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for VLS mechanism ther-modynamics plays a less important role than for VSmechanism. This is the reason that in VS growth1D nanomaterials are mostly well faceted, whereas inVLS growth they are not.Burton et al:[74]investigated the growth of crys-tal planes under a certain supersaturation, and foundout that the formation energy of kinks was larger fora low-indexed, closely packed planes than for a high-indexed, sparsely arranged planes, which implies thatthe higher the index of the plane and the sparser ofthe plane packing, the larger the kink density in thatplane, and vice versa.It was also shown by Burton et al. that the foot-mean-square diffusion distance of a molecule on aplane was given by[74]¸s =p2D¿ = aDexpr³∆Gdes ¡ ∆Gdiff2kBT´(4)where D is the diffusion coefficient, ¿ is the mean staytime of an adsorbed molecule before desorption intothe vapor, aD is the diffusion jump distance, ∆Gdesand ∆Gdiff are the activation energies for desorptionand surface diffusion, respectively. Thus, the diffusiondistance is smaller for a low indexed, closely packedplane with lower free energy. Together with the kinkdensity formulation discussed above, it is natural todraw the conclusion that the higher the free energy ofa plane, the faster the growth velocity of it.Sears[93]has given the nucleation rate as˙ N = Bexp³¡ ∆fkBT´(5)with the formation energy of a critical-sized surfacenucleus ∆f defined by∆f = ¼a®2m½kBTln(S + 1)(6)where B is a constant, a the interlayer spacing for thegrowing plane, ¾ the surface free energy of the stepcreated, and m the atomic weight. From Eqs.(5) and(6), it is straightforward that two-dimensional nucle-ation could be initiated with large supersaturation,especially for those surface planes on which the freeenergy of steps is small, for example, the high-indexedplanes.By solving continuity partial differential equationsunder certain boundary conditions, Ruth et al:[87]derived the kinetic characteristics of the diffusion-controlled whisker growth. The time-dependentlength of the whisker in the initial stage can be simplywritten ash(t) = h0exp(°t) (7)with° = p ¡ p0r½r 2m¼kBT= Sp0r½r 2m¼kBT(8)where h0 is a constant, and ½ is the density of thewhisker. From Eqs.(7) and (8), we can get the growthrate along a specific crystallographic axis, and modelthe final morphology of the materials. However, thereal growth process is much more complex. On onehand, many experimental parameters can play a sig-nificant role in influencing the growth behavior of 1Dnanomaterials, and it is impossible to incorporate allof them in a theoretical model. On the other hand, thecrystallographic peculiarity of a given material makesit unlikely to simply transfer a theoretical model de-veloped for one material to another material. As wewill show in Section 3, the growth models discussedin this section can explain the growth phenomena toan extent, and to get more accurate qualitative de-scription, other experimental parameters have to beconsidered.2.3 ASG mechanismAqueous solution growth (ASG) has a wide mean-ing, and it includes not only low-temperature solutionchemistry and colloid chemistry, hydrothermal chem-istry and solvothermal chemistry, but also electro-chemistry. In a solution phase, far more experimen-tal parameters than in a vapor phase growth shouldbe considered and can be tuned to effectively controlthe growth of 1D nanomaterials. Besides the exper-imental parameters that are common to both vaporand solution phase growth, such as growth tempera-ture for the source and the substrate (if any), growthtime, and vapor partial pressure or solute concentra-tion and precursor types, other important experimen-tal parameters for solution phase growth include ionicstrength, pH value,
surfactant additives, and so on.Two aspects specific to solution growth are notewor-thy: (1) solution is a condensed phase, and the diffu-sion of ions is greatly influenced by the viscosity of thesolution, therefore, diffusion as the rate determiningstep is often encountered; and (2) the grown speciesare mainly ions with positive or negative charges, andthe growth is easier to be affected by foreign addi-tives. Similar to vapor phase growth, however, thecrystallographic characteristic is still the key factorthat determines the final morphology of the nanos-tructures.In ASG approach, three growth fashions havefrequently been observed: (1) ion-by-ion additiongrowth, (2) Ostwald ripening (OR), and (3) orientedattachment (OA). The first growth fashion is the mostgeneral case that we encounter in solution synthesis ofinorganic materials, however, the latter two fashionshave been observed only under special growth condi-tions. OR mechanism, also known as coarsening, canbe described as a diffusion-limited growth of largernanoparticles at the expense of smaller ones, andis well documented in literature [94–96]. The OR mechanism is a thermodynamically favorable process,which can proceed by overcoming a kinetic barrier,namely, dissolution of nanoparticles and transporta-tion of ionic species. OR mechanism generally causesthe dispersity of nanoparticle sizes. OA mechanismis a process where adjacent nanoparticles orient so asto share a common crystallographic axis, and join toform a whole part by eliminating the interface[97–99].This mechanism is also a thermodynamically favor-able process. The kinetic barrier to be overcome isthe transportation and orientation of building blocks.If the orientation cannot be aligned sufficiently andproperly, imperfect OA takes place, where twins,stacking faults, grain boundaries, and dislocationsmay form at the interface.
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