2.1. Field-induced mechanical test

The in situ mechanical loading of nanosized crystals in the FIM experiments was realised using the Maxwell mechanical stress induced by high electric fields. As was shown in these studies, the vast majority of dislocations was removed under the action of the electric field–induced mechanical stresses. So, most of the dislocation-free nanosized crystals were fractured at mechanical stresses corresponded to substantial parts of the ideal strength of solids. This technique was used for uniaxial tensile tests of tungsten and molybdenum nanoneedles and for uniform triaxial (hydrostatic) tensile tests of a tungsten nanocrystal.

methods for characterising the properties of these nanoobjects, as well as computer methods for predicting their behaviour under various external influences. Nanosized metallic crystals occupy a special place among these objects. Due to their remarkable physical and mechanical properties, they can be directly used in various nanodevices; in addition, they are considered as building blocks for the creation of nanocrystalline materials. On the other hand, study of nanosized crystals enables to ascertain the fundamental mechanisms of deformation and fracture inherent in the nanoscale. Fabrication of defect-free nanocrystals and their compression test [1–3], as well as the development of a high-field technique for the preparation and in-situ tensile testing of nanoneedles [4–6], becomes a milestone event in experimental studies of nanosized crystals. Absence of defects (dislocations and twins) in these crystals made it possible to reach extremely high levels of strength, which are close to the value of "theoretical strength". Therefore, molecular dynamics (MD) simulation is the most effective tool for studying atomic mechanisms to

Nanosized crystals of bcc metals are a classical object of MD simulation [7–13]. Currently, considerable attention is paid to metals with a bcc lattice [14–20]. From a physical point of view, bcc metals are more interesting because they provide a greater variety of atomic rearrangements, governing the strength. However, the main difficulty in MD simulation of bcc metal is lack of sufficiently reliable potentials, which limits the accuracy of such simulation. In this connection, the appearance of direct experimental data on the strength of bcc nanocrystals substantially facilitated the problem of selection and verification of these potentials. A great number of works on MD-simulation enabled to predict the key effects controlling the level of strength of nanosized nanocrystals, namely: (i) the size effect, (ii) dependence of strength on orientation, (iii) the temperature dependence of strength, and (iv) dependence of strength on the stress state mode [7–24]. At the same time, the absence of a completed theory of strength of nanosized crystals is a characteristic feature of science of the strength of these objects. Lack of sufficient experimental data is the second feature of state-of-the-art in researches of strength of nanosized crystals. Difficulties in performing mechanical tests of nanospecimens are the reason for this. In this regard, the high-field mechanical tests of nanosized specimens should be indicated. It has made it possible in situ mechanical loading of nanosized specimens up to level close to theoretical strength combined with direct observation of the atomic structure of these objects under well-

In the present work, fundamentals of the atomic mechanisms governing strength of nanosized metallic crystals are described; besides, an attempt is made to explain on this basis the size and orientation effects, temperature dependence of strength, and atomism of fracture of bcc crys-

The in situ mechanical loading of nanosized crystals in the FIM experiments was realised using the Maxwell mechanical stress induced by high electric fields. As was shown in these studies,

reach extremely high levels of strength in crystals.

36 Molecular Dynamics

controlled crystallographic conditions [25, 26].

tals under triaxial uniform (hydrostatic) tension.

2.1. Field-induced mechanical test

2. Methods of physical and numerical experiments

The intrinsic hydrostatic tensile strength of tungsten was experimentally determined using a high-field testing in field-ion microscope (FIM) with needle-shaped specimens (Figure 1a) [6]. The specimens with an initial radius of curvature of about 100 nm and the taper angle of <sup>5</sup> � <sup>15</sup>� were etching in a NaOH solution of 99.98% pure tungsten wires with the <110> texture. The specimen surface was preliminary polished by low-temperature field evaporation [25]. Field ion images were acquired at the voltage of 4–22 kV. For mechanical loading, a high voltage pulse Vp with duration of 20 ns was applied. The local field at specimen surface was determined as

$$F = \frac{F\_0 \times \left(V\_0 + V\_p\right)}{V\_0} \tag{1}$$

where V<sup>0</sup> is the applied voltage corresponding to the threshold field for evaporation F<sup>0</sup> [25, 27]. The evaporation field of tungsten F<sup>0</sup> on the [110] facets at 77 K is 57 V nm�<sup>1</sup> related to an evaporation rate of ~10�<sup>2</sup> atomic layers per second. The electric field decreases severely under

Figure 1. An electron microscopic image of Mo nanotip formed by field evaporation (a) and the sketch of a high-field tension test (b).

the hemispherical cap in the conical part. So, the failure of needle-shaped specimens was usually initiated at the nanosized cap in the region of the ultimate field strength. An electric field applied to a metal specimen induces the Maxwell surface stress

$$
\sigma\_s = \frac{\varepsilon\_0 F^2}{2} \tag{2}
$$

where ε<sup>0</sup> is the electric constant. This stress acts normal to the surface element at all points. The stress state of a needle-shaped specimen is possible to estimate to any plane in the specimen apex section by integration of the stress components at each point on the surface. The Maxwell stress acting over the metal surface produces the force in the axis direction is given by:

$$f\_z = \frac{1}{2} \iint \varepsilon\_0 F^2 \cos \beta dS,\tag{3}$$

According to EAM or FS formalism, the total energy of a system is given by the expression:

Figure 2. The schemes of the nanoneedle tip and loading (r is the protrusion radius) before failure (a) and FIM

) c1, (eV A�<sup>3</sup>

1.885948 4.41 3.25 48.527 96 �33.79621 5.854334 �0.0098221 0.033338

) c1, (eV A�<sup>3</sup>

1.848648 4.1472 3.2572 47.98066 �34.09924 5.832293 0.017494 0.020393

V rð Þ¼ ð Þ <sup>r</sup> � <sup>c</sup> <sup>2</sup> <sup>c</sup><sup>0</sup> <sup>þ</sup> <sup>c</sup>1<sup>r</sup> <sup>þ</sup> <sup>c</sup>2r<sup>2</sup> <sup>þ</sup> <sup>c</sup>3r<sup>3</sup> <sup>þ</sup> <sup>c</sup>4r<sup>4</sup> � �, r <sup>≤</sup> <sup>c</sup>

<sup>φ</sup>ð Þ¼ <sup>r</sup> ð Þ <sup>r</sup> � <sup>d</sup> <sup>2</sup>

(

V rij � � <sup>þ</sup><sup>X</sup>

0, r > c

i6¼j A2 φ rij � �

, r ≤ d 0, r > d

i f r<sup>i</sup>

) c2, (eV A�<sup>4</sup>

Atomic Mechanisms Governing Strength of Metallic Nanosized Crystals

http://dx.doi.org/10.5772/intechopen.75159

) c2, (eV A�<sup>4</sup>

� � (4)

) c3, (eV A�<sup>5</sup>

) c3, (eV A�<sup>5</sup>

) c4, (eV A�<sup>6</sup>

) c4, (eV A�<sup>6</sup>

)

39

)

Utot <sup>¼</sup> <sup>1</sup> 2 X ij

microfractograms of tungsten nanotip acquired at 5.60 kV immediately after failure (b).

) d, A c, (A) c0, (eV A�<sup>2</sup>

) d, A c, (A) c0, (eV A�<sup>2</sup>

Table 1. Potential parameters for W.

Table 2. Potential parameters for Mo.

where the first term is the conventional central pair-potential summation:

f r<sup>i</sup> � � <sup>¼</sup> ffiffiffiffi ri <sup>p</sup> <sup>r</sup><sup>i</sup> <sup>¼</sup> <sup>X</sup>

(

and the second term is the n-body term:

A, (eV A�<sup>1</sup>

A, (eV A�<sup>1</sup>

where dS is an element of surface area, β is the angle between the axis and the normal to that surface facet. The integral is taken over the whole specimen surface. The local Maxwell stress is calculated by integration of the field-induced stress and dividing by the area of the section concerned. The near surface Maxwell stress under the hemispherical envelope of the specimen is virtually hydrostatic and equals to the local surface stress determined by Eq. (3). The stress state in the conical shank region is corresponded to the tensile test with uniaxial tension. It enables both to deform nanocrystal plastically and to break it under uniaxial tension (Figure 1b).

For nanocrystal failure under multiaxial uniform (hydrostatic) tension, a protrusion was formed on the spherical part of specimen. It was created by selection of special schedules for the high-field evaporation of atoms from the nanospecimen surface [19]. This is shown schematically in Figure 2a. Electric field strength and, accordingly, mechanical stresses increase with decrease in the curvature radius of a surface. So, maximal stresses act in this protrusion. This makes it possible to fracture the metal exactly in this volume. It is done by a steep increase in the electric field strength. Appearance of the crater on a nanoneedle surface is the direct evidence that fracture occurs in the local region, where hydrostatic tension acts (Figure 2b).

The Maxwell stress was determined with accuracy of �4%. The systematic error due to uncertainties in the field calibration is �3% (see [28, 29]), and, correspondingly, the systematic error in determination of the Maxwell stress is �6%. The total error in determination of the Maxwell stress is �10%.
