Many artists tend to view metal clay as a bit of a voodoo material. They have a recipe that works (usually the manufacturer's recipe), and superstitiously follow it exactly, right up until it doesn't work or they need to do something different, and then they're at a loss. Understanding the process of sintering can help demystify firing metal clay, and allow us to approach new situations with an educated guess as to what might really work.
Composition of Metal Clay
Metal clay is composed of super-fine particles of metal plus a binder. The metal particles may be all the same identity, such as in silver or copper clay, or they may be a mixture of different metal powders in the cases of bronze or other alloy clays. The binder is present for the express purpose of making the clay malleable, amenable to shaping in various ways. Once the binder burns off in the kiln or torch, what's left is essentially a shape composed of tiny pseudo-spherical particles of metal with lots of air space between them. As you well know, filling a vase full of river rocks leaves a lot more air space than filling that vase with sand. Smaller particles pack more closely, which explains the drive over the years to reduce the particle size of the metal clays. As we see, this has desirable results in terms of strength in the finished product.
Between the point that the binder burns off and the finished product comes out of the kiln, a process called sintering takes place. This is very much like what happens when you dump your ice container into the sink. The individual ice cubes stick together, with holes remaining between the cubes. However, the ice in your sink is above its melting point, so it will eventually puddle in the sink. Ice does sticks together even below its melting point, as is obvious in ice makers left for some time. How does sintering actually happen?
Metal Atoms Moving
The key to understanding sintering is energy. Those particles of metal are actually composed of even smaller balls called atoms. The atoms in the center of the particle are happily surrounded by other metal atoms, but the atoms at the surface only have neighbors below and maybe some to the side. Each atom wants to be surrounded by other atoms, but the surface makes that impossible. Even so, the atoms will try to arrange themselves so as to maximize the connections to neighbors and minimize exposure to the outside world. Those little critters are very social and like to be in the midst of a group. Yes, the atoms can move, IF they have energy.
Consider an empty shoebox sitting on a table. Now pour a bowlful of marbles into the box. The marbles are just a mad jumble, probably mounded up in the center. If the box is jiggled slightly, the marbles will start to move, rearrange and pack tightly. The mound in the center will slowly disappear and the surface will flatten. Those marbles at the top of the pile, touching only a few neighbors (three probably), will eventually wind up in a flat layer surrounded by a hexagon of six neighbors. The atoms deeper down may have neighbors below, above, and in the same layer for a total of twelve. That jiggle applied to the box is heat -- energy that allows the marbles to move.
Now suppose one lonely marble is placed on top of a nice flat, but incomplete, layer. When the jiggling starts, that marble will run around on the surface, here and there, until it finds a hole, whereupon it will drop into the layer with all its friends. Happiness!
What if more heat is added, by jiggling the box more energetically? Then the packing down will happen faster. Unless too much heat is added, at which point the marbles will start to pop out of the lower layers onto the top surface rather than always wanting to drop into holes. That's the melting point -- when so much heat is added that the marbles don't care about staying together nicely. Even more energy might cause atoms to fly out of the box!
When a metal clay project is formed, the metal grains of atoms are separated by binder, touching each other occasionally. The atoms that exist at those points where the grains of metal touch are happier than the atoms off on the surface by themselves. When heat is added, those surface atoms wander over to hold hands with the larger group, forming a neck between the particles. Eventually the particles become more and more connected, and the holes between them become smaller. Atoms migrate from the surface to fill the voids, which causes shrinkage.
As long as energy is available, the movement continues. First the particles stick together, and then it takes time and more energy to fill in the voids. This is why metal clay fired at low temperature or for short times isn't as strong -- the connections within the piece are smaller. For the strongest, densest material higher temperature and longer firing times are advisable.
From this understanding of what really happens on a microscopic level during firing, we can make predictions about what might happen in new situations. Heat provides energy for the connecting process to happen and speeds up the work, so increasing the temperature is good, right up until the point that melting is a concern. Because of inaccuracies in thermocouples and variations in heating distributions within a kiln, it's not wise to try to get too close to the actual melting point. That's why the top firing temperature recommendations are typically at least 50 degrees below the material's melting point.
Even so, at lower temperatures, as with stones or glass, sintering will happen but more slowly. It's wise to fire longer if using a lower temperature. Just because the manufacturer's directions give a certain temperature and time doesn't mean that other choices won't work. Just follow the general guidelines -- the lower the temperature, the longer the time. Firing longer than the recommended time is not an issue, and is probably beneficial, although at some point the tradeoff becomes pretty marginal.
With this picture of the microscopic process, we can also start to understand why sintering on the outside can happen while leaving the core of a piece powdery. It takes both energy AND time to do the work of moving those atoms. If the piece is heated very quickly or the piece is thick, the outside layer may become hot enough to sinter, since the atoms don't have to move very far. But the interior may not get warm as quickly, and atom diffusion distances depends exponentially on temperature, so even a small difference in temperature can result in a huge difference in neck formation. For comparison, moving an atom from the surface of a project into the interior one millimeter away is like driving your car 50,000 miles. Just because the car is at highway speeds doesn't translate to quick arrival. Taking a plane would be better, or a spaceship, and even so it'll still take time.
The upshot is that both time and temperature are important to ensure a well-crafted product. To maximize productive sintering, fire at the highest safe temperature tolerated by the materials in use. To maximize connections between particles, and therefore strength, fire for as long as circumstances allow, factoring in impact on schedule, equipment and personal patience.