What determines the rate of vibration decay of a metal? Suppose we have a tuning fork in a vacuum and strike it.  Is there anything in the theory of metals that would predict that the tuning fork's vibration amplitude would decrease with time.
Put another way, are there internal dampers in metals?  If there are what is this property called, and where could I find the values?
 A: 
In the diagram below, one arm of a tuning fork is firmly attached to a wall (or floor or similar) in point $O$. We'll assume the arm to be a uniform bar.
The green line represents the neutral axis which runs through the centre of gravity of the bar, all the way from $O$ to the free end.
When we exert a force $F$ (for example an impulse force exerted by a hammer) to the bar, the bar deforms elastically, shown as the curved neutral axis. The bar's material that is above the neutral line is being (slightly) elongated, while material under the neutral line is in compression. These deformations cause the elastic response of the bar in the form of a reactive force in the opposite direction of $F$.
When we suddenly remove $F$ the bar snaps back and due to its inertia enters into an oscillatory movement with initial amplitude $A_0$.
However, the constantly changing elongation and compression above and below the neutral axis can only happen by atomic/molecular layers of the material sliding over each other, back and forth during the oscillation of the bar. This sliding is not entirely frictionless and friction work is constantly being dissipated. So the oscillating bar constantly loses energy, even in vacuum.
As a result the amplitude of of oscillation gradually decreased and the oscillation is really a damped oscillation.
A: This concept of damping in metals is called loss factor.
You can model loss factor by considering a complex Young's Modulus, such as
$$E = E_0 (1+j\eta)$$
where $E_0$ is the Young's modulus of the material and $\eta$ is the loss factor. In metals $\eta$ tend to be very small (around 0.001 - 0.02).
