Fundamentals of Amorphous Solids

Structure and Properties

Zbigniew H. Stachurski

• Publisher: Wiley-VCH
• Year: 2015
• Print ISBN: 9783527337071
• eBook ISBN: 9783527682195
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

Long awaited, this textbook fills the gap for convincing concepts to describe amorphous solids.
Adopting a unique approach, the author develops a framework that lays the foundations for a theory of amorphousness. He unravels the scientific mysteries surrounding the topic, replacing rather vague notions of amorphous materials as disordered crystalline solids with the well-founded concept of ideal amorphous solids. A classification of amorphous materials into inorganic glasses, organic glasses, glassy metallic alloys, and thin films sets the scene for the development of the model of ideal amorphous solids, based on topology- and statistics-governed rules of three-dimensional sphere packing, which leads to structures with no short, mid or long-range order. This general model is then concretized to the description of specific compounds in the four fundamental classes of amorphous solids, as well as amorphous polyethylene and poly(methyl)methacrylate, emphasizing its versatility and descriptive power. Finally, he includes example applications to indicate the abundance of amorphous materials in modern-day technology, thus illustrating the importance of a better understanding of their structure and properties.
Equally ideal as supplementary reading in courses on crystallography, mineralogy, solid state physics, and materials science where amorphous materials have played only a minor role until now.

1
Spheres, Clusters and Packing of Spheres

1.1 Introduction

Imagine, Design, Create, Explore

Theory of amorphousness is a science about the structural arrangement of atoms in amorphous solids. It is part of Materials Science, which includes the closely related theory of crystallography. Whilst theory of crystallography is well established, theory of amorphousness is beginning to emerge as a body of science in its own right.

Arrangement of objects leads to creation of patterns. The invention of a repeating pattern as a thoughtful and creative process has ancient beginnings, at first in art as discovered by archaeology and evidenced in mosaics existing in ancient buildings, and later in science as known from old manuscripts; for example the five ideal Greek solids. There are three types of patterns that can fill in Euclidean space contiguously, and to infinity. These are:

• patterns with translational symmetry that possess an underlying lattice
• patterns with fivefold rotational symmetry but without translational symmetry
• random patterns with no lattice and no rotational symmetry.

Two-dimensional examples of such patterns are shown in Figure 1.1. All three are used as conceptual models for atomic arrangements in solids.

Figure 1.1 (a-c) Fragments of two-dimensional patterns representing the three formats of atomic arrangement in solids: crystalline (tiles from Morocco), quasi-crystalline (computer pattern generated by T.R. Welberry of ANU) and amorphous (Aboriginal painting by Ada Ross, Australia).

Crystalline solids have been known and appreciated since antiquity. In modern times the intrinsic elements of symmetry in single crystals of minerals were given attention in 1822 by R. J. Haüy (pronounced

-wee,

as in ‘aside’) in ‘Traité de Cristallographie’. Shortly after, the theoretical treatments of W. H. Miller in 1839 on hkl notation, A. Bravais in 1845 on 14 lattices, A. Schönflies in 1892 and W. Barlow in 1898 on 230 space groups (with many contributions from others) resulted in a complete theory of geometrical crystallography. Perfectly regular and ordered structures of infinite extent are described by geometrical crystallography as perfect (ideal) solids, with positions and arrangements of all atoms defined precisely along specific lattices. Theory of crystallography provides a datum from which the ideal atomic arrangements (and defects) in real materials can be determined. By comparison, no such universal laws or rules are well known for the atomic structure in amorphous solids.

In a historical perspective, it would be interesting to contemplate the following question: if Pythagoras were a statistician rather than deducing perfect harmony from ratios of pure numbers on strings, would we have had a theory of amorphousness in solid- state developed ages ago? Looking back in time, one can draw a direct line from the modern theory of geometric crystallography to the philosophy of pure numbers and rational ratios of antiquity. The René-Just Haüy description of packing of elementary blocks to form a single crystal with a simple relationship between its crystal faces and packing arrangement derives directly from the deductive Pythagorean notion of perfect harmony bas...

Table of contents

• Cover
• Related Titles
• Title Page
• Copyright
• Preface
• Chapter 1: Spheres, Clusters and Packing of Spheres
• Chapter 2: Characteristics of Sphere Packings
• Chapter 3: Glassy Materials and Ideal Amorphous Solids
• Chapter 4: Mechanical Behaviour
• Index
• EULA