A Unit Cell Laboratory Experiment: Marbles, Magnets, and Stacking Arrangements

Abstract

An undergraduate first-semester general chemistry laboratory experiment introducing face-centered, body-centered, and simple cubic unit cells is presented. Emphasis is placed on the stacking arrangement of solid spheres used to produce a particular unit cell. Marbles and spherical magnets are employed to prepare each stacking arrangement. Packing efficiency is calculated using simple measurements of marble or magnet diameters and the dimensions of the stacking arrangement. Edge effects are introduced. Packing efficiency is subsequently calculated for various metal samples employing density measurements and literature atomic radii values. The stacking arrangement for each metal and its corresponding unit cell are determined by comparing packing efficiency values. Estimated percent unoccupied space values for water and air are also determined.

Using Magnet-Embedded Silicone Balls to Construct Stable Models for Close-Packed Crystal Structures

“…This manner of tight connection, however, may lack flexibility, in particular, for laboratory exercises oriented to a large number of students. In other examples, educators developed some alternative connection methods, such as using adhesive tapes, 3 adhesive putty, 5 and glue 6 to connect readily available balls (e.g., table tennis balls, 3 marbles, 5 and transparent plastic balls 6 ). As cost-effective as these methods are, it would always take a relatively long time for students to adhere the model pieces together.…”

“…10 Benefiting from the magnetic connection between neighboring balls, the models can be easily constructed within a shorter time, exhibit good stability and ready extendibility, and are very suitable for more students to practice with. There have also been a few similar models that used magnetic connections, such as the magnetic buckyballs used by Collins 3 and the commercial model kit NaCl Lattice. 11 Superior to these two models (which can only give the simple cubic stacking arrangement), our models of silicone balls with different specifications can be used to construct all four basic crystal structures described in the textbook of general chemistry, including simple cubic, body-centered cubic, facecentered cubic, and hexagonal closest packing.…”

“…The model of “close-packed identical spheres” is a must-learn for beginners studying crystal structures. , In the practical teaching activities, instructors usually demonstrate physical models to help the students understand this part of knowledge. However, it would be best for students to have an opportunity to construct the tangible models by their own hands, and this Journal has reported a few relevant teaching works over the past few years. − For instance, Sunderland et al (2014) adopted the model kit developed by University of WisconsinMadison. , Different from the conventional “ball-and-stick” models of crystal lattices that mainly use metal or plastic short rods to connect hard balls made by wood or plastic, their “crystal structures” are built on a template base, in which the spheres are placed through the fixed long rods sticking up out of the base. This manner of tight connection, however, may lack flexibility, in particular, for laboratory exercises oriented to a large number of students.…”

A Computer-Based Interactive Activity for Visualizing Crystal Structures in Introductory Materials Science Courses

“…Several papers have presented activities utilizing physical spheres, such as latex balls [3] or marbles [4], to build crystal structures. These activities aid students' visualization skills, allowing them to physically manipulate atoms rather than relying on spatial reasoning.…”

Board 14: Materials Division: Measuring Student Learning of Crystal Structures Using Computer-based Visualizations

“…For instance, a student may be able to pinpoint the locations of atoms in a unit cell, yet cannot identify which atoms are located on a given plane. A number of interventions have been developed to help students visualize crystal structures, such as using styrofoam spheres or completing computer activities [1]- [4]. One such activity [5] utilizes OVITO [6], an open-access visualization tool used by materials researchers that enables students to visualize crystal structures on their personal computers.…”