10. PROPERTIES OF DEFECTS IN NANOSTRUCTURED MATERIALS


Alexei E. Romanov
A.F. Ioffe Physico-Technical Institute, Russian Academy of Sciences
Polytechnicheskaya 26
St. Petersburg, 194021, Russia
fax: (812) 247 8924
e-mail: alexei.romanov@ioffe.rssi.ru

For the prediction of the mechanical properties of nanostructured materials (nanocrystals, nanocomposites, nanoscaled films), the behavior of the various defects (dislocations, disclinations, grain boundaries, etc.) plays an important role. To analyze the behavior of defects, it is often necessary to find their elastic fields and energies of these defects.

In nanostructured materials, the elastic properties of defects are strongly modified by the interaction with interfaces. The results of calculating elastic fields for conventional dislocations and disclinations, and Somigliana dislocations in small particles, nanograined materials, and nanoscaled heterophase films are reported here.

On the basis of these results, the stability of defects in nanostructured materials is discussed, and the existence of various critical scales connected with defect strain energy relaxation is predicted. Special attention is paid to the generation of pentagonal symmetry in small particles (which is explained in terms of disclinations) and to the relaxation of misfit strains in thin films (which is connected with the nucleation and motion of misfit dislocations). The other mechanism of strain energy relief in nanoscale film is associated with multiple twinning and is peculiar, for example, to domain formation in ferroelastic and ferroelectric epitaxial films. In this case, analysis of defect properties explains the development of domain patterns with film thickness.

The continuum description of defects in nanoscaled materials is demonstrated to be useful in estimates of stored energy and volume change in nanocrystals, in the analysis of the structural stability of nanomaterials, in the explanation of the yield stress anomalies in the region of nanoscales, etc.

Editor's note: The following outline and figures were used as viewgraphs during Professor Romanov's presentation.

Introduction: The Role of the Theory of Defects in Materials Science and Solid State Physics

History of the Development of the Theory of Defects in the Soviet Union and Russia (see Table 10.1)

Table 10.1
History of the Theory of Defects

Name

Years

Results

Frenkel

1930s

A model for one-dimensional dislocations

A model for point defect formation

Indenbom

1950s

1960s

Theory of dislocation-induced internal stresses

Various applications of the theory of defects

Orlov

1950s

 

1960s

Applications of defect theory to the problems of the physics of strength and plasticity;

Defect kinetics

Slezov

1960s

Theory of segregation and coalescence in the ensemble of point defects

Kosevich

1960s

Mechanics of defects in crystals

Predvoditelev

1970s

Computer modeling of defects

Krivoglaz

1970s

Theory of X-ray diffraction in crystals with defects

Lyubov

1970s

Diffusion and point defects

Orlov

1970s

Theory of radiation-induced defects

Vladimirov

1980s

Cooperative effects in defect ensembles, disclinations

Rybin

1980s

Grain boundaries, disclinations

Likhachev

1980s

Defects in amorphous structures

Ovid'ko

1980s

1990s

Defects in glasses, quasicrystals, liquid crystals

Quasiperiodic grain boundaries, nanocrystals

Romanov

1980s

1990s

Theory of disclinations in solids, defect kinetics

Defects in small particles, thin films and nanocrystals

Gryaznov

1980s

1990s

Pentagonal symmetry in small particles

Stability of defects in nanocrystals

Defects in Small Particles and Nanostructured Materials


Figure 10.1 indicates the various scale lengths of defects and material structures.


Fig. 10.1. Defects and scale levels.

The energy balance of defects within materials, and hence their ultimate stability, will vary according to the nature of the interfaces. Figure 10.2 gives a schematic representation of coherent, semicoherent and incoherent interfaces.


Fig. 10.2. Structure of interfaces (schematic): (a) coherent, (b) semicoherent, (c) incoherent. From G.Gutekunst, J. Mayer, and M. Ruhle, 1997, Philosophical Magazine A, Vol. 75, No. 5, 1329-1355.

Figure 10.3 gives the conditions for establishing the stability of a location and the critical size of a nanocrystallite, L.


Fig. 10.3. Dislocation stability in nanocrystallites.

Condition for Dislocation Stability:

Fimage le b sigmap

Parameters of the Problem:

sigmap                             — Peierls stress

eq   — Effective elastic modulus of matrix

Ve                           — Volume of dislocation stability in a nanocrystallite

caplambda                             — Critical size of a nanocrystallite

Estimation for the Critical Size:

caplambda cong Gb/ sigmap cong 10 - 102 nm

More Precise Results for up_L cong 1:

caplambda cong [v0 + v1(up_L - 1)]Gb/ sigma p

v 0 = 0; v1 cong 0.1sgn (up_L - 1) for sphere with coherent boundary

v0 cong 0.04; v1 cong -0.05 for the cylinder with slipping interface

Table 10.2 lists some of the critical parameters for various metallic materials.

Table 10.2
Dislocation Stability in Various Nanocrystallites
 

Cu

Al

Ni

µ -Fe

G (GPa)

33

28

95

85

b (nm)

0.256

0.286

0.249

0.248

s p (10-2 GPa)

1.67

6.56

8.7

45.5

L (nm), sphere

38

18

16

3

L (nm), cylinder

24

11

10

2

Figure 10.4 gives a hierarchy of stability scales for defects in nanocrystallites.


Fig. 10.4. Hierarchy of stability scales for defects in nanocrystallites.

Figure 10.5 is a high resolution micrograph of a decahedral small particle of Pd.


Fig. 10.5. Structure of small particles. High-resolution micrograph of a decahedral small particle of Pd. There is a splitting of the pentagonal axis (Renou & Penisson).

Possible Directions for Future Developments and Applications of the Theory of Defects for Nanostructured Materials

Analysis of defect interactions at the nanometer scale (computer and analytical modeling)

Investigations of the influence of defects on physical and mechanical properties of nanostructured materials

Predictions of structure-property relationships for nanostructured materials including the results of the modeling in the chain: processing — characterization — applications

The following are particular problems associated with nanostructured materials: