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Phase transformations and phase stability in nanocrystalline materials
Current Opinion in Solid State and Materials Science 9 (2005) 287–295
Phase transformations and phase stability in nanocrystalline materials Yonghua Rong
*
School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, PR China Received 31 March 2006
Abstract The current state of the researches on diffusionless phase transformations, including allotropic, polymorphous and martensitic transformations, and phase stability are reviewed. The behaviors of phase transformation and phase stability in nanocrystalline materials are markedly affected by the non-equilibrium conditions involved in their preparation, as a result, in this review an ideal demonstrating method of critical size for the stability of a high-temperature phase at low-temperatures is suggested, and the intrinsic conditions of the phase stability are clarified. Our recent experiments exhibit that the reversal transformation temperatures of low-temperature phases in nanocrystalline Co bulk metal and Fe–30Ni wt% alloy are significantly raised up over 800 C when their grain sizes are smaller than about 15 nm, while in the reported experiments of nanocrystalline particles or films the reversal transformation temperature lowers with decreasing grain size or is independent of grain size. Therefore, the author suggests that more experiments and theories for phase stability in reversal transformation should be performed. The study of grain growth kinetics of nanocrystalline materials, as a basic of investigating phase stability, is another attention aspect. 2006 Elsevier Ltd. All rights reserved. Keywords: Diffusionless phase transformation; Phase stability; Critical size; Grain-growth; Nanocrystalline material
1. Introduction The researches on the diffusionless phase transformations, including allotropic, polymorphous and martensitic transformation, and phase stability are extended in the category and preparation of nanocrystalline materials due to the need of various applications. Many experiments demonstrate that the transformation from a high-temperature phase to a low-temperature one will be suppressed when the grain (particle) size is smaller than a certain critical size, namely, the stability of the high-temperature phase at lowtemperatures is exhibited. The related theories have emerged to predict the critical size of the high-temperature phase stability and are comparable to the experimental results. However, since the preparation techniques of nano-
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1359-0286/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cossms.2006.07.003
crystalline materials connect with their formation under non-equilibrium conditions, the processing parameters significantly affect structure, which blurs the existence of the critical size and the intrinsic conditions of phase stability. Quite a few experiments were reported on the effect of grain size in nanometer scale on reversal transformation temperature and different size effects were demonstrated, but the related theories have not yet been established to explain these different effects. Kajiwara et al. [1,2] began to investigate martensitic transformation in ultra-fine particles of metals and alloys with nanometer scale in 1986, since then investigations on phase transformation and phase stability in nanocrystalline materials have rapidly went up [3–12]. Kajiwara et al. used ‘‘hydrogen-plasma-metal reaction’’ method to prepare ultra-fine particles of Fe–Ni alloys, pure Co and Co–Fe alloys with the diameters of 20–200 nm. They gave a conclusion that most of the ultra-fine particles for Fe–Ni sample are transformed at about the same Ms (the start temperature of martensitic transformation) as in the bulk,
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from which they doubted of the classical work by Cech and Turnbull [13] that Ms decreases remarkably with decreasing particle size. Zhou et al. [3] prepared ultrafine Fe–Ni (25–35Ni wt%) powders with the particle sizes of 10– 200 nm by levitation melting in liquid nitrogen, and their results supported Kajiwara et al.’s conclusion. However, after that a large number of experimental and theoretical investigations have verified the effect of grain (particle) size on martensitic transformation temperature, that is, Ms decreases remarkably with decreasing particle size, even martensitic transformation is suppressed when the grain (particle) size is smaller than a certain critical size. For example, Kitakami et al.’s experiments [4] indicated that the Co particles with particle sizes smaller than about 20 nm keep fcc structure at room temperature (RT), while the fcc(b) ! hcp(a) martensitic transformation occurs at 693 K in conventional coarse bulk samples. Meanwhile, the critical size of high-temperature fcc phase stable at RT was further calculated as 18 nm for b-multiply twinned icosahedrons or 110 nm for b-Wuff polyhedrons, as shown in Fig. 1. Considering the interface or grain boundary as a dilated crystal and the grain (particle) as a sphere we established a universal theoretical model on the prediction of the critical size of a high-temperature phase stable at lowtemperature in metals [7], alloys and compounds [14]. In addition, the nucleation model of a new phase in nanocrystalline crystals was also established [8], and it shows that the nucleation barrier and critical size of phase transformation are mainly dependent on the strain energy, interphase boundary energy and the grain size, as shown in Fig. 2. The size effect can be ignored when grain size is larger than 100 nm, from which the different behaviors of martensitic transformation between nanocrystals of Fe–Ni and Ni–Ti alloy were explained. However, many experiments indicate that the structure for a given material can vary with preparing methods, even processing parameters in the same method [15]. The effect of the nanocrystalline material preparation condition on phase stability is rather complex
Fig. 1. Calculated energy diagram of a Co fine particle as functions of particle diameter D for three different crystalline states, that is, a b-Wulff polyhedron, and an a-Wulff polyhedron. In this figure, the suffix X stands for b-MT, b-Wulff, and a-Wulff, and the Uca represents the cohesive energy of an a-Co particle. It can be noticed that b phase becomes more stable than a-phase as the particle size reduces.
Fig. 2. Relationship between the free energy of fcc ! bcc transformation and the bcc phase nuclear size in iron with different grain radius R1, interphase boundary energy f1, and a given grain boundary energy f2 = 1.6 J/m2. The squares represent Cahn and Larche work: (a) f1 ¼ cac ¼ 0:8 J/m2, R1 = 10 nm; (b) f1 ¼ cac ¼ 0:8 J/m2, R1 = 50 nm; 0 0 ac 2 2 (c) f1 ¼ cac ¼ 0:8 J/m ; (d) f ¼ c ¼ 0:5 J/m , R1 = 10 nm; (e) 1 0 0 ¼ 0:5 J/m2, R1 = 50 nm; and (f) f1 ¼ cac ¼ 0:5 J/m2. f1 ¼ cac 0 0
due to its connection with non-equilibrium conditions [16], such as vapor-phase deposition, magnetron sputtering, and mechanical ball milling. Therefore, the experimental design of the critical size demonstration and the exploration of the intrinsic conditions (both the necessary and sufficient conditions) of phase stability are very important in understanding the effect of preparation condition on structure. On the other hand, the existence of the critical size of phase stability means that a mixture of two phases with a single grain (particle) in the same size range does not occur, but the opposite case often appears when the grain sizes are around the predicted critical size [2–4,14]. The origin of this phenomenon should be clarified. Fewer researches on the effect of grain (particle) size with nanometer scale on the reversal phase transformation during heating were reported. Various experiments gave different conclusions. The reversal transformation temperature is less affected by particle (grain) size in Fe–Ni alloys [3,17], or lowers with decreasing particle size of anatase TiO2 [10], or lowers with the decrease of Co grain size ranging from 15 to 100 nm, and rises when it is smaller than 15 nm [17]. This difference has not yet been explained. From the above Co experiment it seems that there is also a critical size for the stability of a low-temperature phase at high-temperatures, the related theory has not yet been established. The abnormal thermal stability of nanocrystalline materials, as a basic of phase stability in forward and backward (reversal) transformations, is revealed in many experiments [18–23] and can be explained by different mechanisms of grain-growth kinetics [24–28]. The present review will focus on several basic issues: the ideal demonstrating method of the critical size and intrinsic conditions of phase stability, the phenomenon of a mixture of two phases in the same size range, the effects of preparing method and processing parameters on structure, the
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effect of grain size on the reversal transformation temperature, for understanding the phase transformation behaviors in nanocrystalline metals, alloys and compounds. 2. Critical size of phase stability Some previous experiments [1–3] exhibited that Ms is independent on the particle size, but plenty of recent experiments [4–6,9–11] verified that a high-temperature phase will be stable at low-temperatures when its grain (particle) size is smaller than a certain critical size. Furthermore, the related theories [4,7,8,14,29] were established. Based on analysis of the above results with opposite conclusions, an ideal demonstrating method of critical size is proposed, that is, a nanocrystalline sample is carried out with different annealed duration at some proper temperature in vacuum condition, which can produce different grain sizes but keep the composition unchanged and avoid oxidation disturbing the intrinsic critical size of the phase stability [12,30]. Fig. 3 is the X-ray diffraction spectra of ZrO2 powders annealed at 1573 K for different times [15], where an oxide is taken as an example for avoiding the molestation of oxidation. The variations of particle size and phase structure of ZrO2 with annealing time were determined by X-ray diffraction (XRD), as listed in Table 1. The particle sizes of ZrO2 were confirmed by transmission electron microscopy (TEM), such as the average size of particles about 10 nm of tetragonal (t) ZrO2 for annealing time of 0.5 min. It can be found that for the ZrO2 particles with the average size smaller than 14 nm they are t-phase, for
Fig. 3. X-ray diffraction spectra of ZrO2 powders annealed at 1573 K for 0.5–30 min.
Table 1 The effect of grain size on the phase structure of ZrO2 Held time (min)
0.5 2 3 30
Grain size (nm)
14 18 21 31
Structure t-phase (%)
m-phase (%)
100 51 36 0
0 49 64 100
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those larger than 31 nm, monocline (m) phase, while for those between, a mixture of t-high-temperature and mlow-temperature phases. It clearly demonstrates the size effect on phase stability since conventional coarse-grain (particle) ZrO2 will undergo t ! m martensitic transformation at temperature 1273 K during cooling. The above experiment indicates that the critical particle size of t-high-temperature phase stable at RT for ZrO2 is 14 nm, which is well consistent with our theoretical prediction of 13 nm diameter. Wintere et al. [31] calculated the critical grain size of t-ZrO2 stable at RT as 8 nm (diameter). The critical sizes of t-ZrO2 stable at RT prepared by different conditions have been reported, and they showed a wide range of 12–100 nm, such as 12 nm in zirconia powders synthesized by the gas condensation method [31] and 100 nm in zirconia powders synthesized by sol–gel technique [32]. The non-equilibrium feature of nanocrystalline materials implies that any comparison of experimental observations is meaningful only if the specimens used have comparable crystal size, chemical composition, preparation mode and thermal history [33]. Consequently, only referring to theoretical sense in spite of the preparation employed, the accurate determination of critical size should be carried out by high-temperature phase (such as t-ZrO2) with different sizes (or held different times) cooling from its phase field temperature (such as over 1273 K for t-ZrO2) to RT because such a treatment is close to thermodynamic equilibrium condition, and the results will, in turn, be comparable with the critical size by thermodynamic calculation. In our model of critical size prediction [7,14] a nanocrystalline particle is described as a sphere with diameter d, which is supposed to keep unchanged during phase transformation, containing a shell of thickness d and core (crystallite) with diameter (d 2d). The critical size of phase stability means that when the grain (particle) size of a high-temperature phase is smaller than a certain critical size, the total free energy (both shell and crystallite energies) of the high-temperature phase is lower than that of a low-temperature phase owing to the shell (interface or surface) energy of the high-temperature phase less than that of the low-temperature phase, as a result, the stability of the high-temperature phase at low-temperatures will be demonstrated. If its grain (particle) size is larger than the critical size, the high-temperature phase will completely transform to the low-temperature phase. In this theoretical model the nucleation of new phase in parent phase is not considered. The nucleation theory for phase transformation in nanocrystalline materials [8] clarify the meaning of critical size from another viewpoint, namely, if the grain size R1 of parent phase is small enough in nanometer scale and when it is equal to or smaller than the critical size R0 of new phase nucleation (see Fig. 2), whole grain of parent phase will transform into that of new phase once phase transformation occurs, and in this case the new phase and parent phase cannot coexist in the same grain. This phenomenon cannot occur in conventional coarse-grain
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materials in which the grain size of parent phase is usually in micrometer range and thus always larger than the critical size of new phase nucleation. If the grain size R1 of parent phase is larger than the critical size R0 of new phase nucleation, parent phase maybe partially transform into new phase within its one grain, and thus both the new phase and retained parent phase will coexist within one grain. This phenomenon in nanocrystalline materials is the same as in conventional coarse-grain materials. The critical size means that there is not a mixture of parent phase and new phase with single grain (particle) in the same size range, but such a mixture of two phases do occur, such as 20–40 nm in Co particles [4] and 14–31 nm in ZrO2 particles [15], which is different from the coexistence of new phase and retained parent phase within one grain of original parent phase. The origin of this phenomenon is probably attributed to the difference in the shape of each grain. Experiments revealed that the shape of individual nanocrystalline particle is not spherical, but polyhedral and facetted [4,6,34–37]. Crystallographically different surface has different surface energy, and thus can result in different critical size of phase stability for a given material. For example, the critical size of high-temperature fcc phase of Co particles stable at RT was calculated as 18 nm for b-multiply twinned icosahedrons or 110 nm for b-Wuff polyhedrons by Kitakami et al. [4]. However, in some theories [14,29,31] the shape of particle or grain is simply considered as a sphere, therefore, there is a definite critical size in the stability of a high-temperature phase for a given material. Fig. 4 shows the relation between the calculated critical size (d*) of b-Co and the excess volume (DV) of interface at 300 K [14]. It is clear that If DV varies from 0.05 to 0.3, the distribution of the critical size for b-Co at 300 K ranges from 20 to 65 nm. Since the excess volume of interface or surface is the most important parameter to describe the interface or surface energy, the variation of DV also can be considered to result from the change of the crystal interface or surface shape. Accordingly, the mixture of two phases must appear around the critical size predicted by theoretical calculation since the nanocrystalline grains or particles cannot have an identical shape. It is wor-
Fig. 4. The variation of critical grain size d* with DV for b-Co stable at 300 K.
thy to note that if experimental investigation is carried out in grain (particle) sizes just falling into a mixture of two phases, the critical size effect of phase stability cannot be observed. 3. Intrinsic conditions of phase stability Many experiments indicated that the structures for a given material can vary with different preparing methods, even with the different processing parameters in the same preparing method. For example, by using magnetron sputtering system, we got granular film of Co with the average grain size of 10 nm, consisting of e-hcp (a-Co) martensite and fcc (b-Co) [15] rather than a single fcc (b-Co) high-temperature phase [4] although the grains are smaller than a critical size 18 nm as predicted by Kitakami et al. [4] or 35 nm predicted by us [14]. Our result is different from that of Kitakami et al. [4]. The difference probably originates from processing parameter, such as a much lower sputtering Ar gas pressure of 0.4 Pa we used in comparison to their 13.3–53.3 Pa [4], which maybe give rise to different cooling rates [15]. Why can some experiments demonstrate the size effect on phase stability but others cannot? Therefore, the intrinsic conditions (the necessary condition and sufficient ones) for the stability of a high-temperature phase at low-temperatures must be further clarified to understand the origin of inconsistence between experiments. The phase stability is defined as that the transformation of a high-temperature phase to a low-temperature phase in conventional coarse grain materials is suppressed during cooling. Therefore, the phase stability includes two conditions: 1. As a necessary condition, the high-temperature phase must form during preparation process of nanocrystalline materials. 2. As a sufficient condition, the resultant grains must keep smaller than the critical grain (particle) size during subsequent cooling. In order to verify the intrinsic conditions of the phase stability, a 773 K sputtering temperature was designed for preparing Co granular film to ensure the formation of nanocrystalline b-Co high-temperature phase [15]. Fig. 5 is a dark field image and electron diffraction pattern of Co film sputtered at 773 K inserted. It is shown that a strong fcc [0 0 1] texture and butterfly-like satellites around the main spots, which is identified as the complex diffraction pattern for the beam along fcc [0 0 1] with hcp diffraction spots and {1 1 1}fcc twinning spots. The dark field image in Fig. 5 shows fcc grains with the average size of 40 nm, which is comparable with the critical grain size of 35 nm based on our calculation [14]. This high-temperature sputtering experiment fully demonstrated that at 773 K sputtering the nuclei of fcc b-Co have formed and grew up, then during cooling down to RT some of them can keep fcc structure if these grain sizes still are smaller than
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Fig. 5. Dark field image and electron diffraction pattern inserted of a Co film produced by sputtering at 773 K.
Fig. 6. e-hcp martensites within some fcc parent grains of Co film produced by sputtering at 773 K.
the critical grain size, while the others whose sizes are larger than the critical size will undergo the fcc (b) ! hcp (a) martensitic transformation. In order to determine whether hcp (a)-Co is a single grain or not, the microstructure of grains in higher magnification was observed. It can be clearly seen from Fig. 6 that several bands of e-hcp martensite appear within some larger fcc parent grains, indicating that hcp (a)-Co is the product of martensitic transformation and coexists with retained fcc (b)-Co. No individual e-hcp grain was not observed, which may result from the rather low cooling rate after 773 K sputtering to hinder such a transformation of whole grain. Coexistence of two phases in a nanocrystalline grain due to the occurrence of martensitic transformation was also reported in other materials, such as t-phase and m- martensite in ZrO2 [36,37], R-phase and B19’martensite in NiTi alloy [38]. Since the preparation process of nanocrystalline materials usually connects with their formation under nonequilibrium condition, the processing parameters will markedly affect the resultant structure and, then, the phase transformation behavior. In the present review, the preparing techniques of nanocrystalline materials are roughly classified into two categories. One is that the degree of grain refinement is related to cooling rate, such as vaporphase deposition, magnetron sputtering, hydrogenplasma-metal reaction, and levitation melting in liquid nitrogen. Another is that the degree of grain refinement is
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not related to cooling rate, such as mechanical ball milling, sol–gel, and severe plastic deformation. For example, in vapor-phase deposition, magnetron sputtering etc., the great cooling rate can suppress or partially suppress the nucleation of high-temperature phase during preparation, and thus low-temperature phase [15,39], even amorphous clusters [17] can be obtained. In sol–gel synthesis of nanocrystalline pure ZrO2 powders, one of the synthesis parameters, R (the ratio of molar concentration of water to zirconium n-propoxide) affects the change of structure [32]. The maximum size of undoped ZrO2 nanocrystallites with R = 5 observed for stabilization of 100% metastable t-phase is about 100 nm, and such stability in the largesized nanocrystallites is attributed to strain-induced grain-growth confinement due to a lack of porosity in these particles. In contrast, a significant amount of porosity within the weakly-aggregated ZrO2 nanocrystallites with R = 60 leads to the formation of m-phase at the expense of t-phase. Besides, processing parameters can result in different phase transformation sequences in a material with multi-phase transformations. For example, in well-known Fe there are multi-phase transformations from high-temperature to low-temperature undergoing dFe(bcc) ! c-Fe(fcc) !a-Fe(bcc). Therefore, various cooling rates can give rise to the existence of different phases at RT. Slow cooling may be favorable for the formation of d-Fe, while rapid cooling for that of c-Fe, and more rapid cooling rate for that of a-Fe or even amorphous cluster. During cooling when the grains (particles) are smaller than their critical sizes, respectively, the high-temperature phase, d-Fe(bcc) or c-Fe(fcc), will keep stable at RT. As a consequence, in such materials with multi-phase transformations the size effects or intrinsic conditions of phase stability will be difficultly revealed if experimental conditions are not accurately controlled. From the author’s viewpoint based on the above analysis, in Kajiwara et al.’s experiments [2] the formation of bcc phase in Fe–Ni alloy may be through three approaches rather than one approach of martensitic transformation considered by Kajiwara et al., namely, smaller ultra-fine bcc particles are a stable hightemperature bcc phase like d-Fe or low-temperature phase like a-Fe, while larger ultra-fine bcc particles larger than a critical size are a product of fcc austenite to bcc martensitic transformation. This analysis can make the experiment of Kajiwara et al. be consistent with the classical work of Cech and Turnbull and other experiments as well as theories on size effect of phase stability reported. We can further deduce that in any preparation methods of nanocrytalline materials when grains or particles smaller than the critical size of high-temperature phase exist in a lowtemperature phase at RT, this low-temperature phase, such as e-hcp (a-Co) in Co granular film and a-bcc in Fe–Ni granular film produced by RT deposition, cannot be a product of transformation from the high-temperature phase. In fact, its existence should be attributed to its lower chemical free energy than that of high-temperature phase at RT.
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4. Size effect on reversal transformation Quite a few experiments on the effect of grain (particle) size with nanometer scale on the reversal phase transformation from a low-temperature to a high-temperature phase were reported. Zhou et al. [3] investigated the transformation upon heating for Fe–Ni powders with different sizes of 10–200 nm. Their differential scanning calorimetry (DSC) measurement combined with TEM and XRD analyses indicated that for the particles containing 23–28 wt% Ni, the As (the start temperature of martensite to austenite transformation) ranges from 420 to 530 C and the Af (the finish temperature of martensite to austenite transformation) from 580 to 630 C, and thus the complete temperature range of martensite to austenite in ultra-fine Fe–Ni powders is 420–630 C, falling into the approximately same range for the bulk alloys with such compositions. Accordingly, they concluded that the ultra-fine Fe–Ni powders behave like the bulk during reversal transformation but without an explanation. Similar conclusion was derived by Asaka et al. [17] from experiment of Fe–25.0 at.% Ni nanogranular film that reversal transformation temperature appears to hardly be affected by size at elevated temperatures owing to the less surface energy difference between two phases at elevated temperature. However, Li et al. [10] observed the size dependence of thermal stability of TiO2 nanoparticles. Anatase TiO2 nanoparticles with average particle sizes ranging between 12 and 23 nm synthesized by metalogranic chemical vapor deposition were annealed between 700 and 800 C for 1 h to investigate the phase transformation behavior. The result indicated that the sample with finer initial anatase particles has lower thermal stability and lower transition onset temperature. For instance, at 700 C, the 12 nm particles have 7.9% of rutile (high-temperature phase) whereas the 23 nm ones have only 1.3% rutile, which indirectly verified that the onset temperature of reversal transition from anatase to rutile lowers with decreasing particle size. Their explanation is that the decreased thermal stability in finer nanoparticles was primarily attributed to the reduced activation energy as the size related surface enthalpy and stress energy increased. Kostic et al. [19] found that in nanocrystalline Al2O3 powders the reversal temperatures of the c ! d ! h ! a-Al2O3 phase transformations get remarkably lowered with increasing ball milling time. The introduced mechanical and thermal energies are thought to contribute to the activation energy gap for the observed phase transformation. Liu et al. [23] also demonstrated that temperature and the activation energy for h- to a-Al2O3 reversal transformation decreases with increasing ball milling time due to the promotion of transformation by a large amount of defects generated during milling. In contrary, our recent study observed a remarkable increase of a ! b reversal transformation temperature in nanocrystalline Co created on the surface of a bulk sample by surface mechanical attrition treatment (SMAT) [18]. As shown by DSC curve A in Fig. 7, only an endothermic
Fig. 7. DSC curve (20–1000 C) of Co metal before and after SMAT during heating.
peak at 459.5 C exists for the coarse-grained Co sample without SMAT, while curve B shows two endothermic peaks at 436.9 and 811.5 C, respectively, for the SMAT sample for 60 min, which weighs 33.1 · 103 g taken from the surface layer. Comparing curve B with curve A, the lower temperature peak is recognized to correspond to the reversal transformation in the coarse-grained sample, which is close to the normal 459.5 C, while the second peak at 811.5 C is supposed to be produced by finer grains in the nanocrystalline surface layer. This is verified by the curve C measured from a thinner layer (12.7 · 103 g) with finer grains picked up from the SMAT sample surface since the grain sizes exhibit the gradient distribution along the deformation depth, containing almost one peak at 815 C. XRD analysis and TEM observation confirm the above conclusion. Fig. 8(a) and (b) are a dark field image and an electron diffraction pattern of SMAT Co held 2 min at 500 C (over the temperature of the first endothermic peak), respectively. Fig. 8(a) shows that stable a(hcp) low-temperature phase exhibits the equiaxed grains smaller than about 15 nm, and these stable a(hcp) grains will undergo the reversal transformation above 800 C. Similar result also appears in DSC curves of SMAT Fe–30Ni alloy in our recent experiment [40], in which two endothermic peaks come from the reversal transformation of straininduced bcc martensitie to fcc austenite at 497.1 C and at 815.7 C, respectively. However, comparing with its coarse-grain sample, the As (427.9 C) of hcp to fcc reversal transformation for SMAT Co metal is lowered by about 12 C (see Fig. 7), and the relationship between As and d satisfies with 456.86–293.28/d (15 nm 6 d 6 100 nm) [18], while for SMAT Fe–30Ni alloy the As (485.3 C) of bcc to fcc reversal transformation is raised by about 130 C comparing to bcc martensite sample with coarse-grains obtained by quenched in liquid nitrogen. Our experiments imply that there also exists the critical size (about 15 nm) of phase stability for reversal transformation. In order to explain the difference of phase stability in reversal transformation between nanocrystalline Co metal and Fe–30Ni alloy, the total Gibbs free energy of a nanocrystalline bulk material for a low-temperature phase (a) to a high-temperature phase (b) is expressed as
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Fig. 8. Nanocrystalline grains (hcpa-Co) in the surface layer of Co metal held for 2 min at 500 C after SMAT 60 min: (a) dark field image with g = (100)a and (b) selected area diffraction pattern.
DGa!b ¼ V DGche ðT Þ þ Estr þ Egra ðrÞ þ Evol þ Eint where DGche(T) is the change in free energy per unit volume accompanying a ! b and implicates that high-temperature (T) can supply large chemical driving force in reversal transformation, V is the volume of the high-temperature phase (new phase), Estr is the strain energy accompanying plenty of defects (such as dislocation) produced by SMAT and also is the driving force of reversal transformation [23], and thus both Estr and DGche (T) are negative value. In the above equation Egra(r) is, as a function of grain radius of low-temperature phase (parent phase), the energy induced by the constraining stress of grain boundary, Evol is the strain energy arising from the change of volume in a new phase relative to a parent phase, and Eint is the interface energy between a new phase and parent phase and is usually lower grain boundary energy Egra(r) [8], depending on the structure of interface, coherent degree of interface and the shape of a new phase etc. The Egra(r), Evol and Eint are the resistance of phase transformation, and thus are positive value, of which Evol and Eint are independent on grain size. When DGa!b < 0, the reversal transformation will occur. During SMAT the Estr is produced and the Egra(r) is markedly raised accompanying refinement of grains. If jEstrj > Egra, the start temperature (As) of reversal transformation in a SMAT sample with ultra-fine grains will lower than that of a coarse-grain sample without SMAT, contrarily, if jEstrj < Egra, the As will rise, and they correspond to the drop of 12 C (SMAT Co) and the increase of 130 C (SMAT Fe–30Ni), respectively, when their grains are not enough small, in which the consideration about the Egra(r) of Co metal less than that of Fe–30Ni, or the jEstrj of Co metal greater than that of Fe–30Ni requires to be checked by experiments and theories. When grains are enough small (in our experiments grain size is smaller than about 15 nm), jVDGche(T) + Estrj < Egra(r) + Evol + Eint at the start temperature of reversal transformation in a conventional coarse-grain sample, the reversal transformation will not occur since DGa!b > 0. As a consequence, the larger chemical driving force is required by the increase of temperature so that DGa!b < 0, which corresponds to the case that the second endothermic peak in DSC of SMAT Co or SMAT Fe–30Ni. The thermodynamic consideration mentioned
above can be used to qualitatively explain our experimental phenomena, and the quantitative explanation should be further carried out. It is worth to point out that As can be markedly enhanced by ultra-fine nanocrystalline grains in both SMAT bulk Co metal and Fe–Ni alloy, but this phenomenon has not yet been found in nanocrystalline particles [3,4] or in nanogranular films [35,39]. Consequently, more experiments and the related theories for nanocrystalline particles, films or bulk should be performed to examine whether the stability of a lowtemperature phase at high-temperature occurs only in nano-crystalline bulk materials and has a certain critical size or not. The stability of a low-temperature phase at high-temperatures was realized in nanocrystalline Co metal and Fe– 30Ni alloy prepared by SMAT. The SMAT, accomplished by surface shot peening treatment, creates localized plastic deformation and then leads to grain refinement progressively down to the nanometer region in the surface layer of metallic materials [41]. It has been successfully applied in many materials systems to achieve nanocrystalline surface layer with 15–50 lm thickness [42]. Although microstructure evolution during SMAT shows different features in various materials [43,44], the resultant ultra-fined grains are equiaxed and have plenty of defects, similar to other large strain or severe plastic deformation [33,45,46]. The abnormal thermal stability of nanocrystalline grains in SMAT Co or Fe–Ni samples can be reasonably explained by some of grain-growth kinetics theories, such as solute drag [24], vacancy generation [25] and triple junctions [47]. For example, Fig. 9 shows a minimum on the total molar Gibbs free energy in the vicinity of grain size 15 nm for some alloy [24]. The availability of this minimum implies a possibility to inhibit the grain-growth process and stabilize the nanocrystalline structure if the initial grain size values are lower than those corresponding to that of the Gibbs free energy minimum. The solute drag mechanism mentioned above has been verified by grain-growth in nanocrystalline powders of Pd1xZrx at the supersaturated concentration of x = 0.2, little or no grain-growth is observed up to about 500 C [48]. The solute drag mechanism can well be used to explain the stability of nanocrystalline structure in SMAT Fe–30Ni alloy, but cannot be
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note that recent developments in the fabrication of ultrafine grained bulk metals and alloys have focused on the use of larger strain or severe plastic deformation as a method for achieving microstructure refinement, and the thermal stability of ultra-fine grains is a key issue to phase stability and mechanical properties, accordingly, the study of grain-growth kinetics of ultra-fine grained materials prepared by larger strain or severe plastic deformation is another attention aspect. 5. Conclusions
Fig. 9. Variation of the molar Gibbs free energy G of a binary alloy polycrystal with grain size L at fixed P, T, and fixed overall solute concentration xb = 0.05. The dotted line denotes the Gibbs free energy of the solid solution single crystal with the same xb.
used in SMAT pure Co metal. For nanocrystalline pure metals both vacancy generation mechanism [25,26] and triple junction mechanism [47] can be used to explained the abnormal thermal stability of grain-growth. The study of nanocrystalline Fe powders [26] indicated that when grain size exceeds about 150 nm, a smooth transition from linear to non-linear growth kinetics occurs, as shown in Fig. 10, and the linear-stage growth rate agrees quantitatively with the vacancy generation model, suggesting that the redistribution of excess volume localized in the boundary cores can account for the anomalously high stability with respect to coarsening observed in nanocrystalline samples. The theoretical study based on the triple junction drag model [47] indicated that with low initial K (a dimensionless parameter equal to the product of the triple junction mobility and the average grain size divided by the grain boundary mobility), the growth kinetics is at first linear and becomes parabolic at the later stages only. It is worthy to
Fig. 10. Isothermal evolution of R in ball-milled, nanocrystalline Fe at the indicated annealing temperatures, as determined by a Fourier analysis of X-ray diffraction peak profiles. The straight lines are guides to the eye illustrating linear growth kinetics at initial annealing times; deviations from linearity become apparent when R exceeds 150 nm.
The study of phase transformation in nanocrystalline materials over the 20 years has yielded conclusive proof that a high-temperature phase can stable at low-temperatures when its grain (grain) size is smaller than a certain critical size. The theoretical calculations of critical size have been carried out in some of metals, alloys and compounds. In this review the ideal demonstrating method of critical size, referring to the requirement of grain size distribution, unchanged composition and oxidation-free, are suggested. The intrinsic conditions of phase stability are clarified, namely, the high-temperature phase must form in during preparation of nanocrystalline materials, and then its grain size must keep smaller than a critical grain (particle) size during subsequent cooling. Based on the above viewpoint the effects of preparation methods and processing parameters of nanocrystalline materials on structure are discussed. Since the preparation of nanocrystalline materials usually connects with their formation under non-equilibrium condition, the processing parameters will markedly affect structure, and, in turn, phase transformation behavior. The phenomenon of a mixture of two phases in the same grain size range is observed in many experiments, and its origin is explained by the author as the difference between grain (particle) shapes leading to the distribution of critical size in some extents. Recent our work has shown the stability of a nanocrystalline low-temperature phase at high-temperatures in SMAT bulk Co or Fe–30Ni alloy when its grain size is smaller than a certain grain size (about 15 nm), however, the phenomenon is not observed in their nanocrystalline particles or films reported. In addition, some experiments demonstrate the opposite effect of grain (particle) size, that is, the reversal transformation temperature lowers with decreasing grain (particle) size or is independent on grain (particle) size. Therefore, more experiments for nanocrystalline particles, films or bulk should be performed to examine whether the stability of low-temperature phase at high-temperature occurs only in nanocrystalline bulk materials and has a certain critical size or not, and the related theories should be built. The abnormal thermal stability of nanocrystalline grains is a basic of phase stability, and can be explained by solute drag, vacancy generation or triple junction mechanics. The study of grain-growth kinetics in ultra-fine grained metals and alloys prepared by larger strain or severe plastic deformation will have theoretical and practical sense.
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Acknowledgements The present work was financially supported by the Science and Technology Foundation of Shanghai under Grant Nos. 0159nm045 and 021nm017. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
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Phase transformations and phase stability in nanocrystalline materials Yonghua Rong
*
School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, PR China Received 31 March 2006
Abstract The current state of the researches on diffusionless phase transformations, including allotropic, polymorphous and martensitic transformations, and phase stability are reviewed. The behaviors of phase transformation and phase stability in nanocrystalline materials are markedly affected by the non-equilibrium conditions involved in their preparation, as a result, in this review an ideal demonstrating method of critical size for the stability of a high-temperature phase at low-temperatures is suggested, and the intrinsic conditions of the phase stability are clarified. Our recent experiments exhibit that the reversal transformation temperatures of low-temperature phases in nanocrystalline Co bulk metal and Fe–30Ni wt% alloy are significantly raised up over 800 C when their grain sizes are smaller than about 15 nm, while in the reported experiments of nanocrystalline particles or films the reversal transformation temperature lowers with decreasing grain size or is independent of grain size. Therefore, the author suggests that more experiments and theories for phase stability in reversal transformation should be performed. The study of grain growth kinetics of nanocrystalline materials, as a basic of investigating phase stability, is another attention aspect. 2006 Elsevier Ltd. All rights reserved. Keywords: Diffusionless phase transformation; Phase stability; Critical size; Grain-growth; Nanocrystalline material
1. Introduction The researches on the diffusionless phase transformations, including allotropic, polymorphous and martensitic transformation, and phase stability are extended in the category and preparation of nanocrystalline materials due to the need of various applications. Many experiments demonstrate that the transformation from a high-temperature phase to a low-temperature one will be suppressed when the grain (particle) size is smaller than a certain critical size, namely, the stability of the high-temperature phase at lowtemperatures is exhibited. The related theories have emerged to predict the critical size of the high-temperature phase stability and are comparable to the experimental results. However, since the preparation techniques of nano-
*
Tel.: +86 21 62932558; fax: +86 21 62933910. E-mail address: [email protected]
1359-0286/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cossms.2006.07.003
crystalline materials connect with their formation under non-equilibrium conditions, the processing parameters significantly affect structure, which blurs the existence of the critical size and the intrinsic conditions of phase stability. Quite a few experiments were reported on the effect of grain size in nanometer scale on reversal transformation temperature and different size effects were demonstrated, but the related theories have not yet been established to explain these different effects. Kajiwara et al. [1,2] began to investigate martensitic transformation in ultra-fine particles of metals and alloys with nanometer scale in 1986, since then investigations on phase transformation and phase stability in nanocrystalline materials have rapidly went up [3–12]. Kajiwara et al. used ‘‘hydrogen-plasma-metal reaction’’ method to prepare ultra-fine particles of Fe–Ni alloys, pure Co and Co–Fe alloys with the diameters of 20–200 nm. They gave a conclusion that most of the ultra-fine particles for Fe–Ni sample are transformed at about the same Ms (the start temperature of martensitic transformation) as in the bulk,
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from which they doubted of the classical work by Cech and Turnbull [13] that Ms decreases remarkably with decreasing particle size. Zhou et al. [3] prepared ultrafine Fe–Ni (25–35Ni wt%) powders with the particle sizes of 10– 200 nm by levitation melting in liquid nitrogen, and their results supported Kajiwara et al.’s conclusion. However, after that a large number of experimental and theoretical investigations have verified the effect of grain (particle) size on martensitic transformation temperature, that is, Ms decreases remarkably with decreasing particle size, even martensitic transformation is suppressed when the grain (particle) size is smaller than a certain critical size. For example, Kitakami et al.’s experiments [4] indicated that the Co particles with particle sizes smaller than about 20 nm keep fcc structure at room temperature (RT), while the fcc(b) ! hcp(a) martensitic transformation occurs at 693 K in conventional coarse bulk samples. Meanwhile, the critical size of high-temperature fcc phase stable at RT was further calculated as 18 nm for b-multiply twinned icosahedrons or 110 nm for b-Wuff polyhedrons, as shown in Fig. 1. Considering the interface or grain boundary as a dilated crystal and the grain (particle) as a sphere we established a universal theoretical model on the prediction of the critical size of a high-temperature phase stable at lowtemperature in metals [7], alloys and compounds [14]. In addition, the nucleation model of a new phase in nanocrystalline crystals was also established [8], and it shows that the nucleation barrier and critical size of phase transformation are mainly dependent on the strain energy, interphase boundary energy and the grain size, as shown in Fig. 2. The size effect can be ignored when grain size is larger than 100 nm, from which the different behaviors of martensitic transformation between nanocrystals of Fe–Ni and Ni–Ti alloy were explained. However, many experiments indicate that the structure for a given material can vary with preparing methods, even processing parameters in the same method [15]. The effect of the nanocrystalline material preparation condition on phase stability is rather complex
Fig. 1. Calculated energy diagram of a Co fine particle as functions of particle diameter D for three different crystalline states, that is, a b-Wulff polyhedron, and an a-Wulff polyhedron. In this figure, the suffix X stands for b-MT, b-Wulff, and a-Wulff, and the Uca represents the cohesive energy of an a-Co particle. It can be noticed that b phase becomes more stable than a-phase as the particle size reduces.
Fig. 2. Relationship between the free energy of fcc ! bcc transformation and the bcc phase nuclear size in iron with different grain radius R1, interphase boundary energy f1, and a given grain boundary energy f2 = 1.6 J/m2. The squares represent Cahn and Larche work: (a) f1 ¼ cac ¼ 0:8 J/m2, R1 = 10 nm; (b) f1 ¼ cac ¼ 0:8 J/m2, R1 = 50 nm; 0 0 ac 2 2 (c) f1 ¼ cac ¼ 0:8 J/m ; (d) f ¼ c ¼ 0:5 J/m , R1 = 10 nm; (e) 1 0 0 ¼ 0:5 J/m2, R1 = 50 nm; and (f) f1 ¼ cac ¼ 0:5 J/m2. f1 ¼ cac 0 0
due to its connection with non-equilibrium conditions [16], such as vapor-phase deposition, magnetron sputtering, and mechanical ball milling. Therefore, the experimental design of the critical size demonstration and the exploration of the intrinsic conditions (both the necessary and sufficient conditions) of phase stability are very important in understanding the effect of preparation condition on structure. On the other hand, the existence of the critical size of phase stability means that a mixture of two phases with a single grain (particle) in the same size range does not occur, but the opposite case often appears when the grain sizes are around the predicted critical size [2–4,14]. The origin of this phenomenon should be clarified. Fewer researches on the effect of grain (particle) size with nanometer scale on the reversal phase transformation during heating were reported. Various experiments gave different conclusions. The reversal transformation temperature is less affected by particle (grain) size in Fe–Ni alloys [3,17], or lowers with decreasing particle size of anatase TiO2 [10], or lowers with the decrease of Co grain size ranging from 15 to 100 nm, and rises when it is smaller than 15 nm [17]. This difference has not yet been explained. From the above Co experiment it seems that there is also a critical size for the stability of a low-temperature phase at high-temperatures, the related theory has not yet been established. The abnormal thermal stability of nanocrystalline materials, as a basic of phase stability in forward and backward (reversal) transformations, is revealed in many experiments [18–23] and can be explained by different mechanisms of grain-growth kinetics [24–28]. The present review will focus on several basic issues: the ideal demonstrating method of the critical size and intrinsic conditions of phase stability, the phenomenon of a mixture of two phases in the same size range, the effects of preparing method and processing parameters on structure, the
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effect of grain size on the reversal transformation temperature, for understanding the phase transformation behaviors in nanocrystalline metals, alloys and compounds. 2. Critical size of phase stability Some previous experiments [1–3] exhibited that Ms is independent on the particle size, but plenty of recent experiments [4–6,9–11] verified that a high-temperature phase will be stable at low-temperatures when its grain (particle) size is smaller than a certain critical size. Furthermore, the related theories [4,7,8,14,29] were established. Based on analysis of the above results with opposite conclusions, an ideal demonstrating method of critical size is proposed, that is, a nanocrystalline sample is carried out with different annealed duration at some proper temperature in vacuum condition, which can produce different grain sizes but keep the composition unchanged and avoid oxidation disturbing the intrinsic critical size of the phase stability [12,30]. Fig. 3 is the X-ray diffraction spectra of ZrO2 powders annealed at 1573 K for different times [15], where an oxide is taken as an example for avoiding the molestation of oxidation. The variations of particle size and phase structure of ZrO2 with annealing time were determined by X-ray diffraction (XRD), as listed in Table 1. The particle sizes of ZrO2 were confirmed by transmission electron microscopy (TEM), such as the average size of particles about 10 nm of tetragonal (t) ZrO2 for annealing time of 0.5 min. It can be found that for the ZrO2 particles with the average size smaller than 14 nm they are t-phase, for
Fig. 3. X-ray diffraction spectra of ZrO2 powders annealed at 1573 K for 0.5–30 min.
Table 1 The effect of grain size on the phase structure of ZrO2 Held time (min)
0.5 2 3 30
Grain size (nm)
14 18 21 31
Structure t-phase (%)
m-phase (%)
100 51 36 0
0 49 64 100
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those larger than 31 nm, monocline (m) phase, while for those between, a mixture of t-high-temperature and mlow-temperature phases. It clearly demonstrates the size effect on phase stability since conventional coarse-grain (particle) ZrO2 will undergo t ! m martensitic transformation at temperature 1273 K during cooling. The above experiment indicates that the critical particle size of t-high-temperature phase stable at RT for ZrO2 is 14 nm, which is well consistent with our theoretical prediction of 13 nm diameter. Wintere et al. [31] calculated the critical grain size of t-ZrO2 stable at RT as 8 nm (diameter). The critical sizes of t-ZrO2 stable at RT prepared by different conditions have been reported, and they showed a wide range of 12–100 nm, such as 12 nm in zirconia powders synthesized by the gas condensation method [31] and 100 nm in zirconia powders synthesized by sol–gel technique [32]. The non-equilibrium feature of nanocrystalline materials implies that any comparison of experimental observations is meaningful only if the specimens used have comparable crystal size, chemical composition, preparation mode and thermal history [33]. Consequently, only referring to theoretical sense in spite of the preparation employed, the accurate determination of critical size should be carried out by high-temperature phase (such as t-ZrO2) with different sizes (or held different times) cooling from its phase field temperature (such as over 1273 K for t-ZrO2) to RT because such a treatment is close to thermodynamic equilibrium condition, and the results will, in turn, be comparable with the critical size by thermodynamic calculation. In our model of critical size prediction [7,14] a nanocrystalline particle is described as a sphere with diameter d, which is supposed to keep unchanged during phase transformation, containing a shell of thickness d and core (crystallite) with diameter (d 2d). The critical size of phase stability means that when the grain (particle) size of a high-temperature phase is smaller than a certain critical size, the total free energy (both shell and crystallite energies) of the high-temperature phase is lower than that of a low-temperature phase owing to the shell (interface or surface) energy of the high-temperature phase less than that of the low-temperature phase, as a result, the stability of the high-temperature phase at low-temperatures will be demonstrated. If its grain (particle) size is larger than the critical size, the high-temperature phase will completely transform to the low-temperature phase. In this theoretical model the nucleation of new phase in parent phase is not considered. The nucleation theory for phase transformation in nanocrystalline materials [8] clarify the meaning of critical size from another viewpoint, namely, if the grain size R1 of parent phase is small enough in nanometer scale and when it is equal to or smaller than the critical size R0 of new phase nucleation (see Fig. 2), whole grain of parent phase will transform into that of new phase once phase transformation occurs, and in this case the new phase and parent phase cannot coexist in the same grain. This phenomenon cannot occur in conventional coarse-grain
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materials in which the grain size of parent phase is usually in micrometer range and thus always larger than the critical size of new phase nucleation. If the grain size R1 of parent phase is larger than the critical size R0 of new phase nucleation, parent phase maybe partially transform into new phase within its one grain, and thus both the new phase and retained parent phase will coexist within one grain. This phenomenon in nanocrystalline materials is the same as in conventional coarse-grain materials. The critical size means that there is not a mixture of parent phase and new phase with single grain (particle) in the same size range, but such a mixture of two phases do occur, such as 20–40 nm in Co particles [4] and 14–31 nm in ZrO2 particles [15], which is different from the coexistence of new phase and retained parent phase within one grain of original parent phase. The origin of this phenomenon is probably attributed to the difference in the shape of each grain. Experiments revealed that the shape of individual nanocrystalline particle is not spherical, but polyhedral and facetted [4,6,34–37]. Crystallographically different surface has different surface energy, and thus can result in different critical size of phase stability for a given material. For example, the critical size of high-temperature fcc phase of Co particles stable at RT was calculated as 18 nm for b-multiply twinned icosahedrons or 110 nm for b-Wuff polyhedrons by Kitakami et al. [4]. However, in some theories [14,29,31] the shape of particle or grain is simply considered as a sphere, therefore, there is a definite critical size in the stability of a high-temperature phase for a given material. Fig. 4 shows the relation between the calculated critical size (d*) of b-Co and the excess volume (DV) of interface at 300 K [14]. It is clear that If DV varies from 0.05 to 0.3, the distribution of the critical size for b-Co at 300 K ranges from 20 to 65 nm. Since the excess volume of interface or surface is the most important parameter to describe the interface or surface energy, the variation of DV also can be considered to result from the change of the crystal interface or surface shape. Accordingly, the mixture of two phases must appear around the critical size predicted by theoretical calculation since the nanocrystalline grains or particles cannot have an identical shape. It is wor-
Fig. 4. The variation of critical grain size d* with DV for b-Co stable at 300 K.
thy to note that if experimental investigation is carried out in grain (particle) sizes just falling into a mixture of two phases, the critical size effect of phase stability cannot be observed. 3. Intrinsic conditions of phase stability Many experiments indicated that the structures for a given material can vary with different preparing methods, even with the different processing parameters in the same preparing method. For example, by using magnetron sputtering system, we got granular film of Co with the average grain size of 10 nm, consisting of e-hcp (a-Co) martensite and fcc (b-Co) [15] rather than a single fcc (b-Co) high-temperature phase [4] although the grains are smaller than a critical size 18 nm as predicted by Kitakami et al. [4] or 35 nm predicted by us [14]. Our result is different from that of Kitakami et al. [4]. The difference probably originates from processing parameter, such as a much lower sputtering Ar gas pressure of 0.4 Pa we used in comparison to their 13.3–53.3 Pa [4], which maybe give rise to different cooling rates [15]. Why can some experiments demonstrate the size effect on phase stability but others cannot? Therefore, the intrinsic conditions (the necessary condition and sufficient ones) for the stability of a high-temperature phase at low-temperatures must be further clarified to understand the origin of inconsistence between experiments. The phase stability is defined as that the transformation of a high-temperature phase to a low-temperature phase in conventional coarse grain materials is suppressed during cooling. Therefore, the phase stability includes two conditions: 1. As a necessary condition, the high-temperature phase must form during preparation process of nanocrystalline materials. 2. As a sufficient condition, the resultant grains must keep smaller than the critical grain (particle) size during subsequent cooling. In order to verify the intrinsic conditions of the phase stability, a 773 K sputtering temperature was designed for preparing Co granular film to ensure the formation of nanocrystalline b-Co high-temperature phase [15]. Fig. 5 is a dark field image and electron diffraction pattern of Co film sputtered at 773 K inserted. It is shown that a strong fcc [0 0 1] texture and butterfly-like satellites around the main spots, which is identified as the complex diffraction pattern for the beam along fcc [0 0 1] with hcp diffraction spots and {1 1 1}fcc twinning spots. The dark field image in Fig. 5 shows fcc grains with the average size of 40 nm, which is comparable with the critical grain size of 35 nm based on our calculation [14]. This high-temperature sputtering experiment fully demonstrated that at 773 K sputtering the nuclei of fcc b-Co have formed and grew up, then during cooling down to RT some of them can keep fcc structure if these grain sizes still are smaller than
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Fig. 5. Dark field image and electron diffraction pattern inserted of a Co film produced by sputtering at 773 K.
Fig. 6. e-hcp martensites within some fcc parent grains of Co film produced by sputtering at 773 K.
the critical grain size, while the others whose sizes are larger than the critical size will undergo the fcc (b) ! hcp (a) martensitic transformation. In order to determine whether hcp (a)-Co is a single grain or not, the microstructure of grains in higher magnification was observed. It can be clearly seen from Fig. 6 that several bands of e-hcp martensite appear within some larger fcc parent grains, indicating that hcp (a)-Co is the product of martensitic transformation and coexists with retained fcc (b)-Co. No individual e-hcp grain was not observed, which may result from the rather low cooling rate after 773 K sputtering to hinder such a transformation of whole grain. Coexistence of two phases in a nanocrystalline grain due to the occurrence of martensitic transformation was also reported in other materials, such as t-phase and m- martensite in ZrO2 [36,37], R-phase and B19’martensite in NiTi alloy [38]. Since the preparation process of nanocrystalline materials usually connects with their formation under nonequilibrium condition, the processing parameters will markedly affect the resultant structure and, then, the phase transformation behavior. In the present review, the preparing techniques of nanocrystalline materials are roughly classified into two categories. One is that the degree of grain refinement is related to cooling rate, such as vaporphase deposition, magnetron sputtering, hydrogenplasma-metal reaction, and levitation melting in liquid nitrogen. Another is that the degree of grain refinement is
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not related to cooling rate, such as mechanical ball milling, sol–gel, and severe plastic deformation. For example, in vapor-phase deposition, magnetron sputtering etc., the great cooling rate can suppress or partially suppress the nucleation of high-temperature phase during preparation, and thus low-temperature phase [15,39], even amorphous clusters [17] can be obtained. In sol–gel synthesis of nanocrystalline pure ZrO2 powders, one of the synthesis parameters, R (the ratio of molar concentration of water to zirconium n-propoxide) affects the change of structure [32]. The maximum size of undoped ZrO2 nanocrystallites with R = 5 observed for stabilization of 100% metastable t-phase is about 100 nm, and such stability in the largesized nanocrystallites is attributed to strain-induced grain-growth confinement due to a lack of porosity in these particles. In contrast, a significant amount of porosity within the weakly-aggregated ZrO2 nanocrystallites with R = 60 leads to the formation of m-phase at the expense of t-phase. Besides, processing parameters can result in different phase transformation sequences in a material with multi-phase transformations. For example, in well-known Fe there are multi-phase transformations from high-temperature to low-temperature undergoing dFe(bcc) ! c-Fe(fcc) !a-Fe(bcc). Therefore, various cooling rates can give rise to the existence of different phases at RT. Slow cooling may be favorable for the formation of d-Fe, while rapid cooling for that of c-Fe, and more rapid cooling rate for that of a-Fe or even amorphous cluster. During cooling when the grains (particles) are smaller than their critical sizes, respectively, the high-temperature phase, d-Fe(bcc) or c-Fe(fcc), will keep stable at RT. As a consequence, in such materials with multi-phase transformations the size effects or intrinsic conditions of phase stability will be difficultly revealed if experimental conditions are not accurately controlled. From the author’s viewpoint based on the above analysis, in Kajiwara et al.’s experiments [2] the formation of bcc phase in Fe–Ni alloy may be through three approaches rather than one approach of martensitic transformation considered by Kajiwara et al., namely, smaller ultra-fine bcc particles are a stable hightemperature bcc phase like d-Fe or low-temperature phase like a-Fe, while larger ultra-fine bcc particles larger than a critical size are a product of fcc austenite to bcc martensitic transformation. This analysis can make the experiment of Kajiwara et al. be consistent with the classical work of Cech and Turnbull and other experiments as well as theories on size effect of phase stability reported. We can further deduce that in any preparation methods of nanocrytalline materials when grains or particles smaller than the critical size of high-temperature phase exist in a lowtemperature phase at RT, this low-temperature phase, such as e-hcp (a-Co) in Co granular film and a-bcc in Fe–Ni granular film produced by RT deposition, cannot be a product of transformation from the high-temperature phase. In fact, its existence should be attributed to its lower chemical free energy than that of high-temperature phase at RT.
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4. Size effect on reversal transformation Quite a few experiments on the effect of grain (particle) size with nanometer scale on the reversal phase transformation from a low-temperature to a high-temperature phase were reported. Zhou et al. [3] investigated the transformation upon heating for Fe–Ni powders with different sizes of 10–200 nm. Their differential scanning calorimetry (DSC) measurement combined with TEM and XRD analyses indicated that for the particles containing 23–28 wt% Ni, the As (the start temperature of martensite to austenite transformation) ranges from 420 to 530 C and the Af (the finish temperature of martensite to austenite transformation) from 580 to 630 C, and thus the complete temperature range of martensite to austenite in ultra-fine Fe–Ni powders is 420–630 C, falling into the approximately same range for the bulk alloys with such compositions. Accordingly, they concluded that the ultra-fine Fe–Ni powders behave like the bulk during reversal transformation but without an explanation. Similar conclusion was derived by Asaka et al. [17] from experiment of Fe–25.0 at.% Ni nanogranular film that reversal transformation temperature appears to hardly be affected by size at elevated temperatures owing to the less surface energy difference between two phases at elevated temperature. However, Li et al. [10] observed the size dependence of thermal stability of TiO2 nanoparticles. Anatase TiO2 nanoparticles with average particle sizes ranging between 12 and 23 nm synthesized by metalogranic chemical vapor deposition were annealed between 700 and 800 C for 1 h to investigate the phase transformation behavior. The result indicated that the sample with finer initial anatase particles has lower thermal stability and lower transition onset temperature. For instance, at 700 C, the 12 nm particles have 7.9% of rutile (high-temperature phase) whereas the 23 nm ones have only 1.3% rutile, which indirectly verified that the onset temperature of reversal transition from anatase to rutile lowers with decreasing particle size. Their explanation is that the decreased thermal stability in finer nanoparticles was primarily attributed to the reduced activation energy as the size related surface enthalpy and stress energy increased. Kostic et al. [19] found that in nanocrystalline Al2O3 powders the reversal temperatures of the c ! d ! h ! a-Al2O3 phase transformations get remarkably lowered with increasing ball milling time. The introduced mechanical and thermal energies are thought to contribute to the activation energy gap for the observed phase transformation. Liu et al. [23] also demonstrated that temperature and the activation energy for h- to a-Al2O3 reversal transformation decreases with increasing ball milling time due to the promotion of transformation by a large amount of defects generated during milling. In contrary, our recent study observed a remarkable increase of a ! b reversal transformation temperature in nanocrystalline Co created on the surface of a bulk sample by surface mechanical attrition treatment (SMAT) [18]. As shown by DSC curve A in Fig. 7, only an endothermic
Fig. 7. DSC curve (20–1000 C) of Co metal before and after SMAT during heating.
peak at 459.5 C exists for the coarse-grained Co sample without SMAT, while curve B shows two endothermic peaks at 436.9 and 811.5 C, respectively, for the SMAT sample for 60 min, which weighs 33.1 · 103 g taken from the surface layer. Comparing curve B with curve A, the lower temperature peak is recognized to correspond to the reversal transformation in the coarse-grained sample, which is close to the normal 459.5 C, while the second peak at 811.5 C is supposed to be produced by finer grains in the nanocrystalline surface layer. This is verified by the curve C measured from a thinner layer (12.7 · 103 g) with finer grains picked up from the SMAT sample surface since the grain sizes exhibit the gradient distribution along the deformation depth, containing almost one peak at 815 C. XRD analysis and TEM observation confirm the above conclusion. Fig. 8(a) and (b) are a dark field image and an electron diffraction pattern of SMAT Co held 2 min at 500 C (over the temperature of the first endothermic peak), respectively. Fig. 8(a) shows that stable a(hcp) low-temperature phase exhibits the equiaxed grains smaller than about 15 nm, and these stable a(hcp) grains will undergo the reversal transformation above 800 C. Similar result also appears in DSC curves of SMAT Fe–30Ni alloy in our recent experiment [40], in which two endothermic peaks come from the reversal transformation of straininduced bcc martensitie to fcc austenite at 497.1 C and at 815.7 C, respectively. However, comparing with its coarse-grain sample, the As (427.9 C) of hcp to fcc reversal transformation for SMAT Co metal is lowered by about 12 C (see Fig. 7), and the relationship between As and d satisfies with 456.86–293.28/d (15 nm 6 d 6 100 nm) [18], while for SMAT Fe–30Ni alloy the As (485.3 C) of bcc to fcc reversal transformation is raised by about 130 C comparing to bcc martensite sample with coarse-grains obtained by quenched in liquid nitrogen. Our experiments imply that there also exists the critical size (about 15 nm) of phase stability for reversal transformation. In order to explain the difference of phase stability in reversal transformation between nanocrystalline Co metal and Fe–30Ni alloy, the total Gibbs free energy of a nanocrystalline bulk material for a low-temperature phase (a) to a high-temperature phase (b) is expressed as
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Fig. 8. Nanocrystalline grains (hcpa-Co) in the surface layer of Co metal held for 2 min at 500 C after SMAT 60 min: (a) dark field image with g = (100)a and (b) selected area diffraction pattern.
DGa!b ¼ V DGche ðT Þ þ Estr þ Egra ðrÞ þ Evol þ Eint where DGche(T) is the change in free energy per unit volume accompanying a ! b and implicates that high-temperature (T) can supply large chemical driving force in reversal transformation, V is the volume of the high-temperature phase (new phase), Estr is the strain energy accompanying plenty of defects (such as dislocation) produced by SMAT and also is the driving force of reversal transformation [23], and thus both Estr and DGche (T) are negative value. In the above equation Egra(r) is, as a function of grain radius of low-temperature phase (parent phase), the energy induced by the constraining stress of grain boundary, Evol is the strain energy arising from the change of volume in a new phase relative to a parent phase, and Eint is the interface energy between a new phase and parent phase and is usually lower grain boundary energy Egra(r) [8], depending on the structure of interface, coherent degree of interface and the shape of a new phase etc. The Egra(r), Evol and Eint are the resistance of phase transformation, and thus are positive value, of which Evol and Eint are independent on grain size. When DGa!b < 0, the reversal transformation will occur. During SMAT the Estr is produced and the Egra(r) is markedly raised accompanying refinement of grains. If jEstrj > Egra, the start temperature (As) of reversal transformation in a SMAT sample with ultra-fine grains will lower than that of a coarse-grain sample without SMAT, contrarily, if jEstrj < Egra, the As will rise, and they correspond to the drop of 12 C (SMAT Co) and the increase of 130 C (SMAT Fe–30Ni), respectively, when their grains are not enough small, in which the consideration about the Egra(r) of Co metal less than that of Fe–30Ni, or the jEstrj of Co metal greater than that of Fe–30Ni requires to be checked by experiments and theories. When grains are enough small (in our experiments grain size is smaller than about 15 nm), jVDGche(T) + Estrj < Egra(r) + Evol + Eint at the start temperature of reversal transformation in a conventional coarse-grain sample, the reversal transformation will not occur since DGa!b > 0. As a consequence, the larger chemical driving force is required by the increase of temperature so that DGa!b < 0, which corresponds to the case that the second endothermic peak in DSC of SMAT Co or SMAT Fe–30Ni. The thermodynamic consideration mentioned
above can be used to qualitatively explain our experimental phenomena, and the quantitative explanation should be further carried out. It is worth to point out that As can be markedly enhanced by ultra-fine nanocrystalline grains in both SMAT bulk Co metal and Fe–Ni alloy, but this phenomenon has not yet been found in nanocrystalline particles [3,4] or in nanogranular films [35,39]. Consequently, more experiments and the related theories for nanocrystalline particles, films or bulk should be performed to examine whether the stability of a lowtemperature phase at high-temperature occurs only in nano-crystalline bulk materials and has a certain critical size or not. The stability of a low-temperature phase at high-temperatures was realized in nanocrystalline Co metal and Fe– 30Ni alloy prepared by SMAT. The SMAT, accomplished by surface shot peening treatment, creates localized plastic deformation and then leads to grain refinement progressively down to the nanometer region in the surface layer of metallic materials [41]. It has been successfully applied in many materials systems to achieve nanocrystalline surface layer with 15–50 lm thickness [42]. Although microstructure evolution during SMAT shows different features in various materials [43,44], the resultant ultra-fined grains are equiaxed and have plenty of defects, similar to other large strain or severe plastic deformation [33,45,46]. The abnormal thermal stability of nanocrystalline grains in SMAT Co or Fe–Ni samples can be reasonably explained by some of grain-growth kinetics theories, such as solute drag [24], vacancy generation [25] and triple junctions [47]. For example, Fig. 9 shows a minimum on the total molar Gibbs free energy in the vicinity of grain size 15 nm for some alloy [24]. The availability of this minimum implies a possibility to inhibit the grain-growth process and stabilize the nanocrystalline structure if the initial grain size values are lower than those corresponding to that of the Gibbs free energy minimum. The solute drag mechanism mentioned above has been verified by grain-growth in nanocrystalline powders of Pd1xZrx at the supersaturated concentration of x = 0.2, little or no grain-growth is observed up to about 500 C [48]. The solute drag mechanism can well be used to explain the stability of nanocrystalline structure in SMAT Fe–30Ni alloy, but cannot be
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note that recent developments in the fabrication of ultrafine grained bulk metals and alloys have focused on the use of larger strain or severe plastic deformation as a method for achieving microstructure refinement, and the thermal stability of ultra-fine grains is a key issue to phase stability and mechanical properties, accordingly, the study of grain-growth kinetics of ultra-fine grained materials prepared by larger strain or severe plastic deformation is another attention aspect. 5. Conclusions
Fig. 9. Variation of the molar Gibbs free energy G of a binary alloy polycrystal with grain size L at fixed P, T, and fixed overall solute concentration xb = 0.05. The dotted line denotes the Gibbs free energy of the solid solution single crystal with the same xb.
used in SMAT pure Co metal. For nanocrystalline pure metals both vacancy generation mechanism [25,26] and triple junction mechanism [47] can be used to explained the abnormal thermal stability of grain-growth. The study of nanocrystalline Fe powders [26] indicated that when grain size exceeds about 150 nm, a smooth transition from linear to non-linear growth kinetics occurs, as shown in Fig. 10, and the linear-stage growth rate agrees quantitatively with the vacancy generation model, suggesting that the redistribution of excess volume localized in the boundary cores can account for the anomalously high stability with respect to coarsening observed in nanocrystalline samples. The theoretical study based on the triple junction drag model [47] indicated that with low initial K (a dimensionless parameter equal to the product of the triple junction mobility and the average grain size divided by the grain boundary mobility), the growth kinetics is at first linear and becomes parabolic at the later stages only. It is worthy to
Fig. 10. Isothermal evolution of R in ball-milled, nanocrystalline Fe at the indicated annealing temperatures, as determined by a Fourier analysis of X-ray diffraction peak profiles. The straight lines are guides to the eye illustrating linear growth kinetics at initial annealing times; deviations from linearity become apparent when R exceeds 150 nm.
The study of phase transformation in nanocrystalline materials over the 20 years has yielded conclusive proof that a high-temperature phase can stable at low-temperatures when its grain (grain) size is smaller than a certain critical size. The theoretical calculations of critical size have been carried out in some of metals, alloys and compounds. In this review the ideal demonstrating method of critical size, referring to the requirement of grain size distribution, unchanged composition and oxidation-free, are suggested. The intrinsic conditions of phase stability are clarified, namely, the high-temperature phase must form in during preparation of nanocrystalline materials, and then its grain size must keep smaller than a critical grain (particle) size during subsequent cooling. Based on the above viewpoint the effects of preparation methods and processing parameters of nanocrystalline materials on structure are discussed. Since the preparation of nanocrystalline materials usually connects with their formation under non-equilibrium condition, the processing parameters will markedly affect structure, and, in turn, phase transformation behavior. The phenomenon of a mixture of two phases in the same grain size range is observed in many experiments, and its origin is explained by the author as the difference between grain (particle) shapes leading to the distribution of critical size in some extents. Recent our work has shown the stability of a nanocrystalline low-temperature phase at high-temperatures in SMAT bulk Co or Fe–30Ni alloy when its grain size is smaller than a certain grain size (about 15 nm), however, the phenomenon is not observed in their nanocrystalline particles or films reported. In addition, some experiments demonstrate the opposite effect of grain (particle) size, that is, the reversal transformation temperature lowers with decreasing grain (particle) size or is independent on grain (particle) size. Therefore, more experiments for nanocrystalline particles, films or bulk should be performed to examine whether the stability of low-temperature phase at high-temperature occurs only in nanocrystalline bulk materials and has a certain critical size or not, and the related theories should be built. The abnormal thermal stability of nanocrystalline grains is a basic of phase stability, and can be explained by solute drag, vacancy generation or triple junction mechanics. The study of grain-growth kinetics in ultra-fine grained metals and alloys prepared by larger strain or severe plastic deformation will have theoretical and practical sense.
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