What is Diffusion?
Simply put, diffusion is the phenomenom of material transport by atomic motion. This unit discusses the atomic methods by which diffusion occurs, the maths behind it, and the influence of temperature and materials used, on the rate of diffusion. This unit will introduce the topic of diffusion, how it occurs, and some examples of its use in industry.
Introduction  
If two pieces of different metal are joined together as shown here  for example, copper and nickel, and they are then heated for a long time (but below their melting points), the atoms from the metals migrate, or diffuse into the other. 
One type of diffusion involves the exchange of an atom from it's normal lattice position, to an adjacent vacant lattice site or vacancy. This is known as substitutional or vacancy diffusion. Of course, this process requires the presence of vacancies, and vacancy diffusion depends on the extent of vacancies in the material. It is represented in this animation. 
Steady  State Diffusion
Diffusion is a time  dependent process, and often it is necessary to know how fast it occurs, or the rate of mass transfer. This rate is known as the diffusion flux, J, and is defined as the mass, M, diffusing through a unit cross  sectional area of solid, per unit of time. Therefore,
Where A is the area across which diffusion is occuring, and t is the elapsed diffusion time. If the diffusion flux does not change with time, a steady state condition exists, and this is called steady  state diffusion.
Non  Steady State Diffusion
In real life, most diffusion is non  steady state, i.e. the diffusion "flux", J, varies with time. Look back at the graph showing the concentration gradients between Nickel and Copper. It is how "harsh" this concentration gradient is, that determines this flux, which is how quickly diffusion is occuring. The concentration gradient drives diffusion: a high gradient means a high flux.
This means that the last equation we used is no longer valid. In these situations an equation known as Fick's Second Law is used:
where C is the concentration of the substance you're looking at (measured between 0 and 1). D is known as the diffusion coefficient, and is given in square metres per second.
In real life some simple boundary conditions can be applied to materials. These are that:

x is the distance from the interface you're looking at, and=0 at the surface or interface of the material. 
The instant before diffusion starts, time is taken as zero, and 
Before diffusion starts, all the atoms that will be diffusing are evenly distributed.
Because of these boundary conditions, Fick's Second Law can be simplified to give this simple equation:
Let's see an example of this law in use.
PROBLEM: FICK'S SECOND LAW
The diffusion coefficients for copper in aluminium at 500 and 600^{o}C are 4.8 x 10^{14} and 5.3 x 10^{13}m^{2}/s, respectively. What is the approximate time at 500^{o}C needed to produce the same diffusion result (in terms of Cu at some specific point in Al) as a 10h heat treatment at 600^{o}C?
t_{500}=  (Dt)_{600}  = (5.3 x 10^{13} m^{2}/s) (10 hours)  = 110.4 hours 
D_{500}  4.8 x 10^{14} m^{2}/s 
No hay comentarios:
Publicar un comentario