4. Conclusions

realised at a global (on average) uniform triaxial tension of the entire specimen. Probability of the fluctuation of local stresses in three directions simultaneously is much lower than the probability of fluctuation along one of the directions <100>; so, initiation of instability of nanosized tungsten crystal occurs at local stresses ξcm ≈ 40 GPa. This means that in local regions, the instability

Thus, the strength of nanosized crystals under hydrostatic tension will always be below the strength of an ideal crystal under the same conditions. In this case, the strength of tungsten nanosized crystals under hydrostatic tension is 28 GPa. This is approximately 1.90 times less than the strength of an ideal tungsten crystal. The reason for this is fluctuations of local tensile stresses, which leads to: (i) exceeding of the value of local stresses over global (fluctuations themselves) and (ii) to deviation from triaxial uniform tension within the local region where this transition realises. For nanosized Mo specimens, the first factor results in a decrease in strength

Nowadays, nanoneedles and nanopillars are the most common nanosized specimens, which strength can be determined experimentally. Two main kinds of nanopillars exist, namely: (i) nanopillars obtained by focused ion beam (FIB) technology [43, 44], and (ii) nanopillars obtained by etching of nanocomposites [3]. Surface layer of specimens obtained by FIB technique contains a great number of defects in sub-surface layer, and so their strength does not exceed 1.0–1.5 GPa [43]. The second kind of specimens has no such shortcomings, and so, their strength is much higher. For instance, strength of Mo nanopillars of diameter 300–1000 nm is approximately 9 GPa. This is 6 times greater than strength of nanopillars obtained by FIB technique. However, this strength value is more than 2 times less than the evidence on MD-simulation of compression of defect-free Mo nanopillars of this crystallographic orientation [100]; according to our data, this value is ≈ 20 GPa. This difference can be caused by buckling instability, since at compression tests of nanopillars, it is quite difficult to provide the

A high-field technique of tensile testing in-situ of nanoneedles is free of such disadvantage. In addition, it makes it possible to test the specimens of significantly smaller diameters—from 20 till 125 nm. Data presented in Figure 12 enable to estimate experimentally strength of Mo and W nanocrystals by the value of upper scatter limit of experimental evidence on failure of nanoneedle specimens. This value for W is 23.2 GPа, and for Mo, it is 20.0 GPа. These figures also present the results of MD simulation of tension of cylindrical specimens in the direction [110]. Calculated strength values are approximately 1.4 times greater than the maximum experimental values of the nanopillars strength. At high-field treatment of the tip of nanoneedle specimen, its working volume is "cleaned" from dislocations [4, 19], and so, both decrease the values of strength of nanoneedle specimens, and their scatter may be because of stress raising related to rough lateral surface, which is formed by electrochemical polishing. The results obtained make it possible to identify the main factors leading to a decrease in the strength of nanosized crystals. According to these data, tensile strength of defect-free nanowires is always less than ideal strength. This is due to both surface tension effect (effect of a physical surface) and thermally induced local stress fluctuation (temperature effect). At transition to nanoneedles,

occurs at non-uniform triaxial tension (ξ<sup>11</sup> ≈ 40 GPa; ξ<sup>22</sup> ≈ ξ<sup>33</sup> ≈ 28 GPa).

by 1.43 times, while the second one—by 1.25–1.30 times.

3.4. Strength of nanopillars and nanoneedles

54 Molecular Dynamics

ideal conditions of uniaxial compression.


surface tension in NSC. The first factor governs regularities of strength dependence on temperature and the feature of the bcc!fcc transition under hydrostatic tension. The second one influences the absolute value of nanocrystal strength and determines the main regularities in manifestation of the size effect in nanospecimens of bcc and fcc metals, as well as the orientation dependence of the size effect in nanospecimens of bcc metals.

forming as a result of electrochemical polishing. This means that formation of an atomically

This work was supported by the National Academy of Sciences of Ukraine [grants number

2 National Scientific Center, Kharkov Institute for Physics and Technology, NASU, Kharkov,

[1] Lowry MB, Kiener D, LeBlanc MM, Chisholm C, Florando JN, Morris JW Jr, Minor AM. Achieving the ideal strength in annealed molybdenum nanopillars. Acta Mat. 2010;58:

[2] Bei H, Shim S, Pharr GM, George EP. Effects of pre-strain on the compressive stress–strain response of Mo-alloy single-crystal micropillars. Acta Mat. 2008;56:4762-4770. DOI:

[3] Bei H, Shim S, George EP, Miller MK, Herbert EG, Pharr GM. Compressive strengths of molybdenum alloy micro-pillars prepared using a new technique. Scr Mat. 2007;57:397-

[4] Shpak AP, Kotrechko SO, Mazilova TI, Mikhailovskij IM. Inherent tensile strength of molybdenum nanocrystals. Science and Technology of Advanced Materials. 2009;10(1–9):

, Igor Mikhailovskij<sup>2</sup> and Nataliya Stetsenko<sup>1</sup>

Atomic Mechanisms Governing Strength of Metallic Nanosized Crystals

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

57

smooth surface of nanoneedles is one of the factors to reach the ultimate strength levels.

The authors declare that they have no competing interests.

\*, Olexandr Ovsijannikov<sup>1</sup>

1 G. V. Kurdyumov Institute for Metal Physics, NASU, Kyiv, Ukraine

\*Address all correspondence to: serkotr@gmail.com

5160-5167. DOI: 10.1016/j.actamat. 2010.05.052

10.1016/j.actamat.2008.05.030

400. DOI: 10.1016/j.actamat.2008.05.030

045004. DOI: 10.1088/1468-6996/10/4/045004

Conflict of interest

#0117 U002131; #0117 U006351].

Funding

Author details

Sergiy Kotrechko<sup>1</sup>

Ukraine

References


The maximum attainable experimental values of the strength of Mo and W nanoneedle specimens in the crystallographic direction [110] are approximately 40% less than the results of MD simulation. This may be caused by stress raising due to rough lateral surface of nanoneedle specimens forming as a result of electrochemical polishing. This means that formation of an atomically smooth surface of nanoneedles is one of the factors to reach the ultimate strength levels.
