1. Materials Engineering
Lecture 4:
Solid metal structure.
Impurities and Defects.
Diffusion.
Homogeneous and heterogeneous Systems. Phases.

2. Ideal and Real Solids
Only ideal solids have ideal far order. In real solids, deviations from the far order are observed. Such deviations are referred to as defects.

3. Point defects Point defects are: Vacancies (היעדרויות)
Interstitials (חדירויות)
Self-interstitials (חדירויות עצמיות)
Interstitial impurities (חדירויות ע''י אטום זר)
Substitutions (החלפות)
Complex defects:
Frenkel defect: vacancy + self-intersitial
Point defects on a graphene layer. (Image from Suenaga and Koshino, Nature 468, (2010))
Green: substitutions,
Blue: vacancies
Red: interstitials

4. Linear Defects (dislocations)
Screw dislocation
(נקע בורג)
Edge dislocation
(נקע קצה)
AFM image of an edge dislocation (from

5. Planar defects Twins (תאומים) Stacking faults (מִשגֵי הערמה)
TEM image of planar defects on Si (111) surface

6. Grain boundaries

7. A small exercise

8. Diffusion Vacancy diffusion Impurity atom diffusion
Diffusion is the spread of particles through random motion from regions of higher concentration to regions of lower concentration.
A defect can be described as a quasi-particle. Therefore diffusion of defects complies the same pattern as diffusion of particles.
Vacancy diffusion
Impurity atom diffusion

9. Fick’s Laws Second Fick’s law: First Fick’s law:
Non-stationary (dependent on time) diffusion.
First Fick’s law:
Stationary (i.e. independent on time) diffusion.
J – diffusion flux,
C – concentration,
x – coordinate,
D – diffusion coefficient [cm2 / sec]
►The higher D the faster is the diffusion

10. Temperature dependence of diffusion
Arrhenius dependence:
D0 – preexponential coefficient (specific for each species), (m2 /sec)
Ea – activation energy (specific for each species), (J)
R – gas constant, (R=8.31 J/K)
T – absolute temperature (K, T(K) = T(ºC) + 273)
►The higher the temperature the faster is the diffusion

11. Some experimental data
m2 / sec T ºC Ea
kJ / mol D0
Host metal
Diffusing species
3.0∙ ∙10-15
251
2.8∙10-4
a-Fe (BCC) Fe
1.1∙ ∙10-16
284
5.0∙10-5
g-Fe (FCC)
2.4∙ ∙10-10 80
6.2∙10-7 C
5.9∙ ∙10-11
148
2.3∙10-5
4.2∙10-19
500
211
7.8∙10-5 Cu
4.0∙10-18
189
2.4∙10-5 Zn
4.2∙10-14
144
2.3∙10-4 Al
4.1∙10-14
136
6.5∙10-5
1.9∙10-13
131
1.2∙10-4 Mg
1.3∙10-22
256
2.7∙10-5 Ni

12. Atom and mass percent
What is the composition in atom per cents, of an alloy that consists of 92.5 wt % Ag and 7.5 wt % of Cu?
Solution:
100 gr alloy: 92.5 gr Ag gr Cu
Atom weight Ag = 107, Cu = 64
Atom ratio: Ag = 92.5 / 107 = 0.86, Cu = 7.5 / 64 = Together: 0.87
At. % (Ag) = 0.86/0.87 =0.99 = 99%

13. Homogeneous and Heterogeneous Systems. Phase
A system is a part of the Universe, voluntary chosen for the observation. The rest of the Universe is referred to as the environment
System 1: pure water or water with sugar
System 2: water + oil
System 3: water + oil after some shaking
A homogeneous system has no internal boundaries.
A heterogeneous system has internal boundaries.
Each homogeneous part of a heterogeneous system is referred to as a phase.
Another definition: Phase is a distinctive part of a system
A phase can be continuous or dispersed

14. Examples of homo- and heterogeneous systems.
Gases: always homogeneous
Liquid:
Water-alcohol – homogeneous: solutions
Water-Oil – heterogeneous
Solid:
Bronze (Cu + Zn) solid solution: homogeneous
Steel, Cast (Fe + C): heterogeneous

15. Musts of this lecture Homogeneous and heterogeneous systems; Phase;
Impurities: substitution and interstitial impurities;
Defects: point, linear and grain defects;
Diffusion: impurity and vacancy diffusion;
Stationary and non-stationary diffusion;
Temperature dependence of diffusion.
Calculation of atom and mass compositions.