Nanocrystalline Materials: Synthesis and Properties Part 3 (Nanotechnology)

PROPERTIES OF ISOLATED NANOPARTICLES AND NANOCRYSTALLINE POWDERS

The transition from crystals to nanoparticles is followed by changes in the interatomic distances and lattice constants. For example, when the size of Ag and Au particles decreases from 40 to 10 nm, the lattice constant becomes ~ 0.1% smaller. When the size of Si particles decreases from 10 to 3 nm, the lattice constant increases by 1.1%. The ambiguity of the dimensional effect may be a result of adsorption of impurities or different chemical compositions of particles. One more possible reason is the structural transformations, which are caused by the decrease in the particle size. Reliable experiments did not reveal shrinkage of the lattice constant as the particle size decreased to 10 nm, whereas shortening of interatomic distances for particles of smaller sizes is real enough as compared with bulk substances.

The most probable reason why the lattice constant of small particles changes as compared with its counterpart in a macroscopic substance consists in uncompensated interatomic bonds of surface atoms and hence the surface relaxation. In the case of nanoparticles, the surface relaxation is a maximum on the surface, decreases toward the center of the particle, and may prove to be oscillating under certain conditions. Thus the lattice constant may either increase or decrease as the size of nanoparticles diminishes.[7,8]

The melting temperature Tm drops nonlinearly with decreasing size of small particles of Pb, Sn, Bi, In, Ga, Cu, Ag, Au, and Al. For example, the maximum decrease in the melting temperature of Sn, Ga, and Hg clusters ~ 1 nm in size was 152, 106, and 95 K, respectively.[4] When the radius of CdS colloid nanoparticles was reduced from 4 to 1 nm, Tm dropped nearly by 800 K.[31] According to Refs. [4] and [8], melting temperatures of bulk crystals and small particles >10 nm in size differ insignificantly. The melting temperature decreases when the size of nano-particles becomes less than 10 nm.

Differences in thermodynamic properties of nanopar-ticles and a bulk substance are a result of changes in the phonon spectrum. The phonon spectrum of small particles contains low-frequency modes, which are absent in spectra of bulk crystals. The phonon spectrum of nanoparticles is limited by some minimum frequency on the side of low-frequency vibrations. No such limitation exists for bulk samples. Specific features of the vibration spectrum of nanoparticles affect the low-temperature heat capacity in the first place.

A theoretical analysis, which took into account the quantum-size effect, showed that the low-temperature region (T! 0) has some temperature T0, below which the nanoparticle heat capacity Cv(r) is smaller than the heat capacity Cv of a bulk crystal. At T> T0, the difference DC = Cv(r) —Cv becomes positive, reaches a maximum, and, as the temperature rises further, turns to zero. The difference of the heat capacities DC = Cv(r) —Cv! 0 with increasing size r of the particle. These conclusions agree with experimental data.[33] The heat capacity of Ag nanoparticles 10 nm in size had the quantum-size effect in a magnetic field with B=6 T: at T< 1 K and T> 1 K, the heat capacity of Ag nanoparticles was lower and higher than the heat capacity of bulk silver, respectively. In the absence of the magnetic field, the heat capacity of colloid silver nanoparticles was higher than the heat capacity of bulk Ag over the whole temperature interval studied (Fig. 13).

An examination of phonon densities for coarse-grained Ni and a nanocrystalline nickel powder with particles ~ 10 nm in size showed that the density of phonon states increased in n-Ni as compared with coarse-grained Ni at energies lower than 15 meV.[34]

Specific features of magnetic properties of nanoparti-cles are connected with discreteness of electron and phonon states. In particular, the Curie paramagnetism of a nanoparticle can overlap the Pauli paramagnetism at low temperatures. For example, magnetic susceptibility of lithium nanoparticles of diameter 3.2 nm corresponds to the Pauli paramagnetism at high temperatures and obeys the Curie law at low temperatures.[4] Hg13 clusters are weak paramagnetics in a magnetic field of up to 15 kOe independently of temperature. In a field with H>20 kOe, susceptibility of Hgi3 clusters increases to large paramagnetic values at temperatures below 80 K, although mercury is a diamagnetic.[4]

The phenomenon of superparamagnetism is connected with the small size of ferromagnetic particles. When some critical size Dc is reached, ferromagnetic particles turn to single-domain ones, and, simultaneously, the coercive force Hc becomes a maximum. As the particle size diminishes further, the coercive force drops abruptly to zero as a result of transition to the superparamagnetic state. Typical ferromagnetics acquire the superparamag-netic state when the particle size is less than 1-10 nm.

When the size of Fe nanoparticles decreases from 80 to 8-10 nm, the coercive force Hc increases almost three times. The dimension dependence of Hc for Ni nanopar-ticles exhibits a maximum corresponding to nanoparticles 15 to 35 nm in diameter. As the particle size diminishes from 15 to 12 nm, Hc decreases nearly 5 times.[35] An analysis of the saturation magnetization ls for bulk Ni and a nanocrystalline Ni powder (D =12, 22 and 100 nm)[36] showed that refinement of particles to 12 nm caused an almost twofold decrease in the ls value as compared with bulk Ni.

Fig. 13 Specific heat capacity C of colloidal Ag with D =10 nm at T< 10 K. Measurements were made in the absence of a magnetic field and in a magnetic field B = 6 T. The dashed line shows the specific heat capacity of bulk coarse-grained silver.

Optical dimensional effects show themselves for nanoparticles whose size is smaller than the radiation wavelength and does not exceed 10-15 nm.[37] When fine-grain metal films absorb light, the visible part of the spectrum contains peaks, which are absent in the spectra obtained for bulk metals. For example, granulated films of Au particles 4 nm in diameter have a maximum absorption at l=560-600 nm. Absorption spectra of Ag, Cu, Mg, In, Li, Na, and K nanoparticles also contain maxima in the optical range.[4] Differences in absorption spectra of nanoparticles and bulk metals are explained by the fact that the imaginary part of dielectric permeability is inversely proportional to the particle size. The particle size determines the shape of the low-frequency edge and the absorption bandwidth.

The size of semiconductor nanoparticles is comparable with the Bohr radius of excitons in a macroscopic crystal: the exciton radius changes over broad limits from 0.7 nm for CuCl to 10 nm for GaAs. The decrease in the size of nanoparticles causes displacement of the exciton absorption band to the high-frequency region (”blue” shift). The blue shift is observed for CdS nanoparticles with D < 1012 nm. When the size of ZnO, ZnS, CdS, and CdSe nanoparticles decreases, their luminescence spectra are displaced to the short-wave region.

EFFECT OF THE GRAIN SIZE AND INTERFACES ON PROPERTIES OF BULK NANOSUBSTANCES

Properties of bulk nanomaterials depending on the grain size and the state of grain boundaries have been analyzed in reviews. , , ] At 300 K, the microhardness of bulk nanocrystalline substances is usually several times larger than HV of coarse-grained substances. The growth of HV was observed with decreasing size of n-Fe and n-Ni grains.[41] The microhardness HV of nanocrystalline n-Cu copper (D ~ 16 nm) is ~ 2.5 times larger than that of copper with grains 5 mm in size. However, as the size of n-Cu grains diminishes from 16 to 8 nm, HV decreases by ~ 25%. The decrease in HV is also observed when n-Pd grains are refined from 13 to 7 nm. The microhardness HV of Ni-P, TiAlNb, TiAl, and NbAl3 nanocrystalline alloys drops as the grain size decreases from 60-100 to 6-10 nm.

In a general case, the microhardness of nanosubstances grows as the grain size decreases to some Dc value and drops at D < Dc. Mechanical and elastic properties of nanocrystalline metals are determined not only by a small size of grains, but also by the state of interfaces. Therefore contradictory results on the dimension dependence of the microhardness may be due to different structures of interfaces.

Strength properties of nanosubstances are enhanced with decreasing size of grains. The yield stress of nanocrystalline Pd (D=5-15 nm) and Cu (D=25-50 nm) is 2-3 times higher than the yield stress of coarsegrained metals.[40] The tensile strength of nanocrystalline metals is 1.5-8 times larger than that of coarse-grained metals.

At temperatures from 150 to 300 K, the heat capacity Cp of n-Pd (D=6 nm) and n-Cu (D=8 nm) is 30-50% and ~ 10% higher than the heat capacity of coarse-grained bulk Pd and Cu, respectively. In the interval of 0.06 to 10.0 K, the low-temperature heat capacity of compacted nanocrystalline copper n-Cu with grains 6.0 and 8.5 nm in size proved to be 5-10 times larger than the heat capacity of coarse-grained copper. Measurements of the heat capacity of amorphous, nanocrystalline, and coarsegrained selenium Se over the temperature interval from 220 to 500 K[42] revealed a small increase in the heat capacity of bulk nanocrystalline n-Se as compared with coarse-grained Se at T<375 K. A comparison of the heat capacity of substances in nanocrystalline, amorphous, and coarse-grained states[43] showed that the heat capacity of samples prepared by compaction of nanopowders is largely different from the heat capacity of substances in the coarse-grain state (Table 1). Oppositely, this difference does not exceed 2% for samples prepared by crystallization from the amorphous state. One may think that most of the excess heat capacity of compacted nanomaterials is a result of a large surface area of interfaces, structural distortions, and impurities.

Table 1 Comparison of heat capacity Cp (j mol 1 k J) for the nanocrystalline, amorphous, and coarse-grained polycrystalline states of different substances

Material			State			T (K)
		Nanocrystalline		Amorphous	Coarse-grained
	Synthesis methoda	Crystallite size D (nm) Cp		Cp	Cp
Pd	1	6	37	27	25	250
Cu	1	8	26	—	24	250
Ru	2	15	28	—	23	250
Ni0.8P0.2	3	6	23.4	23.4	23.2	250
Se	3	10	24.5	24.7	24.1	245

The thermal expansion coefficient a is proportional to the heat capacity. Therefore the coefficient a of bulk nanosubstances should be higher than a of coarse-grained polycrystals. Indeed, the coefficient a of nanocrystalline copper n-Cu with grains 8 nm in size on the average is twice as large as a of coarse-grained copper.[44]

A large surface area of interfaces and a high concentration of defects determine an intensive scattering of charge carriers in nanomaterials. A considerable increase in electroresistivity p of nanocrystalline Cu, Pd, Fe, and Ni and various alloys with decreasing size of grains has been noted by many researchers. For example, at temperatures 0< T< 275 K, electroresistivity of n-Cu (D=7 nm) is 7 to 20 times larger than p of common coarse-grained copper.

The effect of the nanostate on magnetic properties of paramagnetics is well pronounced, e.g., in palladium (Fig. 14).[8] At 300 K, susceptibilities of nanocrystalline n-Pd and the initial coarse-grained palladium differ by 8%. According to Ref. [8] such a considerable variation of the susceptibility is a result of the presence of intragrain vacancy complexes in n-Pd, which change the density of electron states at the Fermi level.

The majority of studies into magnetic properties of bulk nanosubstances have dealt with ferromagnetic metals and alloys. A study of submicrocrystalline Ni[45] has confirmed that the coercive force of plastically deformed ferromagnetics is several times larger than Hc of initial metals. However, annealing of submicrocrystalline Ni at T< 470 K causes a decrease in the coercive force, while the grain size remains unchanged. Annealing at higher temperatures leads to a decrease in Hc and an increase in the grain size. Therefore a large coercive force of submicrocrystalline metals and alloys is equally determined by a nonequilibrium state of interfaces on the one hand and a small size of grains on the other hand. Relaxation of interfaces during annealing and growth of grains cause a decrease in Hc.

Fig. 14 Magnetic susceptibility w of nanocrystalline n-Pd and coarse-grained palladium: (From Ref. [8]) (1) annealing w(300, T) and (2) temperature w(T) dependences of the susceptibility for n-Pd; (3) annealing w(300, T) and (4) temperature w(T) dependences of the susceptibility for the initial coarse-grained Pd. The annealing dependences w(300, T) of the susceptibility (curves 1 and 3) were measured at 300 K after annealing at a temperature T and cooling to 300 K.

CONCLUSION

Studies performed in recent decades have considerably improved our understanding of the effects related to the size of grains (crystallites) in solids. For a long time, studies have been focused on small particles (nanoclus-ters) whose properties are intermediate between properties of isolated atoms and polycrystalline solids. The advent of methods for production of compact materials having an extremely fine-grain structure with nanometer-sized grains provided conditions for the study of the structure and properties of solids in the nanocrystalline state. Each of those methods has its virtues and drawbacks, and neither of them is universal because each is applicable to a certain range of substances. Because of their specific structure, properties of nanocrystalline substances differ considerably from those of usual polycrystals. An analysis of the available experimental data shows that not only the grain size (as in isolated nanoparticles), but also the structure and the state of interfaces (grain boundaries) play a significant role in a nanocrystalline solid. The separation of surface effects (connected with interfaces) and volume effects (related to the size of particles) is very important for the theoretical interpretation of the experimental results obtained for isolated nanoparticles and bulk nanocrystalline materials.

Extensive studies of nanocrystalline substances and materials have led to appearance of new sciences, namely, nanocrystalline solid-state physics and chemistry. Therefore it is possible to establish tight contacts between nanomaterials and nanotechnologies, which will present the main motive force of the scientific and technological progress in the 21st century.