Phase diagram of water using Gibbs free energy instead of pressure From my lecture course it was indicated that this is what a phase diagram looks like. 

Is this diagram applicable to water? All the ones I can find online seem to use pressure on the y axis as oppose to G. If if it is applicable to water, where is the triple point on the graph? I understand it's where the 3 phase lines intersect but this doesn't appear to occur on this type of graph.
Phase diagrams are not limited to temperature vs pressure. They can be made with any set of thermodynamic quantities. The diagram in your question is for a particular pressure at which the liquid phase exists. If you changed the pressure, the lines would shift. A triple point will be represented by all three lines intersecting through the same point.