6-1 The phase transformation in Zr based intermetallic alloys during ARB
6-1-1 The transformation of Zr-Ni from nanocrystalline to amorphous phase during ARB
Before discussing the local cluster structures and its structural transformation in this system, it is helpful to examine their equilibrium phase diagram first [180], as depicted in Fig.
6-1. The heat of mixing between HCP Zr and FCC Ni is -49 kJ/mol, which would lead to a strong driving force for the pure elemental Zr and Ni atoms to mix together and to form local ordering. Coupled with the large difference in the atomic radius, r, being 23 % judging from rZr = 0.160 nm and rNi = 0.124 nm, the Zr-Ni system has been considered to be a binary alloy with high glass forming ability upon rapid cooling. The strong tendency for local ordering results in the formation of many equilibrium intermetallic compounds, including Zr2Ni, ZrNi and Zr2Ni7.
From the microstructural evolution and associated two-dimensional Fourier transform shown in Chapter 5-1-1, the vitrification of FCC Ni proceeds relatively more reluctantly than that of HCP Zr in Figs. 5-2 (a) to (c). Undeniably, this could be directly relative to the nature of characteristic between FCC and HCP structures. There are 12 octahdral slip systems for FCC metals competed with those for HCP. Also, the smaller atomic radii and mass of Ni compared with Zr would provide more atoms within a specific space, namely having higher number density than Zr in the same grain size. Both factors let it possess higher diffusion
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mobility and more alternative than Zr atom to quickly restore crystalline while being borne the same condition at high strain rate. On other hand, reduced grain size would lead to the unstable state within grain, e.g. the competition between their surface energy and volume energy in the classic nucleation theory. Hence, FCC or HCP crystals would collapse its long range order rapidly and transfer to short range order clusters when reducing its grain size to a critical value, but Ni could maintain this long range order better than Zr in the same space of their small grain size due to its small atomic radii.
The results of potential energy and HA index both show a pronounced transience at the early stages of ARB cycle. It is well known that one of easier forming compounds in the Zr-Ni alloys is Zr2Ni, which has a body centered tetragonal (BCT) crystalline structure with lattice constants of a=0.65 nm and c=0.53 nm. Other intermetallic compounds include ZrNi5
(cubic), Zr2Ni7 (monoclinic), ZrNi3 (hexagonal), Zr7Ni10 (tetragonal), ZrNi (orthorhombic), etc, based on the equilibrium thermodynamic phase diagram in Fig. 6-1. In general, it prefers to form the intermetallic compounds rather than an amorphous phase through the thermodynamics route. However, there is no information on the relative ease of forming these intermediate phases during the rapid and meta-stable processing of severe deformation at high rates. During the course of ARB under severe shear stress, the induced transient atomic local structures appeared in Fig. 5-20 (c) might be any one of these candidates. But the transient atomic structures might be deformed and deviated from the equilibrium phase structures. Because all intermetallic compounds of Ni-Zr have very complicated crystal structures with unit cell space over 100 cubic angstroms, the complicated Ni-Zr intermetallics require a abundant amount of time to be created [63]. The observed local geometry of 1441, 1661 and 1321 should be associated with such intermediate phases.
By closer examinations of the simulated structures in HA analysis of Zr-Ni, most atoms
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classified as the 1441 pairs are the Ni atoms, implying that the local geometric structures of the 1441 pairs is one of BCC-like short range ordering (or deformed BCC). This BCC-like pairs seem to be the transient atomic arrangement for the FCC structure to transform into the final amorphous phase. It is not clear whether this local atomic pairing is originated from the local formation of the BCT Zr2Ni or the cubic ZrNi5. But it is evident that the transition of the FCC Ni crystals in the current Zr-Ni system will pass a transition stage forming local atomic pairs other than face centered cubic. The evolution of the local pairing structures appears to be rather complicated.
A similar observation of the above transient pairing has also been reported in the MD simulation for the rapid cooling process of Cu[32, 159], where the 1441 and 1661 pairs would have a sudden fluctuation during glass transition. Unlike the process of supercooling where the glass transition is continuous; the amorphization during the current ARB cycle is formed by the strain-induced atomic mixing mechanism during each rolling cycle that will result in a more discrete structure transition than that occurring during supercooling. It follows that the fluctuation phenomenon of the 1441 pair becomes more obvious. Also, the recent simulation work on the rapid quenched Zr-Cu-Al bulk metallic glasses by Fan et al.
[94] has also found the involvement of the BCC Zr-Cu structure.
It is noted that the simulated curves of Zr-Ni in their PRDF and coordinate average are basically stable after the 5th cycle. However, the extracted populations of the local HA pairs still show evident fluctuations in Fig. 5-20. This provides more detailed information on the local short-range order structure transitions which cannot be observed from the RDF, average potential energy, or coordination number.
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6-1-2 The transformation of Zr-Ti from nanocrystalline to amorphous phase during ARB
In the Zr-Ti system, all of analysis results indicate the vitrification is fairly quickly for Zr-Ti during ARB process. Although this tendency is consistent with the observation in experiment [37-39], the reality of their mechanism is still questionable. This refers to the nearly zero for their mixing heat between Zr and Ti and not large difference, only 8%, of atomic radius between tow species (rZr=0.160 nm and rTi=0.148 nm) compared with Zr-Ni system. Zr and Ti are both of the hexagonal close-packed (HCP) structure in addition. For the above characteristics, the Zr-Ti binary system can form an isomorphous phase diagram without any intermetallic compound, but not be considered possessing a high glass-forming ability according to the experimental rules in Chapter 2-1.
The Zr-Ti equilibrium phase diagram [181] is shown in Fig. 6-2. No obvious variation of potential energy in Zr50Ti50, because of the unique characteristic of the completely dissolubility between Zr and Ti atoms together with the near zero mixing enthalpy. It appears that the faster mixing of unlike atoms in Zr50Ti50 is not a result of the potential or mixing enthalpy, but is due to the same HCP structure and the compatible initial hardness for Zr and Ti. The (0002) basal planes of both Zr and Ti lying on the rolling plane could be effectively sheared through with each other, accelerating the thickness reduction and atomic mutual mixing under current high strain rate.
Based on evolution sequence of HA analysis, there is no intermediate atomic paring (like BCC-like pairing detected in Zr-Ni system) formed during the transformation from HCP to amorphous phase. This results suggests that even with the isomorphous Zr-Ti phase diagram nature, this binary system can still be vitrified through the solid state ARB processing at room
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temperature, consistent with the experimental findings as well[37-39]. The solid-state roll-bonding can offer another alternative for systems such as isomorphous Zr-Ti to form amorphous alloys, which can transform the HCP crystalline phase into complete amorphous state in a smooth sequence. During the course of atomic structure transformation, the initial fully ordered atomic close packing (100% of 1421 or 1422 pairings) can be destroyed to occupy only 20% of the overall atomic pairings. Concurrently, the much more random icosahedra and icosahedra-defect 1431, 1541 and 1551 pairs for the amorphous structure gradually become the dominant fraction of ~60%.
6-1-3 The transformation of pure Zr from nanocrystalline to amorphous phase during ARB
Since the Zr and Ti are highly similar elements with the same crystal structure, similar atomic size, hardness and melting point, and both locate on the same IVB column in the Periodical Table, they actually act as twins in many ways. Following the above scheme, it is interesting to ask whether the pure Zr (or Ti) element itself can be vitrified by itself during the same ARB route at room or cryogenic temperatures. There have been a few attempts [67]
to transform the crystalline pure element into the amorphous state, using torsion or ball milling, though the results are still controversial. In our experimental study, the trial using ARB experiments on the pure Zr multi-layers still could not achieve the amorphous phase as the X-ray results shown in Fig. 6-3. This was due to the fact that the applied rolling speed is too low and working temperature is still too high for the pure element to vitrify.
On the other hand, when we adopt the more rapid ARB rolling speed and liquid nitrogen to cool the rolled specimens, the ribbons become too brittle to be rolled repeatedly. The experimental difficulty prevents from the vitrification of pure Zr. However, using the same
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MD simulation method, but replacing the Zr and Ti bi-layer to two pure Zr layers and running the rolling at two rolling speed of 0.001 and 0.025 nm/fs, the result might be stimulating for future experiments.
The HA evolution sequence as a function of ARB cycles for the rolling speed of 0.025 nm/fs exhibits a simple trend, similar to but not exactly the same as the Zr-Ti case. It appears that the vitrification degree of the pure Zr is consistently inferior to Zr-Ti. For example, the ordered 1421 plus 1422 pairs of Zr-Ti can be easily dropped to a minority of 20% after 10 ARB cycles, but the 1421 plus 1422 pairs of pure Zr only decrease to 40% (i.e., still a sizable portion of the persistent HCP pairing). Also, the icosahedra and icosahedra-defect 1431, 1541 and 1551 pairs, with the amorphous-like nature, can occupy ~60% in Zr-Ti, but occupy only 45% in pure Zr.
From the HA index evolution, the pure Zr seems to have the possibility to be vitrified, provided that the ARB rolling speed is sufficiently high and the working temperature is remained to be around 300 K. Experimentally, this is difficult to achieve, since the working temperature tends to rise more with increasing rolling speed. An appropriate cooling technique is necessary. Meanwhile, due to the large gap of the time scale involved in the MD simulation and real experiment, there is always room for questioning the current results (note that the rolling speed in MD is in the range of 10-2 nm/fs and the experimental rolling speed is around 101 mm/s, or 10-8 nm/fs). Nevertheless, it is demonstrated by MD simulation that, under proper cooling and relative faster rolling speed, the crystalline pure Zr element could be able to transform into the amorphous phase. This is demonstrated by both the RDF curves and the HA index. Future experimental improvement is needed to justify the simulated results.
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Here must be noted that the strain rate between two rolling speeds, 0.001 nm/fs (8.35×108 s-1) and 0.025 nm/fs (9.25×109 s-1) is just about 1 order, but present the very distinct results. It could very close in a critical strain rate for the phase transformation between crystalline and amorphous phase. Supposing to ignore the thermal activation generated by severe shear stress during deformation, vitrification can be viewed as a result of competition of stability between long and short rang order, similar to the condition in rapid cooling. When the strain rate is lower, the created defects can be always rearranged and annihilated to maintain the stable-state for crystalline in long range order, just like behaviors shown in Figs. 5-5 to Figs. 5-7. In contrast, when a strain rate is provided high enough to restrict the rearranged period for crystalline phase, a metastable state in short range order is preferred to create for metal atoms within very short deformation period.
6-2 Vitrification transformation in Mg-Cu thin film
As the Mg-Cu equilibrium phase diagram, is presented in Fig. 6-4, implying a possibility of interface reactions of the Mg-Cu intermetallic phases formed in the Mg-Cu multilayer.
There are two intermetallic compounds can form in the Mg-Cu system. In the Cu-rich side, Cu2Mg is a quite stable phase existing in the Mg-Cu system because the radii of major Cu atoms (1.28 Α。), is smaller than surrounding Mg atoms (1.6 Α。), which results in a greater packing fraction to form a Laves phase. In the Mg-rich side, a complex competing crystalline phase, Mg2Cu, can exist in the Mg-Cu system, where the larger atoms is majority. Mg2Cu is an orthorhombic structure but is not as stable as Cu2Mg. For glass formation in the Mg-Cu system, the thermodynamic calculations and experiments [182, 183] indicated that the glass favor forming over the composition range of 12-22%Cu, including a lowest eutectic point at 14.5%Cu. Thus, it is expected that the amorphous phase or the Mg2Cu phase have the chance to form in the lower temperature conditions.
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However, it must be recognized that the amorphous structures have not been generated by MD simulation in this sandwich layers yet, even though higher temperature had been used to offer more kinetic energies for atoms. This may be caused by the employed NVT ensemble that constrained the space on the x and y plane, resulting in a lower degree of freedom for atoms to change their positions extensively in all directions. However, the Mg-Cu amorphous alloys are also difficult to produce by experiment in our laboratory [184]. A transmission electron microscopy (TEM) image of the Mg-Cu multilayer system produced by sputtering is given in Fig. 6-5. The bright zone is the Mg layer with a thickness of 150 nm, and dark zone is the Cu layer with a thickness of 50 nm. The Mg2Cu compound structure was found in this multilayer system when this specimen was annealed at 413 K, as shown in Fig. 6-5. The structural transformation of the specimen during annealing at 413 K is also shown in the X-ray diffraction pattern. The strong peaks at 19.5o and 39.6o imply that the Mg2Cu phase gradually forms along with a decrease of the Cu and Mg peaks.
In contrast, the MD simulations do not show the production of intermetallic compound, Mg2Cu phase, in the current model. This does not only correlate to the constraint of necessary space for phase transformation due to ensemble condition but also relate to the availability of MD method applied on study of nature of diffusion behaviors. It is well known that the diffusion mechanism is a strongly time-dependent behavior with atomic movement. When being in high temperature over melting, the thermal kinetic is high enough for animated the inter-diffusion behavior between two kind of different species. This behavior is presented in the simulation of Mg-Cu under a simple NPT ensemble at an artificial temperature of 2000 K (not shown in this dissertation), but not show in low temperature conditions. This means that studying diffusion behavior in MD method will need much longer time period. Hence, choosing the Monte Carlo method instead of MD might be suitable for this topic.
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6-3 Cyclic loading fatigue in Zr-Cu binary amorphous alloy
6-3-1 The crystallization in cyclic loading fatigue
Generally, the shear-band initiation and propagation during the severe deformation test would result in the structure transition within the amorphous alloys [185], so that some nanocrystallization might be induced along the shear bands. It is of concern whether there would also be any crystallization phenomenon occurred under the cyclic loading as seen in the uniaxial-monotonic loading because the fatigue crack is ordinarily easy to initiate from the sites of those nano-crystals in the BMG. The Zr-Cu equilibrium phase diagram in Fig. 6-6 refers a possibility of intermetallic phases formed in the Zr-Cu system[186]. For real ZrCu at a 50-50 composition according to this diagram, the B2 structure is the stable structure at higher temperatures; it transforms to a B33 structure at lower temperatures, but that will be rather similar to the B2 structure. Few B2 structures are identified in these cyclic loading simulations regardless of stress or severe strain-control mode but those can barely grow into the crystalline phase in progress, as seen Fig. 5-37.
In general, local heating of shear band is viewed as one of cause of crystallization in metallic glass; significant temperature rise in shear may offer enough thermal activation to drive the crystallization. But this viewpoint is not exactly available to our simulation results based on the applied isothermal condition which blocks the possibility of severe temperature change in the system. Hence, the appearance of local ordering phase is a result of another possibility that is strong shear flow enhances atomic mobility and induces the nanocrystalline phase forming in the shear band.
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On the other hand, the nucleation is a time-dependent behavior at different temperatures, e.g., the time lag for nucleation would increase with decreasing temperature at low temperatures. Therefore, if those local ordering structures in Zr-Cu metallic glass can not be in an enough long time, the crystallization is almost impossible to occur from them.
Apparently, in spite of strong shear flow applied from cyclic loading in different conditions (including loading amplitude, period, and strain rate), the circumstance for nucleation is also altered in each progress, and resulting in only repeated appearance and disappearance of those ordering structures.
6-3-2 The structural relaxation in cyclic loading fatigue
Instead of no phase transformation in Zr50Cu50 metallic glass during cyclic loading in this work, the structural behaviors observed from HA pair index during cyclic loading are always in a periodical fluctuation that indicates the domination of structure properties in its cyclic loading fatigue is straightforward structural relaxation. Another evidence is the observation of potential energy variation, which always shows a decrease tendency with increasing loading cycles. Structural relaxation plays an important role that would lead the metallic glass to transfer to lower energy states in the potential energy landscape through the atomic motion when annealing at a high enough temperature, but insufficient for crystallization. The simulation results of HA analysis and potential energy variation apparently prove the structural relaxation can be driven by mechanical method, which can provide enough atomic kinetics to leap over the energy barrier for next metastable equilibrium.
It is difficult to understand the details of structural relaxation through the current HA pair method which only shows the statistics of fraction of simple geometry in short range
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order. But properties of both potential energy and density can reveal some information about the factors of structural relaxation in cyclic loading fatigue. Based on the potential energy results of cyclic loading, it suggests there exists an ideal glass state for a special chemical component, and this ideal glass state could be directly related to its cooling rate. The true phase of the ideal glass state is unclear so far, but can be approached through the repeated structural relaxation by annealing at higher temperatures or mechanical cyclic loading. In the stress-control, it suggests the route to the saturated state (semi-ideal glass state) for structural relaxation is basically in agreement. But increasing loading amplitude helps to shorten the approach time, and extending loading period reduces the cycles for structural relaxation to reach its saturated state.
Furthermore, the tension mode can cause larger dilatation fluctuation than compression one; the Zr50Cu50 metallic glass shows a better resistance for structural relaxation under compression than tension. However, if the applied cyclic strain is large enough to go into plastic range (e.g. εmax = 10%), the saturated state will be higher than that of applied strain within elastic range. There exists two ways in the cyclic loading fatigue. One is to raise its internal energy state within the glass matrix, leading to accumulation of damage to failure finally. Apparently, adding a severe applied strain into plastic range will drive to this tendency, as demonstrated in Fig. 5-42. The other way is to lead the cycled MG to a lower energy state.
The current results show that structural relaxation can induce recovery in the energy state.
6-3-3 Microscopic deformation in cyclic loading
The results of local atomic strain show a homogeneous deformation in the monotonic and cyclic loading. In the monotonic loading cases, the domination of macroscopic strain attributes to the accumulation of irreversible atomic rearrangement. A number of STZ group
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does not rapidly evolve until exceeding overshoot of stress at the applied strain, εmax = 5%. In the cyclic loading case, not only irreversible local shear evens which still dominate the accumulation of local strain but also reversible local elastic deformation affect the development of deformation behaviors in metallic glass.
Generally, the homogenous shear flow in metallic glass typically occurs within supercooled liquid region at high temperatures near the Tg point and provide a well plastic deformation properties. In experiments, most of the metallic glasses show the inhomogeneous deformation with the shear banding mechanism due to the shear localization at high stress concentrations and lower temperatures. In the results of this simulation, the STZs can initiate stochastically and organize to a network-like development in the glass matrix either in monotonic or cyclic loaing in time and space but do not localize. Localization in metallic glass is believed relative to local increase in free volume (positive dilatation), evolution of structure order, stress redistribution, or local heat generation [112]. In the density variation of monotonic loading, the increase of dilatation providing sufficient space for occurrence of a number of plastic flows is indeed observed before going into the plastic region, and plastic shear flows also increase rapidly and lastly in the plastic region. Hence, the difficulty in generation of shear band or localization may be a result of the space limitation in the current model size. It restricts the essential volume for developing a mature shear band, but can exist in a number of STZs groups (embryo shear bands) instead. On the other hand, the small model size will make the redistribution of internal stress or free volumes more easily and quickly in space and add difficulty in shear localization or stress concentration.
In the cyclic loading, the homogeneous deformation in metallic glass is associated with irreversible and reversible atomic rearrangement which are co-exist but account for different percentage in glass matrix during cyclic loading process. When suffering severe deformation
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initially, the irreversible local strains will take most percentage in the glass matrix to release the strain energy and gradually take place of the reversible local deformation. Here extends another issue about the anelastic which is a time dependent elastic behavior in metallic glass but not be well studied in the current works yet. Hence the accumulation of local strain tends to be slow once a balance between two kinds of local atomic strains is achieved in the progress of cyclic loading. Combining with observations in potential energy and density state, it suggests that the behaviors of atomic strains are strongly associated with structural relaxation of metallic glass. The accumulation of local plastic deformation does not go toward failure with increasing energy state and free volumes in metallic glass but, instead, to a steady-state with a lower energy state like the deformation behaviors in homogenous plastic flow.
6-3-4 The phenomenon of dynamic recovery
It is noted that the stress cycles would differ for the elastic and plastic regimes.
Therefore, we have conducted simulations for the strain control mode to three different maximum strain levels, namely, 2.5%, 4% and 10% strain. Figures 5-53 (a), (b) and (c) are the stress-strain curves for 2.5%, 4% (nearly elastic regime) and 10% strain (highly plastic regime). The curve in Fig. 5-53 (a) is basically within the elastic range and is similar to the stress control results, exhibiting a nearly linear relation to applied stress. It also means the energy input from the applied stress is fully loaded and unloaded in each cycle. Contrarily, the stress-strain curve in Fig. 5-53 (c) shows a mechanical hysteresis; the cyclic deformation curve can be divided into four parts: tensile loading, tensile unloading, compressive loading, and compressive unloading. The energy loss during loading and unloading suggests that there have some activities occurred, such as long-range atomic movement or dynamic relaxation/recovery in the Zr-Cu amorphous alloy.