Why is there a difference ?Melting Point of Lead & Tungsten: Find RMSA

[ibysaiyan]

Homework Statement

Hi all, I have a question which is regarding melting point. I know that lindemann's criterion doesn't actually describe the phenomena of melting but is an approximation of what maybe occurring/ an intuitive approach.

So the question is in a tabulated form for lead and tungsten ( assuming crystals) with Youngs modulus, Molar volume and melting temperature given and they want me to describe the terms / details quantitatively.

I have assumed that they want me to essentially find out the root mean square amplitude of the vibrations which will eventually give me a separation distance (not equlibirum) that needs to be at least 10% of a fraction to the inter atomic distance.

Homework Equations

Root mean square of amplitude of atomic vibrations is given by the following equation:

[itex]\sqrt{<u^2>}[/itex] = [itex]\sqrt{KbT/D}[/itex] where D = spring constant.

D = Y[itex]r_{0}[/itex]

The Attempt at a Solution

Data given for lead is:

[itex]T_{m}[/itex] = 3650 K , Molar volume : 0.0953m^3 , Young's modulus: 36*10^10 N/m^2

My approach involved finding out the vibrational energy by kbT. Then equating that to 1/2kx^2 ( here 'x' = r-r0) but first I need to find out spring constant k and separation at equlibirum.

To get 'k' I have used the following equation:
k= Y[itex]r_{0}[/itex]
and for [itex]r_{0}[/itex] , Molar volume = [itex]N_{a}[/itex]b* ([itex]r_{0}[/itex])^3Is the above approach right ? is this how I am mean't to do it ?

Thanks for your replies and merry christmas !Edit: Also one more thing which confuses me slightly .. I know that lindemann's constant is a value which's usually same i.e doesn't vary but I have seen different variation to get it... is the rms of the amplitude of the vibration = C * interatomic distance ? can someone clarify this for me as well. Thanks!

EDIT2: If you have a look on the following links.. you will notice that there is a difference of powers for the mean square amplitude value <u^2> = ..
http://phycomp.technion.ac.il/~phsorkin/thesis/node4.html
http://en.wikipedia.org/wiki/Melting_point

 

[ibysaiyan]

Can someone clairfy to me when exactly does melting occur. Is it when the root mean square of the amplitude gets to about 10% of the inter atomic distance or is it just the mean square of the amplitude ?

Also to find the inter atomic distance.. is that same as 'r0' separation of atoms at equilibrium ?

<u^2> = Cl^2 * a^2 is this the right expression ? Google hasn't helped much on this but has shown some conflicting form.
Thank you..