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The Non-Crystalline State

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Crystallography and Crystal Chemistry

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Abstract

This chapter discusses the non-crystalline state. In it, we make a distinction between amorphous and disordered materials, and we introduce the concept of short-range order. Models of amorphous materials based on either hard spheres or networks are explored, and polymers are specifically discussed in terms of structure, applications, and recyclability. Brief biographies of John Desmond “Des” Bernal and Georgy Theodosiyovych Voronoï are also included.

If you treat glass right, it doesn’t crack. If you know the properties, you can make things; the colour of dusk and night and love. But you can’t control people like that and I really, really wish you could. I want the world to be glass.

—Cath Crowley

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Notes

  1. 1.

    The same definition was used by the Mesopotamians and, as molten metals also flow, led to the confusion that glass was always metal or contained metal.

  2. 2.

    Correlation is a consequence of long-range order and means that if the position of just one unit (atom/ion/molecule) is known, the positions of all other units can be precisely determined.

  3. 3.

    Boris Nikolayevich Delaunay (1890–1980) was a Soviet/Russian mathematician and mountain climber. His surname derives from his ancestor, a French army officer who was captured during Napoleon’s invasion of 1812 and subsequently married a woman from the Tukhachevsky noble family and stayed in Russia. A peak in the Katun Mountains of southern Siberia is named after him.

  4. 4.

    from the Greek olígos (ὀλίγος), “few,” and méros (μέρος), “part”

  5. 5.

    Zachariasen’s first scientific paper, on the crystal structure of BeO, was published in 1925 when he was just 19 years old. He was the sole author. At age 20, he published six more papers, mostly also as sole author. In 1928, at the age of just 22, he became the youngest person to receive a PhD from the University of Oslo.

  6. 6.

    Topology in this context describes the physical arrangement of vertices and polyhedra in a network.

  7. 7.

    Note that V/P ≠ (P/V)−1.

  8. 8.

    The smallest actual repeating unit here is CH2, so one might be tempted to call this polymer polymethylene, (CH2)n, and the systematic structure-based name according to the IUPAC is indeed poly(methylene); however, PE is prepared by polymerizing ethene (CH2=CH2), the double bond here being key to the polymerization process. There is no stable methene/methylene compound, so the traditional name is derived from the smallest unit which is actually used to synthesize the polymer.

  9. 9.

    a state of matter in which long-range order exists along just one or two axes, resulting in properties intermediate between those of conventional liquids and those of solid crystals

  10. 10.

    from the ancient Greek déndron (δένδρον), meaning “tree”

  11. 11.

    An elastomer is a polymeric substance that possesses the quality of elasticity, i.e., the ability to regain its shape after deformation.

  12. 12.

    Natural rubber is derived from latex, which is the sap of the rubber tree (Hevea brasiliensis).

  13. 13.

    from the Greek taktikótiita (τακτικότητα), meaning “regularity”

  14. 14.

    Isomers are molecules or polyatomic ions with identical molecular formulae but distinct arrangements of atoms. Recall that polymorphs are crystalline materials that exist in more than one form.

  15. 15.

    A few other materials also exhibit a negative thermal expansion coefficient, α, including the metastable cubic Zr(WO4)2 phase which has an average α of −7.2 ppm/°C) from absolute zero all the way to its decomposition temperature of 777 °C. It crystallises in space group P213 (No. 198) with zirconium octahedra which are corner-shared to tungsten tetrahedra.

  16. 16.

    now the Plastics Industry Association

  17. 17.

    Phthalates are a group of chemicals used to make plastics softer and more flexible, increase plasticity, decrease viscosity, or decrease friction during manufacture. They are often called plasticizers.

  18. 18.

    Polycarbonate is a group of thermoplastic polymers containing carbonate groups (CO32−) in their chemical structures.

  19. 19.

    Hydrolysis is a chemical reaction in which a water molecule breaks one or more chemical bonds. In this case, –(–OC6H4)2C(CH3)2CO–)–n (PC) + H2O (CH3)2C(C6H4OH)2 (BPA) + CO2. Leaching is the selective removal of a material component, in this case BPA, by dissolution in a liquid.

  20. 20.

    over the objections of the American Chemistry Council, an industry trade association for US chemical companies

  21. 21.

    For example, despite PVDC’s impenetrable barrier to odor and superior heat resistance (i.e., microwavability), SC Johnson removed it from its Saran Wrap product in 2004 because when items containing chlorine end up in municipal incinerators, they can emit toxic chemicals into the environment. Saran Wrap is now made of LDPE.

  22. 22.

    Fluorocarbons, also known as perfluorocarbons or PFCs, are organofluorine compounds with the general formula CxFy.

Works Cited

  1. C. L. Losq, M. R. Cicconi, G. N. Greaves and D. R. Neuville, “Chapter 13: Silicate Glasses,” in Springer Handbook of Glass, J. D. Musgraves, J. Hu and L. Calvez, Eds., Cham, Springer Nature Switzerland AG, 2019, pp. 441–503.

    Chapter  Google Scholar 

  2. N. A. Krishnan, B. Wang, Y. Le Pape, G. Sant and M. Bauchy, “Irradiation- vs. vitrification-induced disordering: The case of α-quartz and glassy silica,” Journal of Chemical Physics, vol. 146, no. 20, p. 204502, 2017.

    Article  PubMed  Google Scholar 

  3. W. H. Zachariasen, “The Atomic Arrangement in Glass,” Journal of the American Chemical Society, vol. 54, no. 10, p. 3841, 1932.

    Article  CAS  Google Scholar 

  4. A. R. Cooper, “W.H. Zachariasen – The Melody Lingers On,” Journal of Non-Crystalline Solids, vol. 49, pp. 1–17, 1982.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Micron School of Materials Science and Engineering, Boise State University, Boise, ID, USA

    Rick Ubic

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  1. Rick Ubic
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Review Questions

Review Questions

  1. 1.

    Explain how network modifiers change the network structure of oxide glasses and what changes can result in the properties of the glass from different network modifiers.

  2. 2.
    1. (a)

      Draw parts of two-dimensional {2,3}, {3,2}, {3,3}, and {4,2} net-works sufficiently large to show representative polygons.

    2. (b)

      What can you determine about the topology of these networks (does sufficient freedom exist to form an amorphous structure)?

    3. (c)

      Which of these networks satisfy Zachariasen’s rules for oxide networks?

  3. 3.

    What is a Voronoi polyhedron?

  4. 4.

    Describe the glass transition temperature.

  5. 5.

    Consider B2O3.

    1. (a)

      Use univalent ionic radii and Pauling’s rules to find the coordinations (NC and NA) and the electrostatic bond valence strength, s, of B–O bonds. Note that r(B+) = 0.35 Å and r(O−) = 1.76 Å.

    2. (b)

      Use Eq. 15.31 (repeated below) to calculate the ionic fraction of these bonds.

      $$ f=1-\exp \left[\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.{\left(\Delta \upchi \right)}^2\right] $$
    3. (c)

      The average B–O bond length is 1.3699 Å. Assuming all bonds are of this length, calculate the bond valence sums for both B and O in this structure. Is B overbonded or underbonded? What about O? Note that r0(B3+–O2−) = 1.371 Å and b = 0.37.

    4. (d)

      What sort of network does B2O3 form (i.e., what is the correct {x,y} notation)?

    5. (e)

      Considering your answers above, sketch part of a three-dimensional B2O3 network.

    6. (f)

      Calculate whether or not B2O3 has the topological ability to form an amorphous structure.

    7. (g)

      How might your calculation in (f) change if Na+ were added as a network modifier? Explain.

  6. 6.

    Consider SiO2.

    1. (a)

      Determine the cation and anion charges (ZSi and ZO) then use the univalent ionic radii, r(Si+) = 0.65 Å and r(O−) = 1.76 Å, and Pauling’s rules to find the coordinations (NSi and NO) and the electrostatic bond valence strength, s, of Si–O bonds.

    2. (b)

      Use Eq. 17.8 to calculate the percent ionicity (P) of these bonds. Assume that χ(Si) = 1.90 and χ(O) = 3.44.

    3. (c)

      The Si–O bond length is 1.62 Å. Calculate the bond valence sums for both Si and O in this structure. Use bond-valence parameters: ro (Si4+–O2−) = 1.624 Å and b = 0.37. Is Si overbonded or underbonded? What about O?

    4. (d)

      What sort of network does SiO2 form (i.e., what is the correct {x,y} notation)?

    5. (e)

      Considering your answers above, sketch part of a three-dimensional SiO2 network.

    6. (f)

      Calculate whether or not SiO2 has the topological ability to form an amorphous structure.

    7. (g)

      How might your calculation in (f) change if Na+ were added as a network modifier? Explain.

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Ubic, R. (2024). The Non-Crystalline State. In: Crystallography and Crystal Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-031-49752-0_18

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