmetry, it may occupy a special position, and the asymmetric unit will be a half of the molecule or even smaller fraction. For example NaCl (Fm-3m) has asymmetric unit of Na4Cl4 (Z = 4), Mg (P63/mmc) has asymmetric unit of Mg2 (Z = 2), but BaTiO3 (P4/mmm) has asymmetric unit of BaTiO3, but Z = 1, why ? If u can answer this u also can answer why ur Al2O3-gamma (Fm-3m) has Z=1 ;-)

Maykel Manawan: But in gamma-Al2O3 case, formula unit is 8.

Dear Aditi, gamma-Al2O3 has few polymorph, here i attached some of them, I picked face centered lattice only. I think 1 of them is ur structure.

Al2O3-gamma-Fd-3m(7.948) file is the structure I was talking about.