Check the attached picture

Check the attached picture

I have no idea about what you are talking "C/2a" but have a look at this link.

There is no such thing as "lattice parameter for tetragonal structure is C/2a." This is meaningless. "C/2a" looks a bit like a space group symbol, but this one doesn't exist. It certainly would not be tetragonal as these would start with something like I4... or P4... In the monoclinic system the closest is C/2c or C/2m. Lattice parameters are not space groups. lattice parameters are the values of a,b,c, alpha, beta, gamma (depending on the symmetry group). In the PDF-2 database there is only one tetragonal pattern for Cu5FeS4 (014-0323) and  the quality is marked as questionable or blank. Its space group is P-421c. In additional to orthorhombic, there are also face centred cubic and one rhombohedral pattern for bornite.

Maykel Manawan has given you the formula to calculate the lattice parameters a,b,c for orthorhombic structures, but you will first need to index the pattern in order to discover the hkl values for each d. An easier way is to match your data with one of the patterns in the database to find which structure fits. Some software programs allow you to tune the lattice parameters in order to find a better fit. 

The answer given by Maykel Manawan gives the formulae to calculate the d-spacing of any set of planes defined by their Miller Indices (hkl) for various crystal structures in terms of the lattice cell dimensions a,b and c. Knowing the values of a,b and c of a specific material allows you to calculate the d-spacings for a given set of Miller indices using Bragg's law. The cubic structure is a special case where a=b=c and it is not necessary to know the value of a.

The question is confusing, as shown in the earlier answers but I assume you want to know the values of a,b and c for the orthorhombic phase of Bornite. These are given in the attached paper by Grguric (1998). The orthorhombic polymorph is in fact a pseudo-tetragonal with a=c and a not=b. Values given by Grguric are:

a = 10.950A

b = 21.862A

c = 10.950A

Space Group Pbca

Incidentally, if you take the formula for the d-spacing for the orthorhombic structure and set a=b=c you will arrive at the formula for a cubic material.

I hope this answers the question you are really asking.

Brian Lent

@ B. Lent:

a) I do not get it, why do you need Braggs law for the calculation of d for a given (hkl) if you have the lattice parameters? From my point of view you can calculate d_hkl for any  hkl without the use of Braggs law. 

b) I don't understand, why you don't need lattice parameter a for a cubic phase if you want calculate d_hkl?

@Brian Lent  @maykel manawan and @Ian J Slipper

Thank you for your complete answer.

I've calculated the a,b and c almost the same as Grguric 's work.

kind of thought and read in a thesis that in tetragonal phase the proportion of (c  devided to two multiply a) is a parameter named "lattice constant", and it is used to compare the selected phase with other similar tetragonals ...and so wanted to know the corresponding proportion for orthorhombic phase.

but as you explained, I guess I was wrong...

for exampe,as I mentioned I've read somewhere,In this thesis

Copper Zinc Tin Sulfide-Based Thin-Film Solar Cells 

Edited by

Kentaro Ito

Shinshu University, Nagano, Japan

at page 63-64 the proportion of c/2a is discussed

Reply to Gert Nolze’s questions:

My reply was in 2 separate but related parts which are both simply different views of the same topic and question. My first comment was to agree with the formulae presented by Manawan, which are used to calculate the d-spacing on the basis of the chosen plane and the unit cell dimensions. End of story, period, pointe finale.

The second part of my reply referred to the calculation of the d-spacing in terms of the Bragg angles obtained from XRD patterns, probably powder diffraction in this case. Pariya mentions an orthorhombic structure in the XRD of “one sample”. The implication is that “other samples” did not exhibit this structure in their diffraction patterns and so the problem becomes the classic case of identifying an unknown phase of an unknown material with an unknown crystal structure. This boils down to exactly what Ian Slipper mentions concerning indexing the pattern and comparing the data against a database or atlas of known compounds. If no match can be found this becomes a very tedious exercise of trial and error unless you have some reason to suspect or guess what the material probably is and for which the lattice cell parameters have been documented, and try to match the pattern with the various structure options. In this particular case values of the unit cell parameters are known (as given by Grguric). A powder XRD of this material (using a Debye-Scherrer camera, for example) should produce self consistent values of 2Theta and a, b and c.

I am also trying to rationalize the notation “C/2a”. The orthorhombic phase of Bornite is classified as “pseudotetragonal”. The values of a,b and c are almost exactly in the ratio 1:2:1. If we use the normal lattice parameters (a and c) for tetragonal symmetry we have a ratio of c/a = 2. In this particular case the tetragonal structure could be represented by 2 cubes of side =a placed side by side or one on top of the other to produce a special case of the tetragonal until cell. It is tempting to consider that this particular case is the origin of the “c/2a” notation with some possible typing error). If not, I can’t understand where it comes from; but I doubt if it is a major concern.

Finally, you write in your first reply to the original question “but have a look at this link”. The link does not appear to be in your answer, nor attached to it. Would you be kind enough to re-enter the link? Thank you.

Index XRD pattern first. select any three peaks whose (hkl) is known. three such equation 1/ d(hkl)^2 = h^2/a^2 + k^2/b^2 +l^2/c^2 for three peaks and three unknowns ( a, b and c) that can give you solution. Solve these equation for a, b and c.

I calculated the orthorhombic system of Nb2O5. Since you have only 3 variables (a, b and c) you have to use 3 indexed peaks to find the parameters. I recommend that you find a peak with only one muller index (Such as (100), (001), or something like that), in these peaks the interplanar distance will the same value of the lattice parameter in question. Then you try to do a system to find the other parameters.

My reseach work on preparation of zeolite from aluminte and silicate from different resources ,I find it difficult to diagnose it by measuring x-rays, The data that I have are 2 theta values, and the wavelength for Cu k alpha

Can you help me with that?