Fundamentals of Radiation Damage- Lecture 3

Question 1

What is Kinchin-Pease model used for?

Answer 1

To model the number of atoms displaced by a PKA. First used to describe interstitial-vacancy pair production in nuclear reactors.

Question 2

Symbol for energy of a PKA

Answer 2

T

Question 3

Assumptions for Kinchin-Pease model

Answer 3

The cascade is a sequence of two-body elastic hard-sphere collisions.
A minimum energy transfer Ed is required for displacement.
The maximum neutron energy available for transfer is the cut-off energy Ec set by loss to the electrons (electronic stopping).
The atoms are randomly distributed so channelling and other effects of crystal structure are ignored.

Question 4

Why is there an upper limit of neutron energy available for transfer Ec?

Answer 4

Energy greater than Ed is lost to electronic stopping and is required to allow the lattice to relax after the atom has been displaced.

Question 5

What is channelling?

Answer 5

In a 3D crystal structure there may be channels through which no atoms are present. An energetic particle may travel into a parallel to these channels and therefore travel much further than predicted.

Question 6

The average number of atoms displaced by a PKA depending on its energy T

Answer 6

0 for T less than Ed.
1 for between Ed and 2Ed.
T/2Ed for between 2Ed and Ec.
Ec/2Ed for T over Ec

Question 7

Displacements vs PKA energy (T) graph

Answer 7

Constant at 0 up to Ed. Vertical up then constant at 1 up to 2Ed. Linear increase until Ec. Constant for above Ec

Question 8

Difference for NRT model

Answer 8

Modified Kinchin-Pease model to include damage efficiency and take into account possibility of ballistic processes recombining the defect as it was produced.
0 displacements up to Ed still.
1 between Ed and 2Ed/0.8
0.8T/2Ed for between 2Ed/0.8 up to infinity.
0.8 is damage efficiency (0.8 for most metals)

Question 9

What are ion-atom or atom-atom collisions governed by?

Answer 9

Interactions between the electron clouds, the electron cloud and the nucleus, and between the nuclei

Question 10

Coulomb equation and what it describes

Answer 10

V(r)=(ε^2)/r
Where ε is a single unit charge, r is separation distance.
Describes the potential energy between two point charges of the same sign

Question 11

Problem with using Coulomb equation for atoms

Answer 11

Atoms have a charged nucleus surrounded by an electron cloud of opposite charge

Question 12

Hard sphere approximation for potential energy

Answer 12

V(r) is 0 for r greater than interatomic radius and is infinity for r less than interatomic radius. This is not a realistic description because electron shells from different atoms can overlap

Question 13

Interatomic potential vs distance graph

Answer 13

V vs r (ion-atom separation). From right to left line just under 0 then curves lower reaching a min at re (spacing between nearest neighbours in the crystal). Then curves up very quickly to almost vertical (crosses x axis). The Coulomb force dominates at large r and central repulsive force dominates at small r. This is simplistic as ion energy matters too (faster can get closer to centre of atom)

Question 14

What is the Bohr radius?

Answer 14

The average distance between the nucleus and electron in a hydrogen atom in its ground state.
Symbol a sub0 and equal to 0.053nm

Question 15

What happens when r is much less than re?

Answer 15

Overlap of valence shells and weak attractive forces (van der Waals) develop

Question 16

What happens when r is between a0 and re?

Answer 16

Closed inner shells begin to overlap. Electrons change levels due to PEP and there is closed shell repulsion.

Question 17

What happens when r is much less than a0?

Answer 17

Coulomb repulsion dominates
R(r)=Z1Z2ε^2/r

Question 18

What happens when r is less than a0?

Answer 18

The nuclear charges are electrostatically screened by the innermost electron shells that have entered internuclear space. The screened Coulomb potential

Question 19

3 important classes of ions in ion-atoms collisions

Answer 19

1. Light energetic ions: E>1MeV, e.g α particle.
2. Highly energetic heavy ions: E about 10^2 MeV, e.g fission fragments (M about 10^2).
3. Lower energy heavy ions: E less than 1MeV, e.g recoils that result from earlier high-energy collision or α-daughter recoil nuclei.

Question 20

Graph of ρ/a vs T for the 3 important classes of ions

Answer 20

ρ/a is ratio of distance of closest approach to the screening radius. All 3 are relatively shallow concave curves down. Low energy heavy (3.) is highest. High energy heavy (2.) starts at ρ/a=1 and is next highest. Light energetic ions (1.) lowest (negative powers of 10) so distance of closest approach is least (closest)

Question 21

What are potentials also used to calculate?

Answer 21

Nuclear and electronic stopping powers.
Range of ions/atoms.

Question 22

What affects damage rates (dpa over distance into solid)?

Answer 22

For same energy ions if heavier mass deposited their energy over a shorter distance resulting in higher damage.

Question 23

Explain the level of damage caused by neutrons

Answer 23

Due to the large collisions means free path of a neutron compared to an ion, the neutron damage energy is low and constant over distances of millimetres

Question 24

How do swelling, hardening and conductivity vary with increasing dpa?

Answer 24

Swelling exponential to then linear increase.
Hardening concave curve increase.
Conductivity exponential decrease.

Question 25

Regions on dose (dpa) vs T/Tm graph

Answer 25

T is temperature this time. Up to T/Tm=0.4 there is radiation hardening and embrittlement regardless of dose. For dpa over 10 and T/Tm up to 0.45 is irradiation creep. Over 10 dpa and between 0.3 and 0.6 T/Tm is phase instability and void swelling. Over 10 dpa and 0.5 to 1 T/Tm is He embrittlement.