Why will clay, when heated to high temperatures,  harden and become waterproof? I have a question

Why will clay, when heated to high temperatures, harden and become waterproof?

 A: Clay minerals form as the products of low-temperature chemical weathering reactions near the earth's surface.  Clay minerals contain hydrogen and oxygen in the form of hydroxyl (for example the composition of kaolinite : $ \mathrm{Al_2Si_2O_5[OH]_4}$ ). If kaolinite is heated above 550-600 C , there is a series of chemical reactions that consumes the clay as a reactant and produces water and other minerals as products. The products of such a relatively low-temperature treatment can be stronger and more moisture resistant than the starting material because of the recrystallization that accompanies the clay dehydration, although not as strong and impervious as produced by firing at higher temperature.
At a temperatures of 1000 C and higher, chemical reactions producing anhydrous alumina and silica oxide drive off more water.  At high temperature, the diffusion transport along grain boundaries (and even through crystals) required for sintering can become significant.
As an aside, it was fortunate for the development of human culture that relatively water-resistant and strong bricks and pots can be manufactured from relatively low temperature firing of clay. The hydrous fluids produced by these reactions at a more easily attainable temperature facilitates solution and re-deposition mass-transport through the microstructure which makes the piece stronger and impermeable.
A: To make the clay "waterproof," the first step is to get the chemically bonded water out of it. That happens as temps rise over 350°C, up to about 800°C. The organic compounds (carbon) have already burned away by that temperature, and what happens next is that other compounds begin to melt and fill the voids left by the attached water molecules (at the micro level.) The silica starts to melt shortly after, and bonds differently to the alumina, with long, flat layers of each connected by rows of oxygen molecules that line up with each other. That is called vitrification, and by then it has hardened, "plugged the holes" (so to speak) and lined up as a barrier to smaller molecules. The other thing that makes clays "waterproof" can happen when excess silica forms glass sheets that coat the clay and prevent water from getting to the clay at all. That is the point of glazes. (Glaze means glass.) The silica can begin to "flow" below its normal melting temperature by adding a flux. Fluxes also change the characteristics of clay to produce different hardening and melting temperatures. Iron oxide is one. It is in most clay and causes the melting (and maturing) temps to drop. That's a simplified overview, but you can easily find more online.
A: From http://matse1.matse.illinois.edu/ceramics/prin.html we get this piece of information from a summary:

The processing of crystalline ceramics follows the basic steps that
  have been used for ages to make clay products. The materials are
  selected, prepared, formed into a desired shape, and sintered at high
  temperatures.

What is sintering?
From http://www.substech.com/dokuwiki/doku.php?id=sintering_of_ceramics we get this definition of ceramic sintering;

Sintering (Firing) of ceramic materials is the method involving
  consolidation of ceramic powder particles by heating the “green”
  compact part to a high temperature below the melting point, when the
  material of the separate particles difuse to the neghbouring powder
  particles.

From the same page this suggests an answer to your question about waterproofing:

During the diffusion process the pores, taking place in the “green
  compact”, diminish or even close up, resulting in densification of the
  part, improvement of its mechanical properties.

A: It is well known that glass will not melt until 3100 degrees Fahrenheit.  Clays are vitrified....lose their water content and become more durable at far lower temperatures.  Not all clays have the same make-up, some are far more dense, durable, water-tight than others.  Glazing was clearly developed because clays are often deficient in their ability to contain liquid...and glass covered clay is a far more useful and durable medium.  It is possible to melt glass on to clay because fluxes act to decrease the melting temperature of glass...in the same way any catalyst can decrease the energy needed for a chemical reaction.  Hope that helps.
A: Among other things in the clay body, the silica content is heated to a state where it is more viscous, though the structural integrity of the body is maintained. As the viscosity of the individual pieces of silica increases, the particles are disordered and come together in a more liquid form. At the point of cooling, vitrification occurs and the individual particles have joined together in a more ordered state. Due to the new order of particles in the vitrified clay body, water cannot pass, provided the integrity of the vitrified clay body is maintained.
At approximately 2385-2420 deg.F the SiO2, among other things, begins to turn from solid particles and crystals into molten SiO2. In the heating process the organic material in the clay is burning off, the water is evaporating, and gaps are being created. However, at the point of many compounds turning more viscous/ or closer to liquid, gaps are also being filled. During the cooling process, the molten compounds have combined, filled gaps, and to some extent maybe even crystallized. There has definitely been some rearranging of structure, fusing many individual particles into one body. There are both physical and chemical changes that occur in the firing.
*It is important to know about viscosity and vitrification to fully understand this simplified explanation.
