Activity pubs.acs.org/jchemeduc
An Example of Body-Centered Cubic Crystal Structure: The Atomium in Brussels as an Educative Tool for Introductory Materials Chemistry Gabriel Pinto* Grupo de Innovación Educativa de Didáctica de la Química, ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, Madrid, Spain 28006 ABSTRACT: When students are introduced to the ways in which atoms are arranged in crystal structures, transposing the textbook illustrations into threedimensional structures is difficult for some of them. To facilitate this transition, this article describes an approach to the study of the structure of solids through a well-known monument, the Atomium in Brussels, Belgium. After a brief introduction to this monument (it represents an unit cell of iron crystal, magnified 165 billion times), a series of questions is proposed to address various topics such as crystal lattice, unit cell, body-centered cube structure, metallic crystals, typical trends for atomic radii in the periodic table, introductory solid structure calculations, and rounding in calculations. Furthermore, this exercise promotes spatial vision in students. The question−answer approach engages the students and most of them gain an appreciation for the three-dimensional structures. Students have expressed keen interest in this type of “tangible” chemistry where a concrete example of everyday life helps them to better understand chemistry topics.
KEYWORDS: First-Year Undergraduate/General, General Public, High School/Introductory Chemistry, Inorganic Chemistry, Public Understanding/Outreach, Analogies/Transfer, Problem Solving/Decision Making, Crystals/Crystallography, Materials Science, Metals
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typical trends for atomic radii in the periodic table, introductory solid structure calculations, and rounding in calculations. This exercise develops an appreciation by the students for threedimensional structures and the spatial components involved.
tudents are introduced to the way in which atoms are arranged in cubic crystal structures in general chemistry classes, but transposing the textbook illustrations into threedimensional structures is difficult for some of them.1 To facilitate this transition, Cady1 proposed the use of models constructed of Styrofoam balls and toothpicks. Online representations and simulators for the various unit cells can also be used to aid student understanding.2 Amey et al.3 described how, since their first use by Dalton ca. 1810, physical molecular models have been employed by chemists to enhance visualization and understanding of the molecular world. Among other examples, they pointed out that giant molecular models have been used to adorn public spaces, such as Jones’ Molecular Matter project4 and, most exceptionally, the Atomium in Brussels, Belgium.5 This article describes an approach to the study of the structure of solids through the Atomium monument in hopes of motivating students to learn concepts associated with this field. After a brief introduction to the Atomium, a series of
INTRODUCTION The Atomium5 was the main pavilion and icon of the 1958 World Fair of Brussels, commonly called Expo 58. It symbolized the democratic will to maintain peace among all the nations, faith in progress, both technical and scientific, and an optimistic vision of the future of a modern technological world for a better life for mankind. At 102 m high, the assembly of tubes and spheres of the Atomium represents the bodycentered cubic structure of an iron crystal, magnified 165 billion (thousand million) times5 and highlights the power of nuclear energy, which was in full development at that time (the 1950s) and which was intended for peaceful use. The Atomium corresponds to a cube centered on one of its vertices and the total mass including the base pavilion is 2400 tons of steel.
questions is proposed to address various topics such as crystal lattice, unit cell, body-centered cube structure, metallic crystals,
Published: May 7, 2012
© 2012 American Chemical Society and Division of Chemical Education, Inc.
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The Atomium was designed by the engineer André Waterkeyn (1917−2005) and the spheres were fitted out by the architects André and Jean Polak.5 Its construction required more than 18 months. Similar to the Eiffel Tower in Paris that was designed and built for the 1889 World Fair (marking the centennial celebration of the French Revolution), the Atomium was to be dismantled after the World Fair, but its success made it a landmark of the city of Brussels and recognized internationally. Today, it is one of the main symbols of Belgium and the most visited monument of Brussels. The Atomium is one of most original and well-known monuments in the world.6 It underwent extensive external and internal restoration between 2004 and 2006. The Atomium is a museum with a permanent exhibition dedicated to Expo 58 and temporary exhibitions with scientific themes and different activities (for example, in the Kid’s sphere, children are invited to spend a night in the monument). Four of the spheres are open to the public. Inside, there are 8 levels, 80 steps to go up, 186 to go down, 4 escalators, and an elevator, which was the fastest of the world in 1958.6 As it can be appreciated in Figures 1 and 2, it is an original and impressive
Figure 2. View of the Atomium in Brussels from a different angle of view with respect to Figure 1. Reproduced with permission. Copyright www.atomium.be - SABAM 2009 - DJ Sharko.
In addition, in general chemistry classes, students are taught that numerical rounding must be done at the end of calculations and that the accuracy of given data must also be considered. This activity could be used to discuss significant figures and precision. Moreover, this activity can be also used to introduce students to the typical periodic trends in the atomic radii.7
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QUESTIONS AND ANSWERS This activity was used as an individual out-of-class assignment for the students. Thus, only a short period of class time was needed for the introduction of the activity and for the final class discussion. There are other possibilities to use the questions with the students. For example, the teacher can ask the questions, followed by a class discussion or students can be divided into groups and work on one question or all the questions. After introducing students to the Atomium as a wellknown European monument, the following questions can be used to link this public structure to topics related to solid structure in chemistry. Question 1
Figure 1. View of the Atomium in Brussels. Reproduced with permission. Copyright www.atomium.be - SABAM 2009 - Frankinho.
According to the information given on several Web sites, tourists’ brochures, and by local tourist guides, the Atomium in Brussels (Figures 1 and 2) represents a “molecule of iron” or “anything about the structure of atoms”. Discuss the accuracy or inaccuracies of these statements and support your answer with the chemical meaning of the monument.
building for everyone but, especially, for chemical educators. Official tours of this monument state that it represents “anything about the structure of the atom”, whereas a Google search refers to the Atomium as an “iron molecule” enlarged more than 6000 times. These examples show that the chemical meaning of the Atomium is confused and misrepresented to the general public.
Question 2
The Atomium represents the crystal structure of iron. With the aid of Figures 1 and 2, other photos,6 and a textbook,8 identify what such structure is. Compare this structure with the structures of other metallic elements, such as the three metals discovered by Spanish researchers.
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ACTIVITY In addition to making the chemical education community aware of this monument, the activity is proposed as a teaching tool for introductory materials or solid-state chemistry topics in a general chemistry course. The activity is formatted with questions and answers. Several questions refer to the geometric relationships of the crystal unit cell. The discussion of some aspects should help students improve their spatial vision.
Question 3
Does each sphere of the monument represent an atom of iron or only a part of an atom of iron? Question 4
The whole monument is made up of 9 spheres (one at each of the 8 vertices or corners of the cube and one in the center), 922
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connected by 20 tubes (12 cube edges plus 2 tubes for each of the 4 cube diagonals). The structure rests on 3 pillars. The diameter of each sphere is 18.0 m, the diameter of the tubes is 3.30 m, and the length of the cube edge tubes is 29.0 m. According to these data,5 what is the length of the diagonal tubes? Question 5
Consider the cube formed by the centers of the eight external spheres of the Atomium and calculate how many spheres are inside that cube.
Figure 4. Space-filling body-centered cubic unit cell.
Question 6
According to the information provided (see for example ref 5), the Atomium represents an iron crystal, magnified 165 billion (thousand million) times. Discuss what that means by considering the metallic radius of iron as 0.126 nm;9 that is, what quantity is being magnified.
the center of each iron atom. This way of representing only the central part of each sphere or atom is usually done in textbooks to facilitate the understanding of the structure as represented in Figure 3. Answer 4
Question 7
If each external sphere is considered centered in each corner of the cube, the length of the cube edge, ledge, according to provided data is 47 m (= 2 × 9 m + 29 m). By the Pythagorean theorem, the diagonal of this cube, d, is given by
The metallic radii of three metals with body-centered cubic structure are 0.152 nm for Li, 0.231 nm for K, and 0.262 nm for Cs.9 Calculate the height (diagonal of the cube) of hypothetical “Atomiums” if they would represent the same relationship size of 165 billion times for these metals. Compare the calculated diagonals (heights) with the diagonal of the “real” Atomium.
d=
3(ledge)2 =
3(47 m)2
(1)
and d is 81.4 m. According to provided data, d is equal to [4(9.0 m) + 2ldia], where ldia is the length of each two of the two tubes of a diagonal. Thus, ldia = 22.7 m. In the information on the Atomium Web site,5 this value is given as 23 m.
Answer 1
Iron metal does not form discrete molecules, but a crystal lattice of atoms of iron. The Atomium does not represent “anything about the structure of the atom”, but it represents the unit cell of the crystal structure of the atoms of iron.
Answer 5
In the indicated cube, there is one sphere in the center and eight 1/8 “pieces” of sphere at each corner. In the same way, the unit cell for a body-centered cubic structure contains only two complete atoms: the central one and the eight 1/8’s that make up each corner. Thus, there are the volumes of two spheres in the cube.
Answer 2
The Atomium represents a body-centered cube structure. It is not easy to identify for students because, in the Atomium, the cube is rotated with respect to the usual representation of a cube, as can be seen in Figure 3. The three metallic elements
Answer 6
By considering 165 × 109 times the metallic radius of iron (0.126 nm), a radius for the sphere of 20.8 m is obtained, that is, 15.5% higher than the data indicated for it (18.0 m). By considering the structure of iron shown in Figure 4, the diagonal across the unit cell, d, is 4 times the radius of the atom, ratom, of iron, and thus, the length of the unit cell, ledge, is given by ledge =
4(ratom) 4(0.126 nm) = = 0.291 nm 3 3
(2)
Figure 3. Body-centered cube structure as usually represented in textbooks (left) and the same structure rotated, resting on a single sphere so that the diagonal of the cube is vertical, as in the Atomium (right).
The length of the unit cell scaled by 165 × 10 is 48.0 m, which is very close to the given value (47.0 m). In fact, there is only a deviation of 2.1%. In other words, the Atomium represents 165 billion times the length of the edge of the unit cell of iron and not of the metallic radius of this element.
discovered by Spaniards, with the name of the discoverer and the year of discover in parentheses are platinum (Antonio de Ulloa, 1748), tungsten (Brothers Juan José and Fermı ́n Fausto de Elhúyar, 1783), and vanadium (Andrés Manuel del Rı ́o, 1801).10 Their crystal structures are body-centered cubic (V and W) similar to iron and face-centered cubic (Pt).9
Answer 7
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In the same way that the height (diagonal) of the Atomium was calculated to be 81.4 m (using eq 1), students can estimate this diagonal for selected metals, for hypothetical “Atomiums”. With the same relationship in size of 165 billion times, and taking into account that the diagonal is 4 times the atomic radius, the length of the diagonal would be 100.3 m for Li, 152.5 m for K, and 172.9 m for Cs. As it can be appreciated, the height of the “Atomium” increases from Fe to K (same period in the periodic table of elements) and it also increases in the order Li < K < Cs
Answer 3
In a body-centered cube structure of a metal, such as iron, the spheres in each corner touch the central sphere, as can be seen in Figure 4. Thus, each sphere of the Atomium represents only 923
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(3) Amey, J. R.; Fletcher, M. D.; Jones, A.; Roberts, E. W.; Roberts, I. O. J. Chem. Educ. 2008, 85, 1361. (4) Jones, G. Molecules Matter. http://www.makeitmolecular.com/ (accessed on Apr 2012). (5) The Atomium Official Website. http://www.atomium.be (accessed Apr 2012). (6) History of the Atomium at Commune Libre de l’Ilot Sacré. http://www.ilotsacre.be/site/en/default_en.htm (accessed on Apr 2012). (7) Pinto, G. J. Chem. Educ. 1998, 75, 725−726. (8) See for example: Kelter, P.; Mosher, M.; Scott, A. Chemistry: The Practical Science; Houghton Mifflin: Boston, MA, 2007. (9) Stark, J. G.; Wallace, H. G. Chemistry Data Book. SI Edition; John Murray: London, 1980. (10) Pinto, G., Rivero, C. Revista UPM 2011, 21, 8−13. Accessible at: http://www.upm.es/sfs/Rectorado/Gabinete%20del%20Rector/ Revista%20UPM/REVISTAUPM21.pdf (accessed on Apr 2012).l (11) Oliver-Hoyo, M. T.; Pinto, G. J. Chem. Educ. 2008, 85, 218− 220. (12) Pinto, G. J. Chem. Educ. 2009, 86, 185−187. (13) Oliver-Hoyo, M. T.; Pinto, G.; Llorens-Molina, J. A. J. Chem. Educ. 2009, 86, 1277−1280. (14) Pinto, G.; Gauthier, C. V. J. Chem. Educ. 2009, 86, 1281−1285.
(same group in the periodic table of elements), as a consequence of the typical trends for atomic radii.
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STUDENTS’ RESPONSE First-year undergraduate engineering students appreciated the question−answer approach and were motivated and interested. They liked the activity and most of them gained an appreciation for the three-dimensional structures. Furthermore, as engineering students, they especially appreciated the significance of the construction of the monument. As discussed in recent previous papers11−14 intended to help instructors include connections between students’ daily experiences and chemical principles taught in the classroom, students have expressed keen interest in this type of “tangible” chemistry where a concrete example of everyday life puts textbook chemistry in context.
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SUMMARY This work discusses a teaching tool that reinforces the work done with unit cells and adds a cross-cultural dimension that is becoming more important in an increasingly interdependent world. By the use of the Atomium at Brussels, Belgium, introductory solids structure calculations can be made more interesting and challenging. Such context enables students to connect the relevance of solid-state chemistry outside the classroom environment. This experience helps students to understand the spatial quality of atoms. Discussion of this kind may encourage students to explore topics in more depth. For example, students can be asked to reproduce the proposed questions by considering other hypothetical geometries for the Atomium, such as simple cubic or face-centered cube, typical of other metals. Also, the discussions with students about public misunderstandings help them to think about the importance of trying to acquire best information through science.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The author declares no competing financial interest.
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ACKNOWLEDGMENTS Marı ́a T. Oliver-Hoyo, Chemistry Department, North Carolina State University at Raleigh is thanked for helpful comments on the manuscript. The author also would like to gratefully recognize the support provided by the Universidad Politécnica de Madrid, under the project “Multiple bonds: chemical education at dif ferent educative levels”. I dedicate this work to my family, because the travels to Brussels with my parents, sister and three brothers, years ago, and with my wife (Elena) and daughters (Elena Lucı ́a and Elisa Marı ́a), in the summer of 2011, gave me the motivation to develop this exercise.
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REFERENCES
(1) Cady, S. G. J. Chem. Educ. 1997, 74, 794−795. (2) See for example: Division of Chemical Education, College of Science (Purdue University). http://chemed.chem.purdue.edu/ genchem/topicreview/bp/ch13/unitcell.php#top (accessed on Apr 2012). Crystallography in a nutschell, by C.E. Strouse. http://www. mic.ucla.edu/X-ray/tutorials.htm (accessed on Apr 2012). First Year Chemistry at The University of Sydney. http://firstyear.chem.usyd. edu.au/calculators/bcc.html (accessed on Apr 2012). 924
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