The "Coral growth" on battery terminals is a combination of the following.
a/ Dissimiliar metals of the battery and connecting terminals.
b/ A cloud of acidic Hydrogen gas that is created when the battery is being charged. Even on so called "sealed " batteries. Very important not to smoke around a "gassing" battery.
Basically what happens is that as the battery gasses off whilst being charged, the moist gas acts as a catalyst on the dissimiliar metals (Lead battery terminal & Tin plated Copper connecting terminal). The re******t chemical reaction is the "Coral" growth around the terminals. If its left alone it will convert all the Tin/Copper terminals to a bluey/white salt (the Coral growth) (Its been too long since I went to High School so I can't recall all the detail of what's what, sorry) now the gas escapes from the battery's vented caps as well as from around the terminals.
16 years around Taxis has taught me that although Vaseline or petroleum jelly is good for earlier cars with lower under bonnet temperatures. Later model (EA on) Falcons underbonnet temperatures are such that "Vaso" melts and evaporates very quickly. High Temp Wheel bearing grease works reasonably well. There is a Tar based spray on anti corrosion product but it tends to dry out after a while and the acid creeps underneath any way.
You will find a car that is driven constanly will create more growth than one thats parked all week. Once upon a time it used to form part of a weekly routine to open the bonnet of our cars and clean, check and adjust things as necessary, that was called "Routine Maintenance". Today its rare to open a bonnet between 15000k services (Known as "Risk Management") because the cars today are so genuinely reliable.
The best method of cleaning it up is as follows; Boil the jug, then pour the boiling hot water onto the terminals. Sprinkle some baking soda onto the terminals and wait till the fizzing stops. Pour the rest of the Boiling water over the terminals. Stand back for 5 minutes to allow to cool. Now undo the terminal bolts and clean and inspect the connecting terminals. Replace any terminals that are obviously weakened. With some fine emery cloth clean up the terminals and then thinly smear a film of wheel bearing grease onto the battery post and the terminals. Replace the bolt if obviously affected by corrosion. Reassemble terminal connections.
If your battery is getting older then it will gas off more and be more suseptible to the coral growth. I remember a time when car batteries lasted virtually the half life of a car about 6 to 8 years. Today your lucky if it lasts the warrenty period of two years.
If your new battery gasses off furiously then you should check the charge rate of the alternator. If its above 14.4volts then your regulator has gone rogue and needs to be replaced. I recall a batch of ED alternators when used in heavy duty Taxi/Cop applications needed to have their regulators changed for this reason.
Hope this helps.