8 Basic properties of nanoparticles – VII

Dr. Anchal Srivastava

Contents of this Unit

1.  Solid disordered nanostructures 1.1.Method of synthesis

1.2.  Failure mechanism of conventional grain sized materials

1.3.  Mechanical properties

1.4 Nanostructured multilayers

1.5 Electrical properties

2.  Summary

Learning Outcomes

• After studying this module, you shall be able to understand
• What are solid disordered nanostructured?
• Their methods of synthesis and failure mechanism of grain sized nanoparticles. Their mechanical, electrical etc. properties.

1. SOLID DISORDERED NANOSTRUCTURES

1.1 Method of synthesis

In this section we will discuss some of the ways that disordered nanostructured solids are made. One method is referred to as compaction and consolidation. As an example of such a process, let us consider how nanostructured Cu-Fe alloys are made. Mixtures of iron and copper powders having the composition Fe₈₅Cu₁₅ are ball milled for 15 h at room temperature. The material is then compacted using a tungsten-carbide die at a pressure of 1 GPa for 24 h. This compact is then subjected to hot compaction for 30 min at temperatures in the vicinity of 400°C and pressure up to 870 MPa. The final density of the compact is 99.2% of the maximum possible density. Figure 7.1 presents the distribution of grain sizes in the material showing that it consists of nanoparticles ranging in size from 20 to 70 nm, with the largest number of particles having 40 nm sizes. Figure 7.2 shows a stress-strain curve for this case. Its Young’s modulus, which is the slope of the curve in the linear region, is similar to that of conventional iron. The deviation from linearity in the stress strain curve shows there is a ductile region before fracture where the material displays elongation. The data show that fracture occurs at 2.8GPa which is about 5 times the fracture stress of iron having larger grain sizes, ranging from 50 to 150 pm. Significant modifications of the mechanical properties of disordered bulk materials having nanosized grains is one of the most important properties of such materials. Making materials with nanosized grains has the potential to provide significant increases in yield stress, and has many useful applications such as stronger materials for automobile bodies. The reasons for the changes in mechanical properties of nanostructured materials will be discussed below.

Figure 7.1 Distribution of sizes of Fe-Cu nanoparticles made by hot compaction methods described in the text.

Figure 7.2 Stress-strain curve for bulk compacted nanostructured Fe-Cu material, showing fracture at a stress of 2.8 GPa.

Nanostructured materials can be made by rapid solidification. One method illustrated in Fig. 7.3 is called “chill block melt spinning.” RF (radiofrequency) heating coils are used to melt a metal, which is then forced through a nozzle to form a liquid stream. This stream is continuously sprayed over the surface of a rotating metal drum under an inert-gas atmosphere. The process produces strips or ribbons ranging in thickness from 10 to 100 pm. The parameters that control the nanostructure of the material are nozzle size, nozzle-to drum distance, melt ejection pressure, and speed of rotation of the metal drum. The need for light weight, high strength materials has led to the development of 85-94% aluminum alloys with other metals such as Y, Ni, and Fe made by this method. A melt spun alloy of Al-Y-Ni-Fe consisting of 10-30-nm Al particles embedded in an amorphous matrix can have a tensile strength in excess of 1.2 GPa. The high value is attributed, to the presence of defect free aluminum nanoparticles. In another method of making nanostructured materials, called gas atomization, a high-velocity inert-gas beam impacts a molten metal. The apparatus is illustrated in Fig 7.4. A fine dispersion of metal droplets is formed when the metal is impacted by the gas, which transfers kinetic energy to the molten metal. This method can be used to produce large quantities of nanostructured powders, which are then subjected to hot consolidation to form bulk samples.

Figure 7.3 Illustration of the chill block melting apparatus for producing nanostructured materials by rapid solidification on a rotating wheel.

Figure 7.4 Illustration of apparatus for making droplets of metals nanoparticles by gas atomization.

Nanostructured materials can be made by electrodeposition. For example, a sheet of nanostructured Cu can be fabricated by putting two electrodes in an electrolyte of CuSO4 and applying a voltage between the two electrodes. A layer of nanostructured Cu will be deposited on the negative titanium electrode. A sheet of Cu2 mm thick can be made by this process, having an average grain size of 27 nm, and enhanced yield strength of 119 MPa.

1.2 Failure mechanism of conventional grain sized materials

In order to understand how nanosized grains affect the bulk structure of materials, it is necessary to discuss how conventional grain-sized materials fail mechanically. A brittle material fractures before it undergoes an irreversible elongation. Fracture occurs because of the existence of cracks in the material. Figure 7.5 shows an example of a crack in a two-dimensional lattice. A “crack” is essentially a region of a material where there is no bonding between adjacent atoms of the lattice. If such a material is subjected to tension, the crack interrupts the flow of stress. The stress accumulates at the bond at the end of the crack, making the stress at that bond very high, perhaps exceeding the bond strength. This results in a breaking of the bond at the end of the crack, and a lengthening of the crack. Then the stress builds up on the next bond at the bottom of the crack and it breaks. This process of crack propagation continues until eventually the material separates at the crack. A crack provides a mechanism whereby a weak external force can break stronger bonds one by one. This explains why the stresses that induce fracture are actually weaker than the bonds that hold the atoms of the metal together. Another kind of mechanical failure is the brittle-to-ductile transition, where the stress-strain curve deviates from linearity, as seen in Fig. 7.2. In this region the material irreversibly elongates before fracture. When the stress is removed after the brittle to ductile transition the material does not return to its original length. The transition to ductility is a result of another kind of defect in the lattice called a dislocation. Figure 7.6 illustrates an edge dislocation in a two-dimensional lattice. There are also other kinds of dislocations such as a screw dislocation. Dislocations are essentially regions where lattice deviations from a regular structure extend over a large number of lattice spacing. Unlike cracks, the atoms in the region of the dislocation are bonded to each other, but the bonds are weaker than in the normal regions. In the ductile region one part of the lattice is able to slide across an adjacent part of the lattice. This occurs between sections of the lattice located at dislocations where the bonds between the atoms along the dislocation are weaker. One method of increasing the stress at which the brittle-to-ductile transition occurs is to impede the movement of the dislocations by introducing tiny particles of another material into the lattice. This process is used to harden steel, where particles of iron carbide are precipitated into the steel. The iron carbide particles block the movement of the dislocations.

Figure 7.5 A crack in two dimensional rectangular lattices.

Figure 7.6 An edge dislocation in two dimensional rectangular lattice.

1.3 Mechanical properties

The intrinsic elastic modulus of a nanostructured material is essentially the same as that of the bulk material having micrometer-sized grains until the grain size becomes very small, less than 5 nm. Young’s modulus is the factor relating stress and strain. It is the slope of the stress-strain curve in the linear region. The larger the value of Young’s modulus, the less elastic the material. Figure 7.7 is a plot of the ratio of Young’s modulus E in nanograined iron, to its value in conventional grain-sized iron Eo, as a function of grain size. We see from the figure that below ~20 nm, Young’s modulus begins to decrease from its value in conventional grain-sized materials.

The yield strength σy of a conventional grain-sized material is related to the grain size by the Hall-Petch equation

σy = σ0 + Kd-(1/2)     (7.1)

where σ0, is the frictional stress opposing dislocation movement, K is a constant, and d is the grain size in micrometers. Hardness can also be described by a similar equation. Figure 7.8 plots the measured yield strength of Fe-Co alloys as a function of d-(1/2), showing the linear behavior predicted by Eq. (7.1). Assuming that the equation is valid for nanosized grains, a bulk material having a 50-nm grain size would have a yield strength of 4.14 GPa. The reason for the increase in yield strength with smaller grain size is that materials having smaller grains have more grain boundaries, blocking dislocation movement. Deviations from the Hall-Petch behavior have been observed for materials made of particles less than 20 nm in size. The deviations involve no dependence on particle size (zero slope) to decreases in yield strength with particle size (negative slope). It is believed that conventional dislocation-based deformation is not possible in bulk nanostructured materials with sizes less than 30 nm because mobile dislocations are unlikely to occur. Examination of small-grained bulk nanomaterials by transmission electron microscopy during deformation does not show any evidence for mobile dislocations.

Figure7.7 Plot of ratio of Young’s modulus E in nanograin iron to its value E0 in conventional granular iron as a function of grain size.

Most bulk nanostructured materials are quite brittle and display reduced ductility under tension, typically having elongations of a few percent for grain sizes less than 30 nm. For example, conventional coarse-grained annealed polycrystalline copper is very ductile, having elongations of up to 60%. Measurements in samples with grain sizes less than 30nm yield elongations no more than 5%. Most of these measurements have been performed on consolidated particulate samples, which have large residual stress, and flaws due to imperfect particle bonding, which restricts dislocation movement. However, nanostructured copper prepared by electrodeposition displays almost no residual stress and-has elongations up to 30% as shown in Fig. 7.9. These results emphasize the importance of the choice of processing procedures, and the effect of flaws and microstructure on measured mechanical properties. In general, the results of ductility measurements on nanostructured bulk materials are mixed because of sensitivity to flaws and porosity, both of which depend on the processing methods.

Figure 7.8 Yield strength of Fe-Cu alloys versus 1/d1/2, where d is the size of the grain.

1.4 Nanostructured multilayers

Another kind of bulk nanostructure consists of periodic layers of nanometer thickness of different materials such as alternating layers of TiN and NbN. These layered materials are fabricated by various vapor-phase methods such as sputter deposition and chemical vapor-phase deposition. They can also be made by electrochemical deposition, which is discussed in Section 7.1. The materials have very large interface area densities. This means that the density of atoms on the planar boundary between two layers is very high. For example, a square centimeter of a 1-pm-thick multilayer film having layers of 2 nm thickness has an interface area of 1000 cm2. Since the material has a density of about 6.5 g/cm³, the interface area density is 154 m²/g, comparable to that of typical heterogeneous catalysts (see Module-VI). The interfacial regions have a strong influence on the properties of these materials. These layered materials have very high hardness, which depends on the thickness of the layers, and good wear resistance. Hardness is measured using an indentation load depth sensing apparatus which is commercially available, and is called a nanoindenter. A pyramidal diamond indenter is pressed into the surface of the material with a load, L(h) and the displacement of the tip is measured. Hardness is defined as L(h)/A(h) where A(h) is the area of the indentation. Typically measurements are made at a constant load rate of -20 mN/s.

Figure 7.9 Stress-strain curve of nanostructured copper prepared by electrodeposition.

Figure 7.10 shows a plot of the hardness of a TiN/NbN nanomultilayered structure as a function of the bilayer period (or thickness) of the layers, showing that as the layers get thinner in the nanometer range there is a significant enhancement of the hardness until -30 nm, where it appears to level off and become constant. It has been found that a mismatch of the crystal structures between the layers actually enhances the hardness. The compounds TIN and NbN both have the same rock salt or NaCl structure with the respective lattice constants 0.4235 and 0.5151 nm, so the mismatch between them is relatively large, as is the hardness. Harder materials have been found to have greater differences between the shear modulus of the layers. Interestingly, multilayers in which the alternating layers have different crystal structures were found to be even harder. In this case dislocations moved less easily between the layers, and essentially became confined in the layers, resulting in an increased hardness.

Figure 7.10 Plot of the hardness of TiN/NbN multilayer materials as a function of the thickness of the layers.

1.5 Electrical properties

For a collection of nanoparticles to be a conductive medium, the particles must be in electrical contact. One form of a bulk nanostructured material that is conducting consists of gold nanoparticles connected to each other by long molecules. This network is made by taking the gold particles in the form of an aerosol spray and subjecting them to a fine mist of a thiol such as dodecanethiol RSH, where R is C₁₂H₂=,. These alkyl thiols have an end group -SH that can attach to a methyl -CH₃, and a methylene chain 8-12 units long that provides steric repulsion between the chains. The chainlike molecules radiate out from the particle. The encapsulated gold particles are stable in aliphatic solvents such as hexane. However, the addition of a small amount of dithiol to the solution causes the formation of a threedimensional cluster network that precipitates out of the solution. Clusters of particles can also be deposited on flat surfaces once the colloidal solution of encapsulated nanoparticles has been formed. In-plane electronic conduction has been measured in two-dimensional arrays of 500-nm gold nanoparticles connected or linked to each other by conjugated organic molecules. A lithographically fabricated device allowing electrical measurements of such an array is illustrated in Figure 7.11. Figure 7.12 gives a measurement of the current versus voltage for a chain without (line a) and with (line b) linkage by a conjugated molecule.

Figure 7.11 Cross sectional view of a lithography fabricated device to measure the electrical conductivity in a two-dimensional array of gold nanoparticles linked molecules.

Figure 7.12 Room temperature current-voltage relationship for a two dimensional cluster array: without linkage (line a) and with the particles linked by a (CN)2C18H12 molecule (line b).

Figure 7.13 Measured current voltage relationship for a two dimensional linked cluster array at the temperatures of 85, 140 and 180 K.

Figure 7.13 gives the results of a measurement of a linked cluster at a number of different temperatures. The conductance G, which is defined as the ratio of the current I, to the voltage is the reciprocal of the resistance: R = V/I= 1/G. The data in Fig. 7.12 show that linking the gold nanoparticles substantially increases the conductance. The temperature dependence of the low-voltage conductance is given by

where E is the activation energy. The conduction process for this system can be modeled by a hexagonal array of single-crystal gold clusters linked by resistors, which are the connecting molecules, as illustrated in Fig. 7.14.

Figure 7.14 Sketch of a model to explain the electrical conductivity in an ideal hexagonal array of single-crystal clusters with uniform intercluster resistive linkage provided by resistors connecting the molecules.

The mechanism of conduction is electron tunneling. The tunneling process is a quantum-mechanical phenomenon where an electron can pass through an energy barrier larger than the kinetic energy of the electron. Thus, if a sandwich is constructed consisting of two similar metals separated by a thin insulating material, as shown in Fig. 7.15, under certain conditions an electron can pass from one metal to the other. For the electron to tunnel from one side of the junction to the other, there must be available unoccupied electronic states on the other side. For two identical metals at T= 0 K, the Fermi energies will be at the same level, and there will be no states available, as shown in Fig. 7.15, and tunneling cannot occur. The application of a voltage across the junction increases the electronic energy of one metal with respect to the other by shifting one Fermi level relative to the other. The number of electrons that can then move across the junction from left to right (Fig. 7.15)in an energy interval dE is proportional to the number of occupied states on the left and the number of unoccupied states on the right, which is

N1(E-eV)f(E-eV)[N2(E)(1-f(E))]

(7.3)

where N1 is the density of states in metal 1, N2 is the density of states in metal 2, and f(E) is the Fermi-Dirac distribution of states over energy, which is plotted in Fig. 7.17. The net flow of current I across the junction is the difference between the currents flowing to the right and the left, which is

where K is the matrix element, which gives the probability of tunneling through the barrier. The current across the junction will depend linearly on the voltage. If the density of states is assumed constant over an energy-range eV (electron volt), then for small V and low T: we obtain

Where,

Gnn = KN₁(E_f)N₂(E_f)e            (7.7)

and Gnn is defined as conductance. The junction, in effect, behaves in an ohmic manner, that is, with the current proportional to the voltage.

Figure 7.15 (a) Metal-insulator-metal junction; (b) density of states of occupied levels and Fermi level before a voltage is applied to the junction; (c) density of states and Fermi level after application of a voltage. Panels (b) and (c) plot the energy vertically and the density of states horizontally, as indicated at the bottom of the figure. Levels above the Fermi level that are not occupied by electrons are not shown.

Figure 7.16 Fermi-Dirac distribution function f(E), indicating equal density in k-space, plotted for the temperatures (a) T = 0 and (b) 0 < T < TF.

4. SUMMARY

• In this module you study
• Different methods for the synthesis of nanostructures
• Failure mechanism behind the conventional grain sized materials. Mechanical and electrical properties of nanostructures.
• Multilayer nanostructure.

Learn More:

1.I. Chang, ‘Rapid solidification processing of nanocrystalline metallic alloys. “ In hand book of

nanostructured materials and nanotechnology, H.S. Nalwa, ed., Academic Press San Seigo, 2000, Vol. 1,

Chapter 11, p. 501.

2.J.E. Gordon, The New Science of Strong Materials, Penguin Books, Middlesex, UK, 1968.

3.C.C. Koch, D.G. Moms, K.Lu, and A. Inoue, Ductility of Nanostructured Materials, MRS Bulletin, Feb. 1999