OK so here is some more Chemistry which I hope will also be useful to Oneworld.
As I have mentioned before, homegeny depends upon the scale you are working at.
So starting inside the atom things are definitely not homogenous.
There is a massive nucleus surrounded by a lot of empty space containing some electrons.
Uniformity is represented by saying that every atom of a particular type is the same as every other atom of that type. For example all hydrogen atoms are the same.
(for those who know about isotopes I am ignoring them)
If we use those atoms to build molecules then again individual molecules are not homegenous since they are often made of different types of atoms. Even those that are combinations of atoms of the same type are not internally homogenous, in much the same way as atoms. So one hydrogen molecule looks much like another.
We represent molecules by the 'ball and stick' models shown in exchemist's post, where the balls are individual atoms and the sticks represent the forces that hold them together.
And yes, these forces are entirely electrical in origin.
For small molecules again all molecules are essentially the same as with atoms and of definite composition, for example methane, ethane propane etc. Individual molecules can be isolated and, in principle at least, you could hand me one molecule of methane.
So a large aggregate (number) of them is homogenous in that there would be the same number per cubic centimetre for each cc on your grid.
Note that we live in a 3D world so we really need to work in terms of volume not area.
This is why I talk of 'bulk clay'.
However clays are in a different category.
That of super large molecules.
Super large molecules happen when a non specific number of atoms join together, unlike methane which always has 4 hydrogens joined to one carbon.
A diamond crystal is an example of this.
You could not, even in principle, hand me one 'molecule' of diamond. Another example would be a common salt crystal.
Clays are like this only their structure is vastly more complex.
But they all still can be represented by balls and sticks.
As regards the sticks or (chemical) bonds there are several types available.
The strength of these bonds are usually measured not in force units but in the energy needed to break them.
Here is a table
Now my table lists intramolecular bonds, which hold the atoms together in simple molecules
and intermolecular bonds which can bind simple molecules such as water to each other hydrogen bonds.
And yes the internal bonds in a single simple molecule are stronger than a single hydrogen bond, in general.
But in large molecules there can be many many hydrogen bonds holding the parts together.
For example in DNA the two strands or chains are held together by literally hundreds of hydrogen bonds this is called 'cross linking'
Clays come in sheets rather than thin strands so the effect is even more marked.
The subject is of such importance that books such as these have been written just about these clay minerals.
Now to return to my original contention.
For pottery the scale Chemistry works at is too fine and we should step up into the realms of mechanical properties.
Here the clay may be considered homogenous for Pottery purposes since it will have come from a relatively thin piece of clay.
I say this because geolically clay may have been laid down in very thick beds, up to thousands of metres thick.
When this happns the clay may be stratified because as the particles which form it settle out of the water the larger, heavier ones settle first so will be at the bottom of any strata which mark the start and finish of a period of formation.
But pottery type clays will be dug out within a couple of metre depths so will be homogenous.
Next post we can examine the mechanical properties that demonstrate this question of homogeny and uniformity.
You may have heard of the Atterberg Limits for field testing clays.