material science_v. rajendran

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Scilab Textbook Companion for

Material Science

by V. Rajendran1

Created byLaxman Ghanasham Sole

B.TechElectronics Engineering

Vishwakarma Institute of Technology, PuneCollege Teacher

Prof. Vijay ManeCross-Checked by

Lavitha Pereira

November 2, 2013

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the Textbook Companion Projectsection at the website http://scilab.in


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Book Description

Title: Material Science

Author: V. Rajendran

Publisher: Tata Mcgraw Hill, New Delhi

Edition: 1

Year: 2012

ISBN: 0-07-132897-1

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Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 5

1 Materials Properties and Requirements 11

2 Crystal Structure 13

3 Characterisation of material 29

4 Cohesion between atoms 33

5 Crystal Imperfections 34

6 Classification of solids 36

7 Elecron theory of Solids 38

8 Statics and Band theory of Solids 45

10 Transport Properties of Semiconductors 56

11 Mechanical Properties 74

12 Thermal Properties 77

14 Luminescence 83

15 Display Devices 85

16 Photoconductivity 87

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18 Dielectric Materials 89

19 Magnetic Materials 101

20 Super Conducting Materials 107

23 Polymer Materials 109

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List of Scilab Codes

Exa 1.1 Resistance of the wire. . . . . . . . . . . . . . . . . . 11Exa 1.2 Extension of a wire. . . . . . . . . . . . . . . . . . . . 11Exa 2.2 Lattice spacing from Miller indices . . . . . . . . . . . 13Exa 2.3 Lattice constant of Sodium . . . . . . . . . . . . . . . 13Exa 2.4 Avogadro Constant . . . . . . . . . . . . . . . . . . . 14Exa 2.5 Lattice spacing from Miller indices . . . . . . . . . . . 14Exa 2.6 Lattice spacing from Miller indices . . . . . . . . . . . 15Exa 2.7 Lattice spacing from Miller indices . . . . . . . . . . . 15Exa 2.8 Lattice spacing from Miller indices . . . . . . . . . . . 16Exa 2.13 Lattice spacing from Miller indices . . . . . . . . . . . 16Exa 2.15 Lattice spacing from Miller indices . . . . . . . . . . . 17Exa 2.16 Number of atoms in Al foil . . . . . . . . . . . . . . . 18Exa 2.17 no of unit cells in 1 kg metal . . . . . . . . . . . . . . 18

Exa 2.18 percentage volume change during structural changes . 18Exa 2.19 Copper Density. . . . . . . . . . . . . . . . . . . . . . 19Exa 2.20 Atomic Radius . . . . . . . . . . . . . . . . . . . . . . 19Exa 20.21 Lattice constant . . . . . . . . . . . . . . . . . . . . . 20Exa 2.22 Glancing angle . . . . . . . . . . . . . . . . . . . . . . 20Exa 2.23 Lattice constant . . . . . . . . . . . . . . . . . . . . . 21Exa 2.24 Plane Drawing . . . . . . . . . . . . . . . . . . . . . . 21Exa 2.25 Interplanar spacing. . . . . . . . . . . . . . . . . . . . 22Exa 2.26 Lattice spacing and deBroglie wavelength . . . . . . . 24Exa 2.27 Lattice constant and atomic radius . . . . . . . . . . 24Exa 2.28 energy of the neutron . . . . . . . . . . . . . . . . . . 25

Exa 2.29 InterPlanar Spacing . . . . . . . . . . . . . . . . . . . 25Exa 2.30 Lattice spacing from Miller indices . . . . . . . . . . . 26Exa 2.31 Number of atoms in Al foil . . . . . . . . . . . . . . . 26Exa 2.32 energy of the neutron . . . . . . . . . . . . . . . . . . 27

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Exa 2.35 deBroglie wavelength of electrons . . . . . . . . . . . . 27

Exa 2.36 Lattice spacing from Miller indices . . . . . . . . . . 28Exa 2.38 Plane Drawing . . . . . . . . . . . . . . . . . . . . . . 28Exa 3.1 wavelength and frequency of Xrays . . . . . . . . . . 29Exa 3.2 wavelength and velocity of electrons . . . . . . . . . . 29Exa 3.3 wavelength and angle for 2nd order bragg reflection. . 30Exa 3.4 Grating spacing and glancing angle. . . . . . . . . . . 31Exa 3.5 wavelength of radiation . . . . . . . . . . . . . . . . . 31Exa 3.6 Energy of thermal neutron . . . . . . . . . . . . . . . 32Exa 3.8 temperature of thermal neutron. . . . . . . . . . . . . 32Exa 4.1 Coulomb interatomic energy. . . . . . . . . . . . . . . 33Exa 5.1 Average distance between dislocations. . . . . . . . . 34

Exa 5.2 Schottky defects per unit cell . . . . . . . . . . . . . . 34Exa 6.1 Wavelength of light emitted from LED . . . . . . . . . 36Exa 6.2 Band gap of given GaAsP . . . . . . . . . . . . . . . . 36Exa 7.1 mobility of electrons in copper . . . . . . . . . . . . . 38Exa 7.2 resistivity of copper . . . . . . . . . . . . . . . . . . . 38Exa 7.3 resistivity of sodium . . . . . . . . . . . . . . . . . . . 39Exa 7.4 mobility of electrons in meatls . . . . . . . . . . . . . 39Exa 7.5 drift velocity of electrons . . . . . . . . . . . . . . . . 40Exa 7.6 mobility of electrons. . . . . . . . . . . . . . . . . . . 40Exa 7.7 Lorentz Number . . . . . . . . . . . . . . . . . . . . . 41

Exa 7.8 Lorentz Number . . . . . . . . . . . . . . . . . . . . . 41Exa 7.9 conductivity of copper . . . . . . . . . . . . . . . . . . 42Exa 7.10 drift velocity of electrons in silver piece . . . . . . . . 42Exa 7.11 resistivity of copper . . . . . . . . . . . . . . . . . . . 43Exa 7.12 mobility and drift velocity of electrons . . . . . . . . . 44Exa 8.1 Fermi energy . . . . . . . . . . . . . . . . . . . . . . . 45Exa 8.2 Density of States . . . . . . . . . . . . . . . . . . . . . 46Exa 8.3 Nordheims Coefficient . . . . . . . . . . . . . . . . . . 47Exa 8.4 Conductivity of Al . . . . . . . . . . . . . . . . . . . . 47Exa 8.5 Fermi distribution Function . . . . . . . . . . . . . . . 48Exa 8.6 Fermi temperature . . . . . . . . . . . . . . . . . . . . 48

Exa 8.7 Density of States . . . . . . . . . . . . . . . . . . . . . 48Exa 8.8 Fermi Velocity . . . . . . . . . . . . . . . . . . . . . . 49Exa 8.9 Fermi Energy . . . . . . . . . . . . . . . . . . . . . . . 49Exa 8.10 Fermi Energy . . . . . . . . . . . . . . . . . . . . . . . 50Exa 8.11 Fermi distribution Function . . . . . . . . . . . . . . . 50

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Exa 8.12 theorotical example . . . . . . . . . . . . . . . . . . . 51

Exa 8.13 theorotical example . . . . . . . . . . . . . . . . . . . 51Exa 8.14 Energies for different probabilities . . . . . . . . . . . 51Exa 8.15 Fermi distribution Function . . . . . . . . . . . . . . . 52Exa 8.16 Fermi Energy . . . . . . . . . . . . . . . . . . . . . . . 53Exa 8.17 Fermi distribution Function . . . . . . . . . . . . . . . 53Exa 8.18 Electron density . . . . . . . . . . . . . . . . . . . . . 54Exa 8.19 concentration of free electrons. . . . . . . . . . . . . . 54Exa 8.20 carrier density and fermi velocity . . . . . . . . . . . . 55Exa 10.1 Intrinsic concentration conductivity and resistivity . . 56Exa 10.2 Fermi Energy . . . . . . . . . . . . . . . . . . . . . . 57Exa 10.3 Resistance of Germanium . . . . . . . . . . . . . . . . 57

Exa 10.4 conductivity of Intrinsic semiconductor . . . . . . . . 58Exa 10.5 Intrinsic Resistivity . . . . . . . . . . . . . . . . . . . 58Exa 10.6 electrical conductivity of boron doped semiconductor . 59Exa 10.7 Hole concentration conductivity and Resistance . . . 59Exa 10.8 Band Gap of Ge . . . . . . . . . . . . . . . . . . . . . 60Exa 10.9 carrier concentration of intrinsic semiconductor . . . . 61Exa 10.10 Electrical conductivity of Si . . . . . . . . . . . . . . . 61Exa 10.11 Fermi energy of Silicon . . . . . . . . . . . . . . . . . 62Exa 10.12 effect of temperature on Fermi level . . . . . . . . . . 62Exa 10.13 Conductivity of Ge. . . . . . . . . . . . . . . . . . . . 63

Exa 10.14 Fermi Energy level . . . . . . . . . . . . . . . . . . . . 63Exa 10.15 Conductivity of Ge. . . . . . . . . . . . . . . . . . . . 64Exa 10.16 Intrinsic concentration of Si . . . . . . . . . . . . . . . 64Exa 10.17 Drift Velocity . . . . . . . . . . . . . . . . . . . . . . . 65Exa 10.18 average no of electron per Cu atom. . . . . . . . . . . 65Exa 10.19 Mobility of Ge . . . . . . . . . . . . . . . . . . . . . . 66Exa 10.20 Hall Potential Difference. . . . . . . . . . . . . . . . . 66Exa 10.21 Mobility of Si . . . . . . . . . . . . . . . . . . . . . . . 67Exa 10.22 Electron concentration and Mobility . . . . . . . . . . 67Exa 10.23 Hall voltage. . . . . . . . . . . . . . . . . . . . . . . . 68Exa 10.24 Relaxation time . . . . . . . . . . . . . . . . . . . . . 68

Exa 10.25 Electron mobility in Silver. . . . . . . . . . . . . . . . 69Exa 10.26 Electron mobility and electric field . . . . . . . . . . . 69Exa 10.27 Electron mobility. . . . . . . . . . . . . . . . . . . . . 69Exa 10.28 Electron mobility and electric field . . . . . . . . . . . 70Exa 10.29 Electron mobility and conductivity . . . . . . . . . . . 70

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Exa 10.30 Drift Velocity . . . . . . . . . . . . . . . . . . . . . . . 71

Exa 10.31 Relaxation time . . . . . . . . . . . . . . . . . . . . . 71Exa 10.32 Electron mobility in Al . . . . . . . . . . . . . . . . . 72Exa 10.33 drift and thermal velocity . . . . . . . . . . . . . . . . 72Exa 11.1 Stress produced in an Al. . . . . . . . . . . . . . . . . 74Exa 11.2 perentage elongation and reduction . . . . . . . . . . . 74Exa 11.3 Brinell Hardness Number . . . . . . . . . . . . . . . . 75Exa 11.4 Tensile strength and fatigue limit of Steel plate . . . . 75Exa 12.1 Change in length due to heating . . . . . . . . . . . . 77Exa 12.2 Change in length due to heating . . . . . . . . . . . . 77Exa 12.3 Steady state heat Transfer. . . . . . . . . . . . . . . . 78Exa 12.4 Compression Stress due to Heating . . . . . . . . . . . 78

Exa 12.5 Heat flux transmitted . . . . . . . . . . . . . . . . . . 79Exa 12.6 Youngs Modulus . . . . . . . . . . . . . . . . . . . . . 79Exa 12.7 temperature Change . . . . . . . . . . . . . . . . . . 80Exa 12.8 compressive Sress. . . . . . . . . . . . . . . . . . . . . 80Exa 12.9 limit to compression stress . . . . . . . . . . . . . . . 81Exa 12.10 Heat energy Requirement . . . . . . . . . . . . . . . . 81Exa 14.1 Penetration depth of electron . . . . . . . . . . . . . . 83Exa 14.2 Luminescent lifetime . . . . . . . . . . . . . . . . . . . 83Exa 15.1 wavelength of light . . . . . . . . . . . . . . . . . . . 85Exa 15.2 Band Gap of GaAsP . . . . . . . . . . . . . . . . . . . 85

Exa 16.1 Pairs generated per second . . . . . . . . . . . . . . . 87Exa 16.2 Wavelength of emitted radiation . . . . . . . . . . . . 87Exa 18.1 Dilectric constant of KCl . . . . . . . . . . . . . . . . 89Exa 18.2 Electronic polarisability of Se atom. . . . . . . . . . . 89Exa 18.3 ratio between electronic and ionic polarability . . . . 90Exa 18.4 Dielectric constant of Ne gas . . . . . . . . . . . . . . 90Exa 18.5 Charge on Capacitor . . . . . . . . . . . . . . . . . . . 91Exa 18.6 Dielectric constant of Ar gas . . . . . . . . . . . . . . 91Exa 18.7 Energy stored in capacitor and polarising the capacitor 91Exa 18.8 ratio of internal field to the applied field . . . . . . . . 92Exa 18.9 Relative permittivity of NaCl . . . . . . . . . . . . . 92

Exa 18.10 Polarisability of Ar. . . . . . . . . . . . . . . . . . . . 93Exa 18.11 Polarisability of He atom . . . . . . . . . . . . . . . . 93Exa 18.12 Polarisability of Ar. . . . . . . . . . . . . . . . . . . . 94Exa 18.13 energy stored in dielectric . . . . . . . . . . . . . . . . 94Exa 18.14 Electronic polarisability of Sulphur . . . . . . . . . . . 94

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Exa 18.15 energy stored in capacitor . . . . . . . . . . . . . . . . 95

Exa 18.16 Polarisation produced in NaCl . . . . . . . . . . . . . 96Exa 18.17 Relative permitivity of NaCl . . . . . . . . . . . . . . 96Exa 18.18 Electric field strength . . . . . . . . . . . . . . . . . . 96Exa 18.19 Polarisability of He atom . . . . . . . . . . . . . . . . 97Exa 18.20 Electric field strength . . . . . . . . . . . . . . . . . . 97Exa 18.21 Dilectric Displacement . . . . . . . . . . . . . . . . . . 98Exa 18.22 Polarisation produced in NaCl . . . . . . . . . . . . . 98Exa 18.23 Polarisation produced in NaCl . . . . . . . . . . . . . 99Exa 18.24 Voltage across Capacitor. . . . . . . . . . . . . . . . . 99Exa 18.25 Charge on Capacitor . . . . . . . . . . . . . . . . . . . 99Exa 18.26 Dilectric Constant . . . . . . . . . . . . . . . . . . . . 100

Exa 19.1 Relative permiability and magnetic force. . . . . . . . 101Exa 19.2 magnetisation and flux density . . . . . . . . . . . . . 101Exa 19.3 Flux density . . . . . . . . . . . . . . . . . . . . . . . 102Exa 19.4 Permiability . . . . . . . . . . . . . . . . . . . . . . . 102Exa 19.5 Magnetic Moment . . . . . . . . . . . . . . . . . . . . 103Exa 19.6 Avrage magnetisation . . . . . . . . . . . . . . . . . . 103Exa 19.7 System Temperature . . . . . . . . . . . . . . . . . . . 104Exa 19.8 Saturation Magnetic field of Gd. . . . . . . . . . . . . 104Exa 19.9 Saturation Magnetisation . . . . . . . . . . . . . . . . 105Exa 19.10 Saturation Magnetisation and saturation flux density . 105

Exa 19.11 Saturation Magnetisationof Gadolinium . . . . . . . . 106Exa 19.12 Magnetic Flux density . . . . . . . . . . . . . . . . . . 106Exa 20.2 Critical Field . . . . . . . . . . . . . . . . . . . . . . . 107Exa 20.3 Critical field through a wire . . . . . . . . . . . . . . . 107Exa 20.4 Critical Temperature for metal . . . . . . . . . . . . . 108Exa 23.1 Sulphur required for final rubber product . . . . . . . 109Exa 23.2 Photon energy to break C C bond . . . . . . . . . . . 109

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List of Figures

2.1 Plane Drawing . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 Plane Drawing . . . . . . . . . . . . . . . . . . . . . . . . . 23

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Chapter 1

Materials Properties and

Requirements

Scilab code Exa 1.1 Resistance of the wire

1 / / Exa mpl e 1 . 1 , p ag e no82 clear

3 clc

4

5 r = 0 . 4 5 * 1 0 ^ - 3 //m6 L = 0 . 3 //m7 r h o = 1 7 * 1 0 ^ - 9 //ohmm8 / / C a l c u l a t i o n s9 R = r h o * ( L / ( % p i * r ^ 2 ) )

10 printf ( The R e s i s t a nc e o f t he w i re i s %. 3 f ohm ,R )

Scilab code Exa 1.2 Extension of a wire


3 clc

11


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4

5 r = 1 . 2 5 * 1 0 ^ - 3 //m6 L =3 //m7 F = 4 9 0 0 //Newton8 e = 2 . 0 5 * 1 0 ^ 1 1 //Pa9 s = F / ( % p i * r ^ 2 * e )

10 printf ( s t r a i n = %. 3 f \ n T h e re f o r e , e x t e n s i o n = %. 3 f ,s , s * 3 )

12


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Chapter 2

Crystal Structure

Scilab code Exa 2.2 Lattice spacing from Miller indices


3 clc

4 // I n t e r c e p t s a re i n t h e r a t i o 3 a : 4 b a lo ng X ,Y andp a r a l l e l t o Z a x i s

5 / /x i n t e r c e p t 3 , y i n t e r c e p t 4 and z i n t e r c e p t

i n f i n i t y6 a = 2 * 1 0 ^ - 1 0 / / 2 A ng st ro m7 h =4

8 k =3

9 l =0

10 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

11 printf ( The l a t t i c e s p a c in g f o r t he p l an e 43 0 i s %. 1f1010 m , d * 1 0 ^ 1 0 )

Scilab code Exa 2.3 Lattice constant of Sodium

1 / / Exa mpl e 2 . 3 , p ag e no31

13


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2 clear

3 clc4

5 d = 9 . 6 * 1 0 ^ 2 //kg/m36 a w t = 2 3

7 n =2

8 a v g = 6 . 0 2 3 * 1 0 ^ 2 6

9 m = n * a w t / a v g

10 a = ( m / d ) ^ ( 1 / 3 )

11 printf ( The l a t t i c e c o n s t a n t od s od iu m i s %. 1 f A ,a * 1 0 ^ 1 0 )

Scilab code Exa 2.4 Avogadro Constant


3 clc

4

5 d = 4 * 1 0 ^ 3 //kg/m36 a w t c s = 1 3 2 . 9

7 a w t c l = 3 5 . 58 a = 4 . 1 2 * 1 0 ^ - 1 0

9 m = d * a ^ 3

10 N = ( a w t c s + a w t c l ) / m

11 printf ( The v a l u e o f A vo ga dr o C o ns t an t % . 4 f 1 0 2 6p e r kg m ol e , N * 1 0 ^ - 2 6 )



3 clc

4 l a m = 1 . 5 4 1 8 * 1 0 ^ - 1 0 //m

14


16/111

5 t h e t a = 3 0 / / i n d e g r e e s

6 h =17 k =1

8 l =1

9 a = l a m * sqrt ( h ^ 2 + k ^ 2 + l ^ 2 ) / ( 2 * sin ( t h e t a * % p i / 1 8 0 ) )

10 printf ( The l a t t i c e c o n s t a n t i s %. 4 f 1010 m ,a*10^10)



3 clc

4 h =1

5 k =0

6 l =0

7 a = 2 . 8 1 4 * 1 0 ^ - 1 0

8 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

9 printf ( The l a t t i c e s p a c in g f o r t he p l an e ( 1 0 0 ) i s %. 3 f1010 m , d * 1 0 ^ 1 0 )



3 clc

4 h =3

5 k =2

6 l =17 a = 4 . 1 2 * 1 0 ^ - 1 0

8 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

9 printf ( The l a t t i c e s p a c in g f o r t he p l an e ( 3 2 1 ) i s %. 4 f1010 m , d * 1 0 ^ 1 0 )

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3 clc

4 // /( i )5 h =1

6 k =0

7 l =18 a = 4 . 2 * 1 0 ^ - 1 0

9 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

10 printf ( \nThe l a t t i c e s p a c i n g f o r t h e p l a n e ( 1 0 1 ) i s%.3 f 1010 m , d * 1 0 ^ 1 0 )

11 // /( i i )12 h =2

13 k =2

14 l =1

15 a = 4 . 1 2 * 1 0 ^ - 1 0

16 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

17 printf ( \nThe l a t t i c e s p a c i n g f o r t h e p l a n e ( 2 2 0 ) i s%.1 f 1010 m , d * 1 0 ^ 1 0 )


1 / / Exa mpl e 2 . 1 3 , p ag e no372 clear

3 clc

4 // ( i )5 h =1

6 k =1

7 l =1

16


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8 a = 4 . 1 2 * 1 0 ^ - 1 0

9 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )10 printf ( \nFor ( 1 1 1) p l an e \nThe l a t t i c e s p a c i n g i s %. 3 f1010 m , d * 1 0 ^ 1 0 )

11 // ( i i )12

13 h =1

14 k =1

15 l =2

16 a = 4 . 1 2 * 1 0 ^ - 1 0

17 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

18 printf ( \n\nFor ( 1 1 2 ) p l an e \nThe l a t t i c e s p a c i n g i s

%.3 f 1010 m , d * 1 0 ^ 1 0 )19 // ( i i i )20

21 h =1

22 k =2

23 l =3

24 a = 4 . 1 2 * 1 0 ^ - 1 0

25 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

26 printf ( \n\nFor ( 1 2 3 ) p l an e \nThe l a t t i c e s p a c i n g i s%.3 f 1010 m , d * 1 0 ^ 1 0 )



3 clc

4 h =2

5 k =2

6 l =07 a = 4 . 9 3 8 * 1 0 ^ - 1 0

8 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

9 printf ( \nThe l a t t i c e s p a c i n g f o r ( 2 2 0 ) p l a n e i s %. 3f1010 m , d * 1 0 ^ 1 0 )

17


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Scilab code Exa 2.16 Number of atoms in Al foil


3 clc

4 a = 0 . 4 0 5 * 1 0 ^ - 1 0 //m5 t = 0 . 0 0 5 //m6 A = 2 5 * 1 0 ^ - 2 //m

7 n = t * A / a ^ 38 printf ( The number o f a to ms i n t h e Al f o i l i s %. 2 f

1 0 2 8 , n * 1 0 ^ - 2 8 )

Scilab code Exa 2.17 no of unit cells in 1 kg metal


3 clc4 a = 2 . 8 8 * 1 0 ^ - 1 0 //5 d = 7 2 0 0 //k/m36 n = 1 / ( d * a ^ 3 )

7 printf ( The number o f u n i t c e l l p r e s e nt i n 1 kgm et al i s %. 4 f 1 0 2 4 , n * 1 0 ^ - 2 4 )

Scilab code Exa 2.18 percentage volume change during structural changes


3 clc

4 r b c c = 0 . 1 2 5 8 * 1 0 ^ - 9

18


20/111

5 r f c c = 0 . 1 2 9 2 * 1 0 ^ - 9

6 a = 4 * r b c c / sqrt (3)7 v b c c = ( a ^ 3 ) / 2

8 a 1 = 4 * r f c c / sqrt (2)

9 v f c c = ( a 1 ^ 3 ) / 4

10 v p = ( v b c c - v f c c )

11 vp = floor ( v p * 1 0 ^ 3 2 )

12 v p = v p * 1 0 ^ - 3 2 / v b c c

13 printf ( The v ol um e c ha n ge i n %% d u r i n g g t h es t r u c t u r a l c ha ng e i s %. 4 f , v p * 1 0 0 )

Scilab code Exa 2.19 Copper Density


3 clc

4 a w t = 6 3 . 5 * 1 0 ^ - 3 // g5 a v g = 6 . 0 2 3 * 1 0 ^ 2 6

6 r = 1 . 2 7 3 * 1 0 ^ - 1 0

7 n =4

8 a = 4 * r / sqrt (2)9 d = n * a w t / ( a v g * a ^ 3 )

10 printf ( The d e n s i t y o f c o pp e r i s %. 4 f gm/m3 ,d )

Scilab code Exa 2.20 Atomic Radius


3 clc4 d = 7 8 6 0

5 m = 5 5 . 8 5

6 n =2

7 a v g = 6 . 0 2 3 * 1 0 ^ 2 6

19


21/111

8 a = ( n * m * 1 0 ^ - 3 / ( a v g * d ) ) ^ ( 1 / 3 )

9 r = a * sqrt ( 3 ) / 410 printf ( \nThe l a t t i c e c o n s t a n t o f a l f ai r o n i s %. 4 f A , a * 1 0 ^ 1 0 )

11 printf ( \nThe a to m i c r a d i us o f a l fai r o n i s %. 5 f 1010 m , r * 1 0 ^ 1 0 )

Scilab code Exa 20.21 Lattice constant

1 / / Exa mpl e 2 . 2 1 , p ag e no422 clear3 clc

4 d = 8 9 6 0

5 m = 6 3 . 5 4

6 n =4

7 a v g = 6 . 0 2 3 * 1 0 ^ 2 6

8 a = ( n * m * 1 0 ^ - 3 / ( a v g * d ) ) ^ ( 1 / 3 )

9 printf ( \nThe l a t t i c e c o n s t a n t o f c o pp e r i s %. 4 f A , a * 1 0 ^ 1 0 )

Scilab code Exa 2.22 Glancing angle


3 clc

4 a = 3 . 8 1 * 1 0 ^ - 1 0 //m5 h =1

6 k =3

7 l =28 l a m = 0 . 5 8 * 1 0 ^ - 1 0

9 n =2

10 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

11 t h e t a = asin ( n * l a m / ( 2 * d ) )

20


22/111

12 printf ( The a n gl e o f g l a n ci n g a t which 2 nd o r de r

d i f f r a c t i o n p at te rn o f N aCl o cc ur s i s %. 2 f ,t h e t a * 1 8 0 / % p i )

Scilab code Exa 2.23 Lattice constant


3 clc

4 h =35 k =0

6 l =2

7 t h e t a = 3 5 / / i n d e g r e e s8 l a m = 0 . 7 * 1 0 ^ - 1 0 //m9 n =1

10 d = n * l a m / ( 2 * sin ( t h e t a * % p i / 1 8 0 ) )

11 printf ( \nThe i n t e r p l a n a r d i s t a n c e f o r ( 3 02 ) p la ne i s%.3 f 1011 m , d * 1 0 ^ 1 1 )

12 a = d * sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

13 printf ( \nThe l a t t i c e c o n s t a n c e i s %. 2 f 1010 m ,a

*10^10)

Scilab code Exa 2.24 Plane Drawing


3 clc4 / / / f o r p l a n e ( 0 , 0 , 1 )5 deff ( z=f (x , y ) , z=x0y0 )6 x = 0 : 0. 2 :3 ; y = x ;

7 // c l f ( ) ;

21


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Figure 2.1: Plane Drawing

8 subplot (311)

9 fplot3d ( x , y , f , a l p h a = 5 , t h e t a = 3 1 )

10

11 / / / F or p l a n e ( 1 , 0 , 1 )12 deff ( z=f (x , y ) , z=x1y0 )13 x = 0 : 0. 2 :3 ; y = x ;

14 // c l f ( ) ;15 subplot (312)

16 fplot3d ( x , y , f , a l p h a = 5 , t h e t a = 3 1 )17

18 / / / F or p l a n e ( 1 , 1 , 1 )19 deff ( z=f (x , y ) , z=x1y1 )20 x = 0 : 0. 2 :3 ; y = x ;

21 // c l f ( ) ;22 subplot (313)

23 fplot3d ( x , y , f , a l p h a = 5 , t h e t a = 3 1 )

Scilab code Exa 2.25 Interplanar spacing

22


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Figure 2.2: Plane Drawing

23


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1 / / Exa mpl e 2 . 2 5 , p ag e no45

2 clear3 clc

4 t h e t a = 1 2 / / i n d e g r e e s5 l a m = 2 . 8 2 * 1 0 ^ - 1 0 //m6 n =1


8 printf ( The i n t e r p l a n a r s p ac i ng i s %. 3 f 1010 m ,d*10^10)

Scilab code Exa 2.26 Lattice spacing and deBroglie wavelength


3 clc

4 t h e t a = 2 7 . 5 / 2 // i n d e g r e e s5 a = 0 . 5 6 3 * 1 0 ^ - 9

6 n =1

7 h =1

8 k =1

9 l =110 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

11 printf ( \nThe l a t t i c e s p a c i n g f o r t h e p l a n e ( 1 1 1 ) i s%.2 f 10 10 m , d * 1 0 ^ 1 0 )

12 l a m = 2 * d * sin ( t h e t a * % p i / 1 8 0 ) / n

13 printf ( \nThe d e B r o g l i e w av el en gt h o f t he n e ut r on si s %. 3 f 1010 m , l a m * 1 0 ^ 1 0 )

Scilab code Exa 2.27 Lattice constant and atomic radius


3 clc

24


26/111

4 h =1

5 k =16 l =0

7 d = 2 * 1 0 ^ - 1 0 //m8 a = d * sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

9 R = a / ( 2 * sqrt ( 2 ) )

10 printf ( The l a t t i c e c o n s t a n t i s %. 3 f 1010 m\nThea t o m ic r a di u s o f t h e c r y s t a l i s %. 1 f 1010 m ,a* 1 0 ^ 1 0 , R * 1 0 ^ 1 0 )

Scilab code Exa 2.28 energy of the neutron


3 clc

4 t h e t a = 2 2 / / i n d e g r e e s5 d = 1 . 8 * 1 0 ^ - 1 0 //m6 n =1

7 h = 6 . 6 2 6 * 1 0 ^ - 3 4

8 m = 9 . 1 * 1 0 ^ - 3 1 //k g

9 e = 1 . 6 * 1 0 ^ - 1 9 //C10 l a m = 2 * d * sin ( t h e t a * % p i / 1 8 0 ) / n

11 E = ( 1 / ( 2 * m ) ) * ( h / l a m ) ^ ( 2 )

12 printf ( \nThe d e B r o g l i e w av el en gt h o f t he n eu tr on i s%.3 f 1010\ n th e e ne rg y o f t he n eu tr on i s %. 2 f

eV , l a m * 1 0 ^ 1 0 , E / e )

Scilab code Exa 2.29 InterPlanar Spacing


3 clc

4

25


27/111

5 h =1

6 k =17 l =1

8 a = 3 * 1 0 ^ - 1 0

9 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

10 printf ( \nThe i n t e r p l a n a r s p ac i ng f o r t he p l a ne ( 1 01 )i s %. 3 f 1010 m , d * 1 0 ^ 1 0 )



3 clc

4 h =3

5 k =2

6 l =1

7 r f c c = 0 . 1 2 7 8 * 1 0 ^ - 9 //m8 a = 4 * r f c c / sqrt (2)

9 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

10 printf ( \nThe l a t t i c e c o ns t a nt = %. 3 f 10610\nThe

i n t e r p l a n a r s p ac i ng f o r t he p l a ne ( 3 21 ) i s %. 3 f 1011 m , a * 1 0 ^ 1 0 , d * 1 0 ^ 1 1 )

Scilab code Exa 2.31 Number of atoms in Al foil


3 clc

4 a = 0 . 4 0 4 9 * 1 0 ^ - 1 0 //m5 t = 0 . 0 0 5 //m6 A = 2 5 * 1 0 ^ - 2 //m7 n = t * A / a ^ 3

26


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8 printf ( The number o f a to ms i n t h e Al f o i l i s %. 2 f

1 0 2 8 , n * 1 0 ^ - 2 8 )

Scilab code Exa 2.32 energy of the neutron


3 clc

4 t h e t a = 2 0 / / i n d e g r e e s

5 d = 2 * 1 0 ^ - 1 0 //m6 n =17 h = 6 . 6 2 6 * 1 0 ^ - 3 4

8 m = 1 . 6 7 * 1 0 ^ - 2 7 //k g9 e = 1 . 6 * 1 0 ^ - 1 9 //C

10 l a m = 2 * d * sin ( t h e t a * % p i / 1 8 0 ) / n

11 E = ( 1 / ( 2 * m ) ) * ( h / l a m ) ^ ( 2 )

12 printf ( \nThe d e B r o g l i e w av el en gt h o f t he n eu tr on i s%.3 f 1010\ n th e e ne rg y o f t he n eu tr on i s %. 4 f

eV , l a m * 1 0 ^ 1 0 , E / e )

Scilab code Exa 2.35 deBroglie wavelength of electrons


3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C5

6 h = 6 . 6 2 6 * 1 0 ^ - 3 4

7 m = 9 . 1 * 1 0 ^ - 3 1 //k g8 e k = 2 3 5 . 2 * e

9 n =1

10 t h e t a = 9 . 2 1

11 l a m = h / sqrt ( 2 * m * e k )

27


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13 printf ( \nThe d e B ro g l i e w av el en gt h o f e l e c t r o n i s %. 3 f 1011 m\nThe i n t e r p l a n a r s p ac i ng i s %. 3 f 1010 m , l a m * 1 0 ^ 1 1 , d * 1 0 ^ 1 0 )



3 clc4 // I n t e r c e p t s a re i n t h e r a t i o 3 a : 4 b a lo ng X ,Y and

p a r a l l e l t o Z a x i s5 / /x i n t e r c e p t 3 , y i n t e r c e p t 4 and z i n t e r c e p t

i n f i n i t y6 a = 2 * 1 0 ^ - 1 0 / / 2 A ng st ro m7 h =4

8 k =3

9 l =0

10 d = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

11 printf ( The l a t t i c e s p a c in g f o r t he p l an e 43 0 i s %. 1

f1010 m , d * 1 0 ^ 1 0 )

Scilab code Exa 2.38 Plane Drawing


3 clc

4 printf ( Same a s e xa mp le 2 . 2 4 o f t h e s ame c h a p t er )

28


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Chapter 3

Characterisation of material

Scilab code Exa 3.1 wavelength and frequency of Xrays


3 clc

4 h = 6 . 6 2 6 * 1 0 ^ - 3 4 / / J s5 e = 1 . 6 * 1 0 ^ - 1 9 //C6 c = 3 * 1 0 ^ 8 //m/s

7 v = 1 0 0 0 0 //V8 l a m _ m i n = ( h * c ) / ( e * v )

9 V = c / l a m _ m i n

10 printf ( \n ( i ) \nThe w a v el e n g th o f Xr a y s e m i tt e dL am da mi n = %. 2 f A \n ( i i ) \nThe f r eq u e nc y o f Xr a y beam e m i tt e d i s %. 1 f 1 0 1 8 Hz , l a m _ m i n * 1 0 ^ 1 0 ,V * 1 0 ^ - 1 8 )

Scilab code Exa 3.2 wavelength and velocity of electrons


29


31/111

3 clc

4 v = 1 0 0 0 0 //V5 i = 2 * 1 0 ^ - 3 //A6 e = 1 . 6 * 1 0 ^ - 1 9 //C7 t =1

8 m = 9 . 1 * 1 0 ^ - 3 1 //k g9 // ( i )

10 n = i * t / e

11 printf ( The no o f e l e c t r o n s s t r i k i n g t h e t a r g e t p e rse con d =%.2 f 1 0 1 6 , n * 1 0 ^ - 1 6 )

12 // ( i i )13 v1 = sqrt ( 2 * e * v / m )

14 // ( i i i )15 l a m = 1 2 4 0 0 / v

16 printf ( \n ( i i ) \nThe v e l o c i t y o f e l e c t r o n =%. 2 f 1 0 7m/ s \n ( i i i ) \n Wa v el en g th o f xr a y s=%. 2 f A , v1* 1 0 ^ - 7 , l a m )

Scilab code Exa 3.3 wavelength and angle for 2nd order bragg reflection


3 clc

4 d = 5 . 6 5 3 4 * 1 0 ^ - 1 0

5 t h e t a = 1 3 . 6 6 6 6 // i n d e g r e e s6 n =1

7 // ( i )8 l a m = 2 * d * sin ( t h e t a * % p i / 1 8 0 ) / n

9 printf ( \n ( i ) \nLambda =%. 3 f1010 m , l a m * 1 0 ^ 1 0 )10 // ( i i )

11 n =212 t h e t a = asin ( n * l a m / ( 2 * d ) )

13 t h e t a = t h e t a * 1 8 0 / % p i

14 printf ( \n ( i i ) \n2nd o r d er Bragg r e f l e c t i o n a t a n g l eTh et a2 = % f , t h e t a )

30


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Scilab code Exa 3.4 Grating spacing and glancing angle


3 clc

4 v = 2 4 8 0 0

5 n =1

6 l a m = 1 . 5 4 * 1 0 ^ - 1 0 //m

7 g a = 1 5 . 8 / / d e g r e e8 // ( i )9 d = n * l a m / ( 2 * sin ( g a * % p i / 1 8 0 ) )

10 printf ( \n ( i ) \n g r at i ng s p a c i n f f o r NaCl c r y s t a l =%f 1010 m , d * 1 0 ^ 1 0 )

11 // ( i i )12 l a m _ m i n = 1 2 4 0 0 / v

13 l a m _ m i n = l a m _ m i n * 1 0 ^ - 1 0

14 t h e t a = asin ( n * l a m _ m i n / ( 2 * d ) )

15 t h e t a = t h e t a * 1 8 0 / % p i

16 printf ( \n ( i i ) \ n g l a n c i n g a n g l e f o r minimum

w a v el e n g th = % f d e g r e e s , t h e t a )

Scilab code Exa 3.5 wavelength of radiation


3 clc

4 l a m = 0 . 7 0 78 * 1 0^ - 1 0

5 w t = 4 26 w t 1 = 4 8

7 l a m 1 = ( l a m * ( w t - 1 ) ^ 2 ) / ( w t 1 - 1 ) ^ 2

8 printf ( \n Wa ve le ng th o f cadmium r a d i a t i o n i s %. 4 f A , l a m 1 * 1 0 ^ 1 0 )

31


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Scilab code Exa 3.6 Energy of thermal neutron


3 clc

4 l a m = 1 0 ^ - 1 0 //m5 h = 6 . 6 2 6 * 1 0 ^ - 3 4

6 m = 1 . 6 7 5 * 1 0 ^ - 2 7

7 e 1 = 1 . 6 0 2 * 1 0 ^ - 1 9 / / e v8 e = ( h ^ 2 ) / ( 2 * m * l a m ^ 2 )

9 e = e / e 1

10 printf ( \nThe e n er g y o f t h er m al n e ut r on w it hw av el en gt h 1 A i s %f eV ,e )

Scilab code Exa 3.8 temperature of thermal neutron


3 clc

4 l a m = 0 . 1 //nm5 T = ( 2 . 5 1 6 ^ 2 ) / ( l a m ) ^ 2

6 printf ( t e m pe ra t ur e o f t he rm al n eu tr on c o r r es p o n d i ngt o 1A i s %. 0 f K ,T )

32


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Chapter 4

Cohesion between atoms

Scilab code Exa 4.1 Coulomb interatomic energy


3 clc

4 R = 2 . 8 1 * 1 0 ^ - 1 0 //m5 e = 1 . 6 * 1 0 ^ - 1 9

6 e p s = 8 . 8 5 4 * 1 0 ^ - 1 2

7 U = - ( e ^ 2 ) / ( 4 * % p i * e p s * R )8 printf ( The Coulomb i n t e r a t o m i c e n e r g y i s %. 2 f eV ,U

* 1 0 ^ 1 9 / 1 . 6 )

33


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Chapter 5

Crystal Imperfections

Scilab code Exa 5.1 Average distance between dislocations


3 clc

4

5 a = 3 . 6 1 5 * 1 0 ^ - 1 0 //m6 t _ a n g = 0 . 7 5 / / i n d e g r e e

7 h =18 k =1

9 l =0

10 d _ 1 1 0 = a / sqrt ( h ^ 2 + k ^ 2 + l ^ 2 )

11 D = d _ 1 1 0 / tan ( t _ a n g * % p i / ( 1 8 0 * 2 ) )

12 printf ( The a v e r ag e d i s t a n c e b et we en t h ed i s l o c a t i o n s i s %. 3 f A , D * 1 0 ^ 6 )

Scilab code Exa 5.2 Schottky defects per unit cell


34


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3 clc

4 l p = 4 . 0 1 8 5 * 1 0 ^ - 1 0 //m5 d e n s = 4 2 8 5 //kg/m36 a v g = 6 . 0 2 2 * 1 0 ^ 2 6

7 w t _ c s = 1 3 2 . 9

8 w t _ c l = 3 5 . 5

9 N = ( d e n s * a v g * l p ^ 3 ) / ( w t _ c s + w t _ c l )

10 s d = ( 1 - N ) * 1 0 0 / 1

11 printf ( The number o f S c ho t tk y d e f e c t s p e r u n i t c e l l= %.3f%% , s d )

35


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Chapter 6

Classification of solids

Scilab code Exa 6.1 Wavelength of light emitted from LED


3 clc

4 e = 1 . 6 0 9 * 1 0 ^ - 1 9 //C5 e g = 1 . 8 //eV6 h = 6 . 6 2 6 * 1 0 ^ - 3 4

7 c = 3 * 1 0 ^ 8 //m/s8 E = e * e g

9 l a m d a = h * c / E

10 printf ( The w av el en gt h o f l i g h t e m it t ed fro m g i ve nLED i s %. 3 f m , l a m d a * 1 0 ^ 7 )

Scilab code Exa 6.2 Band gap of given GaAsP


3 clc

4 l a m = 6 7 1 5 * 1 0 ^ - 1 0 //m

36


38/111


39/111

Chapter 7

Elecron theory of Solids

Scilab code Exa 7.1 mobility of electrons in copper


3 clc

4 r h o = 1 . 7 3 * 1 0 ^ - 8 //Ohmm5 z = 6 3 . 5

6 d = 8 . 9 2 * 1 0 ^ 3 //kg/m3

7 a v g = 6 . 0 2 3 * 1 0 ^ 2 68 e = 1 . 6 * 1 0 ^ - 1 9 //C9 m = 9 . 1 1 * 1 0 ^ - 3 1 //Kg

10

11 n = a v g * d / z

12 s i g = 1 / r h o

13 t a u = s i g * m / ( n * e ^ 2 )

14 m u = s i g / ( n * e )

15

16 printf ( M ob i l i t y o f e l e c t r o n s i n c o pp er i s %. 2 f

10 3 m2/Vs , m u * 1 0 ^ 3 )

Scilab code Exa 7.2 resistivity of copper

38


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1 / / Exa mpl e 7 . 2 , p ag e no161

2 clear3 clc

4 r = 1 . 8 5 * 1 0 ^ - 1 0 //m5 t = 3 * 1 0 ^ - 1 4 // s6 m = 9 . 1 1 * 1 0 ^ - 3 1 //Kg7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 a = r * ( 4 / sqrt ( 3 ) )

9 n e = 2 / a ^ 3

10 r h o = m / ( n e * t * e ^ 2 )

11 printf ( R e s i s t i v i t y o f c o pp er i s %. 3 f 10 8 Ohmm ,r h o * 1 0 ^ 8 )

Scilab code Exa 7.3 resistivity of sodium


3 clc

4

5 r = 1 . 8 5 * 1 0 ^ - 1 0 //m

6 t = 3 . 1 * 1 0 ^ 1 4 // s7 m = 9 . 1 1 * 1 0 ^ - 3 1 //Kg8 e = 1 . 6 * 1 0 ^ - 1 9 //C9 n = 2 5 . 3 3 * 1 0 ^ 2 7

10 r h o = m / ( n * t * e ^ 2 )

11 printf ( The e l e c t r i c R e s i s t i v i t y o f s od iu m a t 0 Ci s %. 3 f 1036 Ohmm , r h o * 1 0 ^ 3 6 )

Scilab code Exa 7.4 mobility of electrons in meatls


3 clc

39


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4

5 r = 1 . 8 5 * 1 0 ^ - 1 0 //m6 t = 3 . 4 * 1 0 ^ - 1 4 // s7 m = 9 . 1 1 * 1 0 ^ - 3 1 //Kg8 e = 1 . 6 * 1 0 ^ - 1 9 //C9 n = 5 . 8 * 1 0 ^ 2 8 // per m3

10 r h o = m / ( n * t * e ^ 2 )

11 printf ( \nThe e l e c t r i c r e s i s t i v i t y of ma t e r i al i s %. 3 f10 8 Ohmm , r h o * 1 0 ^ 8 )

12 m u = e * t / m

13 printf ( \nThe m o bi l it y o f t h e e l e c t r o n i n a m e t a l i s%.2 f 10 3 m2/vs , m u * 1 0 ^ 3 )

Scilab code Exa 7.5 drift velocity of electrons


3 clc

4

5 r h o = 1 . 5 4 * 1 0 ^ - 8 //ohmm

6 E = 1 0 0 //V/m7 n = 5 . 8 * 1 0 ^ 2 8 //m38 e = 1 . 6 * 1 0 ^ - 1 9 //C9 m u = 1 / ( r h o * n * e )

10 v d = m u * E

11 printf ( \ n M ob i li t y o f e l e c t r o n i n s i l v e t r i s %. 4 f 10 3 m2/vs \n\nThe d r i f t v e l o c i t y o f t h ee l e c t r o n i n s i l v e r i s %. 5 f m/ s , m u * 1 0 ^ 3 , v d )

Scilab code Exa 7.6 mobility of electrons


40


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3 clc

45 d = 1 0 . 5 * 1 0 ^ 3 //kg/m36 s i g = 6 . 8 * 1 0 ^ 7 // pe r Ohmm7 w t = 1 0 7 . 9 //kg/m38 e = 1 . 6 * 1 0 ^ - 1 9 //C9 a v g = 6 . 0 2 3 * 1 0 ^ 2 6 //atoms/m3

10

11 n = a v g * d / w t

12 m u = s i g / ( n * e )

13 printf ( The m o b i l i t y o f e l e c t r o n i s % . 3 f 102 m 2 .V / s , m u * 1 0 ^ 2 )

Scilab code Exa 7.7 Lorentz Number


3 clc

4 s i g = 5 . 8 7 * 1 0 ^ 7

5 k = 3 9 0 //W/mk

6 T = 2 9 37 L = k / ( s i g * T )

8 printf ( The L o r e n t z number i s %. 3 f 10 8 W.Ohm/K2, L * 1 0 ^ 8 )

Scilab code Exa 7.8 Lorentz Number

1 / / Exa mpl e 7 . 8 , p ag e no164

2 clear3 clc

4

5 t = 1 * 1 0 ^ - 1 4 // s6 T = 3 0 0 //K

41


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7 m = 9 . 1 1 * 1 0 ^ - 3 1 //Kg

8 e = 1 . 6 * 1 0 ^ - 1 9 //C9 n = 6 * 1 0 ^ 2 8 // per m310 s i g = ( n * t * e ^ 2 ) / m

11 printf ( \ n t h e e l e c t r i c a l c o n d u c t i v i t y i s %. 4 f 107/ohmm , s i g * 1 0 ^ - 7 )

12 k = 1 . 3 8 * 1 0 ^ - 2 3

13 k 1 = n * % p i ^ 2 * k ^ 2 * T * t / ( 3 * m )

14 printf ( \n\n Th er ma l c o n d u c t i v i t y i s %. 2 f W/mk , k 1 )15 L = k 1 / ( s i g * T )

16 printf ( \n\ n t he L o r e n t z number i s %. 4 f 10 8 W.Ohm/k 2 , L * 1 0 ^ 8 )

Scilab code Exa 7.9 conductivity of copper


3 clc

4

5 d = 8 9 0 0 //kg/m3

6 c u = 6 3 . 57 t = 1 0 ^ - 1 4 // s8 a v g = 6 . 0 2 3 * 1 0 ^ 2 3

9 n = a v g * d * 1 0 0 0 / c u

10 m = 9 . 1 * 1 0 ^ - 3 1 //k g11 e = 1 . 6 * 1 0 ^ - 1 9

12

13 s i g = ( n * t * e ^ 2 ) / m

14 printf ( The e l e c t r i c a l c o n d u c t i v i t y i s %. 3 f 1 0 7 /Ohmm , s i g * 1 0 ^ - 7 )

Scilab code Exa 7.10 drift velocity of electrons in silver piece

42


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1 / / Exa mpl e 7 . 1 0 , p ag e no166

2 clear3 clc

4 r h o = 1 . 6 * 1 0 ^ - 8 //Ohmm5 e = 1 . 6 * 1 0 ^ - 1 9 //C6 f e = 5 . 5 * e // J7 a v g = 6 . 0 2 3 * 1 0 ^ 2 3

8 d = 1 . 0 5 * 1 0 ^ 4 / / d e n s i t y9 w t = 1 0 7 . 9 * 1 0 ^ - 3 / / a t o mi c w e i g ht

10 m = 9 . 1 * 1 0 ^ - 3 1 //k g11 c = 3 * 1 0 ^ 8 //m/s12 s i g = 1 / r h o

13 n = a v g * d / w t14 t = s i g * m / ( n * e ^ 2 )

15 printf ( \nThe c o n d u c t i v i t y o f s i l v e r p i e c e i s %. 2 f 1 0 7 p e r Ohmm\n\nThe r e l a x a t i o n t im e i s %. 2 f 101 4 s , s i g * 1 0 ^ - 7 , t * 1 0 ^ 1 4 )

16 l a m = c * t

17 v d = s i g * 1 0 0 / ( n * e )

18 printf ( \n\nThe d r i f t t v e l o c i t y y o f e l e c t r o n s i n t hes i l v e r p i e c e i s % . 2 f m/ s , v d )

Scilab code Exa 7.11 resistivity of copper


3 clc

4 r 1 = 1 . 7 * 1 0 ^ - 8

5 t 2 = 3 0 0

6 t 1 = 7 0 0 + 2 7 3

7 r 2 = r 1 * sqrt ( ( t 1 / t 2 ) )8 printf ( The r e s i s t i v i t y y o f t h e c o p p e r w i r e i s %. 4 f 10 8 Ohmm , r 2 * 1 0 ^ 8 )

43


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Scilab code Exa 7.12 mobility and drift velocity of electrons


3 clc

4

5 r h o = 1 . 5 4 * 1 0 ^ - 8

6 e = 1 . 6 * 1 0 ^ - 1 9 //C7 e f = 5 . 5 * e // J8 n = 5 . 8 * 1 0 ^ 2 8 / / / p er c u b i c m et er9 m = 9 . 1 * 1 0 ^ - 3 1 //k g

10

11 // ( i )12 t = m / ( r h o * n * e ^ 2 )

13 m u = e * t / m

14 printf ( \n ( i ) \nThe r e l a x a t i o n t im e i s %. 2 f 1014 s \nThe m o b i l i t y o f t he e l e c t r o n s i s %. 4 f 103 m2/Vs , t * 1 0 ^ 1 4 , m u * 1 0 ^ 3 )

15

16 // ( i i )17 v d = e * t * 1 0 0 / m

18 printf ( \n\n ( i i ) \ n t h e d r i f t v e l o c i t y o f e l c t r o n i s %. 5 f m/ s , v d )

19

20 // ( i i i )21 vf = sqrt ( 2 * e f / m )

22 printf ( \n\n ( i i i ) \nFermi v e l o c i t y i s %. 2 f 1 0 6 m / s ,v f * 1 0 ^ - 6 )

23

24 // ( i v )25 l a m = v f * t

26 printf ( \n\n ( iv )\nThe mean f r e e p at h i s %. 3 f 10 8 m , l a m * 1 0 ^ 8 )

44


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Chapter 8

Statics and Band theory of

Solids

Scilab code Exa 8.1 Fermi energy


3 clc

4 d _ c u = 8 . 9 6 * 1 0 ^ 3 // d e n s i t y o f cu5 a _ c u = 6 3 . 5 5 / / Ato mic w e ig h t o f cu6 d _ z = 7 1 0 0

7 a _ z = 6 5 . 3 8

8 d _ a l = 2 7 0 0

9 a _ a l = 2 7

10 a v g = 6 . 0 2 3 * 1 0 ^ 2 6

11 h = 6 . 6 2 6 * 1 0 ^ - 3 4

12 m = 9 . 1 * 1 0 ^ - 3 1 //k g13 e = 1 . 6 * 1 0 ^ - 1 9 //C14

15 // ( i )16 n _ c u = d _ c u * a v g / a _ c u17 e _ c u = ( h ^ 2 / ( 8 * m ) ) * ( 3 * n _ c u / % p i ) ^ ( 2 / 3 )

18 e _ c u = e _ c u / e

19 printf ( \n( i ) F or Cu\nThe e l e c t r o n c o n c e n t r a t i o n i n

45


47/111

Cu i s %. 4 f 1 0 2 8 p e r m 3\ n Fe rm i e n e r g y a t 0 k =%

. 4 f eV , n _ c u * 1 0 ^ - 2 8 , e _ c u )2021 // ( i i )22 n _ z = d _ z * a v g * 2 / a _ z

23 e _ z = ( h ^ 2 / ( 8 * m ) ) * ( 3 * n _ z / % p i ) ^ ( 2 / 3 )

24 e _ z = e _ z / e

25 printf ( \n ( i ) F o r Zn\nThe e l e c t r o n c o n c e n t r a t i o n i nZn i s %. 4 f 1 0 2 8 p e r m 3\ n Fe rm i e n e r g y a t 0 k =%. 4 f eV , n _ z * 1 0 ^ - 2 8 , e _ z )

26

27 // ( i )

28 n _ a l = d _ a l * a v g * 3 / a _ a l29 e _ a l = ( h ^ 2 / ( 8 * m ) ) * ( 3 * n _ a l / % p i ) ^ ( 2 / 3 )

30 e _ a l = e _ a l / e

31 printf ( \n ( i ) F or A l\nThe e l e c t r o n c o n c e n t r a t i o n i nAl i s %. 4 f 1 0 2 8 p e r m 3\ n Fe rm i e n e r g y a t 0 k =%. 4 f eV , n _ a l * 1 0 ^ - 2 8 , e _ a l )

Scilab code Exa 8.2 Density of States


3 clc

4 a v g = 6 . 0 2 3 * 1 0 ^ 2 6

5 h = 6 . 6 2 6 * 1 0 ^ - 3 4

6 m = 9 . 1 * 1 0 ^ - 3 1 //k g7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 n = 8 . 4 9 0 5 * 1 0 ^ 2 8

9

10 e f = ( h ^ 2 / ( 8 * m ) ) * ( 3 * n / % p i ) ^ ( 2 / 3 )11 e f = e f / e

12 g a m = 6 . 8 2 * 1 0 ^ 2 7

13 x = ( g a m * sqrt ( e f ) ) / 2

14 printf ( The d e n si t y o f s t a t e s f o r Cu a t t he Fermi

46


48/111

l e v e l f o r T = 0 K i s %. 0 f 1027 m3 , x * 1 0 ^ - 2 7 )

Scilab code Exa 8.3 Nordheims Coefficient


3 clc

4 r n i = 6 3 //n Ohm.m5 r c r = 1 2 9

6 k = 1 1 2 07 c = ( k * 1 0 ^ - 9 ) / ( 0 . 8 * ( 1 - 0 . 8 ) )

8 printf ( The Nord heims c o e e f i c i e n t i s %. 0 f 10 6 Ohmm , c * 1 0 ^ 6 )

Scilab code Exa 8.4 Conductivity of Al

1 / / Exa mpl e 8 . 4 , p ag e no211

2 clear3 clc

4 d = 2 7 0 0 //kh/m35 a w t = 2 7

6 t = 1 0 ^ - 1 4 // s7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 m = 9 . 1 * 1 0 ^ - 3 1 //Kg9 a v g = 6 . 0 2 3 * 1 0 ^ 2 6

10 n = a v g * d * 3 / a w t

11 s i g = ( n * t * e ^ 2 ) / m

12 printf ( The c o n d u ct i v i t y o f Al i s %. 4 f 107 ohmm. ,s i g * 1 0 ^ - 7 )

47


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Scilab code Exa 8.5 Fermi distribution Function


3 clc

4 e 1 = 0 . 0 1 //eV5 e = 1 . 6 * 1 0 ^ - 1 9 //C6 e d = e * e 1

7 T = 2 0 0 //K8 E = 1 / ( 1 + % e ^ ( e d / ( T * 1 . 3 8 * 1 0 ^ - 2 3 ) ) )

9 printf ( The Fermy d i s t r i b u t i o n f u n c t i o n f o r e ne rg y Ei s %. 4 f ,E )

Scilab code Exa 8.6 Fermi temperature


3 clc

4

5 v = 0 . 8 6 * 1 0 ^ 6 //m/s

6 m = 9 . 1 * 1 0 ^ - 3 1 //Kg7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 k = 1 . 3 8 * 1 0 ^ - 2 3 //J/K9 E = ( m * v ^ 2 ) / 2

10 T = E / k

11 printf ( \nThe f e r mi e ne rg y i s %. 3 f 1019 J\nTheF er mi T em pe ra tu re Tf i s %. 2 f 104 K , E * 1 0 ^ 1 9 , T* 1 0 ^ - 4 )

Scilab code Exa 8.7 Density of States


48


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3 clc

45 m = 9 . 1 * 1 0 ^ - 3 1 //Kg6 d E = 0 . 0 1 //eV7 h = 6 . 6 3 * 1 0 ^ - 3 4 / / / J s8 e F = 3 //eV9 e = 1 . 6 * 1 0 ^ - 1 9 //C

10 E 1 = e F * e

11 E 2 = E 1 + e * d E

12

13 n = ( 4 * % p i * ( 2 * m ) ^ ( 1 . 5 ) ) / h ^ 3

14 k = ( ( 2 * 0 . 3 5 2 3 / 3 ) * ( ( E 2 ^ ( 1 . 5 ) - ( E 1 ^ ( 1 . 5 ) ) ) ) )

15 n = n * k16 printf ( The n umber o f s t a t e s l y i n g b etw een t he

e n er gy l e v e l i s %. 2 f 1 0 2 5 , n * 1 0 ^ - 2 5 )

Scilab code Exa 8.8 Fermi Velocity


3 clc4 T f = 2 4 6 0 0 //K5 m = 9 . 1 1 * 1 0 ^ - 3 1 //Kg6 k = 1 . 3 8 * 1 0 ^ - 2 3

7 vf = sqrt ( 2 * k * T f / m )

8 printf ( The F erm i V e l o c i t y i s %. 4 f 1 0 6 m / s , vf* 1 0 ^ - 6 )

Scilab code Exa 8.9 Fermi Energy


3 clc

49


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4 n = 1 8 . 1 * 1 0 ^ 2 8 // p e r c u b i c m

5 h = 6 . 6 2 * 1 0 ^ - 3 4 / / J s6 m = 9 . 1 * 1 0 ^ - 3 1 //Kg7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 e f = ( ( 3 * n / ( 8 * % p i ) ) ^ ( 2 / 3 ) ) * ( ( h ^ 2 ) / ( 2 * m ) )

9 e f = e f / e

10 printf ( The Fermi e ne rg y a t 0 K i s %. 2 f eV , e f )



3 clc

4 n = 1 8 . 1 * 1 0 ^ 2 8 // p e r c u b i c m5 h = 6 . 6 2 * 1 0 ^ - 3 4 / / J s6 m = 9 . 1 * 1 0 ^ - 3 1 //Kg7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 e f = ( ( 3 * n / ( 8 * % p i ) ) ^ ( 2 / 3 ) ) * ( ( h ^ 2 ) / ( 2 * m ) )

9 e f = e f / e

10 printf ( The Fermi e ne rg y a t 0 K i s %. 2 f eV , e f )



3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C5 E d = 0 . 5 * e

6 k = 1 . 3 8 * 1 0 ^ - 2 37 x = 0 . 0 1

8 T = E d / ( k * log ( ( 1 / x ) - 1 ) )

9

50


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10 printf ( T e mp er at ur e a t w hi ch t h e r e i s 1%%

p r o b a b i l i t y t ha t a s t a t e w i t h 0 . 5 eV e ne rg yo c cu p ie d a bo ve t he Fermi e ne rg y l e v e l i s %. 1 f K ,T )

Scilab code Exa 8.12 theorotical example


3 clc4 printf ( T h e o r o t i c a l Exam [ p l e )

Scilab code Exa 8.13 theorotical example


3 clc

4 printf ( T h e o r o t i c a l Exam [ p l e )

Scilab code Exa 8.14 Energies for different probabilities


3 clc

4 e f = 2 . 1

5 k = 1 . 3 8 * 1 0 ^ - 2 36 T = 3 0 0 //K7 e = 1 . 6 * 1 0 ^ - 1 9 // c8 // ( i )9 p 1 = 0 . 9 9

51


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10 E 1 = e f + ( k * T * log ( - 1 + 1 / p 1 ) ) / e

1112 // ( i i )13 p 2 = 0 . 0 1

14 E 2 = e f + ( k * T * log ( - 1 + 1 / p 2 ) ) / e

15

16 // ( i i i )17 p 3 = 0 . 5

18 E 3 = e f + ( k * T * log ( - 1 + 1 / p 3 ) ) / e

19

20 printf ( \nThe e n e r g i e s f o r t he o cc up yi ng o f d e l e c t r o n s a t %d K f o r t he p r o b a b i l i t y o f %. 2 f i s

%. 2 f , T , p 1 , E 1 )21

22 printf ( \nThe e n e r g i e s f o r t he o cc up yi ng o f d e l e c t r o n s a t %d K f o r t he p r o b a b i l i t y o f %. 2 f i s%. 2 f , T , p 2 , E 2 )

23

24 printf ( \nThe e n e r g i e s f o r t he o cc up yi ng o f d e l e c t r o n s a t %d K f o r t he p r o b a b i l i t y o f %. 2 f i s%. 2 f , T , p 3 , E 3 )



3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C5 e d = 0 . 0 2 * e

6 T 1 = 2 0 0

7 T 2 = 4 0 08 k = 1 . 3 8 * 1 0 ^ - 2 3

9 f e 1 = 1 / ( 1 + % e ^ ( e d / ( k * T 1 ) ) )

10 f e 2 = 1 / ( 1 + % e ^ ( e d / ( k * T 2 ) ) )

11 printf ( \nThe F ermi d i s t r i b u t i o n f u n c t i o n f o r t he

52


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g i v e n e n er g y a t %d K i s %. 4 f , T 1 , f e 1 )

12 printf ( \nThe F ermi d i s t r i b u t i o n f u n c t i o n f o r t heg i v e n e n er g y a t %d K i s %. 4 f , T 2 , f e 2 )



3 clc

4 d = 1 0 5 0 0 / / d e n s i t y5 a v g = 6 . 0 2 2 * 1 0 ^ 2 66 a w t = 1 0 7 . 9

7 n = d * a v g / a w t / / p er c u b i c m8 h = 6 . 6 2 * 1 0 ^ - 3 4 / / J s9 m = 9 . 1 * 1 0 ^ - 3 1 //Kg

10 e = 1 . 6 * 1 0 ^ - 1 9 //C11 e f = ( ( 3 * n / ( 8 * % p i ) ) ^ ( 2 / 3 ) ) * ( ( h ^ 2 ) / ( 2 * m ) )

12 e f = e f / e

13 printf ( The Fermi e ne rg y f o r g i ve n m et al i s %. 2 f eV , e f )



3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C5 e d = 0 . 2 * e

6 T 1 = 3 0 07 T 2 = 1 0 0 0

8 k = 1 . 3 8 * 1 0 ^ - 2 3

9 f e 1 = 1 / ( 1 + % e ^ ( e d / ( k * T 1 ) ) )

10 f e 2 = 1 / ( 1 + % e ^ ( e d / ( k * T 2 ) ) )

53


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11 printf ( \nThe F ermi d i s t r i b u t i o n f u n c t i o n f o r t he

g i v e n e n er g y a t %d K i s %. 6 f , T 1 , f e 1 )12 printf ( \nThe F ermi d i s t r i b u t i o n f u n c t i o n f o r t heg i v e n e n er g y a t %d K i s %. 4 f , T 2 , f e 2 )

Scilab code Exa 8.18 Electron density


3 clc4

5 h = 6 . 6 2 * 1 0 ^ - 3 4 / / J s6 m = 9 . 1 * 1 0 ^ - 3 1 //Kg7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 e f = 3 * e

9 k = ( ( 3 / ( 8 * % p i ) ) ^ ( 2 / 3 ) ) * ( ( h ^ 2 ) / ( 2 * m ) )

10 k = e f / k

11 n = k ^ ( 1 . 5 )

12 printf ( The number o f f r e e e l e c t r o n s c o n c e n t r a t i o ni n m et al i s %. 2 f 1 0 28 p er c u b ic m et er ,n

* 1 0 ^ - 2 8 )

Scilab code Exa 8.19 concentration of free electrons


3 clc

4

5 h = 6 . 6 2 * 1 0 ^ - 3 4 / / J s6 m = 9 . 1 * 1 0 ^ - 3 1 //Kg7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 e f = 5 . 5 * e

9 k = ( ( 3 / ( 8 * % p i ) ) ^ ( 2 / 3 ) ) * ( ( h ^ 2 ) / ( 2 * m ) )

54


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10 k = e f / k

11 n = k ^ ( 1 . 5 )12 printf ( The number o f f r e e e l e c t r o n s c o n c e n t r a t i o ni n m et al i s %. 3 f 1 0 28 p er c u b ic m et er ,n* 1 0 ^ - 2 8 )

Scilab code Exa 8.20 carrier density and fermi velocity

1 / / Exa mpl e 8 . 1 8 , p ag e no221

2 clear3 clc

4

5 h = 6 . 6 2 * 1 0 ^ - 3 4 / / J s6 m = 9 . 1 * 1 0 ^ - 3 1 //Kg7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 e f = 7 * e

9 k = ( ( 3 / ( 8 * % p i ) ) ^ ( 2 / 3 ) ) * ( ( h ^ 2 ) / ( 2 * m ) )

10 k = e f / k

11 n = k ^ ( 1 . 5 )

12 printf ( The number o f f r e e e l e c t r o n s c o n c e n t r a t i o n

i n m et al i s %. 2 f 1 0 28 p er c u b ic m et er ,n* 1 0 ^ - 2 8 )

13 v t h = sqrt ( 2 * e f / m )

14 printf ( \nThe t er ma l v e l o c i t y o f e l e c t r o n s i n c o pp eri s %. 3 f 1 0 6 m / s , v t h * 1 0 ^ - 6 )

55


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Chapter 10

Transport Properties of

Semiconductors

Scilab code Exa 10.1 Intrinsic concentration conductivity and resistivity

1 / / Exa mpl e 1 0 . 1 , p ag e no2672 clear

3 clc

4 T = 3 0 0 //K5 m u e = 0 . 4 //m2/Vs6 m u h = 0 . 2

7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 e g = 0 . 7 * e // J9 m = 9 . 1 * 1 0 ^ - 3 1 //k g

10 m e = 0 . 5 5

11 m h = 0 . 3 7

12 h = 6 . 6 2 6 * 1 0 ^ - 3 4

13 k = 1 . 3 8 * 1 0 ^ - 2 3

14 n i = 2 * ( 2 * % p i * k * T / ( h ^ 2 ) ) ^ ( 1 . 5 )

15 n i = n i * ( m ^ 1 . 5 ) * ( m h * m e ) ^ ( 3 / 4 )16 n i = n i * % e ^ ( - e g / ( k * T ) )

17 printf ( \nThe i n t r i n s i c c o nc e n t r at i o n ni =%. 3 f 1 0 1 3/m3 , n i * 1 0 ^ - 1 3 )

18

56


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19 s i g = n i * e * ( m u e + m u h )

20 r h o = 1 / s i g21 printf ( \n I n t r i n s i c C o n d u c ti v i t y , S ig ma =%. 3 f 10 6p e r m 3\n I n t r i n s i c R e s i s t i v i t y , r h o = %. 2 f 106Ohmm , s i g * 1 0 ^ 6 , r h o * 1 0 ^ - 6 )


1 / / Exa mpl e 1 0 . 2 , p ag e no268

2 clear3 clc

4 n i = 1 . 4 5 * 1 0 ^ 1 0 //cm35 n d = 1 0 ^ 1 6 //cm36 k = 1 . 3 8 * 1 0 ^ - 2 3

7 T = 3 0 0

8 e = 1 . 6 * 1 0 ^ - 1 9 //C9 E f = k * T * log ( n d / n i )

10 E f = E f / e

11 printf ( The F ermi e ne rg yy w it h r e s p e c t t o Ef i ni n t r i n s i c Si = %.3 f eV , E f )

Scilab code Exa 10.3 Resistance of Germanium


3 clc

4 n i = 2 . 5 * 1 0 ^ 1 9 //m35 m u e = 0 . 3 9 //m2/Vs

6 m u h = 0 . 1 97 l = 1 0 ^ - 2 //m8 e = 1 . 6 * 1 0 ^ - 1 9 //C9 s i g = n i * e * ( m u e + m u h )

10 R = l / ( s i g * 1 0 ^ - 6 )

57


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11 printf ( The c o n d u c t i v i t y o f i n t r i n s i c Ge i s %. 2 f /

ohmm\nThe R e s i s t a n c e i s %. 0 f , s i g , R )

Scilab code Exa 10.4 conductivity of Intrinsic semiconductor


3 clc

4 n i = 1 . 5 * 1 0 ^ 1 6 //m3

5 m u e = 0 . 1 3 //m2/Vs6 m u h = 0 . 0 5

7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 s i g = n i * e * ( m u e + m u h )

9 printf ( The c o n d u c t i v i t y o f i n t r i n s i c Ge i s %. 2 f 10 4 /ohmm , s i g * 1 0 ^ 4 )

Scilab code Exa 10.5 Intrinsic Resistivity


3 clc

4 n i = 2 . 1 5 * 1 0 ^ 1 3 //cm35 m u e = 3 9 0 0 //cm2/Vs6 m u h = 1 9 0 0

7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 s i g = n i * e * ( m u e + m u h )

9 r = 1 / s i g

10

11 printf ( The c o n d u c t i v i t y o f i n t r i n s i c Ge i s %. 2 f 10 2 /ohmcm\n The i n t r i n s i c r e s i s t i v i t y i s %.0f Ohmcm , s i g * 1 0 ^ 2 , r ) / / a n s w er s n o t m a tc hi n g w i thbook s ans .

58


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Scilab code Exa 10.6 electrical conductivity of boron doped semiconduc-tor


3 clc

4 n i = 2 . 1 * 1 0 ^ 1 9 //m35 m u e = 0 . 4 //m2/Vs6 m u h = 0 . 2

7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 p = 4 . 5 * 1 0 ^ 2 3 //m39 s i g = n i * e * ( m u e + m u h )

10 r = p * e * m u h

11

12 printf ( The c o n d u c t i v i t y o f i n t r i n s i c Ge i s %. 3 f 10 2 /ohmcm\nThe i n t r i n s i c r e s i s t i v i t y i s %. 2 f1 0 4 , s i g , r * 1 0 ^ - 4 )

Scilab code Exa 10.7 Hole concentration conductivity and Resistance


3 clc

4 n = 5 * 1 0 ^ 2 8 //m35 n i = 1 . 4 5 * 1 0 ^ 1 3 //m36 m u e = 1 . 3 5 //m2/Vs7 m u h = 0 . 4 5

8 e = 1 . 6 * 1 0 ^ - 1 9 //C9 p = 4 . 5 * 1 0 ^ 2 3 //m3

10 s i g = n i * e * ( m u e + m u h )

11 r h o = 1 / s i g

12 //r ho= r ho1 0 1 2

59


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13 r = r h o * 1 0 ^ 1 2

14 n d = n / 1 0 ^ 915 p = ( n i ^ 2 ) / n d

16 s i g 2 = n d * e * m u e

17

18 printf ( \nThe i n t r i n s i c c o n d u c t i v i t y i s %. 2 f 10 6/ohmcm\n\nThe i n t r i n s i c r e s i s t i v i t y i s %. 2 f10 5Ohmm\n\ n R e s i s t a n c e = %. 2 f 10 7 Ohm\n\nDonar c o n c e n t r a t i o n i s %. 0 f 1 0 1 9\n\n C on c en t ra t io n o f h o l e i s %. 1 f 106 m3\n\n C o n d u c t i v i t y = %. 1 f p e r ohmm , s i g * 1 0 ^ 6 , r h o* 1 0 ^ - 5 , r * 1 0 ^ - 1 7 , n d * 1 0 ^ - 1 9 , p * 1 0 ^ - 6 , s i g 2 )

Scilab code Exa 10.8 Band Gap of Ge


3 clc

4

5 T = 3 0 0 //K

6 r h o = 2 . 1 2 //ohmm7 m u e = 0 . 3 6 //m2/Vs8 m u h = 0 . 1 7

9 e = 1 . 6 * 1 0 ^ - 1 9 //C10 m = 9 . 1 * 1 0 ^ - 3 1 //k g11 h = 6 . 6 2 6 * 1 0 ^ - 3 4

12 s i g = 1 / r h o

13 n i = s i g / ( e * ( m u h + m u e ) )

14 printf ( \ n C o n d u c t i v i t y = %. 6 f p e r Ohmm\n I n t r i n s i cc a r r i e r c o n c e n t r a t i o n , n i=%. 5 f 1 0 1 8 , s i g , n i

* 1 0 ^ - 1 8 )15

16 k = 1 . 3 8 * 1 0 ^ - 2 3

17 N c = 2 * ( 2 * % p i * k * T / h ^ ( 2 ) ) ^ ( 1 . 5 )

18 N c = N c * ( 0 . 5 * m ) ^ ( 1 . 5 )

60


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19 N v = 2 * ( 2 * % p i * k * T / h ^ ( 2 ) ) ^ ( 1 . 5 )

20 N v = N v * ( 0 . 3 7 * m ) ^ ( 1 . 5 )21 printf ( \nNc=%. 3 f1 0 2 4\nNv=%. 3 f1 0 2 4 , N c * 1 0 ^ - 2 4 , N v* 1 0 ^ - 2 4 )

22 e g = 2 * k * T * log ( sqrt ( N c * N v ) / n i )

23 e g = e g / e

24 printf ( \nThe ba nd g ap o f Ge i s %. 3 f eV , e g )

Scilab code Exa 10.9 carrier concentration of intrinsic semiconductor


3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C5 m = 9 . 1 * 1 0 ^ - 3 1 //k g6 h = 6 . 6 2 6 * 1 0 ^ - 3 4

7 k = 1 . 3 8 * 1 0 ^ - 2 3

8 e g = 0 . 7 * e

9 T = 3 0 0 //K10 n i = 2 * ( 2 * % p i * m * k * T / ( h ^ ( 2 ) ) ) ^ ( 1 . 5 )

11 n i = n i * % e ^ ( - e g / ( 2 * k * T ) )12 printf ( The c a r r i e r c o n c e n t r a t i o n o f an i n t r i n s i c

s e m ic o n d uc t o r i s = %. 2 f 1 0 1 8 p e r m 3 , n i * 1 0 ^ - 1 8 )

Scilab code Exa 10.10 Electrical conductivity of Si


3 clc4 e = 1 . 6 * 1 0 ^ - 1 9 //C5 m = 9 . 1 * 1 0 ^ - 3 1 //k g6 h = 6 . 6 2 6 * 1 0 ^ - 3 4

7 k = 1 . 3 8 * 1 0 ^ - 2 3

61


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8 e g = 1 . 1 * e

9 m u e = 0 . 4 8 //m2 /V. s10 m u h = 0 . 0 1 3 //m2 /V. s11 T = 3 0 0 //K12 n i = 2 * ( 2 * % p i * m * k * T / ( h ^ ( 2 ) ) ) ^ ( 1 . 5 )

13 n i = n i * % e ^ ( - e g / ( 2 * k * T ) )

14

15 s i g = n i * e * ( m u e + m u h )

16 printf ( \nThe c a r r i e r c o n c e n t r a t i o n o f an i n t r i n s i cs e m ic o n d uc t o r i s = %. 2 f 1 0 1 6 p e r m 3\n t h ee l e c t r i c a l c o n d u c t i i v i t y od S i i s %. 3 f 10 3 p e r

Ohmm , n i * 1 0 ^ - 1 6 , s i g * 1 0 ^ 3 )

Scilab code Exa 10.11 Fermi energy of Silicon

1 / / Exa mpl e 1 0 . 1 1 , p ag e no2752 clear

3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C5 e g = 1 . 1 2

6 m e = 0 . 1 27 m h = 0 . 2 8

8 T = 3 0 0

9 k = 1 . 3 8 * 1 0 ^ - 2 3

10

11 e f = ( e g / 2 ) + ( 3 * k * T / 4 ) * log ( m h / m e )

12 printf ( The Fermi e ne rg y o f S i a t 30 0 K i s %. 3 f eV ,ef )

Scilab code Exa 10.12 effect of temperature on Fermi level


62


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3 clc

45 e = 1 . 6 0 * 1 0 ^ - 1 9 //C6 e g = 1 * e

7 k = 1 . 3 8 * 1 0 ^ - 2 3

8 m =4

9 T = 0 . 1 * e * 4 / ( 3 * k * log ( m ) )

10 printf ( Te mper at ur e a t which Fermi l e v e l i s s h i f t e d10%% i s %. f K ,T )

Scilab code Exa 10.13 Conductivity of Ge


3 clc

4

5 e = 1 . 6 * 1 0 ^ - 1 9 //C6 n i = 2 . 4 * 1 0 ^ 1 9 //m37 m u e = 0 . 3 9 //m2/Vs8 m u h = 0 . 1 9 //m2/Vs

9 s i g = n i * e * ( m u e + m u h )10 printf ( The c o n d u ct i v i t y o f Ge a t 300 K i s %. 2 f p er

Ohmm , s i g )

Scilab code Exa 10.14 Fermi Energy level


3 clc4

5 e = 1 . 6 * 1 0 ^ - 1 9 //C6 T 1 = 3 0 0 //K7 T 2 = 3 3 0 //K

63


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8 e g = 0 . 3

9 e g 2 = e g * T 2 / T 110 printf ( E cE f3 30=%.2 f eV\n\nAt 3 30 K , t h e Fe rm ie ne rg y l e v e l l i e s %. 2 f eV , b e ll o w t he c o nd u ct i onband . , e g 2 , e g 2 )

Scilab code Exa 10.15 Conductivity of Ge

1 / / Exa mpl e 1 0 . 1 5 , p ag e no277

2 clear3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C5 e g = 0 . 7 2 * e //eV6 t 1 = 2 9 3 //K7 t 2 = 3 1 3 //K8 k = 1 . 3 8 * 1 0 ^ - 2 3

9 sig1=2

10 n = ( t 2 / t 1 ) * % e ^ ( ( e g / ( 2 * k ) ) * ( ( 1 / t 1 ) - ( 1 / t 2 ) ) )

11 s i g 2 = s i g 1 * n

12 printf ( The c o n d u c t i v i t y o f Ge a t 40 C i s %. 3 f p e r

Ohmm , s i g 2 )

Scilab code Exa 10.16 Intrinsic concentration of Si


3 clc

4 e = 1 . 6 * 1 0 ^ - 1 9 //C

5 m = 9 . 1 * 1 0 ^ - 3 1 //k g6 m m = 0 . 3 1 * m //k g7 h = 6 . 6 2 6 * 1 0 ^ - 3 4

8 k = 1 . 3 8 * 1 0 ^ - 2 3

9 e g = 1 . 1 * e

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10 T = 3 0 0 //K

11 n i = 2 * ( 2 * % p i * m m * k * T / ( h ^ ( 2 ) ) ) ^ ( 1 . 5 )12 n i = n i * % e ^ ( - e g / ( 2 * k * T ) )

13 printf ( The i n t r i n s i c c o n c e n t r a t i o n o f S i a t %d K i s%.4 f 10 1 5 e l e c t r o n s p er m3 , T , n i * 1 0 ^ - 1 5 )

Scilab code Exa 10.17 Drift Velocity

1 / / Exa mpl e 1 0 . 1 7 , p ag e no279

2 clear3 clc

4 h c = 0 . 5 5 * 1 0 ^ - 1 0 //m3//As5 c c = 5 . 9 * 1 0 ^ 7 // pe r Ohmm6 T = 3 0 0 //K7 d m = h c * c c

8 printf ( The d r i f t m o b i l i t y i s g i v en by mu d = %. 1 f 103 m2/Vs , d m * 1 0 ^ 3 )

Scilab code Exa 10.18 average no of electron per Cu atom


3 clc

4

5 s i g = 5 . 9 * 1 0 ^ 7 // pe r Ohmm6 e = 1 . 6 * 1 0 ^ - 1 9 //C7 m u = 3 . 2 * 1 0 ^ - 3 //m2/Vs8 d = 8 9 0 0 / / d e n s i t y

9 a v g = 6 . 0 2 2 * 1 0 ^ 2 310 n i = s i g / ( e * m u )

11 a w t = 6 3 . 5

12 n = a v g * d * 1 0 0 0 / a w t

13 k = n i / n

65


67/111

14 printf ( C o n ce nt ra ti on o f f r e e e l e c t r o n i n p u r e Cu i s

%.2 f 1 0 2 8\nThe a v e ra g e number o f e l e c t r o n sc o n t r i b u t e d p e r Cu atom i s %. 2 f i . e . %. 0 f ,n* 1 0 ^ - 2 8 , k , k )

Scilab code Exa 10.19 Mobility of Ge


3 clc4 i = 5 * 1 0 ^ - 3 //A5 v = 1 . 3 5 // v6 l = 0 . 0 1 //m7 b = 5 * 1 0 ^ - 3

8 t = 1 0 ^ - 3 //m9 a = 5 * 1 0 ^ - 6 //m2

10 v y = 2 0 * 1 0 ^ - 3

11 H = 0 . 4 5 //Wb/m212

13 r h o = v * a / ( l * i )

14 E y = v y / t15 j = i / a

16 k = E y / ( H * j )

17 R h = 3 * % p i * k / 8

18 m u = R h / r h o

19 printf ( The m o b i l i t y o f t h e Ge s am pl e i s %. 2 f m 2/Vs , m u )

Scilab code Exa 10.20 Hall Potential Difference


3 clc

66


68/111

4 I = 2 0 0 //A

5 H = 1 . 5 //Wb/m26 n = 8 . 4 * 1 0 ^ 2 8 / / e l e c t r o n s p e r m37 d = 1 . 0 * 1 0 ^ - 3 //m8 e = 1 . 6 * 1 0 ^ - 1 9 //C9 v = I * H / ( n * d * e )

10 printf ( The H a l l p o t e n t i a l d i f f e r e n c e a pp ea ra nc ebet w ee n t he s hi p i s %. 0 f v , v * 1 0 ^ 6 )

Scilab code Exa 10.21 Mobility of Si


3 clc

4 r h = 3 . 6 6 * 1 0 ^ - 4 //m3/C5 r h o = 8 . 9 3 * 1 0 ^ - 3 //Ohmm6 e = 1 . 6 * 1 0 ^ - 1 9 //C7 n i = 1 / ( r h * e )

8 m u h = r h / r h o

9 printf ( t he c a r r i e r c o nc e nt r at i on o f S i d oped

s p ec i me n i s %. 3 f 1022 m3\n The m o bi l i t y o f S id op ed s p ec i m en i s %. 5 f m 2/Vs , n i * 1 0 ^ - 2 2 , m u h )

Scilab code Exa 10.22 Electron concentration and Mobility


3 clc

4 R h = 3 . 6 6 * 1 0 ^ - 1 1 //m2//As5 s i g = 1 1 2 * 1 0 ^ 7 //ohmm6 e = 1 . 6 * 1 0 ^ - 1 9 //C7 n = 3 * % p i / ( 8 * R h * e )

8 m u = s i g / ( n * e )

67


69/111

9 printf ( \nThe c o n c e n t r a t i o n o f e l e c t r o n s i s % . 0 f

1029 m3\n th e e l e c t r o n m o b i l i t y a t roomt e m p e r a t u r e = % . 3 f m 2 /Vs , n * 1 0 ^ - 2 9 , m u )

Scilab code Exa 10.23 Hall voltage


3 clc

4 I = 5 0 //A5 B = 1 . 5 //T

6 t = 0 . 5 * 1 0 ^ - 2

7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 d = 2 * 1 0 ^ - 2

9 N = 8 . 4 * 1 0 ^ 2 8 //m310 v = B * I / ( N * e * d )

11 printf ( The H a l l v o l t a g e i s %. 2 f 10 7 V , v * 1 0 ^ 7 )

Scilab code Exa 10.24 Relaxation time


3 clc

4 r h o = 1 . 5 4 * 1 0 ^ - 8 //Ohmm5 n i = 5 . 8 * 1 0 ^ 2 8 // per m36 m = 9 . 1 * 1 0 ^ - 3 1 //k g7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 t a u = m / ( r h o * n i * ( e ^ 2 ) )

9 printf ( The r e l a x a t i o n t i m e o f e l e c t r o n s i n m e t a l i s%.2 f 101 4 s , t a u * 1 0 ^ 1 4 )

68


70/111

Scilab code Exa 10.25 Electron mobility in Silver


3 clc

4 s i g = 6 . 2 2 * 1 0 ^ 7 // per ohmm5 n = 5 . 9 * 1 0 ^ 2 8 //m36 e = 1 . 6 * 1 0 ^ - 1 9 //C7 m u = s i g / ( n * e )

8 printf ( The m o bi l it y o f e l e c t r o n s i n S i i s %. 2 f 10 3 m2/Vs , m u * 1 0 ^ 3 )

Scilab code Exa 10.26 Electron mobility and electric field


3 clc

4 r h o = 0 . 1 //Ohmm5 n i = 1 0 ^ 2 0 // per m36 v d = 1 //m/s

7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 m u = 1 / ( r h o * n i * e )

9 E = v d / m u

10 printf ( \nThe m o bi l it y o f t h e e l e c t r o n s i n m a te r ia li s %. 3 f m 2 /Vs \nThe e l e c t r i c f i e l d i s %.1 f V/m ,

mu , E )

Scilab code Exa 10.27 Electron mobility


3 clc

4 s i g = 6 . 2 2 * 1 0 ^ 7 // pe r Ohmm

69


71/111

5 n = 5 . 9 * 1 0 ^ 2 8

6 e = 1 . 6 * 1 0 ^ - 1 97 m u = s i g / ( n * e )

8 printf ( The m o b i l i t y o f e l e c t r o n s i n s i l v e r i s %. 2 f 10 3 m2/Vs , m u * 1 0 ^ 3 )

Scilab code Exa 10.28 Electron mobility and electric field

1 / / Exa mpl e 1 0 . 2 8 , p ag e no286

2 clear3 clc

4 r h o = 0 . 1 //Ohmm5 n i = 1 0 ^ 2 0 // per m36 v d = 1 //m/s7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 m u = 1 / ( r h o * n i * e )

9 E = v d / m u

10 printf ( \nThe m o bi l it y o f t h e e l e c t r o n s i n m a te r ia li s %. 3 f m 2 /Vs \nThe e l e c t r i c f i e l d i s %.1 f V/m ,

mu , E )

Scilab code Exa 10.29 Electron mobility and conductivity


3 clc

4

5 a v g = 6 . 0 2 3 * 1 0 ^ 2 3

6 m = 9 . 1 * 1 0 ^ - 3 1 //k g7 e = 1 . 6 * 1 0 ^ - 1 9 //C8 d = 8 . 9 2 * 1 0 ^ 3 //kg/m39 r h o = 1 . 7 3 * 1 0 ^ - 8 //Ohmm

10 z = 6 3 . 5

70


72/111

11

12 n = a v g * d / z13 s i g = 1 / r h o

14 t a u = s i g * m / ( n * ( e ^ 2 ) )

15 m u = s i g / ( e * n )

16 printf ( \nThe r e l a x a t i o n t im e i s %. 2 f 1011 s \nThem o b i l i t y o f e l e c t r o n s i n c op pe r i s % . 2 f m2/Vs \

nThe c o n d u c t i v i t y o f c op pp er i s %. 2 f 1 0 7 p e rOhmm\n , t a u * 1 0 ^ 1 1 , m u , s i g * 1 0 ^ - 7 )

Scilab code Exa 10.30 Drift Velocity


3 clc

4 r h o = 1 . 5 4 * 1 0 ^ - 8 //ohmm5 E = 1 0 0 //V/m6 n i = 5 . 8 * 1 0 ^ 2 8 //m37 e = 1 . 6 * 1 0 ^ - 1 9 //C8 m u = 1 / ( r h o * n i * e )

9 v d = m u * E10 printf ( The m o b i l i t y o f e l e c t r o n s i n s i l v e r i s %. 4 f

10 3 m2/Vs \nThe d r i f t v e l o c i t y i d %. 5 f m/ s ,mu *10^3 , vd )

Scilab code Exa 10.31 Relaxation time

1 / / Exa mpl e 1 0 . 3 1 , p ag e no288

2 clear3 clc

4 r h o = 1 . 4 3 * 1 0 ^ - 8 //Ohmm5 n i = 6 . 5 * 1 0 ^ 2 8 // per m36 e = 1 . 6 * 1 0 ^ - 1 9 //C

71


73/111

7 m = 9 . 1 * 1 0 ^ - 3 1 //Kg

8 t a u = m / ( r h o * n i * e ^ 2 )9 printf ( The r e l a x a t i o n t i m e f o r e l e c t r o n s i n t hem et al i s %. 2 f 101 4 s , t a u * 1 0 ^ 1 4 )

Scilab code Exa 10.32 Electron mobility in Al


3 clc4

5 R = 6 0

6 r h o = 2 . 7 * 1 0 ^ - 8 //Ohmm7 i = 1 5 //A.8 l =5 //m9 m =3

10 e = 1 . 6 * 1 0 ^ - 1 9 //C11 d = 2 . 7 * 1 0 ^ 3 //kg/m312 a w t = 2 6 . 9 8

13 a v g = 6 . 0 2 3 * 1 0 ^ 2 3

14 n = m * a v g * 1 0 0 0 * d / a w t15 printf ( F re e e l e c t r o n c o n c e n t r a t i o n i s % . 3 f 1 0 2 9

, n * 1 0 ^ - 2 9 )

16 m u = 1 / ( r h o * n * e )

17 printf ( \nThe m o b il i t y o f e l e c t r o n i n al umi ni um i s %. 4 f10 3 m2/vs , m u * 1 0 ^ 3 )

18 v d = m u * i * R * 1 0 ^ - 3 / l

19 printf ( \nThe d r i f t v e l o c i t y o f t h e e l e c t r o n i n A li s %. 1 f 10 4 m/ s , v d * 1 0 ^ 4 )

Scilab code Exa 10.33 drift and thermal velocity

1 / / Exa mpl e 1 0 . 3 3 , p ag e no290

72


74/111

2 clear

3 clc4 R = 0 . 0 2 //Ohmm5 i = 1 5 //A6 m u = 4 . 3 * 1 0 ^ - 3 //m2/Vs7 l =2 //m8 k = 1 . 3 8 * 1 0 ^ - 2 3

9 m = 9 . 1 * 1 0 ^ - 3 1 //k g10 T = 3 0 0 //K11 v = i * R

12 E = v / l

13 v d = E * m u

14 v t h = sqrt ( 3 * k * T / m )15 printf ( \nThe t h er ma l v e l o c i t y o f t h e f r e e e l e c t r o n s

i n c o p p er i s %. 3 f mm/ s \nThe d r i f t v e l o c i t y o f e l e c t r o n s i n c op pe r i s %. 3 f mm/ s , v t h * 1 0 ^ - 5 , v d*10^3)

73


75/111

Chapter 11

Mechanical Properties

Scilab code Exa 11.1 Stress produced in an Al


3 clc

4

5 l d = 2 0 0 0 //k g6 g = 9 . 8 //m/s2

7 r = 0 . 0 0 58 f o r c e = l d * g

9 s t r es s = f o rc e / ( % p i * r ^ 2)

10 printf ( The s t r e s s p ro du ce i n an al umi ni um a l l o y i s%. 1 f MPa, s t r e s s * 1 0 ^ - 6 )

Scilab code Exa 11.2 perentage elongation and reduction


3 clc

4 l f = 5 3 . 7 5 * 1 0 ^ - 3

74


76/111

5 l 0 = 5 0 * 1 0 ^ - 3

6 d f = 9 . 4 * 1 0 ^ - 37 d 0 = 8 . 8 * 1 0 ^ - 3

8 p l = ( l f - l 0 ) * 1 0 0 / l 0

9 p a = ( ( % p i * d f ^ 2 ) - ( % p i * d 0 ^ 2 ) ) * 1 0 0 / ( % p i * d f ^ 2 )

10 printf ( \nThe %% e l o n g a t i o n i s %. 1 f%% a nd \ nth e %%r e d u c ti o n i n a r ea i s %. 3 f%% , p l , p a )

Scilab code Exa 11.3 Brinell Hardness Number


3 clc

4 t s = 9 3 7 //MPa5 b h n = t s / 3 . 4 5

6 printf ( The B r i n e l l H a rd n es s Number i s %. 2 f , b h n )

Scilab code Exa 11.4 Tensile strength and fatigue limit of Steel plate


3 clc

4 p = 3 0 0 0

5 D = 1 0

6 d = 2 . 2

7 H b = 2 * p / ( % p i * D * ( D - sqrt ( D ^ 2 - d ^ 2 ) ) )

8 printf ( \n B r i n e l l H ar dn es s Number o f s t e e l P la te , Hb=%. 1 f\n , H b )

9 t s = 3 . 4 5 * H b10 f l = 0 . 5 * t s

11 printf ( \nThe T e ns i l e s t re n gt h o f s t e e l p l a t e i s %. 3f MPa\n , t s )

75


77/111

12 printf ( \nThe F at ig ue l i m i t o f s t e e l p l a t e i s %. 4 f

MPa , f l )

76


78/111

Chapter 12

Thermal Properties

Scilab code Exa 12.1 Change in length due to heating


3 clc

4

5 a l f e = 8 . 8 * 1 0 ^ - 6 / / p e r k6 l o = 0 . 1 //m

7 d e l T = 9 7 3 //K8 d e l L = a l f e * l o * d e l T

9 printf ( The c ha ng e i n l e n g t h p ro du ce d b y h e a ti n g i s%. 3 f mm , d e l L * 1 0 ^ 3 )

Scilab code Exa 12.2 Change in length due to heating


3 clc

4

5 a l f e = 5 . 3 * 1 0 ^ - 6 / / p e r k

77


79/111

6 l o = 0 . 1 //m

7 d e l T = 9 7 3 //K8 d e l L = a l f e * l o * d e l T9 printf ( The c ha ng e i n l e n g t h p ro du ce d b y h e a ti n g i s

%. 3 f mm , d e l L * 1 0 ^ 3 )

Scilab code Exa 12.3 Steady state heat Transfer

1 / / Exa mpl e 1 2 . 3 , p ag e no351

2 clear3 clc

4 k = 3 7 1 //J/msk5 d e l T = 5 0 // i n d e g r e e s6 d e l x = 1 0 * 1 0 ^ - 3

7 h t = k * d e l T / d e l x

8 printf ( The s t e ad y s t a t e h ea t t r a n s f e r o f 10 mmc op pe r s h e et i s %. 3 f 106 J .m2 . s 1 , h t * 1 0 ^ - 6 )

Scilab code Exa 12.4 Compression Stress due to Heating


3 clc

4 a l f e = 8 . 8 * 1 0 ^ - 6 / / p e r K5 t 1 = 1 3 0 0 //K6 t 2 = 3 2 7 //K7 d e l T = t 1 - t 2

8 E = 3 7 0 //GPa9 e p = a l f e * d e l T

10 s i g = e p * E

11 printf ( \nThe u n c o n s t r a i n e d t h er m al e x p an s i o np ro du ce d by t he h e a ti n g i s %. 4 f 10 3 , e p * 1 0 ^ 3 )

78


80/111

12 printf ( \ n th e c o mp r es s io n s t r e s s p ro du ce d by h e a t in g

i s % . 3 f GPa , s i g )

Scilab code Exa 12.5 Heat flux transmitted


3 clc

4

5 K = 1 2 0 //W/m.K6 t 2 = 4 2 3

7 t 1 = 3 2 3

8 d e l T = t 2 - t 1

9 d e l x = 7 . 5 * 1 0 ^ - 3 //m10 A = 0 . 5 //m211 Q = K * A * ( d e l T / d e l x )

12 h p h = Q * 3 6 0 0

13 printf ( The h e a t f l u x t r a n s mi t t e d t hr ou gh a s h e e tp er h ou r i s %. 2 f 109 J . h1 , h p h * 1 0 ^ - 9 )

Scilab code Exa 12.6 Youngs Modulus


3 clc

4

5 a l f e = 1 7 * 1 0 ^ - 6 / / / p e r K6 t 2 = 2 9 3 //K7 t 1 = 2 3 3 //K8 d e l T = t 2 - t 1

9 s t = 1 1 9 //MPa10 k = a l f e * d e l T

79


81/111

11 printf ( \nThe s t r a i n p ro duc ed i n t e r o d i s %. 2 f

103 , k * 1 0 ^ 3 )12 E = ( s t * 1 0 ^ 6 ) / k13 printf ( \nThe You ng s Mo du lu s o f t h e r o d i s %. 1 f GPa

, E * 1 0 ^ - 9 )

Scilab code Exa 12.7 temperature Change

1 / / Exa mpl e 1 2 . 7 , p ag e no353

2 clear3 clc

4

5 l o = 1 1 . 6 //m6 d e l x = 5 . 4 * 1 0 ^ - 3 //m7 a l f L = 1 2 * 1 0 ^ - 6 / / p e r K8 d e l T = d e l x / ( l o * a l f L )

9 printf ( The maximum t e m p e r a t u r e c a n g e c a n w i t h s t a n dw it ho ut any t he rm al s t r e s s i s %. 2 f K , d e l T )

Scilab code Exa 12.8 compressive Sress


3 clc

4

5 l o = 0 . 3 5 //m6 a l f e = 2 3 . 6 * 1 0 ^ - 6 / / / p e r K7 t 2 = 3 5 8 //K8 t 1 = 2 8 8 //K9 d e l T = t 2 - t 1

10 y m = 6 9 //GPa11 k = a l f e * d e l T

80


82/111

12 printf ( \nThe s t r a i n p ro duc ed i n t e r o d i s %. 3 f

103 , k * 1 0 ^ 3 )13 E = y m * k * 1 0 ^ 914 printf ( \nThe c o m pr e ss i v e s t r e s s p ro du ce d i n Al r od

i s % . 3 f GPa , E * 1 0 ^ - 9 )

Scilab code Exa 12.9 limit to compression stress

1 / / Exa mpl e 1 2 . 9 , p ag e no355

2 clear3 clc

4 a l f e = 2 0 * 1 0 ^ - 6 / / p e r K5 t 1 = 2 9 3 //K6 s i g = 1 7 2 ///MPa7 E = 1 0 0 //GPa8 d e l T = ( s i g * 1 0 ^ 6 ) / ( E * a l f e * 1 0 ^ 9 )

9 printf ( \nTfTi=%. 0 f , d e l T )10 printf ( \n\ n t h e maximum t e m p e r a t u r e a t w hi c h t h e r o d

may b e h e a t ed w i t h o ut \ n e xc e ed i ng a c o m p re s s s i ves t r e s s o f %. 0 f MPa i s %. 0 f K , s i g , d e l T + t 1 )

Scilab code Exa 12.10 Heat energy Requirement


3 clc

4 h _ i r = 4 4 4 // J . kg 1.K15 h _ g r = 7 1 1 // J . kg 1.K1

6 h _ p l = 1 8 8 0 // J . kg1.K17 t 2 = 3 7 3 //K8 t 1 = 3 0 0 //K9 d e l T = t 2 - t 1

10 W =2 //Kg

81


83/111

11

12 / / ( a ) For I r o n13 q = W * h _ i r * d e l T14

15 / / ( b ) f o r G r ap h it e16 q 1 = W * h _ g r * d e l T

17

18 // ( b ) f o r p o l y pr o p yl e n e19 q 2 = W * h _ p l * d e l T

20

21 printf ( The h ea t e ne rg y r e q u i r e d t o r a i s et em p er a tu r e %. 0 f K f ro m i t s t em p er at u re o f \ n i r o n

, g r a p h i t e

material science_v. rajendran

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