Top

Published in:

2011 | OriginalPaper | Chapter

2. Solid-State Chemistry

Author : Bradley D. Fahlman

Published in: Materials Chemistry

Publisher: Springer Netherlands

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The properties of materials is governed by the interactions among its associated sub-units. This chapter will describe the bonding motifs of both crystalline and amorphous solids. Details of common archetypical crystal structures will be given, as well as introductory X-ray crystallography including space group symbolism and X-ray diffraction. Band theory is also provided, which is critical in understanding electrical conductivity and optical properties of crystalline solids. Applications such as superconductivity, fuel cells, and biomaterials are highlighted in this chapter in addition to many others, as we describe the influence of a material’s structure on its associated properties.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter What is Materials Chemistry?

next chapter Metals

Zallen, R. The Physics of Amorphous Solids, John Wiley and Sons: New York. 1983.

Note: there is no empirical evidence that supports the flow of glass over time. That is, there is no analogous glass thickening observed in ancient Roman or Egyptian objects, no degradation in the optical performance of antique telescopes/microscopes, and no change in physical properties of prehistoric artifacts (e.g., dulling of obsidian swords).

Note: electrons in an s-orbital have a finite probability of being found at the nucleus. As the principal quantum number increases, the s-orbitals become more diffuse, leading to electrons being found at distances further from the nucleus. With less attraction toward the nucleus, these electrons are able to orbit the nucleus at speeds approaching the speed of light. When objects move at such high speeds, an increase in relativistic mass occurs, whereby the s-electrons behave as though they were more massive than electrons moving at slower speeds. This mass increase causes the orbiting electrons to be slightly contracted toward the nucleus, decreasing their availability to participate in chemical reactions.

Schroers, J.; Johnson, W. L. “History Dependent Crystallization of Zr₄₁Ti₁₄Cu₁₂Ni₁₀Be₂₃ Melts” J. Appl. Phys. 2000, 88(1), 44–48, and references therein. More information may be obtained from http://www.liquidmetal.com.

For example, see: Dera, P.; Lavina, B.; Borkowski, L. A.; Prakapenka, V. B.; Sutton, S. R.; Rivers, M. L.; Downs, R. T.; Boctor, N. Z.; Prewitt, C. T. Geophys. Res. Lett. 2008, 35, L10301.

(a) Malone, B. D.; Sau, J. D.; Cohen, M. L. Phys. Rev. B 2008, 78, 161202, and references therein. (b) Pfrommer, B. G.; Cote, M.; Louie, S. G.; Cohen, M. L. Phys. Rev. B 1997, 56, 6662, and references therein.

There is an ongoing debate whether the term “pseudopolymorph” should be abandoned, instead designating these compounds as “solvates”. Two viewpoints may be found at: (a) Bernstein, J. Cryst. Growth Design 2005, 5, 1661. (b) Nangia, A. Cryst. Growth Design 2006, 6, 2.

For a nice presentation regarding the thermal characterization of polymorphs, and the implications of polymorphism toward drug design, see: http://www.usp.org/pdf/EN/meetings/asMeetingIndia/2008Session1track3.pdf

For example, see: Perrillat, J. P.; Daniel, I.; Lardeaux, J. M.; Cardon, H. J. Petrology 2003, 44, 773. May be found online at: http://petrology.oxfordjournals.org/cgi/content/full/44/4/773

(a) For instance, the high-pressure polymorphism of silica is described in: Teter, D. M.; Hemley, R. J. Phys. Rev. Lett. 1998, 80, 2145; also available online: http://people.gl.ciw.edu/hemley/192TeterPRL 1998.pdf. (b) McMillan, P. F.; Wilson, M.; Daisenberger, D.; Machon, D. Nature Mater. 2005, 4, 680.

Note: the Miller indices for the (211) plane may also be visualized by extending the unit cell beyond a cell volume of 1 cubic unit. For instance, equivalent planes would also pass through (2,0,0), (0,4,0), and (0,0,4), as well as other extended coordinates. For the (001) plane, the zeroes indicate that the plane does not intercept either the a or b axes.

Cullity, B. D. Elements of X-ray Diffraction, 2nd ed., Addison-Wesley: Reading, Massachusetts, 1978.

For a comprehensive list of SiC physical properties, see: http://www.ioffe.ru/SVA/NSM/Semicond/SiC/bandstr.html#Band

For more details about the structure and applications of SiC, see: http://www.ifm.liu.se/matephys/new_page/research/sic/index.html

Note: CdCl₂ also exists as a hexagonal lattice, analogous to CdI₂.

This is the first of five rules that govern the geometric stability of ionic packing, as proposed by Nobel Laureate Linus Pauling (J. Am. Chem. Soc. 1929, 51, 1010). For more details, see: http://positron.physik.uni-halle.de/talks/CERAMIC1.pdf

(a) Honle, W. J. Solid State Chem. 1983, 49, 157. (b) Perrin, et al. Acta Crystallogr. 1983, C39, 415.

For a recent discovery of a safer cathode alternative, LiFeO₄, see: Kang, B.; Ceder, G. Nature 2009, 458, 190. Information regarding a proposed intercalation mechanism for LiFeO₄ may be found in: Delmas, C.; Maccario, M.; Croguennec, L.; Le Cras, F.; Weill, F. Nature Materials 2008, 7, 665. For a recent method to study the thermal stability of a variety of oxide cathode materials for Li-ion battery applications, see: Wang, L.; Maxisch, T.; Ceder, G. Chem. Mater. 2007, 19, 543.

Qi-Hui, W. Chinese Phys. Lett. 2006, 23, 2202.

For example, see: Ferracin, L. C. et al. Solid State Ionics 2002 , 130, 215.

Willard, M. A.; Nakamura, Y.; Laughlin, D. E.; McHenry, M. E. J. Am. Ceram. Soc. 1999, 82, 3342.

Nakamura, Y.; Smith, P. A.; Laughlin, D. E.; De Graef, M.; McHenry, M. E. IEEE Trans. Magn. 1995, 31, 4154.

http://www.me.psu.edu/sommer/me445/ntcnotes.pdf

(a) Jansen, M.; Letschert, H. P. Nature 2002, 404, 980. (b) Kasahara, A.; Nukumizu, K.; Hitoki, G.; Takata, T.; Kondo, J. N.; Hara, M.;Kobayashi, H.; Domen, K. J. Phys. Chem. A 2002, 106, 6750. (c) Hitoki, G.; Takata, T.; Kondo, J. N.; Hara, M.; Kobayashi, H.; Domen, K. Chem. Commun. 2002, 1698.

Pena, M. A.; Fierro, J. L. G. Chem. Rev. 2001, 101, 1981.

(a) Honle, W. J. Solid State Chem. 1983, 49, 157. (b) Perrin, et al. Acta Crystallogr. 1983, C39, 415.

A nice updated website for past/recent superconductor discoveries is found at http://superconductors.org/type2.htm

For example, see: (a) Emery, V. J.; Kivelson, S. A.; Tranquada, J. M. Proc. Natl. Acad. Sci. 1999, 96, 8814. (b) J. M. Tranquada, H. Woo, T. G. Perring, H. Goka, G. D. Gu, G. Xu, M. Fujita and K. Yamada Nature 2004, 429, 534. (c) Lee, K. H.; Hoffmann, R. J. Phys. Chem. A 2006, 110, 609. (d) http://www.nature.com/nature/journal/v440/n7088/edsumm/e060427-09.html

For instance, see: (a) Lanzara, A.; Bogdanov, P. V.; Zhou, X. J.; Kellar, S. A.; Feng, D. L.; Lu, E. D.; Yoshida, T.; Eisaki, H.; Fujimori, A.; Kishio, K.; Shimoyama, J. -I.; Noda, T.; Uchida, S.; Hussain, Z.; Shen, Z. -X. Nature 2001, 412, 510. (b) Shchetkin, I. S.; Osmanov, T. S. Powder Metall. Metal Ceram. 1993, 32, 1068. (c) Abd-Shukor, R. Solid State Commun. 2007, 142, 587.

One model used to explain superconductivity in YBCO is the reduction of unstable Cu³⁺ sites by redox reactions initiated by electrons passing through the solid in adjacent planes. As an electron passes by a Cu³⁺ ion, it causes an electron to be injected from a neighboring Cu²⁺ ion resulting in a lattice distortion, & hole propagation in the opposite direction. This concept is illustrated at: http://www.chm.bris.ac.uk/webprojects2000/igrant/hightctheory.html

Note: there are two ways to account for charge neutrality in p-type superconductors. First, La_2−xSr_xCuO₄ may be formally written as: La_2−xSr_xCu _1−x ²⁺ Cu _x ³⁺ O₄ where one Cu³⁺ (or a Cu²⁺ with a trapped hole, Cu²⁺(h⁺)) forms for each Sr²⁺ added. Alternatively, the formula may be written as La_2−xSr_xCu²⁺O_4−(x/2), where one oxygen vacancy is formed for every two Sr²⁺ ions added to the lattice.

For example, see: (a) Wojdet, J. C.; Moreira, I.; Illas, F. J. Am. Chem. Soc. 2009, 131, 906. (b) Kamihara, Y.; Watanabe, T.; Hirano, M.; Hosono, H. J. Am. Chem. Soc. 2008, 130, 3296.

A recent issue of the New Journal of Physics was devoted to discoveries related to iron-based HTS: http://www.iop.org/EJ/abstract/1367-2630/11/2/025003

Note: the most promising processing method for YBCO applications involves deposition onto a flexible metal tape coated with buffering metal oxides. Crystal-plane alignment can be introduced into the metal tape itself (via the RABiTS process) or a textured ceramic buffer layer can be deposited on an untextured alloy substrate (the IBAD process). Subsequent oxide layers prevent diffusion of the metal from the tape into the superconductor while transferring the template for texturing the superconducting layer.

For a comprehensive review of recent HTS wire installation projects, and DoE goals related to HTS-based electrical applications, see: http://www.energetics.com/supercon07/agenda.html

Note: there are precedents for crystals with five-fold rotation axes. These crystals are known as quasicrystals, since they exhibit long-range orientational order but are not consistent with lattice translations. For example, see: Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. Phys. Rev. Lett. 1984, 53, 1951. Another nice online summary of quasicrystals is: http://www.tau.ac.il/~ronlif/quasicrystals.html.

Note: the d notation indicates a diamond glide plane, found in diamond or zinc blende extended crystal structures. Whereas glide planes are found in many inorganic-based crystals, screw axes are found predominantly in protein structures.

Note: scattering from the nucleus does not contribute to coherent scattering due to its relatively large mass, precluding its oscillation from the impinging of incident X-rays.

Note: the cosine of angle φ is simply the x component of a unit vector after it is rotated by φ around a unit circle. If the vector is rotated at some constant speed, then its x-value will trace out a cosine wave as a function of time, with amplitude of vector length. Waves of different wavelengths or periods would result in the vectors rotating at different speeds; however, X-ray crystallography uses monochromatic photons of a single wavelength.

An excellent summary of crystallography and systematic absences is given by: http://xrayweb.chem.ou.edu/notes/symmetry.html#absence

(a) http://shelx.uni-ac.gwdg.de/tutorial/english/shelxs.htm; (b) http://www.lks.physik.uni-erlangen.de/diffraction/

Note: another way to state this is that for a single crystal, only a few lattice planes will be oriented at their Bragg angle at any one time.

(a) Yasuda, K.; Ohta, M. J. Dental Res. 1982, 61, 473. (b) Uzuka, T.; Kanzawa, Y.; Yasuda, K. J. Dent. Res. 1981, 60, 883.

For instance, see: Mukoseev, A. G.; Shabashov, V. A.; Pilugin, V. P.; Sagaradze, V. V. Nanostruct. Mater. 1998, 10, 273.

For example, see: http://xrayweb.chem.ou.edu/notes/twin.html

For example, see: Lakes, R. S. Science 1987, 235, 1038.

http://www.ntcresearch.org/pdf-rpts/Bref0606/M04-GT21-06e.pdf

The yield point for metals with gradual elastic–plastic transitions is constructed by drawing a straight line parallel to the elastic portion of the stress vs. strain curve at a specific strain offset, usually 0.002. The intersection of that line and the stress vs. strain curve gives rise to the yield strength, σ_y, of the material.

Garlick, G. D.; Kamb, W. B. J. Geol. Educ. 1991, 39, 398.

For example, see: Fritsch, E.; Massi, L.; Rossman, G. R.; Hainschwang, T.; Jobic, S.; Dessapt, R., found online at: http://www.aigsthailand.com/(A(vlNwUMqNyQEkAAAAMzQ3Mjc5MzItNDRkYy00NjIzLWEyY2YtNTg3YWM4M2EyYjlj2Mm3M88VUzWx_4m4U5KodgkCri41))/FieldTripsDetail.aspx?tID=185&type=Publications&AspxAutoDetectCookieSupport=1

Note: for a thorough treatment of crystal field theory, see Cotton, F. A.. Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry, 6th ed., Wiley: New York, 1999.

Note: the ground-state atomic term symbol for Cr³⁺ is ⁴F, which splits into ⁴T₂, ⁴T₁ and ⁴A₂ for an octahedral transition metal complex. For more information regarding term symbol notation and absorption spectra for transition metal complexes, see: Shriver et al. Inorganic Chemistry, 4th ed., W. H. Freeman: New York, 2006. http://www.scribd.com/doc/6672586/Electronic-Spectroscopy-1

Note: excited electrons give off their energy via infrared emission and thermal interactions with the corundum crystal lattice, referred to as electron–phonon (lattice vibrations) interactions.

For an explanation of the electronic transitions underlying ruby lasers, as well as tunable lasers such as alexandrite, Ti:sapphire, and Nd:YAG, see: Thyagarajan, K. Lasers, Theory and Applications, Plenum Press: New York, 1981.

See Shriver et al. Inorganic Chemistry, 4th ed., W. H. Freeman: New York, 2006 for more details re LMCT and MLCT processes.

For more information regarding the trichroism of iolite and its use as a “Viking compass”, see: http://www.nordskip.com/iolite.html

Note: the Pauli exclusion principle states that each electron must possess a different set of four quantum numbers; that is, two electrons housed in the same orbital (identical n, l, m _l) must be of opposite spin (m _s = ±1/2).

Note: the work function is the solid-state analogy of ionization energy, defined as removing the outermost electron from a gaseous atom. In general, the work function is ca. 1/2 the value of the ionization energy of its corresponding gaseous atoms.

(a) Reif, F. Fundamentals of Statistical and Thermal Physics. McGraw–Hill: New York, 1965. (b) Blakemore, J. S. Semiconductor Statistics. Dover: Canada, 2002.

Note: for AC current, the velocity would be identical to DC, but the electrons would travel back/forth, resulting in a much smaller drift velocity. A nice explanation of the speed of electricity may be found online at: http://www.radioelectronicschool.net/files/downloads/howfast.pdf

Kittel, C. Introduction to Solid State Physics, 8th ed., Wiley: New York, 2004.

For a recent review, see Cheetham, A. K.; Mellot, C. F. Chem. Mater. 1997, 9, 2269. It should be noted that the hydrolytic condensation of trifunctional organosilicon monomers (e.g., RSiCl₃ or RSi(OMe)₃) results in polyhedral oligomeric silsesquioxanes (POSS) – see: http://www.azonano.com/details.asp?ArticleID=1342#_POSSTM_Polymers_Polymerization/Gr. These structures represent the smallest forms of silica, often being denoted as “molecular silica”. Since particle diameters range from 0.07 to 3 nm, these are important architectures for nanoapplications (e.g., see http://www.reade.com/Products/Polymeric/poss.html

Note: a supercritical fluid has intermediate properties of liquid and gas. Typically, the alcogel is placed in an autoclave filled with ethanol. The system is pressurized to 750–850 psi with CO₂ and cooled to 5–10°C. Liquid CO₂ is then flushed through the vessel until all the ethanol has been removed from the vessel and from within the gels. When the gels are ethanol-free, the vessel is heated to a temperature above the critical temperature of CO₂ (31°C). As the vessel is heated, the pressure of the system rises. The pressure of CO₂ is carefully monitored to maintain a pressure slightly above the critical pressure of CO₂ (1050 psi). The system is held at these conditions for a short time, followed by the slow, controlled release of CO₂ to ambient pressure. The length of time required for this process is dependent on the thickness of the gels; this process may last anywhere from 12 h to 6 days.

For a recent review on the synthesis, properties, and applications of aerogels see: Pierre, A. C.; Pajonk, G. M. “Chemistry of Aerogels and Their Applications”, Chem. Rev. 2002, 102, 4243.

Note: the γ-Al₂O₃ crystal structure is best described as a defect spinel structure comprised of a 2×2×2 fcc array of oxide ions with 21/3 aluminum ions divided over the octahedral and tetrahedral interstices. By contrast, α-Al₂O₃ is an HCP array of O²⁻, with Al³⁺ in 2/3 of the octahedral sites. For thermal transformations of alumina, see: Stumpf, H. C.; Russell, A. S.; Newsome, J. W.; Tucker, C. M. Ind. Eng. Chem. 1950, 42, 1398.

For a comprehensive database of zeolite structures refer to: http://www.iza-structure.org/databases/

For a recent review of applications for zeolite thin films, see: Lew, C. M.; Cai, R.; Yan, Y. Acc. Chem. Res. 2009, ASAP.

For comprehensive building models for zeolite frameworks, see: http://www.iza-structure.org/databases/ModelBuilding/Introduction.pdf

For a review of applications for mesoporous zeolites, see: Corma, A. Chem. Rev. 1997, 97, 2373.

For a comprehensive review of hydrothermal methods used to synthesize zeolites, see: Cundy, C. S.; Cox, P. A. Chem. Rev. 2003, 103, 663. A laboratory protocol for the synthesis and characterization of the ZSM-5 zeolite may be found online at: http://materials.binghamton.edu/labs/zeolite/zeolite.html

For F-based zeolite syntheses, see: (a) Koller, H.; Wolker, A.; Eckert, H.; Panz, C.; Behrens, P. Angew. Chem. Int. Ed. Engl. 1997, 36, 2823. (b) Koller, H.; Wolker, A.; Villaescusa, L. A.; Dıaz-Cabanas, M. J.; Valencia, S.; Camblor, M. A. J. Am. Chem. Soc. 1999, 121, 3368.

Comyns, A. E. Focus on Catalysts 2009, 4, 1.

For more information regarding the mechanism for glass formation, see: Royall, C. P.; Williams, S. R.; Ohtsuka, T.; Tanaka, H. Nature Mater. 2008, 7, 556.

Note: it should be noted that glass is not 100% transparent; that is, some incident light is reflected - even in glass that is free from dopant or other inclusion impurities.

Note: in addition to scattering processes, a better rationale for the transparency of glass is due to its electronic band structure, in which the HOMO/LUMO gap is too large to absorb visible light.

It should be known that other oxides are capable of glass network formation, such as B₂O₃, GeO₂, P₂O₅, As₂O₅, As₂O₃, Sb₂O₃, and to a limited degree V₂O₅, ZrO₂ and Bi₂O₃. The oxides of Te, Mo, W, Bi, Ba, Nd, Ti, Zn, Pb, Al, Th and Be are known as conditional glass formers. These may be included in varying concentrations, but will not on their own, yield a glass. These, and other oxides that will not form a glass (including Sc, La, Y, Sn, Ga, In, Mg, Li, Sr, Cd, Rb, Hg, and Cs) are used as network modifiers, to vary the melt viscosity and afford varying properties to the glass.

For more information regarding other crystalline forms, see: Douglas, B. E.; Ho, S. -M. Structure and Chemistry of Crystalline Solids, Springer: New York, 2006.

Note: this is a useful exploitation of the freezing-point depression colligative property, as taught in introductory physical chemistry (e.g., adding salt to icy roads in the winter).

The Complete Book on Glass and Ceramics Technology, NIIR Board of Consultants and Engineers, Asia Pacific Business Press, Inc., 2005.

Some remaining stock of safe, weakly radioactive glass items such as ceramic plates, ore, marbles, etc. may still be acquired online from http://www.unitednuclear.com/

For more details on the history, properties, and fabrication of fiber optics, see: Glass, A. M.; DiGiovanni, D. J.; Strasser, T. A.; Stentz, A. J.; Slusher, R. E.; White, A. E.; Kortan, A. R.; Eggleton, B. J. Bell Labs Techn. J. 2000, Jan. - March, 168.

http://en-us.transitions.com/

For example, see: Armistead, W. H.; Stookey, S. D. Science 1964, 144, 15.

For example, see: Morse, D. L. Inorg. Chem. 1981, 20, 777, and references therein.

Richardson, T. J.; Slack, J. L.; Armitage, R. D.; Kostecki, R.; Farangis, B.; Rubin, M. D.; Appl. Phys. Lett. 2001, 78, 3047.

Asphalt is a black, sticky, viscous liquid that is obtained from crude petroleum. It comprises almost entirely a form of tar called bitumen. The structure of asphalt is actually a colloidal suspension, with small particulates called asphaltenes dispersed through the petroleum matrix. More environmentally friendly aqueous-based asphalt emulsions are currently being used for road repair applications.

For more details regarding the role of C4AF in the hardening mechanisms of Portland cement, see: Meller, N.; Hall, C.; Jupe, A. C.; Colston, S. L.; Jacques, S. D. M.; Barnes, P.; Phipps, J. J. Mater. Chem. 2004, 14, 428, and references therein.

A nice summary of ceramic processing is found online at: http://www.engr.sjsu.edu/~wrchung/images/MatE155/sp06/ceramicsprocessing.pdf

Ratner, B. D.; Hoffman, A. S.; Schoen, F. J.; Lemons, J. E. Biomaterials Science, 2nd ed., Academic Press: New York, 2004.

Aninwene, G. E.; Yao, C.; Webster, T. J. Int. J. of Nanomed. 2008, 3, 257.

Klein, C. Biomaterials. 1990, 11, 509.

LeGeros, R. Z.; LeGeros, J. P. Adv. in Science and Technol., 49, 203.

Pogge, H. B. Electronic Materials Chemistry, Marcel-Dekker: New York, 1996.

Glusker, J. P.; Lewis, M.; Rossi, M. Crystal Structure Analysis for Chemists and Biologists, VCH: New York, 1994.

Larminie, J.; Dicks, A. Fuel Cell Systems Explained, 2nd ed., Wiley: New York, 2003.

West, A. R. Solid State Chemistry and Its Applications, Wiley: New York, 1987.

West, A. R. Basic Solid State Chemistry, 2nd ed., Wiley: New York, 1999.

Moore, E.; Smart, L. Solid State Chemistry: An Introduction, 2nd ed., CRC Press: New York, 1996.

Hurd, C. M. Electrons in Metals, Wiley: New York, 1975.

Elliott, S. The Physics and Chemistry of Solids, Wiley: New York, 1998.

Title: Solid-State Chemistry
Author: Bradley D. Fahlman
Publisher: Springer Netherlands
Book: Materials Chemistry
Print ISBN: 978-94-007-0692-7

Electronic ISBN: 978-94-007-0693-4

Copyright Year: 2011
DOI: https://doi.org/10.1007/978-94-007-0693-4_2

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Premium Partners