Re: The Forces Responsible for Shape Memory Alloys

There have been several questions concerning shape memory alloys and the 
crystal transformations that cause them to return to a previous shape, so 
I won't attempt to go over that information again.  Instead, let's 
examine atomic and molecular bonding to try and get a better 
understanding of the forces involved.

As you suggest, the properties of water are dominated by the hydrogen 
bonding that takes place between adjacent molecules.  Ithica City School 
District has provided a number of animated pages that illustrate 
different types of chemical bonding.  The following link: 

http://ithacasciencezone.com/chemzone/lessons/03bonding/mleebonding/defaul
 leads to 8 antimated pages that illustrate the different types of 
chemical bonds.  Other pages that provide further discussion concerning 
chemical bonding can be found at:  http://
www.newi.ac.uk/buckleyc/bonding.htm and  http://www.tcm.phy.cam.ac.uk/~cjp20/lectures/topic1.pdf

Let's examine the characteristics of hydrogen bonding in water as a way 
of understanding metallic bonding.  Oxygen is highly electronegative, in 
other words, it attracts hydrogen's one electron quite strongly.  As a 
result, the two hydrogens in a water molecule have a strong positive 
charge, since their electrons seem to spend most of their time hanging 
around the oxygen atom.  If water was a linear molecule, i.e. if the 
hydrogen atoms were on opposite sides of the oxygen atom, these 
electrostatic forces would cancel out.  But water, as most people know, 
looks like a Mickey Mouse head (oxygen as the round head, and the 
hydrogen atoms as two large ears).  So each water molecule has a strong 
electrostatic polarity because the water molecule is not linear.  The 
hydrogen atoms of adjacent water molecules are attracted to the negative 
oxygen atoms, and the negative oxygen atoms are attracted to the positive 
hydrogen atoms.

In metals, the electrons are not tightly bound to a particular atom.  
Instead the electrons move about pretty freely between atoms.  The metal 
nucleus has a positive charge because of the protons contained within the 
nucleus which attract any and all electrons near the nucleus.  So, in 
metallic bonding, the nucleus is similar to the hydrogens in a water 
molecule (because they tend to have a positive charge), and the electrons 
are similar to the oxygen (because it tends to have a negative charge).  
Both hydrogen bonding in water and metallic bonding are from similar 
electrostatic forces, with the only difference being that you have 
molecule to molecule forces in water, and atom to atom forces in metals.

Pure metals have unique properties because all of the atoms look alike.  
If you change the position of one row of atoms with respect to another, 
you can make this transformation without breaking any chemical bonds.  
This movement of one row of metal atoms with respect to another is 
referred to as "dislocation movement."  As a result, metals exhibit 
ductility, or the ability to bend prior to breaking.  One of the things 
that is done to strengthen metals is to combine different metals into 
alloys.  At this link: http://web.mit.edu/
3.091/www/pt/pert1.html you can 
see the change in atomic radius for each element.  When you combine two 
different metals into an alloy, different atomic radius makes it more 
difficult for the atoms to move with respect to each other; it makes it 
more difficult for a dislocation to move through the metal.

Let's think of an alloy as having a box full of baseballs with a few 
softballs thrown in.  The softballs pin the rows of baseballs together, 
preventing them from moving as easily as they would without the softballs 
being present.  If you have a certain ratio of baseballs to softballs, 
they will try and arrange themselves into a regular pattern.  A typical 
shape memory alloy may have an atomic composition of 50% titanium and 50% 
nickel.  The atomic radius of nickel is 1.24 angstroms and the atomic 
radius of 1.45 angstroms.  In this case, we can expect that in a shape 
memory alloy crystal, every other atom will be nickel, and every other 
atom will be titanium.

In the case of shape memory alloys, you can only move them a small amount 
before they no longer can remember their initial shape.  At

http://pubs.acs.org/cen/topstory/7906/7906notw1.html
and  

http://doc.tms.org/ezMerchant/prodtms.nsf/ProductLookupItemID/MMTA-0103-
we learn that shape memory 
alloys can only be deformed between 3 and 8% before they undergo 
inelastic deformation.  So in the case of shape memory alloys, the amount 
of deformation that they undergo appears to be too small for the atoms to 
actually jump from one position to another.  Instead, it appears that we 
can deform the alloy a bit, but the softballs are still close to the 
whole that they were budged out of and want to settle back into that hole 
if they are given a chance.  If you deform the shape memory alloy too 
much, the softballs lose track of the places they were located, and 
therefore, they cannot return to their initial shape.  So essentially the 
force generated by a shape memory alloy is caused by the attraction for 
metal atoms to settle back into their old, regular position, rather than 
being slightly displaced from that position.

Although I haven't checked it out, Phil, I bet that a shape memory alloy 
decreases in density a bit when it is strained, and increases in density 
when it returns to it's original position.

You might wonder how much force is generated by materials changing from 
one crystal form to another.  You mentioned that a force is generated 
when water freezes into ice.  The early settlers in Utah (and possibly 
other locations) mined granite blocks out of the mountains by drilling 
holes in the granite, filling those holes with water, and letting them 
freeze overnight.  The force of the water freezing and increasing in 
volume was sufficient to split the granite.  I will leave you with one 
last example.  Graphite has a density of 2.2 grams per cubic centimeter; 
diamond has a density of 3.5 grams per cubic centimeter.  To convert 
graphite to diamond, all one has to do is to put the graphite under a 
pressure of a bit over one million pounds per square inch and heat it up 
to increase the speed of the reaction.  So, I suspect that if you 
confined a diamond, if you heat it up to maybe 1500C, it will exert a 
force on its surroundings of more than a million pounds per square inch.  

Thanks for a most interesting question.