Maltese Cross, Rock Salt and Inter-ionic Distance - Episode I

The common salt that we use daily to make our food palatable contains a wealth of scientific information which an inquisitive mind can explore without end. The beauty and staggering amount of hierarchical complexity even of simple things is what make Physics an enchanting subject. One can't imagine how much informative even a bit of work would turn out to be in Science and especially so in Physics.

A few days ago, at the beginning of Pongal holidays, I felt like growing NaCl crystals and I believed what the heck? it should be very simple. I requested my better half for a lot of  rock salt ( we call  salt in impure form just taken out of sea without any further ado in Tamizh as கல் உப்பு). She looked at me askance. Then with a creepy smile I explained to her What I was going to do. Accustomed with my sudden fits of scientific inquiry she provided me with precious table salt. I took a beaker with ~150 ml potable water and boiled it bubbling hot and added the salt until the salt refused to be dissolved further (that is what is called in scientific mumbo jumbo  as Saturated Solution). Well I left that beaker undisturbed for a while until all the dirt and dust settle down and poured an aliquot of that in petri dishes. 



NaCl Crystal with Maltese Cross Pattern


Another view of NaCl Single Crystal clearly Showing the Sides
I was a bit disappointed as I expected a perfect cube but instead I got a tetragonal one. But It seems to me to be a possible habit that can be obtained by stacking unit cells of NaCl. It is nice looking with a beautiful Maltese cross pattern inside.


A Maltese Cross Batch

How Beautiful ! But What causes this strange looking pattern. I mused over it for a while. A possible explanation is that growth of NaCl crystal is faster along edges and corners resulting in a cubic shell within shell within shell morphology and Maltese cross pattern. Well this is a sort of itching point for me. So let me step over this and go on to tell you what I did next. 

I took the crystal to my department lab (Under Graduate Physics Laboratory, Dr.Zakir Husain College,Ilayangudi) and measured its dimensions using a Traveling Microscope with a least count of 0.001 cm. These dimensions are:

KAZ Measuring The NaCl Crystal Dimensions

All the World's a Stage Including My Mobile

Breadth x Width x Height dimensions of the crystal were measured to be 0.487 cm x  0.487 cm x 0.247 cm ( I felt a bit lazy and measured the breadth or width only and took them to be equal as the crystal seems to have a square face. But this should never be done in any serious scientific pursuit ).Then multiplying these together gave the volume of the crystal as  $5.86 \times {10^{ - 8}}{m^3}$.(CAUTION: When applying numbers to any equation or formula the resulting numerical value should be rounded off to have the same number of significant digits as the least number of significant digits in the numbers we are applying. THIS IS MOST IMPORTANT and Unfortunately also MOST IGNORED. Read HERE).

Then I weighed the crystal using the digital balance in the lab.It has accuracy to only three decimal figures and when put the crystal on the weighing stage the reading danced between 0.12 g and 0.13 g. 

Weighing the Crystal - Reading Danced Between 0.12 g

and 0.13 g But Never Settled Down
So, I took the weight to be 0.13 g as it seemed a bit to be more lingering over this value. The density of NaCl is then obtained as,


But here again the ghost of significant digits haunts us. The mass of the crystal has been determined to only two significant digits. So our answer has to be rounded off to two significant digits too. With this in mind  we have $22.00 \times {10^2}kg.{m^{ - 3}} = 2200kg.{m^{ - 3}}$. The reported value is $21.65 \times {10^2}kg.{m^{ - 3}} = 2200kg.{m^{ - 3}}$ to two significant digits which coincides exactly with our experimental value. Remarkable achievement instead of my crude methods. Must be a fluke?. OK, it does not matter. Let us pass on to the next step.Let us calculate inter-ionic spacing of NaCl  crystal. Please Wait for More.

(Continues...)