X-ray Cystallography -Calculating Density

[Losh]

Hi,

In our lab session on x-ray crystallography we found values for d, the plane separation using Bragg's law and from that we are supposed to find the density of the crystals (Lithium Fluoride, Rubidium Chloride and Potassium Chloride). However, when we calculated the densities they were much higher than the accepted values. I suggested that this might be because we assumed that the unit cell contains no empty space, so I recalculated the densities assuming that about 25% of the cells are empty (packing efficiency for face centred cubic crystals is about 75%) and therefore has no mass and got values much closer to what would be expected.

My lab partner thinks I'm wrong and that we don't need to consider empty space though so I'm not sure whether this is correct?

Thank you in advance for any help.

 

[Bob S]

How many atoms of potassium and chlorine are in a potassium chloride crystal that weighs about 75 grams?

Bob S

 

[Gokul43201]

Losh: Please show the complete calculation - it's not clear what steps you took to go from d-spacings to the density.

 

[Losh]

Ok. We were told that one side of a unit cell of any of the crystals was 2d so we calculated the volume of a unit cell from that (2d)^3. Then we calculated the mass of a unit cell by using the fact that there are 4 atoms of each of the 2 elements in 1 unit cell and by calculating the mass of one atom of each element from data tables of atomic weight and then summing to get the total mass of the atoms in the cell. Then we found density by doing M/V.

I thought we might have to account for the empty space in the cell though since the mass we used was the total mass of the atoms in the cell but the volume we used was the total volume with empty space included? I don't know it may just be me being stupid!

Thanks again.

 

[Gokul43201]

Let's back up a couple of steps. There is not a single unique value of d, which is the spacing between a set of parallel planes, and for different families of planes you have different d-values. Each value is derived from a specific reflection, using Bragg's Law.

So, to start over, what value of d-spacing did you use for the calculation, and why? Did you index the peaks, etc. Please start from the beginning - it's difficult to diagnose where the error may be without the whole story.

 

[Bob S]

Back to my previous question, rephrased. What is the gram-molecular weight of the potassium chloride molecule, and how many molecules are in it? How many atoms are in it?

Bob S

 

[zhanghe]

Dear Losh,
let the calculation method alone first, the way you understand the "density" is wrong, the density is just mass/volume, please tell me total mass and total volume, i will give you the density, i don't care about the volume is empty or half empty or not, so your partner is right. According to volume is from XRD, i guess there must be something wrong with the "d", please pay attetion to the extinction effect in Brag, sometimes you get (100) is not real (100), for example, maybe in fact (200), so the "d" may be underestimated.