# Physics of Crystals: Drude, where’s my electron?

Did you know that physics involves the study of crystals? From radios, diodes, metals, medical technology, smart phones, and more; crystals have been vital to the development of our modern world.

Well before quantum mechanics had first been discovered people had already began to understand some of the fascinating effects of electricity and magnetism through the use of crystals. In 1861 Maxwell had formulated a series of equations that defined how electricity and magnetism could be linked to one another using Faraday’s observations, whom in 1845 had already discovered some of the first evidence that light was itself an electro-magnetic effect. All of this had already happened when Hall found himself busy in 1879 measuring magnetic forces on charges in wires and attempting to describe how these effects changed the resistance of wires. These observations and early electrical experiments that scientists completed in an attempt to describe the electro-magnetic phenomena of the world around them were both astounding and eye opening to a world never before seen by humans. And yet almost none of their observations had even begun to construct a theory of how the materials themselves could possibly allow these phenomena.

A particular discovery that led to one of the first working theories behind why metals were able to conduct was spurred off by J.J. Thompson’s discovery of the electron in 1897. Metals are themselves a kind of crystal with many free electrons that when allowed to coalesce into a larger piece of metal, also known as a bulk material, are able to have these electrons flow through them as is the case for copper wire. Paul Drude first used that discovery in 1900 in conjunction with the highly successful kinetic theory of gases to formulate a working model of conduction of heat and electricity in metals. He formulated four basic assumptions that gave an insight into some of the quantitative and qualitative properties behind bulk metals. Those assumptions are:

1. The electrons experience no interactions between collisions*
2. Collisions are instantaneous
3. Any electron picked at random will experience a relaxation time $\tau$ such that this will be the probabilistic time between electron-ion collisions.
4. Electrons only achieve thermal equilibrium with their surroundings through collisions

#### *(external fields will cause effects on the electron gas, but no resulting forces cause any interactions i.e. an external electric field would interact with the charged particles, but the movement of the electrons within the system does not cause interactions for other electrons)

###### Description: The above picture represents the collisions that electrons (tiny blue dots) would be undergoing with the ions (larger red dots). It should be noted that this is absolutely NOT how electrons actually travel in metals. This is only a model that was relatively successful in a pre-quantum mechanical physics world view.

However, Drude’s model is absolutely flawed. In his time, how light was emitted and absorbed by atoms had not yet been understood. The quantization of energy levels for electron orbitals and the inability for electrons to exist between these energy barriers had not been discovered. However, even without this knowledge of the world he was able to apply previously successful ideas and gather some accurate information about the magnificent world of crystals.

To me, this is important. Physics is much more a way of critical analysis and educated guesses about the world than it is applying a kind of absolute knowledge of what we already know. It is important to understand that in the face of the unknown physicists and many other professions do not simply stop and find themselves lost. The art of discovering the physical properties of the universe that is about us is as much an applied philosophical quest as it is one that stands within the art and creativity of the minds that pursue it. Developing a wide array of models and testing these ideas is vital to discovering new and never before seen properties about the unknown.

Over the next few days we shall explore the details of this model and how its early successes helped give early scientists a means by which we could begin to describe some of the different effects going on within the different metals. The assumptions by Drude are wildly inaccurate, however they have a wide array of successes that come with their overall failure.

###### Also, I am going to make so many more puns.

Confused about what’s going on here? Great! Send your questions and comments to (JoshingWithPhysics@gmail.com) or respond in the comments section below! I want to make sure that you are able to get a detailed and clear understanding of this fascinating world! Your feedback is absolutely vital.

Best wishes,

Josh Lofy