Mechanical Behaviour of Materials Volume 1: Micro- and Macroscopic C
Advances in technology are demanding ever-increasing mastery over the materials being used: the challenge is to gain a better understanding of their behaviour, and more particularly of the relations between their microstructure and their macroscopic prope
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Annex 1 gives background notions dealing with atomic and molecular structures in an abbreviated way, for the convenience of the user of the book. On the other hand, it is also easy to gather useful information on the web.
A1.1 Types of Bonds The main types of chemical bonds are listed in Table A1.1. Table A1.1 Types of bonds Type of bonds Covalent Metallic Ionic Van der Walls Hydrogen bond
Mechanism Shared electrons Free electrons cloud Electrostatic attraction Molecular attraction Dipoles attraction
Order of magnitude (kJ/mole) 102 102 102 101 1
Adding a repulsive term to the attractive one gives the usual expression for the energy: B A U D m n (A1.1) r r (A, B positive; B is Born’s constant1 ) where r is the distance between the atoms m is of the order of 10 n D 1 for ionic bonds, D 6 for van der Waals bonds For an ionic crystal the attractive force is qq0 /r2 , where q, q0 are the charges on the ions. 1
Max Born (1882–1970), Nobel Prize winner, was a German physicist.
D. Franc¸ois et al., Mechanical Behaviour of Materials: Volume 1: Micro- and Macroscopic Constitutive Behaviour, Solid Mechanics and Its Applications 180, DOI 10.1007/978-94-007-2546-1, © Springer ScienceCBusiness Media B.V. 2012
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Annex 1: Atomic and Molecular Structures
For NaCl, A D e2 , where e is the charge on the electron and D 1.7475 is Madelung’s constant2 .
A1.2 Crystalline Solids – Elements of Crystallography A1.2.1 Symmetry Groups Figure A1.1 shows the elements of symmetry and the corresponding HermannMauguin symbols3 , an integer for axes of symmetry and m for a mirror plane. The notation 2/m corresponds to common axis and normal to the mirror plane. The following operations are identical 2N 2 1N 3N 3 1N 4N 4 1N 6N 6 1N 3 2N 3m
Fig. A1.1 Point groups of symmetry and the corresponding Hermann-Mauguin symbols 2
Erwin Madelung (1881–1972) was a German physicist. Charles Victor Mauguin (1878–1958) was a French mineralogist; Carl Hermann (1898–1961) was a German mineralogist.
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A1.2 Crystalline Solids – Elements of Crystallography
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A1.2.2 Crystallographic Systems The crystallographic systems are listed in Table A1.2. Table A1.2 Crystallographic systems (Barrett and Massalski 1988) Hermann-Mauguin symbol (32 point System Characteristics Symmetry element groups) Examples Triclinic
Three unequal axes, no pair at right-angles a ¤ b ¤ c, ’ ¤ “ ¤ ” ¤ 90º Monoclinic Three unequal axes, one pair not at right angles a¤b¤c ’ D ” D 90ı ¤ “ Orthorhombic Three unequal axes, all at right angles a¤b¤c ’ D “ D ” D 90ı Tetragonal
None
1
K2 CrO7
One binary axis of rotation or one mirror plane
2, 2N .D m/ 2/m
S“, CaSO4 2H2 O (gypsum)
3 orthogonal binary axes of rotation or 2 perpendicular mirror planes One quaternary axis of rotation or of rotationinversion 4 ternary axes of rotation
222, 2 mm 2/m2/m2/m
S’, U’, Ga Fe3 C (cementite)
4, 4N , 422, 4 mm,4N 2m 4/m, 4/m2/m2/m
Sn“ (white) TiO2
Three axes at right angles, two equal a D b ¤ c, ’ D “ D ” D 90ı Cubic Three equal axes, all at right angles a D b D c,
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