The Science of Construction Materials

Per Freiesleben Hansen edited by Ole Mejlhede Jensen

The Science of Construction Materials

1 C

Prof. Ole Mejlhede Jensen Technical University of DenmarkDept. Civil Engineering2800 Kgs. LyngbyBrovej, Bldg. 118Denmarkomj@byg.dtu.dk

ISBN: 978-3-540-70897-1 e-ISBN: 978-3-540-70898-8 DOI 10.1007/978-3-540-70898-8Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2009935456

Translation from the Danish edition: Materialefysik for Bygningsingeniører - Beregningsgrundlag by Per Freiesleben Hansen, © Statens Byggeforskningsinstitut, Hørsholm, Denmark 1995. All rights reserved.© Springer-Verlag Berlin Heidelberg 2009This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is per-mitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Photographs: The photos in this book come from different sources and are reproduced by permission. For a list of the origin of these illustrations see Appendix E.

Cover illustration: Paul Stutzman, Nat. Inst. of Sci. and Techn., USA; for details please refer to Appendix E.

Cover design: eStudio Calamar S.L, Figueres/Berlin

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Springer is part of Springer Science+Business Media (www.springer.com)

This book is scientifically sponsored by the Educational Activities Committee, EAC, of the International Union of Laboratories and Experts in Construction Materials, Systems and Structures, RILEM.

Contents

Contents

List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

1. Systems of matter1.1 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2

Structure of the atom 1.2Elements 1.2Isotopes 1.3

1.2 Relative atomic mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3

1.3 Relative molecular mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4

1.4 Amount of substance - the mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5The Avogadro constant 1.5

1.5 Molar mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6

1.6 Mixture of substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7Concentration 1.7

1.7 The ideal gas law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8

1.8 Ideal gas mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9Atmospheric air 1.9Humidity 1.9

1.9 Real gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10The van der Waals equation 1.11The van der Waals constants 1.11

1.10 Intermolecular forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.12The Lennard-Jones potential 1.12The Lennard-Jones parameters 1.13Hydrogen bond 1.13

1.11 Critical temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.14The van der Waals isoterms 1.14The critical point 1.15Critical constants 1.16

1.12 SI units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.17Base units 1.17Derived units 1.17Prefixes 1.17Special units 1.18

List of key ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.19

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.201.1: Corrosion of iron – stray current 1.201.2: Air hardening of lime mortar 1.211.3: Foaming of aerated concrete 1.221.4: Accelerated testing of concrete 1.23

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Contents

1.5: Molar mass of atmospheric air 1.241.6: Chemical shrinkage by hardening of Portland cement 1.25

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.27

Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.30

2. Thermodynamic concepts2.1 Thermodynamic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2

System types 2.22.2 Description of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3

2.3 Thermodynamic variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4

2.4 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6Thermodynamic temperature scale 2.6Other temperature units 2.6

2.5 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7Work and heat 2.7The concept of work 2.8Mechanical work 2.8Volume work 2.9Surface work 2.10Electrical work 2.10

2.6 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11Heat capacity of a system 2.12Specific heat capacity 2.12Heating of a system of substances 2.13Symbols and units 2.13

2.7 Thermodynamic process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14Process conditions 2.15Process types 2.15

List of key ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.182.1: Measuring the adiabatic heat development of concrete 2.182.2: Mechanical work in tensile testing of a steel rod 2.192.3: Volume work by evaporation of water 2.202.4: Surface work by atomization of water 2.212.5: Electrical work by galvanizing of steel 2.222.6: Heating of mortar by employing hot mixing water 2.24

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.24

Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.28

3. First law3.1 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2

Energy and energy conservation 3.2Energy forms 3.2Kinetic energy 3.2Potential energy 3.3Chemical energy 3.3Summary 3.3

3.2 First law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4Internal energy as a state function 3.5

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3.3 Internal energy U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6Symbols and units 3.7Internal energy and heat capacity 3.7

3.4 Enthalpy H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8Enthalpy H as a state function 3.8Symbols and units 3.9Enthalpy and heat capacity 3.9

3.5 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10Joule’s law 3.11

3.6 Isothermal change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12

3.7 Adiabatic change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13Adiabatic equations 3.14Course of adiabats 3.15

3.8 Thermochemical equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16Reaction enthalpy 3.16Reaction equations 3.16Reaction heat 3.17Thermochemical calculation 3.17Calculation rules 3.18

3.9 Standard enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19Pressure-dependence of enthalpy 3.20Temperature-dependence of enthalpy 3.20

3.10 Reaction enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21Calculation procedure 3.22

List of key ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.23

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.243.1: Temperature rise in hardening plaster of Paris 3.243.2: Computerized calculation of the evaporation heat of water 3.263.3: Heat development and hydration of clinker minerals 3.273.4: Fire resistance of plaster 3.283.5: Measurement of hydration heat with a solution calorimeter 3.303.6: Computerized enthalpy calculation 3.32

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.33

Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.38

4. Second law4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2

Spontaneous processes 4.2Thermodynamic equilibrium 4.2Thermodynamic process 4.3

4.2 The Carnot cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4Thermal efficiency 4.4The Carnot cycle 4.5

4.3 Second law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7Entropy S 4.7

4.4 Temperature dependence of entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9

4.5 Entropy change, ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10

4.6 Entropy change by phase transformation . . . . . . . . . . . . . . . . . . . . . . . . 4.12

4.7 Standard entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13

4.8 Reaction entropi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.15

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Calculation procedure 4.164.9 Chemical equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.17

The constant growth of entropy 4.17Thermodynamic equilibrium condition 4.18

4.10 The concept of entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.19Micro states 4.19The probable disorder 4.20The Boltzmann relation 4.20Can entropy decrease? 4.21Phase transformation and disorder 4.21

List of key ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.244.1: Transformation of tin at a low temperature – ”tin pest” 4.244.2: Dehydration of gypsum when grinding Portland cement 4.264.3: Computerized calculation of the partial pressure of sat. water vap. 4.274.4: Differential thermal analysis of cement paste – DTA 4.294.5: Vapour pressure of mercury – occupational exposure limit 4.314.6: Control of relative humidity RH by salt hydrates 4.32

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.34

Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.37

5. Calculations of equilibrium5.1 The Gibbs free energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2

Definition of free energy G 5.2The G function differential 5.2Spontaneous processes 5.3Free reaction energy 5.4

5.2 The Clapeyron equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5Phase equilibrium in single-component system 5.6Integration of the Clapeyron equation 5.6

5.3 The Clausius-Clapeyron equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7Integration of the Clausius-Clapeyron equation 5.8

5.4 Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9

5.5 Thermodynamic equilibrium constant . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12Equilibrium condition 5.13Determination of activity 5.13

5.6 Temperature dependence of equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 5.14

List of key ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.16

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.175.1: Loss of strength by high-temperature curing of concrete 5.185.2: Steel manufacture – reduction of iron ore in blast furnace 5.195.3: Capillary condensation in porous construction materials 5.215.4: Computerized calculation of the partial pressure of sat. water vap. 5.235.5: Adsorption of water in hardened cement paste 5.255.6: Precipitation of salt in porous materials – salt damages 5.28

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.31

Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.35

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6. Electrochemistry6.1 Electric current and charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2

Electric current 6.2Electric charge 6.3The Faraday constant 6.3

6.2 Electric potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4Field strength 6.4Electric potential 6.4Electric work 6.5

6.3 Electric conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6Conductivity 6.6Conductance 6.7

6.4 Electrochemical reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8Electrochemical cell 6.8Redox reaction 6.9Electrochemical process 6.9

6.5 Electrochemical potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11The electrochemical potential 6.11Daniell cell 6.12

6.6 The Nernst equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13Electric work contribution 6.13The Nernst equation 6.13

6.7 Temperature dependence of the potential . . . . . . . . . . . . . . . . . . . . . . 6.156.8 Notation rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.16

Cell diagram 6.16Cell reaction 6.17

6.9 Standard potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.19Standard hydrogen electrode 6.19Potential of single electrode 6.19

6.10 Passivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.21Anode reaction with passivation 6.21Reinforcement corrosion 6.22

List of key ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.23

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.256.1: Oxidation of metals in water – pH dependence 6.256.2: Calculating and producing a Pourbaix diagram for iron Fe 6.276.3: Measurement of pH with glass electrode – membrane potential 6.296.4: Electrochemical measurement of thermodynamic standard values 6.306.5: Hydrogen reduction with polarization – hydrogen brittleness 6.32

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.34

Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.38

APPENDIX A

Mathematical appendix

1. Numerical calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2Input data A.2Specification of uncertainty A.2Significant digits A.2Mathematical uncertainty calculation A.3

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Approximate uncertainty calculation A.4Example:Thermodynamic calculation of the ion product and pH of water A.6Literature A.8

2. Dimensional analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.8Fields of application A.8Limitations A.8Physical dimension A.9Types of dimension A.9Dimensional-homogeneous equation A.10The Buckingham pi teorem A.10Determination of pi parameters A.11Rewriting of pi parameters A.12Synthetic base units A.13Calculation examples A.14Examples:Non-steady convective cooling of concrete cross-sections A.14Capillary cohesion in particle systems A.17Literature A.19

3. Newton-Raphson iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.19Example:Calculation of amount of substance, the van der Waals equation A.20Literature A.20

4. Cramer’s formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.20Example:Solution of linear equation system A.22Literature A.22

5. Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.22Example:Influence of the force-fibre angle on the compressive strength of wood A.24Literature A.25

6. Exact differential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.26Example:Change of state, ideal gas A.27Literature A.28

7. Gradient field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.28Example:Calculation of gradient and curve integral A.30Literature A.30

8. Maxwell’s relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.31State quantities A.31Fundamental equations A.31Maxwell’s relations A.32Substance parameters A.33Examples:Joule’s law for ideal gas A.34Influence of pressure on the entropy of condensed substances A.35Temperature change for adiabatic compression of substances A.35Pressure increase in case of heating with delayed expansion A.36Literature A.37

9. Debye-Huckel’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.37Ions in solutions A.37Activity coefficient A.38

page x

Acknowledgements for illustrationsAcknowledgements for illustrations

EAcknowledgements for illustrations

List of symbols

List of symbols

The list contains symbols and indices used throughout the book. Note: in some cases

the same symbol has been used for a mole-specific and a mass-specific quantity,

for example for specific heat capacity (c). In such cases, the value concerned will be

specified by the unit. Also, thermodynamic state functions such as U , H, G and S, which

may occur as both extensive and intensive quantities, are described by the same

symbol. Again, the applied unit shall be noted. These notation rules have been chosen

to limit the use of indices and thus further the legibility. In the list, non-dimensional

and abstract quantities are indicated by (–).

A area of cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (m2)A nucleon number in atom nucleus (mass number) . . . . . . . . . . . . . . . (−)A the Helmholtz free energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J); (J/mol)Ar relative atomic mass m/mu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)a activity of substance component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)

a the van der Waals constant (correction of pressure) . . (m6Pa/mol2)a stoichiometric coefficient in reaction equation . . . . . . . . . . . . . . . . . (−)(aq) ions or gases in aqueous solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)b the van der Waals constant (correction of volume) . . . . . . . (m3/mol)b stoichiometric coefficient in reaction equation . . . . . . . . . . . . . . . . . (−)

C heat capacity of system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J/K)c mole-specific heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J/molK)c mass-specific heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J/kgK)ci molar concentration of component (i) . . . . . . . . . . (mol/m3); (mol/�)cp heat capacity at constant pressure (isobaric) . . . . . . . . . . . . (J/molK)

cV heat capacity at constant volume (isochoric) . . . . . . . . . . . . (J/molK)c�� standard concentration 1 mol/� . . . . . . . . . . . . . . . . . . . . . . . . . . (mol/�)c stoichiometric coefficient in reaction equation . . . . . . . . . . . . . . . . . (−)d stoichiometric coefficient in reaction equation . . . . . . . . . . . . . . . . . (−)det() determinant of () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)

dim() physical dimension of () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)E electric field strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (V/m)E modulus of elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (MPa)e electric elementary charge ∼ 1.602 · 10−19 C . . . . . . . . . . . . . . . . . (C)eV electron volt, energy unit ∼ 1.602 · 10−19 J . . . . . . . . . . . . . . . . . (eV)

e− symbol for electron in reaction equation . . . . . . . . . . . . . . . . . . . . . . . (−)F force (vector quantity) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (N)Fx force, component in x direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (N)F the Faraday constant ∼ 96500 C/mol . . . . . . . . . . . . . . . . . . . (C/mol)G the Gibbs free energy in thermodynamic system . . . . . . (J); (J/mol)

G��T standard free energy at temperature T . . . . . . . . . . . . . . . . . . . (J/mol)

ΔrG free reaction energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J); (J/mol)G electric conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ω−1

(g) gaseous state (”gas”) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)H enthalpy content in thermodynamic system . . . . . . . . . . . (J); (J/mol)

H��T standard enthalpy at temperature T . . . . . . . . . . . . . . . . . . . . . (J/mol)

ΔrH reaction enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J); (J/mol)I electric current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A); (C/s)Ka thermodynamic equilibrium constant . . . . . . . . . . . . . . . . . . . . . . . . . . (−)k Boltzmann constant R/N ∼ 1.38 · 10−23 J/K . . . . . . . . . . . . . . (J/K)

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List of symbols

L linear dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (m)� litre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (�)(�) liquid state (”liquid”) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)ln() natural logarithm of () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)log10() base 10 logarithm of () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)

M molar mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (kg/mol); (g/mol)Mr relative molecular mass m/mu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)m mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (kg)mu atomic mass constant ∼ 1.6606 · 10−27 kg . . . . . . . . . . . . . . . . . . . . . (kg)mi molality of component (i) in mixture . . . . . . . . . . . . . . . . . . . . (mol/kg)

N neutron number in atom nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)N the Avogadro constant ∼ 6.022 · 1023 mol−1 . . . . . . . . . . . . . . . (mol−1)n amount of substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (mol)n degree of polymerization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)p pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Pa)

pc critical pressure for real gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Pa)pi partial pressure of (i) in gas mixture . . . . . . . . . . . . . . . . . . . . . . . . . (Pa)ps partial pressure of saturated water vapour . . . . . . . . . . . . . . . . . . . . (Pa)ptot total pressure in mixture of gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Pa)p�� standard pressure 101325 Pa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Pa)

pH pH value: pH = −log10(a(H+)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)Q heat added to a system from its surroundings . . . . . . . . . (J); (J/mol)Q electric charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (C); (A · s)R gas constant ∼ 8.314 J/molK . . . . . . . . . . . . . . . . . . . . . . . . . (J/molK)R electric resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Ω)

RH relative humidity p/ps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (%); (−)r0 equilibrium distance, Lennard-Jones potential . . . . . . . . . . . . . . . . . (m)S entropy content in system . . . . . . . . . . . . . . . . . . . . . . . (J/K); (J/molK)S��

T standard entropy at temperature T . . . . . . . . . . . . . . . . . . . . . (J/molK)ΔrS reaction entropy during process . . . . . . . . . . . . . . . . . . (J/K); (J/molK)

(s) solid state (”solid”) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)(SHE) standard hydrogen electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)T thermodynamic temperature (273.15 + θ) . . . . . . . . . . . . . . . . . . . . . (K)Tc critical temperature for real gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (K)U internal energy in a thermodynamic system . . . . . . . . . . . (J); (J/mol)

ΔU increase in internal energy during process . . . . . . . . . . . . . (J); (J/mol)u absolute humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (g/m3)V volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (m3); (�)Vmix volume of a mixture or solution . . . . . . . . . . . . . . . . . . . . . . . . . . (m3); (�)Va electric potential at the point (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (V)

ΔV increase in volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (m3)ΔV electric potential difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (V)V �� electrochemical standard potential against (SHE) . . . . . . . . . . . . . (V)υc critical volume for real gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (m3/mol)W work done on a system by its surroundings . . . . . . . . . . . (J), (J/mol)

wi mass fraction of component (i) in a mixture . . . . . . . . . . . . . . . . . . . (−)xi mole fraction of component (i) in a mixture . . . . . . . . . . . . . . . . . . . (−)x�� mole fraction of pure solvent; x�� = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . (−)Z proton number in atom nucleus (atomic number) . . . . . . . . . . . . . . (−)z transfer number for electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)

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List of symbols

α coefficient of volume expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (K−1)β coefficient of linear expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (K−1)γ heat capacity ratio cp/cV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)γ activity coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)Δ increase in parameter value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)

ε strain ΔL/L0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)εu ultimate strain for a material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)ε residual term, regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)η thermal efficiency, cyclic process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)Φ(r) Lennard-Jones potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J); (J/mol)

Φ0 Lennard-Jones constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (J); (J/mol)κ compressibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Pa−1)λ thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . (kJ/mhK); (W/mK)λ free mean path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (m)μ prefix micro-, corresponding to 10−6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)

Π non-dimensional parameter group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)� density of a substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (kg/m3)�i mass concentration of component (i) in a mixture . . . . . . . . . . (kg/m3)ρ electric resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Ωm)σ electric conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (Ω−1m−1)

σ surface tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (N/m)θ temperature, degrees Celsius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (oC)Ω number of micro states in a system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (−)

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Preface

Preface

Preface to the English editionThis book on the Science of Construction Materials is the English version of theDanish textbook Materialefysik for Bygningsingeniører (Statens Byggeforsk-ningsinstitut - Danish Building Research Institute, Hørsholm, 1995). The trans-lation has been done by a team consisting of Professor Ole Mejlhede Jensen,Technical University of Denmark and Kirsten Aakjær, BA, Aalborg University.Comments on the English version were kindly supplied by Professor Sidney Dia-mond, Purdue University. Help with reproduction of the line figures was given byTrine Bay, MSc student, and help with the final text editing was given by SaraLaustsen, PhD student. Transfer of copyright was kindly granted by the familyof Per Freiesleben Hansen. Financial support for the translation was donated bythree Danish foundations: COWIfonden, Knud Højgaards fond, and Larsen &Nielsen fonden.

A number of modifications were made during the preparation of the Englishversion of the textbook. Some of these have been necessitated by the translation,such as references to sources in Danish being changed to international references.Other corrections were made concerning a few apparent errors in the text. Allline figures have been redrawn, and many photos have been substituted. How-ever, in general, the English version is close to the Danish text. In addition tothe textbook, a separate book of exercises exists. The exercises differ in extentand complexity and are organized to further the understanding and use of thesubjects in the textbook. Based on this teaching concept, the subject of ba-sic construction materials has been taught successfully in Denmark through 20years.

Per Freiesleben Hansen(1936-2002)

Per Freiesleben Hansen at hisdesk, October 2001. The Danishtextbook was written during a 10-year period. It was his pedagog-ical intention that ”the studentsshould not be given a lunch pack-et, but be taught how to makeone themselves - and then theyshould be given a sharp knife.”

It is more than two decades ago that Per Freiesleben Hansen initiated thewriting of this textbook. This initiative was necessitated by the developmentwithin construction materials research from 1960 to 1985. In this period theresearch moved form being a simple study of the properties of different materialstowards being a theoretically based specialist discipline. In the decade since thepublication of the Danish textbook, the development has gone much further.In particular, complex computer simulation has become increasingly used as analternative to measurement and direct calculation has been replaced by complexcomputer modelling. In this situation it is very important that the computerprogrammers build their algorithms on sound materials science. And likewise,it is very important that the user of the programs has an understanding offundamental physics and chemistry that allows a critical interpretation of theoutput from the black box of complexity; the sharp knife of materials sciencethat the textbook provides is more needed than ever.

It is our hope that this English version will contribute to enhancing thedevelopment of the science of construction materials internationally.

Lyngby, June 2009O.Mejlhede Jensen

Extract from the preface to the Danish editionIn its classical form, the science of construction materials is a descriptive, empiri-cal discipline related to certain types of materials, e.g. the study of the propertiesof wood, steel, concrete and plastics. This traditional division of the science intothe separate studies of the different material types is appropriate as long as thepurpose is to collect, disseminate and use knowledge about the simple physi-cal and chemical properties of specific materials. Through generations, research,

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Preface

teaching and engineering practice have all functioned within this framework with-out problems.

However, during the last few decades the nature of the research being pursuedwithin construction materials has changed. Increasingly, construction materialsresearch is carried out by specialists within theoretical disciplines such as physics,chemistry and physical chemistry. The methods used for investigations have be-come more sophisticated and it is often necessary to ”interpret” the results beforethey become meaningful for the practical civil engineer.

This development has given rise to an unfortunate gap between research andengineering practice in the field of construction materials. Fundamental researchhas gradually been fragmented into a number of narrow specialist disciplines,making it difficult for the researchers to communicate fundamental new knowl-edge in a form that can be utilized by the building materials engineer. This schismbecomes more and more noticeable as research has resulted in development of anumber of new building materials.

Within civil engineering education, an attempt to surmount these problemswas the introduction of the specialist discipline ”Materials Science”, which aimsat describing the macroscopic properties of materials based on their atomic andmolecular structures. An early exponent of this specialist discipline was vanVlack. His ”Elements of Materials Science” was introduced into the civil engi-neering education at the Technical University of Denmark in the late 1960’es.

Materials Science according to these principles has been shown to be readilyaccepted within the fields of electrical and mechanical engineering. In these fieldswell-defined materials are used, and well-defined requirements are established fortheir mechanical or electrical properties. However, within the field of constructionmaterials, Materials Science has not been accepted to the same degree. Only in afew cases has this discipline lead to knowledge transfer of permanent significanceto the practical civil engineer. The main reasons for this are the following:

• Materials Science is a theoretical science of materials which is based on thescientific disciplines of the researcher, and therefore reflects the reality on thebuilding site only to a limited extent.

• The materials problems faced by civil engineers are as much related to acomplex interaction of materials, structure and environments as they are tothe properties of the pure materials themselves.

As used in the title of this book, the concept of Materials Physics [Editor: directtranslation of the original Danish title] can be defined as having the followingcharacteristics:

• Materials Physics is a theoretical science of materials formulated with respectto the special concerns of the civil engineer.

At a theoretical level, materials science is interdisciplinary. Also, Materials Physicsincludes elements of other sciences, e.g. chemical thermodynamics, mathemati-cal analysis and numerical methods. An essential task in Materials Physics is tocombine parts of these specialist fields into a practical set of calculation tools forbuilding materials engineers.

The borderland of materials science where technical development and educa-tional work meet is fascinating – and difficult – at the same time. Therefore, Iexpress my great appreciation to many colleagues for their specialist inspiration,ideas and sound advice given to me during this work.

Aalborg, August 1994P.Freiesleben Hansen

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Introduction

Introduction

The form of the textbook aims to make it fit for self-study. This has been achievedby the following additions to the theoretical subject matter.

• At the end of each theoretical section a number of check-up questions andexercises are given in order to make it possible for the reader to test hisunderstanding of the text.

• The book contains a large number of thoroughly-prepared examples, showingthe application of formulas and calculation expressions, and demonstratingat the same time the application of the theoretical text to specific engineeringwork.

• The book also contains a mathematical appendix with descriptions of themathematical-physical methods that are often used to solve practical designproblems and an appendix of tables that covers the application of the theo-retical text to normal problems in materials science.

• The book is provided with an elaborate subject index making it possible totrack theory, examples, tables and exercises separately.

This publication is both a casebook and workbook; however, it is the author’shope that it will also be used as a reference book by practising civil engineers,and thus serve as a source of inspiration during the work with technical tasks inmaterials science at different levels.

Contents of the bookBefore working with this book, readers may find it useful to get an overview ofthe subjects dealt with in the different chapters. Therefore, readers should firstread through the following overview and browse through the chapters concerned.

Chapter 1. Substance systems reviews a number of elementary, but funda-mental definitions and concepts that are used to describe the compositionand properties of substances. A large number of the addressed subjects arecontained in the curriculum of mathematical-physical university entrance ex-ams.

Chapter 2. Thermodynamic concepts contains an overview of the most es-sential concepts and definitions included in the thermodynamic descriptionof substances. In the explanation of thermodynamics a number of preciseterms concerning systems, state functions and process types are employed.The meaning of these concepts and their application to practical substancesystems are explained.

Chapter 3. First law introduces the simple, but perfectly general principle ofthe conservation of energy as expressed through the first law of thermodynam-ics. The development of calculation rules for this principle is explained andthe practical application of these rules is demonstrated to specific technicalproblems in material technology.

Chapter 4. Second law deals with the concept entropy, which is the basisfor solving equilibrium problems in physical chemistry. Through the entropyconcept of the second law, equilibrium conditions for substance systems isdeveloped and the application of these conditions is illustrated by solution ofpractical problems within material science.

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Introduction

Chapter 5. Calculations of equilibrium deals with the concepts free energyand thermodynamic equilibrium constants, two quantities that form the ba-sis of a number of essential technical calculation methods for equilibriumsystems. The practical application of these quantities is demonstrated by anumber of typical problems within materials technology.

Chapter 6. Electrochemistry explains the most essential definitions and con-cepts within the field that can be called equilibrium electrochemistry. Theaim is, among others, to present the design basis of the subsequent treatmentof the science of corrosion.

Appendix A. Mathematical appendix contains a survey of selected mathema-tical-physical methods that are often used for solution of practical problems.These include numerical processing and uncertainty calculation, dimensionalanalysis, linear regression, iterative root finding, etc.

Appendix B. Tables contains a selection of tabular data covering the most fre-quent types of problems within the science of construction materials: physicalconstants, overview of the properties of elements, including table of the el-ements, thermochemical data of inorganic and organic substances and ions,and a table of the vapour pressure of water.

Appendix C. Solutions to check-up questions and exercises contains a sys-tematic overview of solutions to all check-up questions and exercises in thebook.

Appendix D. Subject index refers to theoretical sections, examples, problems,figures and tables in the book.

Structure of the bookThe layout of the book aims at making the study an active process. From experi-ence, parts of the explained text may appear to be somewhat abstract – perhapseven recondite – until successfully applied to one’s own specific problems andpractical examples. In its layout and treatment of subjects the book reflects thisphilosophy of learning.

For a start, try to go through for example chapter 1 and familiarize yourselfwith the “signals” given in the text and with the organization of the subjects.

Calculation expressions are directly followed by an example showing howto apply the expression by solving a practical problem. These examples arepreceded by a black square.

Theoretical sections are followed by a number of brief check-up questions, tocheck whether the text has been understood correctly. These control questionsare preceded by a white square that can be checked off when the question hasbeen answered. Solutions to control questions are given in Appendix C.

Definitions are framed in the text by a bold line. Such bold-line frameindicates the definitions and concepts that form the theoretical foundationof the text.

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Introduction

Essential calculation expressions and formulas are framed by a thin line.Such thin-line frames indicate the expressions that form the practicalcalculation tools.

The individual chapters are concluded by a list of key ideas giving an overviewof definitions, concepts and calculation expressions introduced within them.

After each chapter, a number of examples are given, typically six major ex-amples with thoroughly prepared and discussed calculation examples. Theseexamples are preceded by black squares. The examples have been carefullychosen so that they illustrate the application of the theory to practical engi-neering problems.

Minor exercises – typically 20 – are given at the end of each chapter to facil-itate the learning of the theoretical subjects. The exercises are preceded bywhite squares; the exercises also show how to apply the explained theory bysolving practical problems within materials science. Solutions to exercises aregiven in Appendix C.

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Introduction

A chemical laboratory fromthe 19th century; above and ontop of the tiled tabletop, exam-ples of the former, often homemadeequipment for chemical tests can beseen.

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