Crystalline materials are the opposite of amorphous. They have a regular atomic structure where the atoms are neatly arranged with a simple organization that can be described by a unit cell. The face-centered cubic (fcc) model built with the Solid State Model Kit is an example of one such unit cell. Although we often do not think of them that way, most metals are crystalline. They are often polycrystalline, meaning that they contain many individual crystals packed together in what is call a grain structure. This crystallinity is what gives metals much of the familiar behaviors we associate with them, such as malleability and ductility.
Most crystalline solid structures contain missing atoms, called defects, impurity atoms of other elements, and misaligned planes of atoms called dislocations. Impurity atoms, defects, and dislocations all have an important impact on the physical and chemical properties of the solid. For example, copper wire is easy to bend because the structure contains planes of atoms that can slip easily past one another. The planes that dislocations move along are called slip planes. A slip plane can be observed in the face-centered cubic (fcc) model by picking up one of the bottom corners of the model so that half of the model slides up. Amorphous materials do not contain such planes.
Many students have heard of atoms, but few have an understanding of how the arrangement of atoms can affect the properties of materials. In addition, most students do not know what the word amorphous means. Our goal is to introduce the concepts of crystalline and amorphous structures and the link between structure and properties. Students should be encouraged to come up with different experiments after observing and discussing the differences between the two materials.
One difference that can be observed by the students is the pits that have been made in the steel base where the ball has bounced on it. These pits are a direct result of the impact producing many dislocations and causing permanent deformation. If the ball starts out with an initial amount of kinetic energy then some of the energy lost with each bounce goes into the movement of the dislocations, the misaligned planes of atoms. Such pits are not seen in the amorphous metal because the random arrangement of atoms in this material precludes dislocations. Thus energy is not lost in the movement of dislocations in the amorphous material.
There are several ways in which the ball loses kinetic energy: sound, random collisions with the sides of the tubes, and friction with the air. Assuming these factors are the same, on average, for both bases, the difference in the bouncing of the ball must be due mainly to the difference in energy transfer between the ball and each surface. The fact that the ball bounces longer on the amorphous metal surface indicates a much different energy transfer interaction than that of the stainless steel base. The difference in "reboundability" (coefficient of restitution) of the ball bearing with each metal surface is due to differences in how the atoms pack.
The coefficient of restitution represents the degree to which an impact is elastic. Upon collision, one or both of the objects mar deform, and this deformation may be elastic or plastic (permanent). A perfectly elastic impact, in which the kinetic energy loss is zero, would have a coefficient of restitution of one. A perfectly inelastic impact, where all of the energy goes into plastic deformation, will have is no rebound and a coefficient of restitution of zero. The coefficient of restitution can be determined for the two cases in this demonstration by measuring the height from which the ball is dropped (h1) and the height of the first bounce (h2).
Coefficient of Restitution = e = (h1/h2)1/2
Stainless steel is a crystalline metal made primarily from iron with a few percent of additional elements such as carbon, chromium, and sometimes nickel. Steel has an ordered, repeating pattern of atoms, while the Vitreloy amorphous metal is comprised of five elements (41.2% zirconium, 22.5% beryllium, 13.8% titanium, 12.5% copper, and 10.0% nickel). The different atomic radii of atoms in Vitreloy promote its highly disordered arrangement. The different sized marbles in a jar can be used to represent this amorphous arrangement of atoms. With all of the different atomic sizes it is difficult for the atoms to pack neatly.
It is important to note, however, there are many amorphous materials that are not made up of a collection of differently sized atoms. When a material is molten the atoms are farther apart because they have more thermal energy, their arrangement is irregular and random. If a material can be frozen (i.e. quenched) into the solid state fast enough, crystallization can be prevented and the random arrangement can be trapped in a tightly-packed solid form. This occurs because the atoms do not have enough time to arrange themselves in an ordered structure.
Because there are no planes of atoms in an amorphous material, the atoms are gridlocked into the glassy structure, making the movement of groups of atoms very difficult. One consequence of this atomic gridlock, is that some amorphous metals are very hard. Vitreloy is more than two times harder than stainless steel. However, besides being a very hard material, this amorphous alloy has a low elastic (or Young's) modulus.
Demonstrate the relationship between wavelength and frequency by watching the ball bounce on the amorphous metal surface. Explain that the distance the ball travels in one bounce represents the wavelength of a photon of electromagnetic radiation. The time it takes for the ball to bounce once represents the frequency of the photon. As the "wavelength" decreases the frequency of the bouncing ball increases demonstrating the inverse relationship of the formula c = ln.
By the end of the 8th grade, students should know that:
Energy cannot be created or destroyed, but only changed from one form into another.
Energy appears in different forms. Heat energy is in the disorderly motion of molecules; chemical energy is in the arrangement of atoms; mechanical energy is in moving bodies or in elastically distorted shapes; gravitational energy is in the separation of mutually attracting masses.
