CP (commercially Pure) titanium is, as was stated, titanium in its purest unallyoyed form. Sources are variable, most being from the USA, Russia, or China, but also from Europe. CP titanium has excellent corrosion resistance, but its strength-to-weight ratio is rather poor, especially compared with 3/2.5 Ti and even some modest steels. Unless you're building bike frames or other structural elements, however, this really isn't much of an issue. There are four grades of CP Ti that originate in the USA, with the different grades being designated by oxygen content. Other countries grade their titanium differently, but with some poking around you can usually figure out what is what even with different "names" from the various grading systems. CP's yield strength varies from 25-65 ksi (thousand pounds per square inch), and the grading system worls with Grade 4 having the highest yield strength and Grade 1 having the lowest. Again, probably only an issue in load-bearing structural projects.
6Al/4V titanium is 90% titanium, 6% aluminum, and 4% vanadium. It is the brainchild of the aerospace industry, with an excellent strength-to-weight ratio and it accounts for about 50% of the overall titanium usage in the USA. It tends to be less ductile, but again, if you aren't making tubes you'll not notice this. 6/4's shear modulus value is less than 3/2.5 titanium, which can be a probelm with repeated torsion (probably not an issue with knives). It is more expensive and harder on tools, so it is costly and difficult to get it to do what you want.
An alternative is 3Al/2.5V titanium, which is sort of a magical compromise between the CP and 6/4 alloy. Probably the bottom line, though, is for use in knife manufacturing, they're all pretty much the same. Any arguments?
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