- Email: [email protected]
Direct imaging of a first-order liquid-liquid phase transition in undercooled molten PdNiP alloys and its thermodynamic implications
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Direct imaging of a first-order liquid-liquid phase transition in undercooled molten PdeNieP alloys and its thermodynamic implications Y.F. Lo, X.C. Wang, Z.D. Wu, W.Z. Zhou, H.W. Kui⁎ Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, People's Republic of China
A R T I C L E I N F O
A B S T R A C T
Keywords: Bulk metallic glass (BMG) PdeNieP Short-range orders Nucleation and growth and latent heat First-order liquid-liquid phase transition Structure of liquids
Polyamorphic transition is the transition between two amorphous states or two liquid states (LLT) at a fixed composition of a substance. Experience in LLT is limited. Besides, its nature remains largely unknown as it occurs under the experimental conditions of high pressure/temperature (P/T) or high undercooling. In this study, we found that some undercooled PdeNieP melts undergo a LLT. Contrary to all earlier studies, PdeNieP specimens that contain the structural changes that occur at different stages of the LLT can be prepared for electron microscopy. HRTEM (high resolution transmission electron microscope) establishes that it is a first-order phase transition. From thermodynamics, a first-order phase change is accompanied by a latent heat. Here it was measured by a DSC (differential scanning calorimeter). A first-order LLT has important thermodynamic implications. First, it reconfirms that a liquid has different kinds of short-range-orders (SROs). Second, the firstorder LLT implies that the SROs of a liquid are divided into distinct groups, each containing either a SRO or a number of different SROs, but not all. Physically, each group represents a real liquid. Third, the SRO(s) in a group can be assigned an independent Gibbs free energy, GSRO(P, T, c = composition) and the thermodynamics of the liquids can be described in terms of these GSRO.
1. Introduction Polymorphism refers to the first-order phase transition between two crystalline phases at a fixed composition of a substance. The best example is perhaps found in pure iron where it changes from face-centered-cubic to body-centered-cubic forms at 1183 K and 1 atmospheric pressure. Polyamorphism refers to the transition between two amorphous/liquid phases at a fixed composition of a substance. The first glassy-state polyamorphic transition was observed in ice under high P and low T [1]. The transition is sharp and the authors suggested that it is a first-order phase transition. The first liquid-state polyamorphic transition or liquid-liquid phase transition (LLT), was observed in meltquenched Y2O3-Al2O3 glasses [2]. An as-prepared glassy specimen always consists of both low- and high-density polyamorphs, mixing up with each other. They are separated from each other by sharp boundaries, indicating that a nucleation and growth mechanism has taken place. However, this observation is not a rigorous proof for a first-order phase transition (explained below). As of today, in experiments, the harsh conditions, including, (i) high T (and often high P); and/or (ii) deep in the undercooling regime where crystallization is prone to occur, continue. As a result, preparation of specimens that contain structural changes that occur at different stages of a polyamorphic transition has
⁎
not been possible for detailed electron microscopic analysis. Despite these difficulties, both experimental [3–10] and theoretical studies [11–16] confirm that polyamorphic transitions take place in systems with different kinds of bonding. There is a conceptual difficulty in accepting a first-order LLT. At present a liquid/glass is considered to consist of different kinds of SROs [17–35], coming from its constituent clusters [33–36]. The relative amount of these SROs changes continuously with T and P, but in dynamic equilibrium with each other when T and P are fixed. Since the structural change occurring in a first-order phase transition is abrupt, a first-order LLT is therefore inconsistent with the current view of the structure of liquids. If a LLT is a first-order phase transition, it can be represented by,
′ L → L + L′ (L′ from nucleation and growth) → L,
(1)
where L and L′ have the same composition. Eq. (1) can be interpreted as follows. The LLT takes place at a temperature below the transition temperature (for observable rate). In the first reaction (first arrow), nucleation and growth of L′ occurs in L. In the second reaction (second arrow), all L is transformed into L′. In a rigorous experimental proof of a first-order LLT, direct evidence must be obtained to settle an important issue, which is: L′ is the only phase that appears in L, which eventually
Corresponding author. E-mail address: [email protected] (H.W. Kui).
http://dx.doi.org/10.1016/j.jnoncrysol.2017.07.020 Received 28 April 2017; Received in revised form 8 June 2017; Accepted 25 July 2017 0022-3093/ © 2017 Published by Elsevier B.V.
Please cite this article as: Lo, Y.F., Journal of Non-Crystalline Solids (2017), http://dx.doi.org/10.1016/j.jnoncrysol.2017.07.020
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
of negative heat of mixing. As a result, LSD soon became a controversial issue in glass science [39]. Recently, it was demonstrated by HRTEM and SAXS that LSD occurs in some PdeNieP bulk metallic glasses (BMGs) [39,40], i.e., the decomposition can be described by Eq. (3). Now in Eq. (3), there are two different phases, ℓ1 and ℓ2. The next question is: What is the nature of the two different phases, ℓ1 and ℓ2, in a spinodally phase-separated PdeNieP BMG? Wu et al. [41] were able to provide partial answer to this question. By means of HRTEM, EDX (energy dispersive X-ray) and X-ray diffraction, the authors were able to differentiate ℓ1 and ℓ2 in two respects. First, ℓ1 and ℓ2 have different compositions. Second, they have different SROs. The difference in SROs is confirmed through their structure factors obtained from X-ray studies. In one of them, say ℓ1, it contains a right shoulder in the second peak. According to earlier experience [27,42–46], this liquid is taken to have an icosahedral SRO symmetry. For clarity, it is denoted by i-SRO below. It must be noted that i-SRO is a symbol for the structure factor of ℓ1, which may contain more than one type of clusters [47,48]. The structure factor of the other liquid, ℓ2, denoted by ℓ-SRO, either has a left shoulder or has both a right shoulder and a left shoulder in the second peak. The symmetry of this second SRO is not known. From the theory of spinodal decomposition, the i-SRO and ℓ-SRO together form a metastable liquid miscibility gap (MLMG) in the undercooling regime of molten PdeNieP. The MLMG was more recently determined by Zhou et al. [49]. The transformations of PdeNieP melts inside the MLMG were earlier explored by Wu et al. [39–41,49–52]. In this work, transformations of PdeNieP melts outside, but in the vicinity of the MLMG were studied. Indeed, we found a first-order LLT there, which is reported in this article. The existence of both the firstorder LLT and LSD will shed new light on the thermodynamics of liquids.
consumes all L. All previous studies have failed to achieve this. In a first-order phase transition, the first partial derivatives of the molar Gibbs free energy of a substance, G, namely, −(∂G/∂T)P = S (molar entropy), and (∂ G/∂P)T = V (molar volume), are discontinuous. To determine whether a transition is of first-order or higher-order, one approach is to measure if there is any abrupt change in V at/below the transition temperature. Another approach is related to S. As discussed in the last paragraph, a rigorous proof of a first-order phase change involves: (i) the emergence and subsequent growth of L′ in L (by nucleation and growth mechanism); and (ii) the complete consumption of L by L′ only. Since L and L′ are different phases, they have different entropies or equivalently there is an abrupt change in −(∂G/∂ T)P = S as L′ appears in L. These two conditions can be realized experimentally if TEM specimens that contain the structural changes occurring at different stages of a LLT can be prepared. In this work, this entropic approach was chosen for the establishment of a first-order LLT. From thermodynamics, a first-order phase change is accompanied by a latent heat (enthalpy change). In this work, the molar latent heat of the first-order LLT was measured by DSC. A liquid can also decompose into two liquids of different compositions, called phase-separation. There are two different decomposition mechanisms, which are liquid nucleation and growth (LNG), and liquid spinodal decomposition (LSD). On a phase diagram, the phase field that includes both LNG and LSD is called a liquid miscibility gap. Both LNG and LSD are discussed individually below. A LNG can be represented by,
ℓ → ℓ′ + ℓ2 (ℓ2 from nucleation and growth) → ℓ1 + ℓ2 ,
(2)
in which the parent matrix is formed by phase ℓ. The first reaction is the nucleation and growth of phase ℓ2 in ℓ. As the domains of ℓ2 grow, their composition remains constant while that of the matrix is changing. For clarity, it is denoted by ℓ′. A downhill diffusion field is set up right in front of the ℓ′/ℓ2 interfaces. In the second reaction, after the completion of the decomposition, the newly formed phase still has a composition of ℓ2. It co-exists with the parent matrix which now has a composition of ℓ1. ℓ1 and ℓ2 are two different phases. A liquid spinodal decomposition, LSD, can be represented by,
ℓ → composition modulation → ℓ1 + ℓ2 .
2. Materials and experimental PdeNieP ingots were prepared by one of the following two methods, depending on the composition. In the first method, Pd and Ni granules, and Ni2P powders, all of purity better than 99.9%, were used. The Ni2P powders were first sintered into a pellet. Then the right proportion of Pd and Ni granules and the Ni2P pellet were put into a clean fused silica tube and alloying was by rf (radio frequency) induction heating under Ar atmosphere. In the second method, Pd, Ni2P, and P powders, all of purity better than 99.9%, were used. First, the right proportion of the different kinds of powders was sintered into a pellet [53]. Then an as-formed pellet was put into a clean fused silica tube and melted by induction heating under Ar atmosphere. In both methods, a typical ingot formed had a eutectic microstructure, with a diameter of ~4 mm (or a mass of ~0.3 g). A fluxing technique [39–41,49–52] has been found to be effective in transforming molten PdeNieP alloys into BMGs. In the experiment, a PdeNieP ingot and some B2O3 (called the fluxing agent) of mass ~1.3 g, were put into a clean fused silica tube of inner diameter 11 mm and outer diameter 13 mm as shown in Fig. 1a. The system was first evacuated by a mechanical pump to ~10− 2 Torr. Then it was heated up to ~ 1300 K (above its liquidus, Tl) by a torch. The high temperature heat-treatment was applied for a time period of ~4 h before it was cooled down again by some chosen kinetic paths. Six different cooling paths were arranged for the system, which are: (A) first quenched in a tin bath of constant temperature Ta (Ta = 593, 598 or 613 K) for an intermediate isothermal annealing, with a time period of τ (≤ 20 min). After the isothermal annealing, the system was water-quenched to room temperature. This is the process [39–41] earlier used to demonstrate the existence of amorphous spinodal decomposition in PdeNieP BMGs, in which the annealing temperature was 613 K and τ ~ 20 min; (B) air-cooled to room temperature [54]; (C) first quenched in a tin bath of Ta = 503 K for 1.5 min and then waterquenched to room temperature; (D) water-quenched to room
(3)
Initially, there is a homogeneous liquid of composition ℓ. In the early stage of the spinodal decomposition, composition modulation is slowly built up in ℓ. In the absence of stress such as in a liquid, the composition modulation is isotropic and random. As time increases, the composition modulation sharpens. Meanwhile some characteristic wavelength dominates the spinodal morphology. When the spinodal decomposition completes, the spinodal morphology is described as the intertwining of an ℓ1 liquid subnetwork and an ℓ2 subnetwork. It is noted that ℓ1 and ℓ2 are different phases. Phase separation of a liquid into two liquids of different compositions is a common phenomenon in materials science. It must, however, be pointed out that spinodal decomposition is commonly observed in systems only with a positive heat of mixing. This is consistent with Cahn's theory of spinodal decomposition. Chen and Turnbull [37], by TEM methods, were the first to observe amorphous/liquid phase separation (LPS) in a metallic glass (Pd-Si glassy ribbons). Later, Chou and Turnbull [38] demonstrated that the LPS is consistent with a LSD by using small angle X-ray scattering (SAXS). The observed LSD is unexpected because Pd-Si has a negative heat of mixing. It is against Cahn's prediction. To get around the problem, Chen and Turnbull [37] proposed that there exists a SRO in undercooled molten Pd-Si, which generates a local hump in the Gibbs free energy blade, G(T, P, C = composition), allowing the formation of two locally stable liquid phases, ℓ1 and ℓ2. It is noted that ℓ1 and ℓ2 are two different phases. After these two reports, direct evidence of LSD could not be found in the next four decades, both in Pd-Si (Chen and Turnbull's result could not be repeated elsewhere) and in other glass formers 2
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 1. (a) Schematic diagram showing the experimental set-up of a fluxing experiment; (b) schematic diagram showing the experimental set-up of a molten PdeNieP specimen in a thin-wall fused silica tube quenched in water; (c) schematic diagram showing the experimental set-up to measure, T vs. t, in paths (B), (C), and (D); (d) Results of, T vs. t, for paths (B) to (E).
spinning is estimated to be on the order of 106 K s− 1 [56–57]. For clarity, Table 1 summarizes what the different cooling paths are about and the respective cooling rates achieved by them. An as-prepared specimen was characterized by X-ray diffraction. The scanning rate of the diffractometer was chosen to be 0.25 degree/ min and the step of the measurement was 0.1 degree. The X-ray source was Cu Kα line, which has a wavelength of 1.54 Å. The microstructure was studied by HRTEM and EDX line mapping. The enthalpy change or latent heat between i-SRO and ℓ-SRO was measured by DSC.
temperature; (E) A clean fused silica tube, which was tapered to a sealed end as shown in Fig. 1b, was first prepared. The thickness of the wall of the tapering part of the tube was less than 200 μm. In the experiment, a fluxed PdeNieP ingot was put into the fused silica tube and the system was evacuated by a mechanical pump to ~ 10− 2 Torr. It was then heated up until the metal ingot inside was completely melted. Ar gas was next introduced from the top, pushing the alloy melt into the tapering fused silica tube. Finally the system was inserted into water for rapid quenching [55]; and (F) wheel spinning [56–57]. It is of interest to measure, at least semi-quantitatively, the quenching rates achieved in paths (B), (C), (D), and (E). The experimental arrangement for this purpose for paths (B), (C), and (D) is shown in Fig. 1c. In a fluxing experiment, a thermocouple sheathed in another fused silica tube of smaller diameter was added. In a cooling cycle, the thermocouple served to record, T vs. t (time). For path (E), in a controlled experiment, the tapering part of a fused silica tube (Fig. 1b) was filled with B2O3 instead of a molten alloy. A thermocouple was inserted directly into the molten flux to measure: T vs. t. The experimental results for the various cooling paths are shown in Fig. 1d. The cooling rates for paths (B), (C), (D) and (E) were found to be 3.5, 7.4, 18.9, and 1000 K s− 1, respectively. It must be emphasized that these cooling rates are only qualitatively correct. The cooling rate achieved in wheel
3. Results Before moving on to discuss the experimental results obtained in this work, some basic results obtained in Ref. [41] are reproduced here for comparison and reference purpose. The HAADF, EDX line mapping and HRTEM images of a Pd42Ni40P18 BMG (composition inside the MLMG) that has undergone LSD are shown in Fig. 2. Because Eq. (3) is obeyed, the as-formed specimen is called a spinodal BMG. The HAADF image shown in Fig. 2a shows that there is mass/thickness contrast, indicating that the spinodal BMG is not of uniform composition. Fig. 2b is the EDX line mapping taken along the dashed line shown in Fig. 2a. It displays composition variation along the dashed line, consistent with
Table 1 Different cooling paths used to prepare various PdeNieP specimens. Description of the cooling paths
Measured average dT/dt
Path A: Initially the system was at a temperature above Tl. It was quenched in a tin bath of Ta (593, 598 or 613 K) and then thermally annealed at Ta for a time period τ ≤ 20 min. Finally it was water-quenched to room temperature. Path B: The system was directly air-cooled from above Tl to room temperature. Path C: Initially the system was at a temperature above Tl. It was quenched in a tin bath of Ta = 503 K and then thermally annealed at Ta with τ = 1.5 min. Finally it was water-quenched to room temperature. Path D: The system was directly water-quenched from above Tl to room temperature. Path E: Molten PdeNieP enclosed in a thin-wall fused silica tube at T > Tl was water-quenched to room temperature. Path F: Thin foils were prepared by wheel spinning method.
Not applicable
3
− 3.5 K s− 1 Not applicable − 19 K s− 1 − 103 K s− 1 − 106 K s− 1
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 2. Microstructure of a Pd42Ni40P18 specimen that has undergone LSD. (a) HAADF shows that its composition is non-uniform; (b) EDX line mapping along the dashed line shown in (a), again showing that the composition varies; (c) HRTEM image taken from the white areas in (a), showing that they are amorphous; and (d) HRTEM image taken from the black areas in (a) showing that they are amorphous.
variation in them (see ref. [41]). It can therefore be concluded that the lever rule can qualitatively predict the height of the left shoulder in the second peak of their structure factors. The MLMG in undercooled molten PdeNieP is basically a right angle prism [49]. Fig. 4 shows the actual data obtained by the authors, on a cross-section of the MLMG at ~ 800 K. The open circles represent compositions that undergo LSD while the closed circles are those that reject LSD or they are outside the MLMG. In this work, three alloy compositions rejecting LSD were chosen for study, which are: Pd40Ni40P20 (on the boundary of the MLMG; Tg = 585 K and Tℓ = 923 K), Pd59Ni25P16 (outside the MLMG; Tg = 590 K and Tℓ = 971 K), and Pd40Ni45P15 (outside the MLMG; Tg = 580 K and Tℓ = 1073 K). For clarity, they are represented by inverted open triangles.
the HAADF result. Fig. 2c is a HRTEM image taken from the brighter areas in Fig. 2a, showing that it is amorphous. Fig. 2d is a HRTEM image taken from the darker areas in Fig. 2a, showing that it is also amorphous. Fig. 3a shows the MLMG of the alloy system, PdeNieP. For liquids with compositions along the top horizontal line, they only have i-SRO. The vertex of the MLMG (with the symbol “X”) has a composition of ~ Pd50Ni36P14. A liquid with this composition only has ℓ-SRO. Inside the MLMG, spinodal BMGs of compositions marked by closed squares, hexagons, and triangles are studied by X-ray diffraction method. According to ref. [41], a left shoulder in the second peak of the structure factor of a PdeNieP spinodal BMG is attributed to ℓ-SRO (in the Introduction section, in Eq. (3), ℓ2 is chosen as ℓ-SRO and ℓ1 is chosen to be i-SRO). By applying the lever rule to Fig. 3a, spinodal Pd80 − xNixP19 BMGs (all closed squares in Fig. 3a) have the least amount of ℓ-SRO; an intermediate amount of ℓ-SRO in spinodal Pd82 − xNixP18 BMGs (all closed hexagons in Fig. 3a); and the most amount of ℓ-SRO in spinodal Pd82.5 − xNixP17.5 BMGs (all closed triangles in Fig. 3a). Fig. 3b, taken from Ref. [41], shows the structure factors of these spinodal BMGs. The structure factors of spinodal Pd80 − xNixP19 BMGs exhibit a tiny left shoulder (Fig. 3b(i)). Despite the fact that the left shoulder is small, previous experience shows that HAADF can easily detect the composition variation in them (see, for example, Fig. 5 in ref. [50]). The structure factors of spinodal Pd82 − xNixP18 BMGs have a clear left shoulder and HAADF can detect the composition variation in them (see ref. [41]). The structure factor of spinodal Pd82.5 − xNixP17.5 BMGs have a prominent left shoulder and HAADF can detect the composition
3.1. Pd40Ni40P20 HRTEM shows that Pd40Ni40P20 specimens prepared by paths (A), (B), (C), (D), (E) and (F) are amorphous - bulk metallic glasses (BMGs) in paths (A) to (E) and glassy ribbons in path (F). HAADF images (Fig. 5a) are all homogeneous, indicating that the compositions of the glassy specimens are uniform. EDX line mapping displays random signal, further confirming that they are homogeneous (experimental results not shown). The structure factor obtained by X-ray diffraction studies contains a right shoulder in the second peak (Fig. 5b). This characteristic structure factor is often taken to be an indication that the glassy specimens have an icosahedral symmetry as mentioned earlier 4
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 3. (a) Spinodal PdeNieP BMGs of compositions marked by geometric symbols are prepared. (b) Structure factors of (i) spinodal Pd80 − xNixP19 BMGs; (ii) spinodal Pd82 − xNixP18 BMGs; and (iii) spinodal Pd82.5 − xNixP17.5 BMGs, are shown.
a BMG. HAADF image does not display any mass/thickness contrast, suggesting that it is of uniform composition. EDX line mapping also confirms that it is a homogeneous BMG. In X-ray analysis, the second peak of the structure factor consists of a right shoulder, showing that the BMG has i-SRO. Structurally, it is similar to that of a Pd40Ni40P20 BMG discussed above. The result is shown in Table 2.
[27,42–46]. A left shoulder is nowhere to be seen. The results obtained here are the same as those described in ref. [41]. For clarity, the SRO of the glassy specimens is denoted by i-SRO. Table 2 lists the experimental results of Pd40Ni40P20.
3.2. Pd59Ni25P16 3.2.1. Path (A); Ta = 593 K and τ = 1 min HRTEM shows that a melt of this composition can be quenched into
3.2.2. Path (A); Ta = 593 K and τ = 5 min HRTEM shows that an as-prepared specimen is a BMG (Fig. 6a). Fig. 4. A cross-section of the MLMG in PdeNieP. The open circles represent compositions which undergo LSD while closed circles are those that reject LSD. PdeNieP alloys studied in this work are represented by inverted open triangles. The exact compositions are: Pd40Ni40P20, Pd59Ni25P16 and Pd40Ni45P15.
5
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
[50], the BMG must contain ℓ-SRO. The question is: Why could not the HAADF and EDX line mapping methods detect the presence of ℓ-SRO in the BMG, just like that in a Pd40.5Ni40.5P19 spinodal BMG, which is displayed in Fig. 5 in ref. [50]? It may be argued that perhaps the volume fraction of ℓ-SRO present in the BMG is just too little to be detected by HAADF and EDX. In the next effort, the volume fraction of ℓSRO was increased. For clarity, the result obtained in this part of the experiment is listed in Table 2. 3.2.3. Path (A); Ta = 593 K and τ = 10 min HRTEM (Fig. 7a) shows that a Pd59Ni25P16 melt can be transformed into a BMG. HAADF (Fig. 7b) shows that there is no mass/thickness contrast or equivalently the BMG is of uniform composition. EDX line mapping was employed to measure any composition variation in the BMG. The measurement was made along the red line shown in Fig. 7b. The result is shown in Fig. 7c, where only random signal is exhibited, showing that the BMG is of uniform composition, in good agreement with the HAADF result. The structure factor determined from X-ray diffraction of the BMG is shown in Fig. 7d. It displays a strong right shoulder and also a strong left shoulder in the second peak. The strong left shoulder predicts the presence of a substantial volume fraction of ℓ-SRO in the BMG. If the BMG had undergone a phase-separation reaction (Eqs. (2) and (3)), HAADF and EDX line mapping must have been able to detect a composition variation (Fig. 2). Therefore, it can be concluded that the appearance of the ℓ-SRO has nothing to do with a phase-separation mechanism or Eqs. (2) and (3) can be ruled out. Furthermore, since there is no composition change when i-SRO transforms into ℓ-SRO, it can be concluded that the transformation observed here is a LLT. The result is summarized in Table 2. 3.2.3.1. Is the LLT a first-order or higher-order phase transition?. The two conditions for a transformation to be of first-order as explained in Eq. (1) are: (i) the emergence of ℓ-SRO in i-SRO; and (ii) subsequently all iSRO is consumed by ℓ-SRO only. HRTEM was used to find the phase distribution of i-SRO and ℓ-SRO in Pd59Ni25P16 specimens of Ta = 593 K and τ in the range of 1 ≤ τ ≤ 300 min. In the experiment, an electron diffraction pattern was taken at a certain site. A software, named, “DigitalMicrograph”, was then used to acquire a 1dimenional linear intensity from the 2-dimensional electron diffraction pattern. The 1-dimensional linear intensity was then used to determine the structure factor at that site. After thorough studies, only two different structure factors were found, which are shown in Figs. 8a(i) and (ii). The former is characterized to have a right shoulder in the second peak while the latter has both a right shoulder and a left shoulder. The one in Fig. 8a(i) is taken to be due to i-SRO. Earlier Wu et al. [41] found that the structure factor of ℓ-SRO contains either a left shoulder or both a left shoulder and a right shoulder. As a result, the structure shown in Fig. 8a(ii) cannot be attributed to ℓ-SRO alone at this point. The experimentally measured phase distributions of i-SRO and ℓSRO from HRTEM studies in Pd59Ni25P16 specimens are given below. In the TEM bright field images shown in Figs. 8b through f, when electron diffraction reveals a certain site (radius of the electron beam ≈ 100 nm) having i-SRO, it is painted red; otherwise, it is painted green. Fig. 8b displays the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 1 min. In all those thin areas suitable for TEM studies, they are all red. Fig. 8c depicts that of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 3 min. It shows the emergence of a tiny green area in a red matrix. Fig. 8d(i) shows the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 5 min. The green areas have increased substantially when compared with those shown in Fig. 8b and c. It was also found that the electron diffraction technique can be used to mark the boundary between a green area and a red area. An example is shown in Fig. 8d(ii), marked by a dashed line. When an electron beam is entirely on the left of the boundary, only structure
Fig. 5. (a) HAADF image of a Pd40Ni40P20 BMG, showing that there is no mass/thickness contrast or the specimen is of uniform composition; and (b) the structure factor of the Pd40Ni40P20 BMG, showing that there is a right shoulder in its second peak. A left shoulder is nowhere to be seen.
HAADF shows that mass/thickness contrast is absent (Fig. 6b), i.e., the BMG is of uniform composition. Fig. 6c shows the result of EDX line mapping measured along the red line marked in Fig. 6b. The random signal again indicates that the BMG is of homogeneous composition. HRTEM, HAADF and EDX line mapping suggest that the BMG is homogeneous. The BMG was studied by X-ray diffraction method and the measured structure factor is shown in Fig. 6d. In the second peak, besides a strong right shoulder, a left shoulder begins to emerge (It is small and an arrow is used to mark its position.). According to Fig. 3b(i) and Fig. 5 in ref. 6
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Pd50Ni25P16. The last section describes a novel first-order LLT. Since a first-order phase transition is accompanied by an abrupt change in enthalpy (or latent heat), a DSC was used to measure it. In the experiment, before the actual thermal runs, the DSC was made to go through test runs with aluminum specimens (mass about 50 g). After an aluminum specimen was inserted into the sample holder of the DSC, the system was allowed to sit at 323 K for 1 min. Then it was heated up, at a heating rate of 40 K/min, to 593 K for prolonged thermal annealing, for a time period of 22.5 min. After the thermal annealing, the system was cooled down again to room temperature. This cycle was repeated 4 more times and the results are shown in Fig. 7a. Analysis shows that the fluctuation in the DSC runs is less than 0.3 mW. The same cycle was then applied to amorphous Pd59Ni25P16 specimens (mass about 50 g) that were initially completely occupied by iSRO. The isothermal annealing time was longer, about 300 min so as to make sure that all i-SRO had changed to ℓ-SRO (see Fig. 8f). The first thermal scan of one of these PdeNieP specimens (mass = 53 g) is shown as black line in Fig. 9b. After the 300 min isothermal annealing, the system was cooled down to room temperature. A second cycle was next applied to the same specimen and the second thermal scan is shown as red line in Fig. 9b. After the DSC experiment, the sample was removed for microstructural studies. Extensive HRTEM study showed that it was free of any crystallinity. Fig. 9c shows a TEM real image of the specimen, indicating that it is a homogeneous specimen. Fig. 9d is an electron diffraction pattern of the specimen, where only halos are found. The 2-dimensional electron diffraction is then converted into a 1-dimensional one to determine the structure factor. The as-determined structure factor (not shown here) is identical to the one shown in Fig. 8a (ii) or equivalently, the specimen is completely occupied by ℓ-SRO. The difference between the black and red lines in Fig. 9b is substantially larger than 0.3 mW, which is the resolution of the instrument. It therefore confirms that the transformation, i-SRO → ℓ-SRO, is an exothermic one and the enthalpy change (as calculated from the area between the blue and red line and calibrated) is 3690 J/mol. This is a lower bound for the actual enthalpy change as there was heat release when the specimen was heat from 323 to 593 K for isothermal annealing. The DSC studies therefore again confirm that the transformation, i-SRO → ℓ-SRO, is a first-order phase transition.
Table 2 Cooling paths (A) to (F) and the corresponding SROs observed in PdeNieP specimens of different compositions. Path
Pd40Ni40P20
Pd59Ni25P16
Pd40Ni45P15
A
Ta = 598 K; τ = 15 min; iSRO
Crystalline
B C
i-SRO i-SRO
Ta = 593 K; (a) τ = 1 min: i-SRO only; (b) τ = 5 min: i-SRO and ℓ-SRO; (c) τ = 10 min: i-SRO and ℓ-SRO, but no composition change. Therefore, it is an LLT (details in Section 3.2.3). (d) τ = 300 min: ℓ-SRO only; establishes that it is a first-order LLT (details in Section 3.2.3.1.). Crystalline i-SRO
D
i-SRO
i-SRO
E F
i-SRO i-SRO
i-SRO i-SRO
Crystalline i-SRO and ℓ-SRO (first-order LLT) i-SRO and ℓ-SRO (first-order LLT) i-SRO i-SRO
factor of the kind in Fig. 8a(i) are found. On the other hand, when an electron beam is completely on the right of the boundary, only structure factor of the kind shown in Fig. 8a(ii) are found. Fig. 8e shows the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 10 min. Now the green area exceeds the red area. Again, boundaries of the kind shown in Fig. 8d(ii) exist (not shown here). Fig. 8f shows the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 300 min. It is all green, implying that the transition from red to green has completed. Three conclusions can be drawn from the phase distribution determination. First, the BMG shown in Fig. 8f is completely occupied by ℓ-SRO. The structure factor for this BMG is the same as the one shown in Fig. 8a(ii). It can therefore be concluded that the structure factor of a liquid with ℓ-SRO contains both a right shoulder and a left shoulder in the second peak. Second, Fig. 8b through f establish that the LLT, iSRO → ℓ-SRO, is a first-order phase transition because: (i) it is a nucleation and growth mechanism; and (ii) the amorphous specimen shown in Fig. 8f is completely occupied by ℓ-SRO and in the process, only ℓ-SRO is found to consume i-SRO. Third, since a first-order phase transition is an abrupt change, i-SRO and ℓ-SRO must be distinct from each other. Equivalently, all of the short-range orders available to molten PdeNieP are divided into distinct groups and each group represents a physical liquid. According to thermodynamics, each group (containing SROs that belong to this group) can be assigned an independent Gibbs free energy, for example, Gi-SRO and Gℓ-SRO.
3.2.4. Other paths Pd59Ni25P16 specimens prepared by path (B) are crystalline. Specimens prepared by paths (C), (D), (E), and (F) are all amorphous with i-SRO. The results are summarized in Table 2. 3.3. Pd40Ni45P15
3.2.3.2. Latent heat measurement of the first-order LLT occurring in
With reference to Fig. 4, the composition of this alloy is outside the Fig. 6. Microstructure of a Pd59Ni25P16 BMG prepared by path (A) with Ta = 593 K and τ = 5 min. (a) HRTEM image, showing that the specimen is amorphous; (b) HAADF image, showing that the specimen is of uniform composition; (c) EDX line mapping, further illustrating that the specimen is a homogenous BMG; and (d) the structure factor has a strong right shoulder (right arrow) and a small left shoulder (left arrow).
7
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 7. Microstructure of a Pd59Ni25P16 BMG prepared by path (A) with Ta = 593 K and τ = 10 min. (a) HRTEM image, showing that the specimen is amorphous; (b) HAADF image, showing that the specimen is of uniform composition; (c) EDX line mapping, further illustrating that the specimen is a homogenous BMG; and (d) structure factor, containing a strong rightshoulder as well as a strong left-shoulder.
Moreover, since it is easier for i-SRO to nucleate out than ℓ-SRO as a PdeNieP melt is cooled from above its Tl to Trt (Table 2), the structure of a liquid with ℓ-SRO is presumably more complicated than that of a liquid with i-SRO. As mentioned earlier, when quenched into its MLMG, an undercooled homogeneous PdeNieP melt undergoes LSD, splitting into two liquids or ℓ → ℓ1 (i-SRO) + ℓ2 (ℓ-SRO). Fig. 3a displays the MLMG. It shows that ℓ1 or i-SRO has a composition of Pd80 − xNixP20, where x
MLMG. The experimental results are summarized in Table 2. The transformation observed is a first-order LLT.
4. Discussions Because of the presence of the right shoulder in the second peak of the structure factor, ℓ-SRO is also taken to have icosahedral symmetry, which explains why ℓ-SRO resists strongly against crystallization.
Fig. 8. (a(i) and a(ii)) Two distinct electron diffraction patterns were found. For clarity they are transformed into structure factors (1-D normalized intensity). The inset in each figure is an enlarged picture of the second peak of the structure factor; (b) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 1 min.; (c) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 3 min.; (d(i)) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 5 min.; (d(ii)) The green area and the red area are separated from each other by a boundary (dashed line); (e) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 10 min.; and (f) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 300 min. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
8
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 9. DSC studies of the reaction, i-SRO → ℓ-SRO. (a) Calibration of the DSC; (b) The black line is the first thermal scan and the red line is its second thermal scan; (c) TEM real image of the specimen after the two thermal scans in (b), showing that it is free of crystallinity; (d) electron diffraction of the PdeNieP specimen after the two thermal scans in (b) and only halos are found. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
more NieP or PdeP bonds for there are less P atoms. This implies that ℓ-SRO has a more ordered structure. With this picture in mind and together with the fact that both i-SRO and ℓ-SRO are taken to have an icosahedral symmetry, it is not surprising that the structure factor of iSRO and that of ℓ-SRO are similar to each other. Based on these considerations, the first-order LLT found in this work is likely to be similar to a first-order order-disorder transition in crystalline solids. Wilde et al. [59] measured the heat of crystallization of Pd40Ni40P20 at its melting temperature (Tm ≈ 890 K), which is about 9391 J/mol. The entropy of crystallization is therefore 10.55 J/mol K. In this study, the enthalpy change (or latent heat) of the first-order LLT at 593 K is 3690 J/mol. The equilibrium transition temperature from i-SRO to ℓSRO is not known. As an approximation, the entropy of the LLT is estimated from, 3690/593 (J/mol K) = 6.22 J/mol K. It shows that the entropy of the LLT is 59% of the entropy of crystallization. The large change (59%) is consistent with the proposal that the LLT is related to
varies from 0 to 80. Physically, i-SRO can be regarded as a liquid solution. On the other hand, ℓ2 has a fixed composition (~ Pd50Ni36P14), indicating it behaves as a liquid metallic compound or the relative positions of Pd, Ni, and P in ℓ-SRO are basically fixed. It can therefore be concluded that the configurational entropy of i-SRO is larger than that of ℓ-SRO. Alternatively, the nature of i-SRO and ℓ-SRO, which together constitute the MLMG, can be analyzed semi-quantitatively in terms of the concept of enthalpy of formation. According to ref. [58], the enthalpies of formation for NieP, PdeP, and PdeNi are, respectively, −61, −66, and 0 kJ/mol. Assume that these values are qualitatively correct for Pd, Ni, and P that are arranged in a liquid structure with icosahedral symmetry. Then i-SRO, with a composition of Pd80 − xNixP20, where x varies from 0 to 80, has too many P atoms to maximize the number of NieP or PdeP bonds. As a result, i-SRO is likely to be disordered. On the contrary, ℓ-SRO, with a composition of ~Pd50Ni36P14, can form 9
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 11. (a) Free energy blades of the i-SRO phase and ℓ-SRO phase are drawn on a 2dimensional composition diagram of PdeNieP. Point H has a composition of Pd40Ni40P20 and point K has a composition of ~ Pd50Ni36P14; (b(i)) Free energy curves, one for i-SRO and the other one for ℓ-SRO, along the composition line joining points H and K; and (b(ii)) merging of the two free energy curves shown in part (b(i)). A composition range in which its curvature is negative is formed.
Fig. 10. (a) Free energy curves of L, i-SRO and ℓ-SRO before merging; and (b) Formation of the miscibility gap upon the merging together of the three free energy curves in (a).
occur at T = 593 K. Fig. 11a depicts the Gibbs free energy blade of the liquid that exhibits i-SRO at a temperature of 593 K (denoted by Gi-SRO) and that of the liquid with ℓ-SRO (denoted by Gℓ-SRO). Notably, they are two separate, independent G blades. The G blade for L (in Fig. 10) does not exist. Fig. 11a only shows portions of Gi-SRO and Gℓ-SRO. They can be extended to cover the entire composition range. An analog can be drawn from a crystalline solid, in which the Gibbs free energies for a face-centered cubic structure, Gf.c.c.(P, T, c), and a body-centered cubic structure, Gb.c.c.(P, T, c), are two independent functions. Each GSRO may consist of irregular features, such as dips, that occur at special compositions (with special atomic arrangements) where the values of GSRO are particularly low. The groove- and cone-shape structures in Fig. 11a are typical irregularities on the otherwise smooth Gi-SRO and Gℓ-SRO blades, respectively. Collectively, these irregularities create a GSRO landscape, similar to the concept of ‘potential energy hyperspace’ or ‘energy landscape’ [61–63] in glass science, although the latter refers to the various mechanically stable glass structures of a substance at a fixed composition. Fig. 11a shows the triangular MLMG (the triangle LSK connected by dashed lines) and its vicinity at Ta = 593 K, with Gi-SRO and Gℓ-SRO in place. Geometrically, Gi-SRO is chosen to be groove-like with a minimum at Pd40Ni40P20 for two reasons: (i) as discussed before, i-SRO behaves as a liquid solution; and (ii) it is shown in ref. [51,52] that Pd40Ni40P20 in the glass state is exceptionally stable. Also geometrically, Gi-SRO is chosen to open up faster for P ≥ 20 at.%, but slower for P ≤ 20 at.%. The choice is based on the experimental results shown in Fig. 3 in ref.
an order-disorder change. Recently, Stolpe et al. [60] found an LLT in an undercooled Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 melt (a Vitreloy) by using synchrotron XRD. The authors associated the LLT with a change in heat capacity and entropy. They found that the entropy change of the LLT is only about 6% of the entropy of crystallization of the Vitreloy alloy, much less than that (59%) found in this work. Since the two liquids (before and after the LLT) described in the work of Stolpe et al. are not well characterized, the origin of the large difference in the entropy of LLT between this work and that of Stolpe et al. cannot be assessed at this point. Earlier, a thermodynamic model [50] based on Chen and Turnbull's suggestion [37] was proposed to explain the origin of the MLMG. The details are shown in Fig. 10a through b. Fig. 10a shows three Gibbs free energy curves, which are: (i) a conventional liquid free energy curve L that consists of SROs from all available types of clusters; (ii) a liquid free energy curve of i-SRO; and (iii) a liquid free energy curve of ℓ-SRO. The horizontal axis in the figure is along a composition direction that passes through both ℓ-SRO and i-SRO. Fig. 10b shows the creation of a miscibility gap when i-SRO and ℓ-SRO merge into L. The merging together is possible because it is not necessary to meet long-range order, as in crystalline solids. The thermodynamic model in Fig. 10a through b can explain the MLMG, but fails to explain the first-order LLT that occurs just outside the MLMG. Fig. 11a through c show a revised 3-dimensional thermodynamic model for the liquid spinodal decomposition and first-order LLT that 10
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Nat. Mater. (2007) 192–197. [6] G.N. Greaves, M.C. Wilding, S. Fearn, D. Langstaff, F. Kargl, S. Cox, Q. Vu Van, O. Majérus, C.J. Benmore, R. Weber, C.M. Martin, L. Hennet, Science (2008) 566–570. [7] R. Shimizu, M. Kobayashi, H. Tanaka, Phys. Rev. Lett. 112 (2014) 125702. [8] J.Z. Li, W.K. Rhim, C.P. Kim, K. Samwer, W.L. Johnson, Acta Mater. 59 (2011) 2166–2171. [9] S. Wei, F. Yang, J. Bednarcik, I. Kaban, O. Shuleshova, A. Meyer, R. Busch, Nat. Commun. 4 (2013) 2083. [10] S. Lan, M. Blodgett, K.F. Kelton, J.L. Ma, J. Fan, X.L. Wang, Appl. Phys. Lett. 108 (2016) 211907. [11] P.H. Poole, F. Sciortino, U. Essmann, H.E. Stanley, Nature 360 (1992) 324–328. [12] P.H. Poole, T. Grande, C.A. Angell, P.F. McMillan, Science 275 (1997) 322–323. [13] P.G. Debenedetti, Metastable Liquids, Princeton University Press, Princeton, NJ, 1997. [14] J.R. Errington, P.G. Debenedetti, Nature 409 (2001) 318–321. [15] I. Saika-Voivod, P.H. Poole, F. Sciortino, Nature 412 (2001) 514–517. [16] S. Sastry, C.A. Angell, Nature 2 (2003) 739–743. [17] D. Turnbull, J. Chem. Phys. 20 (1952) 411–424. [18] F.C. Frank, Proc. R. Soc. Lond. 215A (1952) 43–46. [19] G.D. Scott, Nature 188 (1960) 908–909. [20] G.D. Scott, Nature 194 (1962) 956–957. [21] J. Bernal, Proc. R. Soc. Lond. 280A (1964) 299–322. [22] J.L. Finney, Proc. R. Soc. Lond. 319A (1970) 495–507. [23] G.S. Cargill, J. Appl. Phys. 41 (1970) 12–29. [24] P. Chaudhari, D. Turnbull, Science 199 (1978) 11–21. [25] P.H. Gaskell, Nature 276 (1978) 484–485. [26] P.H. Gaskell, J. Non-Cryst. Solids 32 (1978) 207–224. [27] S. Sachdev, D.R. Nelson, Phys. Rev. Lett. 53 (1984) 1947–1950. [28] D.R. Nelson, F. Spaepen, Solid State Phys. 42 (1989) 1–90. [29] T. Egami, W. Dmowski, Y. He, R.B. Schwarz, Metall. Mater. Trans. 29A (1998) 1805–1809. [30] H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimaki, T. Lippmann, G. Reiter, Nature 408 (2000) 839–841. [31] J. Saida, M. Matsushita, A. Inoue, Appl. Phys. Lett. 79 (2001) 412–414. [32] A. Inoue, A. Takeuchi, Acta Mater. 59 (2011) 2243–2267. [33] H.W. Sheng, W.K. Luo, F.M. Alamgir, J.M. Bai, E. Ma, Nature 439 (2006) 419–425. [34] X.J. Liu, G.L. Chen, X. Hui, T. Liu, Z.P. Lu, Appl. Phys. Lett. 93 (2008) 011911. [35] N.A. Mauro, V. Wessels, J.C. Bendert, S. Klein, A.K. Gangopadhyay, M.J. Kramer, S.G. Hao, G.E. Rustan, A. Kreyssig, A.I. Goldman, K.F. Kelton, Phys. Rev. B 83 (2011) 184109. [36] P.F. McMillan, M. Wilson, M.C. Wilding, D. Daisenberger, M. Mezouar, G.N. Greaves, J. Phys. Condens. Mater. 19 (2007) 415101. [37] H.S. Chen, D. Turnbull, Acta Metall. 17 (1969) 1021–1031. [38] C.P. Chou, D. Turnbull, J. Non-Cryst. Solids 17 (1975) 169–188. [39] S. Lan, Y.L. Yip, M.T. Lau, H.W. Kui, J. Non-Cryst. Solids 358 (2012) 1298–1302. [40] Z.D. Wu, X.H. Lu, Z.H. Wu, H.W. Kui, J. Non-Cryst, J. Non-Cryst. Solids 385 (2014) 40–46. [41] Z.D. Wu, W.Z. Zhou, Y.F. Lo, S. Lan, H.W. Kui, J. Non-Cryst. Solids 410 (2015) 51–57. [42] P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Phys. Rev. B 28 (1983) 784–805. [43] A. Mizuno, S. Matsumura, M. Watanabe, S. Kohara, M. Takata, Mater. Trans. 46 (2005) 2799–2802. [44] K.F. Kelton, A.K. Gangopadhyay, T.H. Kim, G.W. Lee, J. Non-Cryst. Solids 352 (2006) 5318–5324. [45] S.Y. Wang, C.Z. Wang, M.Z. Li, L. Huang, R.T. Ott, M.J. Kramer, D.J. Sordelet, K.M. Ho, Phys. Rev. B 78 (2008) 184204. [46] M. Inui, K. Maruyama, Y. Kajihara, M. Nakada, Phys. Rev. B 80 (2009) 180201. [47] H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimaki, T. Lippmann, G. Reiter, Nature 408 (2000) 839–841. [48] F. Spaepen, Nature 408 (2000) 781–782. [49] W.Z. Zhou, Z.D. Wu, Y.F. Lo, H.W. Kui, J. Non-Cryst. Solids 432 (2016) 420–425. [50] M.T. Lau, S. Lan, Y.L. Yip, H.W. Kui, J. Non-Cryst. Solids 358 (2012) 2667–2673. [51] Z.D. Wu, S. Lan, H.W. Kui, Metall. Mater. Trans. A 45 (2014) 2399–2404. [52] S. Lan, Z.D. Wu, M.T. Lau, H.W. Kui, J. Non-Cryst. Solids 373–374 (2013) 5–12. [53] P.L. Maitrepierre, J. Appl. Phys. 40 (1969) 4826–4834. [54] H.W. Kui, A.L. Greer, D. Turnbull, Appl. Phys. Lett. 45 (1984) 615–618. [55] H.S. Chen, D. Turnbull, Acta Metall. 17 (1969) 1021–1031. [56] H.H. Liebermann, C.D. Graham, IEEE Trans. Magn. 12-6 (1976) 921–923. [57] H.S. Chen, C.D. Miller, Rev. Sci. Instrum. 41 (1970) 1237–1238. [58] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesion in Metals - Transition Metal Alloys, Elsevier Science Publishers B.V., Amsterdam, 1989. [59] G. Wilde, G.P. Gorler, R. Willnecker, J. Fecht, J. Appl. Phys. 87 (2000) 1141–1152. [60] M. Stolpe, I. Jonas, S. Wei, Z. Evenson, W. Hembree, F. Yang, A. Meyer, R. Busch, Phys. Rev. B 93 (2016) 014201. [61] F.H. Stillinger, T.A. Weber, Science 225 (1984) 983–989. [62] F.H. Stillinger, Science 267 (1995) 1935–1939. [63] C.A. Angell, MRS Bull. 33 (2008) 544–555.
[41], where it was found that the glass forming ability decreases rapidly with P ≥ 20 at.%, but slowly for P ≤ 20 at.%. Gℓ-SRO, as discussed before, behaves like a liquid intermetallic compound. Geometrically, it is chosen to have a shape as shown in Fig. 11a, with the vertex at a composition of ~Pd50Ni36P14. The choice is again based on the composition-dependent glass forming ability of PdeNieP alloys as listed in Fig. 3 of ref. [41]. Consider a straight line HK in the MLMG, with point R on it. A point, such as H, K, or R, represents a composition. A vertical plane (not shown) is then introduced into the figure with its bottom edge sitting on the line HK. It cuts through both Gi-SRO and Gℓ-SRO. The intersecting curves are shown in Fig. 11b(i). Thermodynamics then predicts that a homogeneous liquid of composition, R (either with i-SRO or ℓ-SRO symmetry), decomposes into a mixture of two liquids, which are H (iSRO) and K (ℓ-SRO), to reduce the overall Gibbs free energy of the system. There are two decomposition modes for R to choose from: nucleation and growth or spinodal decomposition. Kinetically, the spinodal reaction is preferred as reaction barrier is absent. This mechanism is made possible by the fact that liquids do not have any longrange order. As a result, Gi-SRO and Gℓ-SRO can join together, forming a hump in G for LSD to take place, as shown in Fig. 11b(ii). Table 2 shows that it is easier to nucleate out i-SRO than ℓ-SRO. If R is quenched to Trt rapidly, only i-SRO survives. On the other hand, if an intermediate thermal annealing (or slow quenching rate) is employed, a spinodal mechanism occurs in R: i-SRO → i-SRO + ℓ-SRO. For compositions below the composition line of Pd80 − xNixP20 and outside, but in the vicinity of, the MLMG (such as Pd59Ni25P16 and Pd40Ni45P15 as shown in Fig. 4), it is clear that Gi-SRO > Gℓ-SRO (Fig. 11a and b(ii)). Thermodynamics predicts that only first-order phase transitions are possible between them. It can then be concluded that with a fast quenching rate, a PdeNieP melt is quenched into i-SRO (Table 2). A subsequent thermal annealing will transform it into ℓ-SRO by a first-order process. If on the other hand the cooling rate is slow enough, there is enough time for the first-order LLT to take place: iSRO → ℓ-SRO. 5. Conclusions Five conclusions can be drawn from the experimental results. First, a liquid-liquid phase transition (LLT) is observed in the undercooling regime of molten PdeNieP. The reaction can be represented by, L → L + L′ (L′ from nucleation and growth) → L′, where L and L′ have i-SRO and ℓ-SRO, respectively, and they have the same composition. Second, electron microscopy (an entropic approach to classify the order of a phase transition) establishes that the LLT is a first-order phase transition. Third, the latent heat of the LLT is measured. Its lower bound value is 3690 J/mol. Fourth, because it is a first-order LLT, the SROs of undercooled PdeNieP are divided into groups and each group containing one or more SROs. Furthermore, each group of SROs represents a physical liquid. Fifth, each group of SROs can be assigned a Gibbs free energy, GSRO(P, T, c). As a result, the thermodynamics of liquids can be described in terms of these GSRO(P, T, c). References [1] O. Mishima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393–395. [2] S. Aasland, P.F. McMillan, Nature 369 (1994) 633–636. [3] Y. Katayama, T. Mizutani, W. Utsumi, O. Shimomura, M. Yamakata, K. Funakoshi, Nature 403 (2000) 170–173. [4] M.H. Bhat, V. Molinero, E. Soignard, V.C. Solomon, S. Sastry, J.L. Yarger, C.A. Angell, Nature 48 (2007) 787–790. [5] H.W. Sheng, H.Z. Liu, Y.Q. Cheng, J. Wen, P.L. Lee, W.K. Luo, S.D. Shastri, E. Ma,
11
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Direct imaging of a first-order liquid-liquid phase transition in undercooled molten PdeNieP alloys and its thermodynamic implications Y.F. Lo, X.C. Wang, Z.D. Wu, W.Z. Zhou, H.W. Kui⁎ Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, People's Republic of China
A R T I C L E I N F O
A B S T R A C T
Keywords: Bulk metallic glass (BMG) PdeNieP Short-range orders Nucleation and growth and latent heat First-order liquid-liquid phase transition Structure of liquids
Polyamorphic transition is the transition between two amorphous states or two liquid states (LLT) at a fixed composition of a substance. Experience in LLT is limited. Besides, its nature remains largely unknown as it occurs under the experimental conditions of high pressure/temperature (P/T) or high undercooling. In this study, we found that some undercooled PdeNieP melts undergo a LLT. Contrary to all earlier studies, PdeNieP specimens that contain the structural changes that occur at different stages of the LLT can be prepared for electron microscopy. HRTEM (high resolution transmission electron microscope) establishes that it is a first-order phase transition. From thermodynamics, a first-order phase change is accompanied by a latent heat. Here it was measured by a DSC (differential scanning calorimeter). A first-order LLT has important thermodynamic implications. First, it reconfirms that a liquid has different kinds of short-range-orders (SROs). Second, the firstorder LLT implies that the SROs of a liquid are divided into distinct groups, each containing either a SRO or a number of different SROs, but not all. Physically, each group represents a real liquid. Third, the SRO(s) in a group can be assigned an independent Gibbs free energy, GSRO(P, T, c = composition) and the thermodynamics of the liquids can be described in terms of these GSRO.
1. Introduction Polymorphism refers to the first-order phase transition between two crystalline phases at a fixed composition of a substance. The best example is perhaps found in pure iron where it changes from face-centered-cubic to body-centered-cubic forms at 1183 K and 1 atmospheric pressure. Polyamorphism refers to the transition between two amorphous/liquid phases at a fixed composition of a substance. The first glassy-state polyamorphic transition was observed in ice under high P and low T [1]. The transition is sharp and the authors suggested that it is a first-order phase transition. The first liquid-state polyamorphic transition or liquid-liquid phase transition (LLT), was observed in meltquenched Y2O3-Al2O3 glasses [2]. An as-prepared glassy specimen always consists of both low- and high-density polyamorphs, mixing up with each other. They are separated from each other by sharp boundaries, indicating that a nucleation and growth mechanism has taken place. However, this observation is not a rigorous proof for a first-order phase transition (explained below). As of today, in experiments, the harsh conditions, including, (i) high T (and often high P); and/or (ii) deep in the undercooling regime where crystallization is prone to occur, continue. As a result, preparation of specimens that contain structural changes that occur at different stages of a polyamorphic transition has
⁎
not been possible for detailed electron microscopic analysis. Despite these difficulties, both experimental [3–10] and theoretical studies [11–16] confirm that polyamorphic transitions take place in systems with different kinds of bonding. There is a conceptual difficulty in accepting a first-order LLT. At present a liquid/glass is considered to consist of different kinds of SROs [17–35], coming from its constituent clusters [33–36]. The relative amount of these SROs changes continuously with T and P, but in dynamic equilibrium with each other when T and P are fixed. Since the structural change occurring in a first-order phase transition is abrupt, a first-order LLT is therefore inconsistent with the current view of the structure of liquids. If a LLT is a first-order phase transition, it can be represented by,
′ L → L + L′ (L′ from nucleation and growth) → L,
(1)
where L and L′ have the same composition. Eq. (1) can be interpreted as follows. The LLT takes place at a temperature below the transition temperature (for observable rate). In the first reaction (first arrow), nucleation and growth of L′ occurs in L. In the second reaction (second arrow), all L is transformed into L′. In a rigorous experimental proof of a first-order LLT, direct evidence must be obtained to settle an important issue, which is: L′ is the only phase that appears in L, which eventually
Corresponding author. E-mail address: [email protected] (H.W. Kui).
http://dx.doi.org/10.1016/j.jnoncrysol.2017.07.020 Received 28 April 2017; Received in revised form 8 June 2017; Accepted 25 July 2017 0022-3093/ © 2017 Published by Elsevier B.V.
Please cite this article as: Lo, Y.F., Journal of Non-Crystalline Solids (2017), http://dx.doi.org/10.1016/j.jnoncrysol.2017.07.020
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
of negative heat of mixing. As a result, LSD soon became a controversial issue in glass science [39]. Recently, it was demonstrated by HRTEM and SAXS that LSD occurs in some PdeNieP bulk metallic glasses (BMGs) [39,40], i.e., the decomposition can be described by Eq. (3). Now in Eq. (3), there are two different phases, ℓ1 and ℓ2. The next question is: What is the nature of the two different phases, ℓ1 and ℓ2, in a spinodally phase-separated PdeNieP BMG? Wu et al. [41] were able to provide partial answer to this question. By means of HRTEM, EDX (energy dispersive X-ray) and X-ray diffraction, the authors were able to differentiate ℓ1 and ℓ2 in two respects. First, ℓ1 and ℓ2 have different compositions. Second, they have different SROs. The difference in SROs is confirmed through their structure factors obtained from X-ray studies. In one of them, say ℓ1, it contains a right shoulder in the second peak. According to earlier experience [27,42–46], this liquid is taken to have an icosahedral SRO symmetry. For clarity, it is denoted by i-SRO below. It must be noted that i-SRO is a symbol for the structure factor of ℓ1, which may contain more than one type of clusters [47,48]. The structure factor of the other liquid, ℓ2, denoted by ℓ-SRO, either has a left shoulder or has both a right shoulder and a left shoulder in the second peak. The symmetry of this second SRO is not known. From the theory of spinodal decomposition, the i-SRO and ℓ-SRO together form a metastable liquid miscibility gap (MLMG) in the undercooling regime of molten PdeNieP. The MLMG was more recently determined by Zhou et al. [49]. The transformations of PdeNieP melts inside the MLMG were earlier explored by Wu et al. [39–41,49–52]. In this work, transformations of PdeNieP melts outside, but in the vicinity of the MLMG were studied. Indeed, we found a first-order LLT there, which is reported in this article. The existence of both the firstorder LLT and LSD will shed new light on the thermodynamics of liquids.
consumes all L. All previous studies have failed to achieve this. In a first-order phase transition, the first partial derivatives of the molar Gibbs free energy of a substance, G, namely, −(∂G/∂T)P = S (molar entropy), and (∂ G/∂P)T = V (molar volume), are discontinuous. To determine whether a transition is of first-order or higher-order, one approach is to measure if there is any abrupt change in V at/below the transition temperature. Another approach is related to S. As discussed in the last paragraph, a rigorous proof of a first-order phase change involves: (i) the emergence and subsequent growth of L′ in L (by nucleation and growth mechanism); and (ii) the complete consumption of L by L′ only. Since L and L′ are different phases, they have different entropies or equivalently there is an abrupt change in −(∂G/∂ T)P = S as L′ appears in L. These two conditions can be realized experimentally if TEM specimens that contain the structural changes occurring at different stages of a LLT can be prepared. In this work, this entropic approach was chosen for the establishment of a first-order LLT. From thermodynamics, a first-order phase change is accompanied by a latent heat (enthalpy change). In this work, the molar latent heat of the first-order LLT was measured by DSC. A liquid can also decompose into two liquids of different compositions, called phase-separation. There are two different decomposition mechanisms, which are liquid nucleation and growth (LNG), and liquid spinodal decomposition (LSD). On a phase diagram, the phase field that includes both LNG and LSD is called a liquid miscibility gap. Both LNG and LSD are discussed individually below. A LNG can be represented by,
ℓ → ℓ′ + ℓ2 (ℓ2 from nucleation and growth) → ℓ1 + ℓ2 ,
(2)
in which the parent matrix is formed by phase ℓ. The first reaction is the nucleation and growth of phase ℓ2 in ℓ. As the domains of ℓ2 grow, their composition remains constant while that of the matrix is changing. For clarity, it is denoted by ℓ′. A downhill diffusion field is set up right in front of the ℓ′/ℓ2 interfaces. In the second reaction, after the completion of the decomposition, the newly formed phase still has a composition of ℓ2. It co-exists with the parent matrix which now has a composition of ℓ1. ℓ1 and ℓ2 are two different phases. A liquid spinodal decomposition, LSD, can be represented by,
ℓ → composition modulation → ℓ1 + ℓ2 .
2. Materials and experimental PdeNieP ingots were prepared by one of the following two methods, depending on the composition. In the first method, Pd and Ni granules, and Ni2P powders, all of purity better than 99.9%, were used. The Ni2P powders were first sintered into a pellet. Then the right proportion of Pd and Ni granules and the Ni2P pellet were put into a clean fused silica tube and alloying was by rf (radio frequency) induction heating under Ar atmosphere. In the second method, Pd, Ni2P, and P powders, all of purity better than 99.9%, were used. First, the right proportion of the different kinds of powders was sintered into a pellet [53]. Then an as-formed pellet was put into a clean fused silica tube and melted by induction heating under Ar atmosphere. In both methods, a typical ingot formed had a eutectic microstructure, with a diameter of ~4 mm (or a mass of ~0.3 g). A fluxing technique [39–41,49–52] has been found to be effective in transforming molten PdeNieP alloys into BMGs. In the experiment, a PdeNieP ingot and some B2O3 (called the fluxing agent) of mass ~1.3 g, were put into a clean fused silica tube of inner diameter 11 mm and outer diameter 13 mm as shown in Fig. 1a. The system was first evacuated by a mechanical pump to ~10− 2 Torr. Then it was heated up to ~ 1300 K (above its liquidus, Tl) by a torch. The high temperature heat-treatment was applied for a time period of ~4 h before it was cooled down again by some chosen kinetic paths. Six different cooling paths were arranged for the system, which are: (A) first quenched in a tin bath of constant temperature Ta (Ta = 593, 598 or 613 K) for an intermediate isothermal annealing, with a time period of τ (≤ 20 min). After the isothermal annealing, the system was water-quenched to room temperature. This is the process [39–41] earlier used to demonstrate the existence of amorphous spinodal decomposition in PdeNieP BMGs, in which the annealing temperature was 613 K and τ ~ 20 min; (B) air-cooled to room temperature [54]; (C) first quenched in a tin bath of Ta = 503 K for 1.5 min and then waterquenched to room temperature; (D) water-quenched to room
(3)
Initially, there is a homogeneous liquid of composition ℓ. In the early stage of the spinodal decomposition, composition modulation is slowly built up in ℓ. In the absence of stress such as in a liquid, the composition modulation is isotropic and random. As time increases, the composition modulation sharpens. Meanwhile some characteristic wavelength dominates the spinodal morphology. When the spinodal decomposition completes, the spinodal morphology is described as the intertwining of an ℓ1 liquid subnetwork and an ℓ2 subnetwork. It is noted that ℓ1 and ℓ2 are different phases. Phase separation of a liquid into two liquids of different compositions is a common phenomenon in materials science. It must, however, be pointed out that spinodal decomposition is commonly observed in systems only with a positive heat of mixing. This is consistent with Cahn's theory of spinodal decomposition. Chen and Turnbull [37], by TEM methods, were the first to observe amorphous/liquid phase separation (LPS) in a metallic glass (Pd-Si glassy ribbons). Later, Chou and Turnbull [38] demonstrated that the LPS is consistent with a LSD by using small angle X-ray scattering (SAXS). The observed LSD is unexpected because Pd-Si has a negative heat of mixing. It is against Cahn's prediction. To get around the problem, Chen and Turnbull [37] proposed that there exists a SRO in undercooled molten Pd-Si, which generates a local hump in the Gibbs free energy blade, G(T, P, C = composition), allowing the formation of two locally stable liquid phases, ℓ1 and ℓ2. It is noted that ℓ1 and ℓ2 are two different phases. After these two reports, direct evidence of LSD could not be found in the next four decades, both in Pd-Si (Chen and Turnbull's result could not be repeated elsewhere) and in other glass formers 2
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 1. (a) Schematic diagram showing the experimental set-up of a fluxing experiment; (b) schematic diagram showing the experimental set-up of a molten PdeNieP specimen in a thin-wall fused silica tube quenched in water; (c) schematic diagram showing the experimental set-up to measure, T vs. t, in paths (B), (C), and (D); (d) Results of, T vs. t, for paths (B) to (E).
spinning is estimated to be on the order of 106 K s− 1 [56–57]. For clarity, Table 1 summarizes what the different cooling paths are about and the respective cooling rates achieved by them. An as-prepared specimen was characterized by X-ray diffraction. The scanning rate of the diffractometer was chosen to be 0.25 degree/ min and the step of the measurement was 0.1 degree. The X-ray source was Cu Kα line, which has a wavelength of 1.54 Å. The microstructure was studied by HRTEM and EDX line mapping. The enthalpy change or latent heat between i-SRO and ℓ-SRO was measured by DSC.
temperature; (E) A clean fused silica tube, which was tapered to a sealed end as shown in Fig. 1b, was first prepared. The thickness of the wall of the tapering part of the tube was less than 200 μm. In the experiment, a fluxed PdeNieP ingot was put into the fused silica tube and the system was evacuated by a mechanical pump to ~ 10− 2 Torr. It was then heated up until the metal ingot inside was completely melted. Ar gas was next introduced from the top, pushing the alloy melt into the tapering fused silica tube. Finally the system was inserted into water for rapid quenching [55]; and (F) wheel spinning [56–57]. It is of interest to measure, at least semi-quantitatively, the quenching rates achieved in paths (B), (C), (D), and (E). The experimental arrangement for this purpose for paths (B), (C), and (D) is shown in Fig. 1c. In a fluxing experiment, a thermocouple sheathed in another fused silica tube of smaller diameter was added. In a cooling cycle, the thermocouple served to record, T vs. t (time). For path (E), in a controlled experiment, the tapering part of a fused silica tube (Fig. 1b) was filled with B2O3 instead of a molten alloy. A thermocouple was inserted directly into the molten flux to measure: T vs. t. The experimental results for the various cooling paths are shown in Fig. 1d. The cooling rates for paths (B), (C), (D) and (E) were found to be 3.5, 7.4, 18.9, and 1000 K s− 1, respectively. It must be emphasized that these cooling rates are only qualitatively correct. The cooling rate achieved in wheel
3. Results Before moving on to discuss the experimental results obtained in this work, some basic results obtained in Ref. [41] are reproduced here for comparison and reference purpose. The HAADF, EDX line mapping and HRTEM images of a Pd42Ni40P18 BMG (composition inside the MLMG) that has undergone LSD are shown in Fig. 2. Because Eq. (3) is obeyed, the as-formed specimen is called a spinodal BMG. The HAADF image shown in Fig. 2a shows that there is mass/thickness contrast, indicating that the spinodal BMG is not of uniform composition. Fig. 2b is the EDX line mapping taken along the dashed line shown in Fig. 2a. It displays composition variation along the dashed line, consistent with
Table 1 Different cooling paths used to prepare various PdeNieP specimens. Description of the cooling paths
Measured average dT/dt
Path A: Initially the system was at a temperature above Tl. It was quenched in a tin bath of Ta (593, 598 or 613 K) and then thermally annealed at Ta for a time period τ ≤ 20 min. Finally it was water-quenched to room temperature. Path B: The system was directly air-cooled from above Tl to room temperature. Path C: Initially the system was at a temperature above Tl. It was quenched in a tin bath of Ta = 503 K and then thermally annealed at Ta with τ = 1.5 min. Finally it was water-quenched to room temperature. Path D: The system was directly water-quenched from above Tl to room temperature. Path E: Molten PdeNieP enclosed in a thin-wall fused silica tube at T > Tl was water-quenched to room temperature. Path F: Thin foils were prepared by wheel spinning method.
Not applicable
3
− 3.5 K s− 1 Not applicable − 19 K s− 1 − 103 K s− 1 − 106 K s− 1
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 2. Microstructure of a Pd42Ni40P18 specimen that has undergone LSD. (a) HAADF shows that its composition is non-uniform; (b) EDX line mapping along the dashed line shown in (a), again showing that the composition varies; (c) HRTEM image taken from the white areas in (a), showing that they are amorphous; and (d) HRTEM image taken from the black areas in (a) showing that they are amorphous.
variation in them (see ref. [41]). It can therefore be concluded that the lever rule can qualitatively predict the height of the left shoulder in the second peak of their structure factors. The MLMG in undercooled molten PdeNieP is basically a right angle prism [49]. Fig. 4 shows the actual data obtained by the authors, on a cross-section of the MLMG at ~ 800 K. The open circles represent compositions that undergo LSD while the closed circles are those that reject LSD or they are outside the MLMG. In this work, three alloy compositions rejecting LSD were chosen for study, which are: Pd40Ni40P20 (on the boundary of the MLMG; Tg = 585 K and Tℓ = 923 K), Pd59Ni25P16 (outside the MLMG; Tg = 590 K and Tℓ = 971 K), and Pd40Ni45P15 (outside the MLMG; Tg = 580 K and Tℓ = 1073 K). For clarity, they are represented by inverted open triangles.
the HAADF result. Fig. 2c is a HRTEM image taken from the brighter areas in Fig. 2a, showing that it is amorphous. Fig. 2d is a HRTEM image taken from the darker areas in Fig. 2a, showing that it is also amorphous. Fig. 3a shows the MLMG of the alloy system, PdeNieP. For liquids with compositions along the top horizontal line, they only have i-SRO. The vertex of the MLMG (with the symbol “X”) has a composition of ~ Pd50Ni36P14. A liquid with this composition only has ℓ-SRO. Inside the MLMG, spinodal BMGs of compositions marked by closed squares, hexagons, and triangles are studied by X-ray diffraction method. According to ref. [41], a left shoulder in the second peak of the structure factor of a PdeNieP spinodal BMG is attributed to ℓ-SRO (in the Introduction section, in Eq. (3), ℓ2 is chosen as ℓ-SRO and ℓ1 is chosen to be i-SRO). By applying the lever rule to Fig. 3a, spinodal Pd80 − xNixP19 BMGs (all closed squares in Fig. 3a) have the least amount of ℓ-SRO; an intermediate amount of ℓ-SRO in spinodal Pd82 − xNixP18 BMGs (all closed hexagons in Fig. 3a); and the most amount of ℓ-SRO in spinodal Pd82.5 − xNixP17.5 BMGs (all closed triangles in Fig. 3a). Fig. 3b, taken from Ref. [41], shows the structure factors of these spinodal BMGs. The structure factors of spinodal Pd80 − xNixP19 BMGs exhibit a tiny left shoulder (Fig. 3b(i)). Despite the fact that the left shoulder is small, previous experience shows that HAADF can easily detect the composition variation in them (see, for example, Fig. 5 in ref. [50]). The structure factors of spinodal Pd82 − xNixP18 BMGs have a clear left shoulder and HAADF can detect the composition variation in them (see ref. [41]). The structure factor of spinodal Pd82.5 − xNixP17.5 BMGs have a prominent left shoulder and HAADF can detect the composition
3.1. Pd40Ni40P20 HRTEM shows that Pd40Ni40P20 specimens prepared by paths (A), (B), (C), (D), (E) and (F) are amorphous - bulk metallic glasses (BMGs) in paths (A) to (E) and glassy ribbons in path (F). HAADF images (Fig. 5a) are all homogeneous, indicating that the compositions of the glassy specimens are uniform. EDX line mapping displays random signal, further confirming that they are homogeneous (experimental results not shown). The structure factor obtained by X-ray diffraction studies contains a right shoulder in the second peak (Fig. 5b). This characteristic structure factor is often taken to be an indication that the glassy specimens have an icosahedral symmetry as mentioned earlier 4
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 3. (a) Spinodal PdeNieP BMGs of compositions marked by geometric symbols are prepared. (b) Structure factors of (i) spinodal Pd80 − xNixP19 BMGs; (ii) spinodal Pd82 − xNixP18 BMGs; and (iii) spinodal Pd82.5 − xNixP17.5 BMGs, are shown.
a BMG. HAADF image does not display any mass/thickness contrast, suggesting that it is of uniform composition. EDX line mapping also confirms that it is a homogeneous BMG. In X-ray analysis, the second peak of the structure factor consists of a right shoulder, showing that the BMG has i-SRO. Structurally, it is similar to that of a Pd40Ni40P20 BMG discussed above. The result is shown in Table 2.
[27,42–46]. A left shoulder is nowhere to be seen. The results obtained here are the same as those described in ref. [41]. For clarity, the SRO of the glassy specimens is denoted by i-SRO. Table 2 lists the experimental results of Pd40Ni40P20.
3.2. Pd59Ni25P16 3.2.1. Path (A); Ta = 593 K and τ = 1 min HRTEM shows that a melt of this composition can be quenched into
3.2.2. Path (A); Ta = 593 K and τ = 5 min HRTEM shows that an as-prepared specimen is a BMG (Fig. 6a). Fig. 4. A cross-section of the MLMG in PdeNieP. The open circles represent compositions which undergo LSD while closed circles are those that reject LSD. PdeNieP alloys studied in this work are represented by inverted open triangles. The exact compositions are: Pd40Ni40P20, Pd59Ni25P16 and Pd40Ni45P15.
5
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
[50], the BMG must contain ℓ-SRO. The question is: Why could not the HAADF and EDX line mapping methods detect the presence of ℓ-SRO in the BMG, just like that in a Pd40.5Ni40.5P19 spinodal BMG, which is displayed in Fig. 5 in ref. [50]? It may be argued that perhaps the volume fraction of ℓ-SRO present in the BMG is just too little to be detected by HAADF and EDX. In the next effort, the volume fraction of ℓSRO was increased. For clarity, the result obtained in this part of the experiment is listed in Table 2. 3.2.3. Path (A); Ta = 593 K and τ = 10 min HRTEM (Fig. 7a) shows that a Pd59Ni25P16 melt can be transformed into a BMG. HAADF (Fig. 7b) shows that there is no mass/thickness contrast or equivalently the BMG is of uniform composition. EDX line mapping was employed to measure any composition variation in the BMG. The measurement was made along the red line shown in Fig. 7b. The result is shown in Fig. 7c, where only random signal is exhibited, showing that the BMG is of uniform composition, in good agreement with the HAADF result. The structure factor determined from X-ray diffraction of the BMG is shown in Fig. 7d. It displays a strong right shoulder and also a strong left shoulder in the second peak. The strong left shoulder predicts the presence of a substantial volume fraction of ℓ-SRO in the BMG. If the BMG had undergone a phase-separation reaction (Eqs. (2) and (3)), HAADF and EDX line mapping must have been able to detect a composition variation (Fig. 2). Therefore, it can be concluded that the appearance of the ℓ-SRO has nothing to do with a phase-separation mechanism or Eqs. (2) and (3) can be ruled out. Furthermore, since there is no composition change when i-SRO transforms into ℓ-SRO, it can be concluded that the transformation observed here is a LLT. The result is summarized in Table 2. 3.2.3.1. Is the LLT a first-order or higher-order phase transition?. The two conditions for a transformation to be of first-order as explained in Eq. (1) are: (i) the emergence of ℓ-SRO in i-SRO; and (ii) subsequently all iSRO is consumed by ℓ-SRO only. HRTEM was used to find the phase distribution of i-SRO and ℓ-SRO in Pd59Ni25P16 specimens of Ta = 593 K and τ in the range of 1 ≤ τ ≤ 300 min. In the experiment, an electron diffraction pattern was taken at a certain site. A software, named, “DigitalMicrograph”, was then used to acquire a 1dimenional linear intensity from the 2-dimensional electron diffraction pattern. The 1-dimensional linear intensity was then used to determine the structure factor at that site. After thorough studies, only two different structure factors were found, which are shown in Figs. 8a(i) and (ii). The former is characterized to have a right shoulder in the second peak while the latter has both a right shoulder and a left shoulder. The one in Fig. 8a(i) is taken to be due to i-SRO. Earlier Wu et al. [41] found that the structure factor of ℓ-SRO contains either a left shoulder or both a left shoulder and a right shoulder. As a result, the structure shown in Fig. 8a(ii) cannot be attributed to ℓ-SRO alone at this point. The experimentally measured phase distributions of i-SRO and ℓSRO from HRTEM studies in Pd59Ni25P16 specimens are given below. In the TEM bright field images shown in Figs. 8b through f, when electron diffraction reveals a certain site (radius of the electron beam ≈ 100 nm) having i-SRO, it is painted red; otherwise, it is painted green. Fig. 8b displays the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 1 min. In all those thin areas suitable for TEM studies, they are all red. Fig. 8c depicts that of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 3 min. It shows the emergence of a tiny green area in a red matrix. Fig. 8d(i) shows the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 5 min. The green areas have increased substantially when compared with those shown in Fig. 8b and c. It was also found that the electron diffraction technique can be used to mark the boundary between a green area and a red area. An example is shown in Fig. 8d(ii), marked by a dashed line. When an electron beam is entirely on the left of the boundary, only structure
Fig. 5. (a) HAADF image of a Pd40Ni40P20 BMG, showing that there is no mass/thickness contrast or the specimen is of uniform composition; and (b) the structure factor of the Pd40Ni40P20 BMG, showing that there is a right shoulder in its second peak. A left shoulder is nowhere to be seen.
HAADF shows that mass/thickness contrast is absent (Fig. 6b), i.e., the BMG is of uniform composition. Fig. 6c shows the result of EDX line mapping measured along the red line marked in Fig. 6b. The random signal again indicates that the BMG is of homogeneous composition. HRTEM, HAADF and EDX line mapping suggest that the BMG is homogeneous. The BMG was studied by X-ray diffraction method and the measured structure factor is shown in Fig. 6d. In the second peak, besides a strong right shoulder, a left shoulder begins to emerge (It is small and an arrow is used to mark its position.). According to Fig. 3b(i) and Fig. 5 in ref. 6
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Pd50Ni25P16. The last section describes a novel first-order LLT. Since a first-order phase transition is accompanied by an abrupt change in enthalpy (or latent heat), a DSC was used to measure it. In the experiment, before the actual thermal runs, the DSC was made to go through test runs with aluminum specimens (mass about 50 g). After an aluminum specimen was inserted into the sample holder of the DSC, the system was allowed to sit at 323 K for 1 min. Then it was heated up, at a heating rate of 40 K/min, to 593 K for prolonged thermal annealing, for a time period of 22.5 min. After the thermal annealing, the system was cooled down again to room temperature. This cycle was repeated 4 more times and the results are shown in Fig. 7a. Analysis shows that the fluctuation in the DSC runs is less than 0.3 mW. The same cycle was then applied to amorphous Pd59Ni25P16 specimens (mass about 50 g) that were initially completely occupied by iSRO. The isothermal annealing time was longer, about 300 min so as to make sure that all i-SRO had changed to ℓ-SRO (see Fig. 8f). The first thermal scan of one of these PdeNieP specimens (mass = 53 g) is shown as black line in Fig. 9b. After the 300 min isothermal annealing, the system was cooled down to room temperature. A second cycle was next applied to the same specimen and the second thermal scan is shown as red line in Fig. 9b. After the DSC experiment, the sample was removed for microstructural studies. Extensive HRTEM study showed that it was free of any crystallinity. Fig. 9c shows a TEM real image of the specimen, indicating that it is a homogeneous specimen. Fig. 9d is an electron diffraction pattern of the specimen, where only halos are found. The 2-dimensional electron diffraction is then converted into a 1-dimensional one to determine the structure factor. The as-determined structure factor (not shown here) is identical to the one shown in Fig. 8a (ii) or equivalently, the specimen is completely occupied by ℓ-SRO. The difference between the black and red lines in Fig. 9b is substantially larger than 0.3 mW, which is the resolution of the instrument. It therefore confirms that the transformation, i-SRO → ℓ-SRO, is an exothermic one and the enthalpy change (as calculated from the area between the blue and red line and calibrated) is 3690 J/mol. This is a lower bound for the actual enthalpy change as there was heat release when the specimen was heat from 323 to 593 K for isothermal annealing. The DSC studies therefore again confirm that the transformation, i-SRO → ℓ-SRO, is a first-order phase transition.
Table 2 Cooling paths (A) to (F) and the corresponding SROs observed in PdeNieP specimens of different compositions. Path
Pd40Ni40P20
Pd59Ni25P16
Pd40Ni45P15
A
Ta = 598 K; τ = 15 min; iSRO
Crystalline
B C
i-SRO i-SRO
Ta = 593 K; (a) τ = 1 min: i-SRO only; (b) τ = 5 min: i-SRO and ℓ-SRO; (c) τ = 10 min: i-SRO and ℓ-SRO, but no composition change. Therefore, it is an LLT (details in Section 3.2.3). (d) τ = 300 min: ℓ-SRO only; establishes that it is a first-order LLT (details in Section 3.2.3.1.). Crystalline i-SRO
D
i-SRO
i-SRO
E F
i-SRO i-SRO
i-SRO i-SRO
Crystalline i-SRO and ℓ-SRO (first-order LLT) i-SRO and ℓ-SRO (first-order LLT) i-SRO i-SRO
factor of the kind in Fig. 8a(i) are found. On the other hand, when an electron beam is completely on the right of the boundary, only structure factor of the kind shown in Fig. 8a(ii) are found. Fig. 8e shows the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 10 min. Now the green area exceeds the red area. Again, boundaries of the kind shown in Fig. 8d(ii) exist (not shown here). Fig. 8f shows the result of a Pd59Ni25P16 TEM specimen with Ta = 593 K and τ = 300 min. It is all green, implying that the transition from red to green has completed. Three conclusions can be drawn from the phase distribution determination. First, the BMG shown in Fig. 8f is completely occupied by ℓ-SRO. The structure factor for this BMG is the same as the one shown in Fig. 8a(ii). It can therefore be concluded that the structure factor of a liquid with ℓ-SRO contains both a right shoulder and a left shoulder in the second peak. Second, Fig. 8b through f establish that the LLT, iSRO → ℓ-SRO, is a first-order phase transition because: (i) it is a nucleation and growth mechanism; and (ii) the amorphous specimen shown in Fig. 8f is completely occupied by ℓ-SRO and in the process, only ℓ-SRO is found to consume i-SRO. Third, since a first-order phase transition is an abrupt change, i-SRO and ℓ-SRO must be distinct from each other. Equivalently, all of the short-range orders available to molten PdeNieP are divided into distinct groups and each group represents a physical liquid. According to thermodynamics, each group (containing SROs that belong to this group) can be assigned an independent Gibbs free energy, for example, Gi-SRO and Gℓ-SRO.
3.2.4. Other paths Pd59Ni25P16 specimens prepared by path (B) are crystalline. Specimens prepared by paths (C), (D), (E), and (F) are all amorphous with i-SRO. The results are summarized in Table 2. 3.3. Pd40Ni45P15
3.2.3.2. Latent heat measurement of the first-order LLT occurring in
With reference to Fig. 4, the composition of this alloy is outside the Fig. 6. Microstructure of a Pd59Ni25P16 BMG prepared by path (A) with Ta = 593 K and τ = 5 min. (a) HRTEM image, showing that the specimen is amorphous; (b) HAADF image, showing that the specimen is of uniform composition; (c) EDX line mapping, further illustrating that the specimen is a homogenous BMG; and (d) the structure factor has a strong right shoulder (right arrow) and a small left shoulder (left arrow).
7
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 7. Microstructure of a Pd59Ni25P16 BMG prepared by path (A) with Ta = 593 K and τ = 10 min. (a) HRTEM image, showing that the specimen is amorphous; (b) HAADF image, showing that the specimen is of uniform composition; (c) EDX line mapping, further illustrating that the specimen is a homogenous BMG; and (d) structure factor, containing a strong rightshoulder as well as a strong left-shoulder.
Moreover, since it is easier for i-SRO to nucleate out than ℓ-SRO as a PdeNieP melt is cooled from above its Tl to Trt (Table 2), the structure of a liquid with ℓ-SRO is presumably more complicated than that of a liquid with i-SRO. As mentioned earlier, when quenched into its MLMG, an undercooled homogeneous PdeNieP melt undergoes LSD, splitting into two liquids or ℓ → ℓ1 (i-SRO) + ℓ2 (ℓ-SRO). Fig. 3a displays the MLMG. It shows that ℓ1 or i-SRO has a composition of Pd80 − xNixP20, where x
MLMG. The experimental results are summarized in Table 2. The transformation observed is a first-order LLT.
4. Discussions Because of the presence of the right shoulder in the second peak of the structure factor, ℓ-SRO is also taken to have icosahedral symmetry, which explains why ℓ-SRO resists strongly against crystallization.
Fig. 8. (a(i) and a(ii)) Two distinct electron diffraction patterns were found. For clarity they are transformed into structure factors (1-D normalized intensity). The inset in each figure is an enlarged picture of the second peak of the structure factor; (b) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 1 min.; (c) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 3 min.; (d(i)) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 5 min.; (d(ii)) The green area and the red area are separated from each other by a boundary (dashed line); (e) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 10 min.; and (f) Phase distribution in a Pd59Ni25P16 BMG with Ta = 593 K and τ = 300 min. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
8
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 9. DSC studies of the reaction, i-SRO → ℓ-SRO. (a) Calibration of the DSC; (b) The black line is the first thermal scan and the red line is its second thermal scan; (c) TEM real image of the specimen after the two thermal scans in (b), showing that it is free of crystallinity; (d) electron diffraction of the PdeNieP specimen after the two thermal scans in (b) and only halos are found. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
more NieP or PdeP bonds for there are less P atoms. This implies that ℓ-SRO has a more ordered structure. With this picture in mind and together with the fact that both i-SRO and ℓ-SRO are taken to have an icosahedral symmetry, it is not surprising that the structure factor of iSRO and that of ℓ-SRO are similar to each other. Based on these considerations, the first-order LLT found in this work is likely to be similar to a first-order order-disorder transition in crystalline solids. Wilde et al. [59] measured the heat of crystallization of Pd40Ni40P20 at its melting temperature (Tm ≈ 890 K), which is about 9391 J/mol. The entropy of crystallization is therefore 10.55 J/mol K. In this study, the enthalpy change (or latent heat) of the first-order LLT at 593 K is 3690 J/mol. The equilibrium transition temperature from i-SRO to ℓSRO is not known. As an approximation, the entropy of the LLT is estimated from, 3690/593 (J/mol K) = 6.22 J/mol K. It shows that the entropy of the LLT is 59% of the entropy of crystallization. The large change (59%) is consistent with the proposal that the LLT is related to
varies from 0 to 80. Physically, i-SRO can be regarded as a liquid solution. On the other hand, ℓ2 has a fixed composition (~ Pd50Ni36P14), indicating it behaves as a liquid metallic compound or the relative positions of Pd, Ni, and P in ℓ-SRO are basically fixed. It can therefore be concluded that the configurational entropy of i-SRO is larger than that of ℓ-SRO. Alternatively, the nature of i-SRO and ℓ-SRO, which together constitute the MLMG, can be analyzed semi-quantitatively in terms of the concept of enthalpy of formation. According to ref. [58], the enthalpies of formation for NieP, PdeP, and PdeNi are, respectively, −61, −66, and 0 kJ/mol. Assume that these values are qualitatively correct for Pd, Ni, and P that are arranged in a liquid structure with icosahedral symmetry. Then i-SRO, with a composition of Pd80 − xNixP20, where x varies from 0 to 80, has too many P atoms to maximize the number of NieP or PdeP bonds. As a result, i-SRO is likely to be disordered. On the contrary, ℓ-SRO, with a composition of ~Pd50Ni36P14, can form 9
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Fig. 11. (a) Free energy blades of the i-SRO phase and ℓ-SRO phase are drawn on a 2dimensional composition diagram of PdeNieP. Point H has a composition of Pd40Ni40P20 and point K has a composition of ~ Pd50Ni36P14; (b(i)) Free energy curves, one for i-SRO and the other one for ℓ-SRO, along the composition line joining points H and K; and (b(ii)) merging of the two free energy curves shown in part (b(i)). A composition range in which its curvature is negative is formed.
Fig. 10. (a) Free energy curves of L, i-SRO and ℓ-SRO before merging; and (b) Formation of the miscibility gap upon the merging together of the three free energy curves in (a).
occur at T = 593 K. Fig. 11a depicts the Gibbs free energy blade of the liquid that exhibits i-SRO at a temperature of 593 K (denoted by Gi-SRO) and that of the liquid with ℓ-SRO (denoted by Gℓ-SRO). Notably, they are two separate, independent G blades. The G blade for L (in Fig. 10) does not exist. Fig. 11a only shows portions of Gi-SRO and Gℓ-SRO. They can be extended to cover the entire composition range. An analog can be drawn from a crystalline solid, in which the Gibbs free energies for a face-centered cubic structure, Gf.c.c.(P, T, c), and a body-centered cubic structure, Gb.c.c.(P, T, c), are two independent functions. Each GSRO may consist of irregular features, such as dips, that occur at special compositions (with special atomic arrangements) where the values of GSRO are particularly low. The groove- and cone-shape structures in Fig. 11a are typical irregularities on the otherwise smooth Gi-SRO and Gℓ-SRO blades, respectively. Collectively, these irregularities create a GSRO landscape, similar to the concept of ‘potential energy hyperspace’ or ‘energy landscape’ [61–63] in glass science, although the latter refers to the various mechanically stable glass structures of a substance at a fixed composition. Fig. 11a shows the triangular MLMG (the triangle LSK connected by dashed lines) and its vicinity at Ta = 593 K, with Gi-SRO and Gℓ-SRO in place. Geometrically, Gi-SRO is chosen to be groove-like with a minimum at Pd40Ni40P20 for two reasons: (i) as discussed before, i-SRO behaves as a liquid solution; and (ii) it is shown in ref. [51,52] that Pd40Ni40P20 in the glass state is exceptionally stable. Also geometrically, Gi-SRO is chosen to open up faster for P ≥ 20 at.%, but slower for P ≤ 20 at.%. The choice is based on the experimental results shown in Fig. 3 in ref.
an order-disorder change. Recently, Stolpe et al. [60] found an LLT in an undercooled Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 melt (a Vitreloy) by using synchrotron XRD. The authors associated the LLT with a change in heat capacity and entropy. They found that the entropy change of the LLT is only about 6% of the entropy of crystallization of the Vitreloy alloy, much less than that (59%) found in this work. Since the two liquids (before and after the LLT) described in the work of Stolpe et al. are not well characterized, the origin of the large difference in the entropy of LLT between this work and that of Stolpe et al. cannot be assessed at this point. Earlier, a thermodynamic model [50] based on Chen and Turnbull's suggestion [37] was proposed to explain the origin of the MLMG. The details are shown in Fig. 10a through b. Fig. 10a shows three Gibbs free energy curves, which are: (i) a conventional liquid free energy curve L that consists of SROs from all available types of clusters; (ii) a liquid free energy curve of i-SRO; and (iii) a liquid free energy curve of ℓ-SRO. The horizontal axis in the figure is along a composition direction that passes through both ℓ-SRO and i-SRO. Fig. 10b shows the creation of a miscibility gap when i-SRO and ℓ-SRO merge into L. The merging together is possible because it is not necessary to meet long-range order, as in crystalline solids. The thermodynamic model in Fig. 10a through b can explain the MLMG, but fails to explain the first-order LLT that occurs just outside the MLMG. Fig. 11a through c show a revised 3-dimensional thermodynamic model for the liquid spinodal decomposition and first-order LLT that 10
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Y.F. Lo et al.
Nat. Mater. (2007) 192–197. [6] G.N. Greaves, M.C. Wilding, S. Fearn, D. Langstaff, F. Kargl, S. Cox, Q. Vu Van, O. Majérus, C.J. Benmore, R. Weber, C.M. Martin, L. Hennet, Science (2008) 566–570. [7] R. Shimizu, M. Kobayashi, H. Tanaka, Phys. Rev. Lett. 112 (2014) 125702. [8] J.Z. Li, W.K. Rhim, C.P. Kim, K. Samwer, W.L. Johnson, Acta Mater. 59 (2011) 2166–2171. [9] S. Wei, F. Yang, J. Bednarcik, I. Kaban, O. Shuleshova, A. Meyer, R. Busch, Nat. Commun. 4 (2013) 2083. [10] S. Lan, M. Blodgett, K.F. Kelton, J.L. Ma, J. Fan, X.L. Wang, Appl. Phys. Lett. 108 (2016) 211907. [11] P.H. Poole, F. Sciortino, U. Essmann, H.E. Stanley, Nature 360 (1992) 324–328. [12] P.H. Poole, T. Grande, C.A. Angell, P.F. McMillan, Science 275 (1997) 322–323. [13] P.G. Debenedetti, Metastable Liquids, Princeton University Press, Princeton, NJ, 1997. [14] J.R. Errington, P.G. Debenedetti, Nature 409 (2001) 318–321. [15] I. Saika-Voivod, P.H. Poole, F. Sciortino, Nature 412 (2001) 514–517. [16] S. Sastry, C.A. Angell, Nature 2 (2003) 739–743. [17] D. Turnbull, J. Chem. Phys. 20 (1952) 411–424. [18] F.C. Frank, Proc. R. Soc. Lond. 215A (1952) 43–46. [19] G.D. Scott, Nature 188 (1960) 908–909. [20] G.D. Scott, Nature 194 (1962) 956–957. [21] J. Bernal, Proc. R. Soc. Lond. 280A (1964) 299–322. [22] J.L. Finney, Proc. R. Soc. Lond. 319A (1970) 495–507. [23] G.S. Cargill, J. Appl. Phys. 41 (1970) 12–29. [24] P. Chaudhari, D. Turnbull, Science 199 (1978) 11–21. [25] P.H. Gaskell, Nature 276 (1978) 484–485. [26] P.H. Gaskell, J. Non-Cryst. Solids 32 (1978) 207–224. [27] S. Sachdev, D.R. Nelson, Phys. Rev. Lett. 53 (1984) 1947–1950. [28] D.R. Nelson, F. Spaepen, Solid State Phys. 42 (1989) 1–90. [29] T. Egami, W. Dmowski, Y. He, R.B. Schwarz, Metall. Mater. Trans. 29A (1998) 1805–1809. [30] H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimaki, T. Lippmann, G. Reiter, Nature 408 (2000) 839–841. [31] J. Saida, M. Matsushita, A. Inoue, Appl. Phys. Lett. 79 (2001) 412–414. [32] A. Inoue, A. Takeuchi, Acta Mater. 59 (2011) 2243–2267. [33] H.W. Sheng, W.K. Luo, F.M. Alamgir, J.M. Bai, E. Ma, Nature 439 (2006) 419–425. [34] X.J. Liu, G.L. Chen, X. Hui, T. Liu, Z.P. Lu, Appl. Phys. Lett. 93 (2008) 011911. [35] N.A. Mauro, V. Wessels, J.C. Bendert, S. Klein, A.K. Gangopadhyay, M.J. Kramer, S.G. Hao, G.E. Rustan, A. Kreyssig, A.I. Goldman, K.F. Kelton, Phys. Rev. B 83 (2011) 184109. [36] P.F. McMillan, M. Wilson, M.C. Wilding, D. Daisenberger, M. Mezouar, G.N. Greaves, J. Phys. Condens. Mater. 19 (2007) 415101. [37] H.S. Chen, D. Turnbull, Acta Metall. 17 (1969) 1021–1031. [38] C.P. Chou, D. Turnbull, J. Non-Cryst. Solids 17 (1975) 169–188. [39] S. Lan, Y.L. Yip, M.T. Lau, H.W. Kui, J. Non-Cryst. Solids 358 (2012) 1298–1302. [40] Z.D. Wu, X.H. Lu, Z.H. Wu, H.W. Kui, J. Non-Cryst, J. Non-Cryst. Solids 385 (2014) 40–46. [41] Z.D. Wu, W.Z. Zhou, Y.F. Lo, S. Lan, H.W. Kui, J. Non-Cryst. Solids 410 (2015) 51–57. [42] P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Phys. Rev. B 28 (1983) 784–805. [43] A. Mizuno, S. Matsumura, M. Watanabe, S. Kohara, M. Takata, Mater. Trans. 46 (2005) 2799–2802. [44] K.F. Kelton, A.K. Gangopadhyay, T.H. Kim, G.W. Lee, J. Non-Cryst. Solids 352 (2006) 5318–5324. [45] S.Y. Wang, C.Z. Wang, M.Z. Li, L. Huang, R.T. Ott, M.J. Kramer, D.J. Sordelet, K.M. Ho, Phys. Rev. B 78 (2008) 184204. [46] M. Inui, K. Maruyama, Y. Kajihara, M. Nakada, Phys. Rev. B 80 (2009) 180201. [47] H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimaki, T. Lippmann, G. Reiter, Nature 408 (2000) 839–841. [48] F. Spaepen, Nature 408 (2000) 781–782. [49] W.Z. Zhou, Z.D. Wu, Y.F. Lo, H.W. Kui, J. Non-Cryst. Solids 432 (2016) 420–425. [50] M.T. Lau, S. Lan, Y.L. Yip, H.W. Kui, J. Non-Cryst. Solids 358 (2012) 2667–2673. [51] Z.D. Wu, S. Lan, H.W. Kui, Metall. Mater. Trans. A 45 (2014) 2399–2404. [52] S. Lan, Z.D. Wu, M.T. Lau, H.W. Kui, J. Non-Cryst. Solids 373–374 (2013) 5–12. [53] P.L. Maitrepierre, J. Appl. Phys. 40 (1969) 4826–4834. [54] H.W. Kui, A.L. Greer, D. Turnbull, Appl. Phys. Lett. 45 (1984) 615–618. [55] H.S. Chen, D. Turnbull, Acta Metall. 17 (1969) 1021–1031. [56] H.H. Liebermann, C.D. Graham, IEEE Trans. Magn. 12-6 (1976) 921–923. [57] H.S. Chen, C.D. Miller, Rev. Sci. Instrum. 41 (1970) 1237–1238. [58] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesion in Metals - Transition Metal Alloys, Elsevier Science Publishers B.V., Amsterdam, 1989. [59] G. Wilde, G.P. Gorler, R. Willnecker, J. Fecht, J. Appl. Phys. 87 (2000) 1141–1152. [60] M. Stolpe, I. Jonas, S. Wei, Z. Evenson, W. Hembree, F. Yang, A. Meyer, R. Busch, Phys. Rev. B 93 (2016) 014201. [61] F.H. Stillinger, T.A. Weber, Science 225 (1984) 983–989. [62] F.H. Stillinger, Science 267 (1995) 1935–1939. [63] C.A. Angell, MRS Bull. 33 (2008) 544–555.
[41], where it was found that the glass forming ability decreases rapidly with P ≥ 20 at.%, but slowly for P ≤ 20 at.%. Gℓ-SRO, as discussed before, behaves like a liquid intermetallic compound. Geometrically, it is chosen to have a shape as shown in Fig. 11a, with the vertex at a composition of ~Pd50Ni36P14. The choice is again based on the composition-dependent glass forming ability of PdeNieP alloys as listed in Fig. 3 of ref. [41]. Consider a straight line HK in the MLMG, with point R on it. A point, such as H, K, or R, represents a composition. A vertical plane (not shown) is then introduced into the figure with its bottom edge sitting on the line HK. It cuts through both Gi-SRO and Gℓ-SRO. The intersecting curves are shown in Fig. 11b(i). Thermodynamics then predicts that a homogeneous liquid of composition, R (either with i-SRO or ℓ-SRO symmetry), decomposes into a mixture of two liquids, which are H (iSRO) and K (ℓ-SRO), to reduce the overall Gibbs free energy of the system. There are two decomposition modes for R to choose from: nucleation and growth or spinodal decomposition. Kinetically, the spinodal reaction is preferred as reaction barrier is absent. This mechanism is made possible by the fact that liquids do not have any longrange order. As a result, Gi-SRO and Gℓ-SRO can join together, forming a hump in G for LSD to take place, as shown in Fig. 11b(ii). Table 2 shows that it is easier to nucleate out i-SRO than ℓ-SRO. If R is quenched to Trt rapidly, only i-SRO survives. On the other hand, if an intermediate thermal annealing (or slow quenching rate) is employed, a spinodal mechanism occurs in R: i-SRO → i-SRO + ℓ-SRO. For compositions below the composition line of Pd80 − xNixP20 and outside, but in the vicinity of, the MLMG (such as Pd59Ni25P16 and Pd40Ni45P15 as shown in Fig. 4), it is clear that Gi-SRO > Gℓ-SRO (Fig. 11a and b(ii)). Thermodynamics predicts that only first-order phase transitions are possible between them. It can then be concluded that with a fast quenching rate, a PdeNieP melt is quenched into i-SRO (Table 2). A subsequent thermal annealing will transform it into ℓ-SRO by a first-order process. If on the other hand the cooling rate is slow enough, there is enough time for the first-order LLT to take place: iSRO → ℓ-SRO. 5. Conclusions Five conclusions can be drawn from the experimental results. First, a liquid-liquid phase transition (LLT) is observed in the undercooling regime of molten PdeNieP. The reaction can be represented by, L → L + L′ (L′ from nucleation and growth) → L′, where L and L′ have i-SRO and ℓ-SRO, respectively, and they have the same composition. Second, electron microscopy (an entropic approach to classify the order of a phase transition) establishes that the LLT is a first-order phase transition. Third, the latent heat of the LLT is measured. Its lower bound value is 3690 J/mol. Fourth, because it is a first-order LLT, the SROs of undercooled PdeNieP are divided into groups and each group containing one or more SROs. Furthermore, each group of SROs represents a physical liquid. Fifth, each group of SROs can be assigned a Gibbs free energy, GSRO(P, T, c). As a result, the thermodynamics of liquids can be described in terms of these GSRO(P, T, c). References [1] O. Mishima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393–395. [2] S. Aasland, P.F. McMillan, Nature 369 (1994) 633–636. [3] Y. Katayama, T. Mizutani, W. Utsumi, O. Shimomura, M. Yamakata, K. Funakoshi, Nature 403 (2000) 170–173. [4] M.H. Bhat, V. Molinero, E. Soignard, V.C. Solomon, S. Sastry, J.L. Yarger, C.A. Angell, Nature 48 (2007) 787–790. [5] H.W. Sheng, H.Z. Liu, Y.Q. Cheng, J. Wen, P.L. Lee, W.K. Luo, S.D. Shastri, E. Ma,
11