Solid State Chemistry Taught as a Comprehensive University Course for Chemistry Students Elena V. Boldyreva Novosibirsk State University, Division of Solid State Chemistry, Pirogova, 2, 630090, Novosibirsk, Russia The importance of solid state chemistry both for fundamental chemical science and for modern technology seems to be recognized generally. Nonetheless, teaching solid state chemistry does not seem to be adequate ( I ) . According to the results of the questionnaire reviewed in (I):
...there is no mmprehensive course on solid state chemistry at universities intended not for narrow specialists hut for all chemistm students. Instead of an inteerated course students ufln are h6ven separate pam of it rlrmrnts of rtystallography, elcmrnts of solid rtate physlrs. or even narrow sprrtal pnhlems that are the 9ub~ectof thew teacher invratagations. The problem of teaching solid state chemistry a s a comprehensive course seems to be a n urgent one. According to M. Stanley Whittingham from State University of New York a t Binghamton, the work of one out of every three chemists is related in some way to solid state chemistry (I). I n the present contribution I would like to relate our experience-giving a comprehensive course "Introduction to Solid State Chemistry" intended for all third-year undereraduate chemistrv students (aooroximatelv 100 students . per year) a t Novosibirsk State University. If other comprehensive solid state chemistry courses are taught elsewhere, it would be fruitful to use this Journal for exchange of information.. o~inions.and exoerience. The main goal of a n integrated, comprehensive course is to give the students a general idea of the defmition of solid s t a t e chemistrv, its place among other chemical disciplines, the ma& probiems arising%hen reagent(s) orland product(s) of a chemical reaction are solid, and how these problems are to be solved. We try to teach the students "the language" used when dealing with solid state (ranging from metal alloys to bioorganic molecular crystals), rather than go into details concerning structure, properties, and reactivitv of oarticular solids. Students to be soeciallv trained i h soid state chemistry get more detailed 'cours& (in materials science, solid state physics, crystallography, heterogeneous kinetics, experimental techniques, thermodvnamics of ~ o i n defects. t . . .) a vear later. The -general outline of thecourse is given in ~ a h 1. e
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A
Principles Guiding the Course 1 Trach~ngof ~ o h drtate ehem~stryi s closely related to other chemlcal courses A general ~deathat hrlp~dur to make the muse compact, logical and not fragmentary was to consider all the models used in solid state chemistry in comparison with corresponding models known in "molecular chemistry". We aim to demonstrate the interrelation between "molecular" and "crystal" models and, at the same time, stress the difference between "molecular" and "crystal" thinking. Group theory provides us the language, unifying the whole course and allowing us to compare molecular and crystal models. When considering imperfect solids, we make a link between "classical thermodynamics of electrolyte solutions" and the thermodynamics of defects in solids. Heterogeneous kinetics is mnsidered as compared to the homogeneous one.
Table 1. General Structure of the Course 1. General Introduction
Solid state chemistry as a part of chemistry. Preparative, analytical,physical solid state chemistry. The role of solid state chemistry in modern materials science and chemical engineering. 2 Perfect Solids Atomic structure. Electronic structure. Physical properties determined by perfect structure. Effectof perfect structure on chemical reactions. 3. Real (Imperfect) Solids
Main types of imperfections (defect),their effect on the atomic and electronic structure. Real structure. Properties determined by real structure. Effect of imperfections on chemical reactions. 4. General Conclusion The interrelation between ideal structure, real structure, and physical and chemical properties of solids. Spatial propagation of the reactions of solids. The main problems of solid state thermodynamics and solid state kinetics. Metastable states and solid chemistry. Control of the reactivity of solids. Control of the properties of solid materials.
2. From the beginning to the end of the coune, examples are homowed from both inorganic and organic solid state chemistry, including biomimetic reactions. We consider metals, ceramics, molecular crystals, glasses, ionic salts, ete. and demonstrate, that all these different solids have something in common, related to their aggregation state. 3. One- and two-dimensional periodic models are used widely to introduce the main concepts, as the subject of student exercises, and to check understanding. 4. The course is subdivided into blocks. Each new hlock is intmdueed by a lecture. Then students are expected to get necessary training at the seminan (with the help of a tutor) and at home solving various problems. At the end of the block one more summarizing lecture is given. We try not to overload the students with empirical fads during lectures hut to give them a general idea of the subject. Details are considered during seminars. BY the end of the semester the students are expected to prepare a review on one of the general topics, using the Lecture and seminar nates, as well as special scientificliterature. Examples of todcs are listed in the "General Conclusion"part
To give some idea of how these principles are realized practically, I would like to comment on the program. Volume 70
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Table 2. General Comparison of the Description of the Symmetry of Molecules and Crystals
Molecules Symmetry operations
Any point
operations
Group, Point characterizing symmetry the symmetry group (all point operations)
Crystals Point operations mnsistent with translational symmetry + Space operations 1) Space group (all point and
space operations)
2) Point group s(point operations)
3) Crystallographicclass (all point operations + point contributions of space
- -
oneratinncl -. ..-. .-,
4) Translation group (all
translations) + Bravais group
5) Crystallographicsystem (all
point operaiions of the Bravais lattice) The number of possible symmetry groups
Infinitein principle
Finite in principle (for three dimensional periodic structures only 230 space groups,32 point groups. 14 translation groups and 7 crystallographic systems are possible)
Figure 1. General view of solid state chemistry as a scientificdiscipline. The Appendix also contains some exam~lesof the oroblems suggested to the studcnts for individual study. detailed information also is available on request.
ore
Introduction to Solid State Chemistry Course Outline 1. Introduction
The topics covered in the introductory lecture are given in Table 1. The main idea of this introductory lecture can be summarized by the diagram in Figure 1. I stress that within any "subdivision"of solid state chemistry, inorganic, organic, or coordination compounds can be considered. We discuss the role of solid state chemistry in modem life. I first demonstrate numerous examples of new materials present in the classroom. remind of others present outside, and finally give a general table of various applications of solid state chemistry ramina from metals or functional ceramics production-to the creation of new medicines.
2 Perfect Solids
2a. Description of a Perfect Solid The main unifying idea when teaching the chemistry of ofsolids fmm perfect solids is to consider all the . properties . the point of view of symmetry. First, symmetry of "static structures", the symmetry of atomic positions is considered. We use the language of group theory (1)to compare the symmetry of molecules and the symmetry of periodic structures (crystals) and (2) to introduce the basic concepts of crystallography, necessary for practical work with solids. Table 2 and examples 1-3 in the Appendix may give some idea of how it is done. During practical training i n symmetry, students also solve some problems, preparing them for the lectures devoted to vibrational and eleitronic properties of periodic structures (See example 5-6 in the Appendix). The next step is to consider vibrations in crystals from the point of view of symmetry. In contrast to traditional 552
Journal of Chemical Education
solid state physics courses ( 2 4 ) , we start this topic not by the consideration of the vibrations of linear chains, but by comparing vibrational spectra of, say the C03'- ion (a) as an isolated ion (b) in the crystals of CaC03(aragonite) ( c ) in the crystals of CaC03(calcite)(5). Because the conce~tof ~ositionalsvmmetrv is known to the students from the l&res onBymmetry of solids, it is easy to show the effect of the crystalline surrounding of the vibrational spectra of some species. Further examdes are chosen from chemistrv of molecular (organic) soiids. The effect of interactibns between the molecules on the "intramolecular" vibrations in molecular crystals (Davydov splitting) is considered also (5, 6). Only then do we start discussing vibrations in crystals where no complex "individual species" (like an organic molecule or a COBion) can be found: metals, simple oxides, halides of alkaline metals, etc. The effect of translational symmetry on the vibrations is then discussed, and comparison is made with the effect of point symmetry on the vibrations. Vibrations in periodic chains formed (a) by identical and (b) bv different atoms are considered rather traditionallv (24:. The concept of acoustic and optic phonons is intrdduced. Finallv. ".we comoare two different ao~roachesto the description of vibrations in solid-starting from a molecule and starting from a periodic chain of identical speciesand discuss the advantages and the disadvantages of each model when applied to this or that class of solids. The electrot& structure of solids also is considered from the point of view of symmetry. We do not follow the traditional presentation for courses of solid state physics (free electrons-weak bond approximation-strong bond approximation) (241, but rather treat them in the manner used by R. Hoffmann (7) or R. Evarestov (8). Just as electronic structure of a molecule is "modulated" by point group symmetry, the electronic structure of solids is symmetry adapted, but for periodic structures translational symmetry is of no less importance than point symmetry We considered the electronic structure of one- and two-dimensional structures because these wstems are much easier for calculations and, at the samctime, allow us to introduce the main concepts. Finally, generalization is made for ~~
..
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the three-dimensional periodic structures. Some experimental data andlor results of computer simulation of the electronic structure of three-dimensional solids are suggested for the interpretation of students. 26. Properties of Perfect Solids This part of the course illustrates the influence of ideal atomic and electronic structure on the physical and chemical properties of solids. This problem was ~ a r t l discussed v whei &sidering vibrationLin solids or electronic structure of solids above. However, a special block is also devoted to the problem. First of all, those ~rouertiesof crvstals are considered that can be &terpre&d only on the basis of our knowledge of the symmetry of the structure. Anisotro~vof solid state prupe&es is &scussed in this part of thg&urse. It is of great help for us that students are familiar with tensors from the previously studied courses in mathematics and physics. When illustrating the anisotropy of solid state properties we use not on% " t r a d i t i o n a l ~ ~ a m ~from les crystal physics (941),but also show (for the first time during the course) the anisotropy of the interface propagation during solid state reaction. Problems of spatial development of solid state reactions are discussed in detail later. After that the properties of solids are considered.At this point we introduce description of solids (a) as a net of polyhedera and (b)as close packings.
We consider the structures of nonwstalline solids as compared with periodic crystal struct;res, stressing not only the differences, but also similarities (See Table 3). When discussing amorphous structures, concepts of polyhedral nets and irregular close packings are used widely. In general, our approach to teaching this part of the course is close to those described in a number of publications (15 -19). Experimental techniques of studying noncrystalline solid state also are discussed briefly. 2e. Factors Determining Structures of Solids Prediction of Cwstal Structures Crystal ~ n g i n e e n ' n ~ Metastable Structures of Solids. This part of the course is of special importance for reparative solid state chemistry, & partic&, for materials science and crystal engineering. It also is of great importance for proper understanding of the reactivity of solids. All the factors are subdivided into thermodynamic and kinetic ones. Thermodynamic factors determine the equilibrium structure; whereas, kinetic factors are mainly to be taken into account, when the structure, obtained under peculiar experimental conditions, is to be predicted. We consider the role of the radii and electronic structure of atoms, forming a crystal structure, discuss the SSD (structural sortini diagramsktechnique (201. The concept of optimizing packing density (21) is considered. We also eive some eeneral idea of different methods of calculatine packing e&rgies for solids, belonging to different classes: metal. ionics. and molecular crvstals (21-23). When discussihg kinetic factors, the &ncept's of tdpotaxy and e ~ i t a x vare introduced (24). "To~ochemical~rinciole"also is remkded once more and dis&ssed in a Ader sense.
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The usefulness of the concepts when interpreting properties of silicates. oxides. halides. halweenides. metals. and molecular crystals is discussed: We cksider various ways of representing "empty space within a solid" (concepts of "free volume", "packing density", "reaction cavity") and dis3. Real (Impedect) Solids cuss the role of " e m.~" t vsoace" . in determinina chemical properties of solids intercalation and inclusion phenomIn this part of the course various possible deviations ena, and organic solid state reaction. Radiolvsis of inorfrom ideal atomic and electronicstructure (various t w e s of ganic salts-also serve a s examples. " ~ o ~ o c h e m i c a l defects) are considered. Most important ii this blockis principle" also is f ~ s introduced t within this block of the (1) to discuss with the students the influenceof the defects on course. physical properties and chemical reactions of solids and (2) to eive a eeneral idea of the role of interfaces in solid state 2c. Experimental Study of Perfect Atomic and Electronic Structure of Solids and Their Vibrational Properties To be able to consider these two problems adequately, it This part of the course is rather traditional (13,14). Diffraction and spectroscopic techniques are considered. Speis necessary first to "learn a new language". We try to cial attention is paid to the variants of the methods with make a link with the part of the course devoted to perfect good spatial resolution (microspectroscopy, local difsolids, exploiting the concept of symmetry when considerfractometry using Synchrotron irradiation sources). ing defects. At the same time, some new concepts also are to be introduced, as compared with treatment of ideal sol2d. Noncrystalline Solids: Amorphous Solids, Incommenids. That is why we start this block from new definitions. surate Phases, and Quasicrystals 3a. Various Dpes of Defects in Solids Liquid Crystals (General Introduction) Up to this part of the course (2a-24, we deal only with classiiication of defects crystalline solids (with the exception of the very first introorigin of defeds ductory lecture). However, importance of noncrystalline equilibrium /nonequilbrium defeds (general introduction) solid state rewires that a special block of the course influence of defects on properties of solids (generalintroducshould be devoted to it. tion) Structural and electronic defects are introduced. includTable 3. General Comparison of the Structures ing vacancies, interstitials, impurities, dislocation$, stackof Various Solids ing faults, shear structures,. -main boundaries. and heterogeieous inclusions. Long-range Order Periodicity Thermally, mechanically, and radiation-induced defects are considered. After that each type of defect is considered Crystals in more detail. Quasicrystals 3b. Point Defects in Solids Incommensurate thermodynamics of pomt defects in solids (including point structures defects in compounds,; mobility of point defens Amorphous solids 'the influenceof point defecta on physical properties of solids experimental study of point defects Volume 70 Number 7 July 1993
553
interaction of point defects clusters, ass&iates, and superstructures effect of point defects on chemical reactions Our treatment of thermodynamics of point defects is based to a large extent on the "classical " textbooks on the matter (25,261; that is, it follows the traditions of "classical" thermodynamics of diluted electrolyte solutions. Thermodynamics of point defects gives an opportunity to show once more in this part of the course the close interrelation of solid state chemistry with other chemical disciplines. Students usuallv are i m ~ r e s s e dto see that the main laws of solution th"ermodynknics are applicable to "structural elements"-vacancies and interstitials--of the crystal At the same time, we discuss new factors, arising in a solid as compared with a solution. First of all, the role of mechanical stress is discussed. Structure distortions induced in a crystal by point defects are considered. These distortions manifestthemselves in physical and chemical properties of solids. When discussiw diffusion of point defec&, we also take into account not-bnly gradienis of concentration an&or electric field, but also field of mechanical stress ("uo-hill diffusion"). (10.271. . , . Soecial attention is oaid to the ;&libria "solid-gas" in nonstoichiometric solidi(25, 28). Various possible reasons of the existence of nonstoichiometric solids are discussed. When discussing the effect of the defect on *~hvsical ~ r o ~ e r t i ewe s . widelv use " * again the concept of symmetry, in particular of site symmetry. Experimental techniques of studying point defects are considered in comparison with the application of the same techniques to the study of ideal solids. For example, we discuss, what differences are to be expected
.
(a) in the powder diffraction patterns, (b) in single crystal diffaction patterns, (c) in optical absorption spectra of several solid samples, if all the samples represent the same polymorph of the same chemical compound, but differ in the type and the concentration of defects. Techniques peculiar for the study of point defects are considered. First of all, various types of electrophysical measurements (conductivity measurements, etc.) are wnsidered. The effect of point delects on chemical reactions is hardly described in "traditional" 122.29) textbooks on solid state chemistry. However, a number of monographs and reviews, specially devoted to the subject, is available (3043). 3c. Dislocations in Solids main types of dislocations energy of dislocation deformation of atomic and electronic structure mobility of dislocations effect of dislocations on the mechanical properties experimental study of dislocations influence of dislocations on the chemical reactions Dislocations are imoortant for solid state chemistrv for several reasons. First, dislocations are the sites in the crystal, where chemical reactivity is changed. Second, dislocations play a crucial role in the relaxation of mechanical stress in solids, in sintering, and in fracture. Mechanical stress is known to be one of the most important factors affecting solid state reactivitv. Sinterine and fracture are important in preparative &lid state chemistry, namely in materials science. Teaching of dislocations in our course is based partly on the "classical" monoera~hson the subiect (34. 35). However, the influence of dislocations on c h ~ m i creactivity ~l is not considered in such monographs. To consider this prob-
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554
Journal of Chemical Education
lem, we analyzed numerous original publications on reactivity of solids. When discussing the role of dislocations in fracture or sintering, we return once again to the problem of internlation between the momholow -" (or the texture) of a solid material and its characteristics. 3d. Interphases and Interfaces Solid surfaces .Interfaces "solid-vacuum" .Interface "solid-gas" 'Interface "solid-liquid" Interface "solid-solid" The differencein the electric potentials. Point defects and electnn-hole equilibria. Mechanical stress field. Dislocation structure of interface Experimental study and computer simulation of the interfaces 'Interfaces and solid state chemistry: properties of materials ' chemical reactions
This block ofthe course is of crucial importance, because solid state chemistry is to a large extent the chemistry of the interfaces. However, the topic is usually either omitted or not treated adequately in traditional textbooks. The most helpful reviews were written by H. Schmalzried and his co-workers (36.37). Some monographs on semiconductors physics (38) A d books on electr>dik (39). where point defects and electron-hole equilibria are treated in detail, also were helpful. Mechanical stress field a t the interfaces also is considered in the original monographs and reviews (27,40). 4. General Conclusion
The main ma1 of this concluding block of the course is to summarizethe abundant mate2al studied during the course. The students are expected to be ready to make such a summary themselves, a& a tutor helps them and controls the results. Appendix Some examples of problems suggested to students for individual study. 1A. Find all the symmetry operations, characterizing the symmetry of a regular triangle (Fig 2a). Write down the symbols of the operations (a)in Schoenfliess ~spectmspcopic") system, (b)in international ("crystallographic")system. Write down the matrices of all the operations. Use Kelli's table to test if these operations form a p u p . Write down the svmhol of the m u n . .
.
.
. "
rh, in international ("crystallu~~aphic") system. of the symmetry p u p . How should Find the suh&~o-oupa
we deform the triangle to make its symmetry carrespond to the symmetry of the subgroups? Write down the cwrdinates of general and special equivalent nositions. 1B Consider five diITerent structures, periodic in one dmension only, formed by regular triangles (Fig.2, b-0. e For each u f ' ~ hstructures: Find the symmetry operations, characterizing the symmetry. Compare them with the symmetry operation characteristic for an individual triangle. Prove that the svmmetrv form a .. noun. - onerations . . Find the subgroups of the space group. Find space group, polnr group, crystallographic claaa, translatlun (Bravais) group. Is the space group s-orphous or not? Write down the cmrdinates of general and special equivalent positions for the space gmup. Answer the same questions if in all the structures (h-0 triangles rotate freely
(a) for Lit ions
(b) for C?+ ions
Figure 2. A regular triangle (a) and five differentstructures, periodic
in one dimension, formed by regular triangles (b-f). Examples for the training problem 1.
Write down the corresponding quasichemical equations, using Kroeger symbols. Why are the defects, arising in MgO and in COOwhen doping the crystals with Lif,different? Calculate the equilibrium concentrations of the defects in doped crystals of MgO and COO: (a) as a fundion of the impurity concentration (partial pressure of oxygen in contact with the sample being constant), (b) as a function of the partial pressure of oxygen in contact with the sample (the impurity concentration being constant). Suggest the experimental techniques to study the defects in these solids. What physical and chemical properties of MgO and CoO may be expected to be sensitive to the concentration of the defects in these solids? 10. Exdain whv solid samoles of o-ethoxv-trans-cinnamie acii show dikerent reactihty in respect t6 photodirnerization, depending on the solvent from which they are recrystallivprl .--- --. 11. Explain why reduction of NiO by hydrogen proceeds via formation and growth of Ni-nuclei and the kinetics of the
2. An international symbol of the space group of a two-di-
mensional periodic structure is suggested. Write the mrdinates of general and special equivalent position. Can a structure described bv this mace m u n be chiral? Do equivalent directions exist in thk shuetke? What are their symbols? Do polar directions exist in this structure? What are their symbols? TT I to predict the anisotropy of various Drop&ies such as thermal expansion, p&arizatian, o&ieal and mechanical nro~erties. diffusion. electrical wnduc. . tivity Is it possible to expect different edges of a hypothetical two-dimensional crystal of this symmetry to show different reactivity in respect to: a. dissolution b. interaction with gases c. sublimation? 3. Space group of the crystal structure of %O, is P2 2 2 Parameters of the elementary cell are a = 12.50 1 , l d l 15.196 A, c = 5.448 A. Density is 6.214 g/em3. Coordinates of how many Re and 0 atoms should be defined to describe the structure unambiguously? 4. Suggest the way of transforming the structure of Si into the structure ofSiOz, r e q u i ~ ag minimum of atomic displacements. Write down the transition matrice. 5. Compare the symmetry of a free COZ2-ion with the positional symmetry of the ion in the structures of (a) arage nite and (b) calcite. Can the positional symmetry be i n f l u e n d by a deformation of the structures? 6. Compare the positional symmetry of Zn" in two polymorphs of ZnS-sphalerite and wurtzite. 7. In the vibrational spectrum of the crystals of K2SiFsa triple degenerate vibration of SiFs2-ion, Flu, is observed (v = 488 m & . Try to explain why in the crystals of B a S i b this vibration is split into two: Flu --t A2, + E, (vl = 472 em-', v2 = 506 em-'). 8. A band structure calculated for some solid compound is suggested for the interpretation of the students. The students are expected to show energy gaps, to comment on the band width, to show possible electronic transitions, and to estimate their energies. 9. What defects arise in the aystals of MgO when a small part of Mg& ions is substituted isomorphically (a) for Lit ions? (b) for y3+ions? What defecta arise in the crystals of CoO when a small part of Co2+ions is substituted isomorphically
Solvent, from which the samples are recrystallized
Product formed ~ n d e r irrad atlon of solld sampes
ether benzene ethanol
truxillic acid truxinic acid no reaction occurs
process is autocatalytic. Consider the interface Ni-NiO formed and discuss, what is changed in the crystal of NiO a v a result of the formation of Ni-nucleus. How can these changes influence (a) the growth of nucleus and (b) the formation of new nuclei? Suggest experiments to test your hypothesis.
Literature Cited New Yo*, 1976. 4. Blskemare, J. S. Solrd StotrPhyaiw Cambridge University h a : Cambridge, 1986.
5. P d e f
H.;Mathieu,J-P.SmtrssdeVibmtionetSymt~de8Cliafff;Gordonend
B-4, Pans,1970. 6. Dsvydov. A. S . T h w ofLighf Absorption by Molecular Cmstdls; lad. Aksd. Nauk Ukr SSR: Kiw, 1951(in Ruslanl. 7. Hoffman, R. Sdrd. and S u W s : A Chmldh Vmw on Bondiw in Ex*"& turns:VCH Publishers: New Yo*, 1988.
Strur-
8. Evarestov,R.:Smimw,Y MefhaBofGroup Theo'y in Quantum ChmratyofSolrds: I d Leningrad. Univ: k n i n g a d . 1987 (in R u s s w l .
9. Nye, J. F Phwical Pmpr(les lefC'ysff11: Their Repmwnation & nmw8 andMa. f-s; Oxford Reas: Clarendm, 1957. 10. Vainatein, B. K, Ed.Mdarn Cryaallogmphy; Nauka: Moa-, 1979,Val.4 (inRus-
.-.,A"-.
17. Dratias, D.Rpehrrcha 1888,N 178,788-798. 18. Villain. J. R p e h m h 19W, N 250, 1498-1506. 19. Jamsen, T. 2. Klist. 1992,198,N 112,1132. 20. Roy, R.Sdid Stofe Imics 1988,3W3,3-22. 21. K t a W c d & x A M o k c u l a ~Crystals:Naulta: Moaeow, 1971(in Russian). 22. West, A R. SolidStnts Chmlnryond itsApplimtion; Wilqr: Chicheater, 1984. 23. ~ e a t mR.: , cavezzotti,~.~ ~ s t ~ e f ~ e f ~ e f ~ e f n d o ~f m ~p &n~l el ~a l o ~ ~ ~ ~ l e ; p ~ p ~ t , Ed.; Elaevier:Amsterdam, 1990,161-210. 2.4. O m d d , H. R.; Guoter, J. R In 2976 C ~ y a I dGmwth and Motoriols: Kaldi* E.; Scheel, H. J.. Eds; Nolth Holland Publishing Company: Amsterdam, 1977. 25. Sehmalzried. H; Nevrotakx A. F~sfka'pp~hemodynam
