Motivating Students to Learn about the Science of Materials

Proceedings of 2013 JSEE Annual Conference – Niigata August 29-30, 2013

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Motivating Students to Learn about the Science of Materials

K. Arimoto1, H. Melia2 and M.F. Ashby3

1. Senior External Education Consultant, Education Division, Granta Design Ltd., Cambridge, UK 2. Teaching resources Team Leader, Education Division, Granta Design Ltd., Cambridge, UK 3. Engineering Department, University of Cambridge, Cambridge, UK

Abstract

In order to innovate rather than just make incremental change to a product, engineers need a deep understanding of the science of materials. Engineering students, therefore, especially those who are not materials specialists, should be given the basic scientific knowledge and vocabulary to equip them to choose and use materials wisely. A connection must be made between the materials properties in which engineers are interested and the underlying science. In this study, a visual approach has been taken. Charts showing how atomic characteristics relate to materials properties have been created using the elements database in CES EduPack, (a world-leading materials teaching resource). Characteristics of the elements in the Periodic table are illustrated and other teaching examples for fundamental subjects are suggested.

Keywords: Materials education, elements database, periodic table, science-led approach, CES EduPack.

1. Introduction

Industrial products are created using a variety of materials, such as metals, ceramics, polymer, elastomers, and hybrids. All are based on the 92 stable elements that we have at our disposal. How do the fundamental properties of these elements – the atomic number and weight, the nuclear stability, the crystal structure, the cohesive energy etc. – influence the engineering properties that are essential for design? A deep scientific knowledge is an essential prerequisite to the use of new materials in innovative ways. Students, therefore, should be given opportunities to explore a higher level of scientific information on materials. In this study, charts were created using the Elements database of CES EduPack [1], which show how properties of materials can be explained scientifically from atomic characteristics.

This paper describes the contents and applications of the CES Elements database. It shows how charts help students think scientifically about materials [2]. The paper concludes with a discussion of how a fundamental approach of the science of materials can be accessed further through recommended reading.

2. The CES Elements database 2.1 The database and its contents

An understanding of the elements is at the root of the science of materials. They have periodic characteristics in their order of atomic numbers, captured in their grouping the Periodic Table of the Elements. The CES EduPack suite of databases includes comprehensive cover of the Elements of the Periodic table. The records are ordered by atomic number and are segregated into folders corresponding to the rows of the Periodic Table. Each record contains data for the crystal structure, physical, mechanical, thermal, diffusion, surface energy, electrical, magnetic, nuclear, and cost properties. The properties contained in the database are listed in the table below. Each record contains data for the properties listed in Table 1. Each field name is linked to a “science note” that provides a definition and background. Thus the database provides not only data but also the underlying background to the property and its relationship to other properties.

The properties can be plotted, compared, combined and displayed as material-property charts [3], illustrated below. Each row of the periodic table including the lanthanides and actinides can be color-coded using envelopes to identify their periodicity.

Students can learn to create property charts in a few minutes using the CES EduPack software. The visual presentations of data is engaging and the “science notes” described below encourage students to absorb the fundamental knowledge of materials science that they need. The examples that follow illustrate how students can not only learn about the characteristics of individual elements but also explore the relationships between properties and


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even estimate properties in an intelligent way. Lastly, it is shown how the elemental properties mirror the properties of common engineering materials – further motivating students to learn the science.

Table 1. The field names in the CES EduPack “Elements” database.

2.2 Atomic characteristics

Atomic weight is plotted against the atomic number for the elements, using the elements database of CES EduPack, as shown in Figure 1. It can be seen that the atomic weight rises almost linearly with increasing atomic number.

Figure 1 Atomic weight vs. atomic number Figure 2 Binding energy per nucleon vs. atomic number.

The nuclear stability of an element is measured by the binding energy per nucleon. This property is plotted against atomic number in Figure 2. The most stable nuclei (those with the greatest binding energy) cluster around iron. It is clear from this plot that elements with a higher atomic number than iron will generally favour decay by

Properties of the Elements The element Thermal properties Electrical properties Symbol Melting temperature Electrical resistivity at 300K Periodic table row Boiling point T - dependence of resistivity Periodic table column Heat of fusion Free electron concentration Atomic number Heat of vaporization Electron mobility Atomic weight Cohesive energy Hall coefficient, RH Date of discovery Thermal expansion coefficient at 300K Work function Specific heat capacity Standard electrode potential Structure and physical properties

Debye temperature

Crystal structure Thermal conductivity at 300K Magnetic properties Space group Magnetic classification Lattice parameter, a Diffusion data Magnetic susceptibility Atomic radius Pre-exponential, lattice self-diffusion Atomic volume Activation energy, lattice self-diffusion Nuclear properties Molar volume Pre-exponential, g-b diffusion Neutron absorption cross section State at 300K (Metal / Non-metal) Activation energy, g-b diffusion Neutron scattering cross section Phase at 300K (Solid / Liquid / Gas) Binding energy per nucleon Density at 300K Surface energies Surface energy, solid Mechanical properties Surface energy, liquid Young's modulus at 300K Shear modulus at 300K Bulk modulus at 300K Poisson's ratio T- dependence of modulus


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fission whilst those lower than iron will generally favour fusion, and that fission releases, at most, a few hundred keV per event, whereas fusion can release many thousands. It is known that the total mass of individual protons and neutrons in a nucleus is larger than the mass evaluated from its atomic weight. This mass-discrepancy can be calculated by students from the binding energy per nucleon using Einstein’s celebrated equation E = mc2 for the mass–energy equivalence.

Property data for both the atomic radius and the crystal structure are included in the elements database. Figure 3 charts atomic radius against atomic number for each element and illustrates how atomic radius changes across each row of the Periodic Table from column to column. This periodic characteristic is highlighted by two additional lines linking elements in columns 1 and 8 in Figure 3. This cyclic feature in the atomic radius is reflected in the density of elements, as described in Section 2.3, below.

The lattice constant, a, is plotted against atomic radius in Figure 4, illustrating the way in which HCP, FCC, and BCC crystal structures line up in ways characteristic of the structure. Figure 5 illustrates the relation between atomic radius and atomic volume. The data cluster in a narrow band regardless of crystal structures. These charts help students to understand clearly the size of atoms in each element, atom packing within crystal structures, and the definition of lattice parameters. Students can further investigate the above relationship for other crystal structures such as diamond-cubic using the database.

Figure 3 Atomic radius vs. atomic number. Figure 4 Lattice parameter vs. atomic radius.

Figure 5 Atomic volume vs. atomic radius. Figure 6 Cohesive energy vs. atomic number. Charts showing how other atomic characteristics vary with atomic number (and thus across the Periodic Table)

can be used for students to discover similar trends to those of Figures 1, 2, and 3. As an example, the cohesive energy, defined as the energy per mol required to separate atoms in a solid into the neutral atoms at infinity, is


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charted against their atomic number as shown in Figure 6. Students will notice that the configuration of data points for each row of the periodic table is the opposite of that in Figure 3 for the atomic radius. Students can explore configurations of the same kind by plotting the work function and the density of free electrons. The electron mobility, for instance, has the same trend as atomic radius shown in Figure 3.

2.3 Relations between atomic characteristics and materials properties

It is meaningful for students to recognize how atomic characteristics relate to materials properties relevant for engineering design, such as density, Young’s modulus, and heat capacity. Here we show charts created using CES EduPack with the Elements database as examples of the way they can be used to enhance student’s scientific thinking.

The density of an element is its mass per unit volume. It is thus possible to calculate density by dividing the atomic mass by the atomic volume, both of which are contained in the database. However, it is useful for students first to examine how atomic weight and atomic volume relate to density of the HCP, FCC and BCC crystal structures as shown in Figure 7 and 8, respectively. Specific envelopes linking data points of the elements in each row of the periodic table show a general trend that matter is denser with decreasing atomic volume or increasing atomic weight for the elements.

Students can be challenged to compare the density listed in the database with that derived from atomic properties. They will find that density ρ ( in units of kg/m3), the atomic volume VA (in units of m3) and the atomic weight Ar(E) (in units of kg/kmol, for convenience). The three are related by:

( )1000*

r

v A

A E=A V

ρ (1)

where Av is Avogadro’s number (6.022×1023). Figure 9 shows the comparison between the density measured by conventional means and that calculated from atomic parameters. As expected, the two coincide. The small deviations from perfect linearity reflect inaccuracies in published density measurements.

It is beneficial for students to understand that the cohesive energy plays a fundamental role in determining many materials properties, such as Young’s modulus, melting temperature, thermal expansion coefficient, activation energy for lattice diffusion and surface energy [3]. The cohesive energy measures the strength of the bonds between atoms in a solid. Figures 10 and 11 are charts for Young’s modulus and surface energy against cohesive energy, respectively. The correlation is revealed in the figures, and can be discussed further by students [3].

It is known that heat capacity per unit volume is inversely proportional to atomic volume [5]. The relation can be confirmed by students in Figure 12. The reason why the atomic volume contributes to the heat capacity should be explored by students [5].

Electromagnetic properties of materials have their origins in atomic characteristics. As examples, the electrical conductivity is proportional to the density of free electrons and to the electron mobility [3] and the saturation magnetisation is related to the number of Bohr magnetons per atom and the atomic volume [3]. Students can be challenged to explore these and other relationships using CES EduPack to cement their scientific knowledge.

Figure 7 Density vs. atomic volume. Figure 8 Density vs. atomic weight.


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Figure 9 Density by eq.(1). Figure 10 Young’s modulus vs. cohesive energy.

Figure 11 Surface energy and cohesive energy. Figure 12 Heat capacity and atomic volume. 2.4 Connecting the scientific knowledge back to the world of engineering materials.

By creating similar charts in both the Elements database and the Level 2 or 3 Engineering Materials database of CES EduPack, students can explore how the properties of the elements are mirrored in the materials made from those elements. They can also explore any differences, and discuss how mankind has been able to manipulate the properties of materials through changes to composition (carbon steels), microstructure (aluminum alloys) and architecture (composites). 3. Other Fundamental Subjects to Learn More of the Science of Materials

A number of excellent texts are available to give students further insight into the fundamentals of materials [4-7]; most include large numbers of worked examples and exercises. Other texts take a different, design-led approach in with material selection to meet engineering design requirements is the primary focus [8]. A few, such as [3], combine the two approaches, using design requirements to introduce a property and bring out its engineering relevance, then “drilling down” to explore its fundamental origins in atomic characteristics, chemistry and microstructure. This approach, combined with an introduction to manufacturing processes for shaping, joining and finishing materials [9, 10] (also covered in the CES EduPack software), offers a more rounded materials education for non-materials specialists. 4. Conclusion

In order to make innovative products and to resolve problems occurring in their production and use, it is increasingly expected that engineering students should have a sound understanding of the science of materials, even


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if materials science is not their primary field. This paper describes the way in which charts of material properties, created using CES EduPack with the Elements database, provide and engaging way to introduce engineering students to the fundamentals of material behavior. Charts show that properties of actual materials can be explained scientifically from atomic characteristics. It is found that these charts excite students’ interest in the science of materials and deepen their knowledge. The approach is backed up by teaching texts with numerous examples of the chart-based approach. References 1. CES EduPack 2013, Granta Design, Cambridge UK ( www.grantadesign.com ). 2. Silva, A., Fry, M., Arimoto, K. and Ashby, M. F., “Tradition and Innovation in the Education of Materials and

Engineering Students”, JSEE annual conference international session proceedings, 2012, pp. 82-87. 3. Ashby M.F., Shercliff, H. and Cebon, D. “Materials: Engineering, Science, Processing and Design”, 2nd

Edition, Butterworth Heinemann, Oxford, UK. 2010.

4. Callister, W. D. Jr. and Rethwisch, D. (2010) Materials Science and Engineering, an Introduction. 8th Edition, John Wiley and Sons, NY, USA.

5. Budinski K.G. and Budinsky M.K. (2009), Engineering Materials, Properties and Selection, 9th Edition, Prentice Hall, London, UK.

6. Fulay, P., Wright, W., Askeland, D.R. (2011), The Science and Engineering of Materials, 6th Edition, Wadsworth, California. USA.

7. Shackelford, J., (2008) “Introduction to Materials Science for Engineers”, 7th Edition, Prentice Hall, London UK.

8. Ashby M.F., “Materials Selection in Mechanical Design”, 4th Edition, Butterworth Heinemann, Oxford, UK. 2011.

9. ASM Handbook, Vol. 22A: Fundamentals of Modeling for Metals Processing, ASM International, 2009. 10. ASM Handbook, Vol. 22B: Metals Process Simulation, ASM International, 2010. Biography Kyozo Arimoto is a consultant at Arimotech Ltd. which he founded in 2002, and also at Granta Design Ltd. since 2013. He has worked on heat treatment simulation for around 20 years and helped develop a commercial code that is used worldwide. He has published over 35 articles on heat treating simulation. He works with Granta as Senior External Education Consultant and is the principal distributor of CES EduPack in Japan.

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Motivating Students to Learn about the Science of Materials