A good bicycle frame must be both stiff and flexible at the same time.   It must be stiff enough to resist being deformed by the force of pedaling.   Pedaling can cause the frame to flex laterally due to tension on the chain and vertically due to the downward force on the pedals.  Energy spent bending and flexing the frame is wasted energy.  A good bike frame must minimize the amount of energy wasted in flexing and maximize the energy transferred to the rear wheel.   However, a perfectly stiff frame would be much too uncomfortable to ride; every little bump and vibration in the road would be transmitted through the frame to the rider.

For decades, steel has been the material of choice for quality bike frames because of the combination of stiffness and flexibility in its alloys.  By proper choice of tube material and geometry, a master frame builder can build a steel frame with almost any desired combination of ride characteristics.

The "XLM" titanium mountain bike by Merlin bikes.

Unfortunately steel is dense, so builders have looked into lighter alternatives.    Aluminum has become a popular choice because of its low cost and density, but it must have thicker tubes because it is so much softer than steel. The thick tubes cause less flexibility, making it less comfortable.  Carbon fiber is also an option, but it is harder to work with and is more expensive.

The flexibility and stiffness of titanium make it a perfect material for these glasses. (V. Holtgrewe)

Recently, titanium has become a popular material for bike frames.  Like most metals, pure titanium is too soft for structural use and must be alloyed to have the desired structural properties.  Titanium is usually mixed with aluminum and vanadium to form an alloy which is harder and stiffer than pure titanium, the most common alloy consisting of 3% Al and 2.5% V.  These frames are as light as aluminum yet retain the desirable combinations of stiffness and flexibility of the best steel frames.

What are other future possibilities?  A metal matrix is a heterogeneous mixture of a substance such as ceramic within a metal.  These materials have been used in the aerospace industry and are just starting to find applications as bike frame materials.

Reger/Goode/Mercer:  Chemistry Principles and Practice,  2/e,  p. 456–457