材料科学基础英文版课件_(12)
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= ~3.810-4
For most metals, the value near the melting point is in the range of 10-3 to 10-4
• Volume defects
Dislocations External surfaces Grain boundaries Twin boundaries Stacking faults Phase boundaries
Pores, cracks, inclusions, and second phases
where Hv is the increase in enthalpy per mole of vacancies introduced (the vacancy formation energy) The increase in entropy:
where Sv is the increase in thermal entropy per mole of vacancies introduced The increase in the free energy of the system due to the vacancy formation:
Formation – leading to an increase of internal energy – free energy increase (G = H - TS, H=U+PV, U - H - G ) Formation – leading to an increase of entropy (randomness) –free energy decrease At a given temperature, there must be a concentration of point defects at which the free energy of the system has a minimum value.
Point Defects – Point Defects in Metals (5)
Or
(G = H - T S)
is in units of the mole fraction and can also be represented by = Nv/N where Nv is the number of vacancies at
• Thermal equilibrium vacancies and interstitials
• Quenching-induced nonequilibrium vacancies and interstitials
• Irradiation-induced nonequilibrium vacancies and interrstitials
equilibrium for a certain amount of material and N is the total number of atomic sites
Point Defects – Point Defects in Metals (6)
~3 for most metals e.g. iron (Fe): Hv is ~1.4 eV per atom, the melting points is 1808K (1535oC), the equilibrium vacancy concentration is
Point Defects – Point Defects in Metals (1)
1. Vacancies and Interstitials (self-interstitials)
Frenkel pair: vacancy + interstitial
Schottky defect: moving an atom to the surface produces a vacancy
ChapterΒιβλιοθήκη Baidu5
Imperfections in Solids
Lecturer: Shenhua SONG
Outline
• Point defects
1. Point defects in metals 2. Point defects in ceramics
• Linear defects • Plane defects
G = H - T S
Point Defects – Point Defects in Metals (4)
The molar free energy of the crystal containing Xv mole of vacancies:
where GA is the molar free energy of the vacancy-free crystal The equilibrium concentration of vacancies can be calculated by the condition:
• Deformation-induced nonequilibrium vacancies
Point Defects – Point Defects in Metals (2)
Why there is a thermal equilibrium concentration for vacancies or interstitials (self-interstitials)
Point Defects – Point Defects in Metals (3)
Derivation of equilibrium vacancy concentration
The increase in enthalpy for introducing Xv mole of vacancies in one mole of material (Xv: the mole fraction of vacancies):
For most metals, the value near the melting point is in the range of 10-3 to 10-4
• Volume defects
Dislocations External surfaces Grain boundaries Twin boundaries Stacking faults Phase boundaries
Pores, cracks, inclusions, and second phases
where Hv is the increase in enthalpy per mole of vacancies introduced (the vacancy formation energy) The increase in entropy:
where Sv is the increase in thermal entropy per mole of vacancies introduced The increase in the free energy of the system due to the vacancy formation:
Formation – leading to an increase of internal energy – free energy increase (G = H - TS, H=U+PV, U - H - G ) Formation – leading to an increase of entropy (randomness) –free energy decrease At a given temperature, there must be a concentration of point defects at which the free energy of the system has a minimum value.
Point Defects – Point Defects in Metals (5)
Or
(G = H - T S)
is in units of the mole fraction and can also be represented by = Nv/N where Nv is the number of vacancies at
• Thermal equilibrium vacancies and interstitials
• Quenching-induced nonequilibrium vacancies and interstitials
• Irradiation-induced nonequilibrium vacancies and interrstitials
equilibrium for a certain amount of material and N is the total number of atomic sites
Point Defects – Point Defects in Metals (6)
~3 for most metals e.g. iron (Fe): Hv is ~1.4 eV per atom, the melting points is 1808K (1535oC), the equilibrium vacancy concentration is
Point Defects – Point Defects in Metals (1)
1. Vacancies and Interstitials (self-interstitials)
Frenkel pair: vacancy + interstitial
Schottky defect: moving an atom to the surface produces a vacancy
ChapterΒιβλιοθήκη Baidu5
Imperfections in Solids
Lecturer: Shenhua SONG
Outline
• Point defects
1. Point defects in metals 2. Point defects in ceramics
• Linear defects • Plane defects
G = H - T S
Point Defects – Point Defects in Metals (4)
The molar free energy of the crystal containing Xv mole of vacancies:
where GA is the molar free energy of the vacancy-free crystal The equilibrium concentration of vacancies can be calculated by the condition:
• Deformation-induced nonequilibrium vacancies
Point Defects – Point Defects in Metals (2)
Why there is a thermal equilibrium concentration for vacancies or interstitials (self-interstitials)
Point Defects – Point Defects in Metals (3)
Derivation of equilibrium vacancy concentration
The increase in enthalpy for introducing Xv mole of vacancies in one mole of material (Xv: the mole fraction of vacancies):