Nonlinear lattice kink pulses: existence and action on defects in - - PowerPoint PPT Presentation

Nonlinear lattice kink pulses: existence and action

• n defects in crystals.

With application to radiation damage and the ‘long range effect’. Cross-discipline research using results from:

• 1. charged particle tracks in crystals of muscovite mica .......
• 2. numerical modelling in 2-D an 3-D (molecular dynamics)..

and conditions imposed by de Broglie matter waves......

• F. Mike Russell

Heriot-Watt University, Edinburgh, EH14 4AS, UK

and Rutherford Appleton Laboratory, Chilton, UK (Retired)

Alex P. Chetverikov.

Saratov State University, Astrakhanskaya 83, Saratov-410012, Russia

The topics

• The study of swift particle interactions in solids is difficult

because:

• They are hidden inside a solid, involve movement of atoms and

there are few electrical effects so are hard to observe.

• Some remaining problems – all involve non-linear effects.
• No clear evidence for energetic subsonic breathers in MD

studies of metals

• So what is cause of so-called ‘Long Range Effect’ in metals and

semiconductors over distances >1.5mm?

• Unexplained fossil tracks of particles in crystal of muscovite

• Most experiments study gross effects resulting from irradiation

but fossil tracks in crystals show what actually happens at the atomic level.

• Numerical modelling useful and MD is very powerful.
• Main results
• Kink solitons but not mobile breathers are seen in MD studies
• f metals – but kinks have short range << 1 micron.
• So kinks must gain energy from stored energy in the lattice to

explain observed results from experiments.

• If true then explains 45 year old problem in recorded tracks in

mica and also Long Range Effects.

• Application of results to radiation damage in metals.
• How to test kink pulse predictions.

Breathers and kinks

Breathers and kinks.

Impulse

Plots show creation of mobile lattice excitations in a chain of interacting particles by a kinetic impulse. a) Chain with on-site potentials. Breather has internal oscillations and leaves no residual displacement of particles behind. Self-focussing and very stable. (This is a quodon.)

Impulse

b) Chain with no on-site potentials. Kink is laterally unstable and decays

• quickly. Leaves a trail of displaced

particles that slowly decays. What does MD tell us?

Evidence for kink pulses gaining energy from a lattice.

1. Charged particle tracks in muscovite crystals.

Relativistic muons lose energy by just two main processes: electronic and nuclear scattering [transfer of kinetic energy]. Electronic processes lead to recording a continuous track by precipitation of impurity. Nuclear scattering occurs infrequently but should create atomic cascades. Where is the evidence for these cascades? The tracks of muons show only fan-shaped appendages that are consistent with a cascade origin – except that they are far too long. These fans are inconsistent with a breather origin.

• 2. Molecular dynamic studies of atomic cascades.

Simulated cascades arising from collisions of swift atoms in a gold crystal show clear evidence for lattice excitations moving at supersonic speed. Measurements on these excitations show that they are kink-pulses. They are not breathers.

• 3. These results can be unified if kink pulses gain energy from the lattice.

MD results.

MD cascade results. (Kai Nordlund) Thin slice essential: kink pulses hidden in full 3D data.

A single frame from a video of an atomic cascade in a gold crystal. Initial impact site The frame shows a slice just two atoms thick taken from the full 3D

• cascade. The slice included the

impact site. Multiple kink-pulses in line abreast

The many short sections of self- assembled ‘multiple kink pulses’ form a continuous expanding envelope. This kink pulse envelope moves

• utwards at super-sonic speed.

Speed of the kink pulses.

Speed of kink pulse in different chain directions.

Digital data retains information despite manipulation of images. Plots of the distance moved by kink pulses in given time. The distance is in units of atomic spacing ~0.27nm. Speed is ~ 2 X speed of sound. The expansion of the cascade envelope is also shown. It is very fast initially but then slowly collapses and fades away. Next, the shape of the kink pulse.

Instantaneous positions of atoms in chain near a kink pulse front from MD data.

Plot shows displacements of atoms (R) from their equilibrium positions relative to the atomic spacing. (Average of several kinks

in same multiple kink pulse.)

The kink involves just one atom carrying most of the energy and momentum, followed by a trail of displaced atoms. The variation of R immediately behind the kink is important.

There is no simple mathematical expression for this wave form.

Review of MD results.

Review of evidence from MD cascade in gold crystal.

• Extracting a thin slice from the MD data revealed non-linear atomic

motions usually hidden in 3-D plots. Good technique – similar to mica..

• Showed behaviour of kink pulses in 2-D sheets.

Justifies study of kink pulses in 2-D arrays.

• Showed the creation of many kink pulses from a single collision.

Justifies search for kink pulses in interactions of swift particles in crystals

• Showed evidence of self-assembly of pulses.
• Kink pulses move at supersonic speed along chains.
• No clear evidence for breathers.

Next, a study of kinks in 2-D arrays.

Kink pulses in 2-D triangular lattice. Morse interactions.

Similar to potassium sheet in muscovite crystal lattice. Moving pulse front Three particles are simultaneously given equal initial velocities that are in phase. They create three kink pulses that propagate at supersonic speed. The particles in the tail are displaced from their initial positions. Consistent with a kink soliton. Tail causes some sideways displacement of atoms in adjacent chains. Next, energy distribution in this kink pulse.

Energy density distribution in kink pulse in 2-D sheet.

This is for the previous three kink pulse. A single kink pulse on an isolated 1-D chain is not dispersed. A single kink pulse moving along a chain in a 2-D sheet loses energy by coupling to the adjacent chains.

Significant loss after going 100 atomic steps.

With multiple kink pulses in line abreast the kink pulses near the centre are ‘protected’ by the adjacent kink pulses. Energy moves sideways across the chains and is lost from the kink pulse at the sides. Rate of lateral spreading.

Lateral spreading angle 2θ of kink pulses.

The speed of a kink pulse depends on its energy. Plot shows how lateral spreading velocity varies with forward

• velocity. V1 is speed of sound.

Kinks in MD data lie in this region

Which gives a total spreading angle 2θ of about 4 degrees.

Next, multiple kink pulses in line abreast.

Propagation of multiple kink pulses in a 2-D sheet with 8 kink pulses abreast.

The speed of a kink pulse decreases as its energy decreases. Since energy is lost from the sides of the moving front the sides move more slowly than the centre. The front develops a curved shape. The MD results showed kink pulses. Now we look for them in recorded tracks in crystals of muscovite.

The crystal structure of muscovite. Show sample

Muscovite is optically transparent and a good insulator. It is very stable chemically. It can be cleaved in to thin sleets. The split occurs in the (001)-plane at the sheet of potassium atoms. The potassium atoms have a large spacing of 0.53nm. They form a triangular array. Impurity atoms are precipitated in the potassium region where the silicate layers move apart. What is seen in muscovite crystals.

Typical sheet of muscovite mica showing fossil tracks of quodons and a proton.

quodons proton

Scale bar: 1 cm.

Crystals of muscovite mica grow deep underground at high pressure and temperature. New crystals contain a mobile interstitial impurity of about 1% of iron. During cooling the impurity reaches super-saturation and precipitates at nucleation sites, forming ribbons of black magnetite. Such sites are created by large movements of atoms in quodons or breathers. Next, the unexplained tracks in mica.

Photo (negative) of sheet of muscovite showing tracks of muons and ‘fans’.

fans The electric charge on the muons causes energy loss by electronic

• processes. This triggers the

recording process to record the tracks of the muons. The only other process for energy loss is by nuclear scattering, which creates atomic cascades. This is the most probable cause for the fan-shaped appendages. There is no other know cause for the fans. Too big to be crystal defects. More examples of fans.

More examples of fans in muscovite crystals.

Note the scale bars. Some fans are 15cm long! These fans look like the expected shape of multiple kink pulses – but they are many orders of magnitude too long. Allowing for lateral spreading of multiple kink pulses the expected range in gold is ~120nm. In the 2-D case of mica the expected range is ~1 micron. Next we look at the properties of these fans and compare with those expected

• f multiple kink pulses .

Properties of fans: angular distribution in (001)-plane Φ and the total angular width of fans 2Θ.

.

Chain direction

The fans are clustered about chain directions but the centre line can deviate by Φ. The total lateral spreading angle 2Θ is never less than ~4 degrees, as predicted from the modelling in 2-D arrays. How to create fans.

Diagram showing how individual nuclear scattering events merge by lateral spreading to form a continuous multiple kink pulse provided they are created nearly simultaneously.

Relativistic particle such as muon. Nearly simultaneous nuclear scattering producing kink pulses. This is typical of channelling particles moving in potassium (001)-plane in muscovite. Alternative high energy way to create nearly simultaneous multiple kink pulses is in an atomic cascade. But the expected range is far too short to explain the fans observed.

Relationship between length of fans and the concentration

• f stored energy.

Natural crystals of muscovite accept variable amounts of iron impurity during their growth. (0% to 1.7%)

1 per unit cell

Below about one impurity atom per 200 unit cells of muscovite the recording process fails to operate.

The amount of iron available is found from the total amount precipitated, which is proportional to the area Ap. (The ribbons of magnetite have constant thickness.) So the concentration is Ap/V.

The plot shows the range of kink pulses is proportional to the impurity concentration

• r the amount of stored or latent energy.

Pushing defects.

Defect sweeping by multiple kink pulses: long range effect.

A single kink pulse is unlikely to move an interstitial because the lattice can locally adjust laterally. If multiple kink pulses are self-assembled to be in line abreast or into a plane then different behaviour is expected. This is because the lattice will be restricted in adjusting laterally. The intense compression in the kink pulse front will produce a potential hill or wall. It will be easier for a defect to be swept forward than to pass over the potential wave. This surfing of defects, especially of interstitials, should contribute to long range effects. Inner structure of fans

Inner structure of fans: striations.

Scale bar: 1cm.

Each line corresponds to a local energy maximum in the energy in the multiple kink pulse front. Lines can have widths of 0.8 micron or more, and spacing of 1 micron or more. All lines lie exactly in chain directions. The amount of decoration with magnetite varies along the tracks of the multiple kink pulses as the energy gained/lost varies. The lateral periodicity is probably due to a Benjamin-F​eir instability. Origin of cascade

Application to radiation damage and the Long Range Effect.

These results relate to: 1) Why breathers are not seen in MD studies of atomic cascades in metals. 2) The fan shaped patterns in crystals of muscovite associated with relativistic charged particles. 3) The type of nonlinear lattice excitation that can propagate >1.5mm in single crystals of Copper. 4) Annealing of radiation damage in metals. 5) The existence of Long Range Effects in absence of quodons/breathers. 6) The sweeping forward of crystal defects by multiple kink pulses. Possible sudden build-up of defects at grain boundaries.

Extension to silicon.