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Metastable intermetallic phases in the Al-Sm system
Materials Today Communications 21 (2019) 100673
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Metastable intermetallic phases in the Al-Sm system a
a
S.H. Zhou , F.Q. Meng , M.J. Kramer a b
a,b
a
a
a
, R.T. Ott , F. Zhang , Z. Ye , S. Jain
a,b
a,b,⁎
, R.E. Napolitano
T
Division of Materials Science and Engineering, Ames Laboratory, DOE, USA Department of Materials Science and Engineering, Iowa State University, USA
ARTICLE INFO
ABSTRACT
Keywords: Intermetallic Metastability X-ray diffraction CALPHAD Devitrification
The thermodynamic landscape involving several metastable phases in the glass-forming Al-Sm system is assessed, integrating experimental measurements and first principles calculations into a comprehensive CALPHAD description. The phases examined here include Al41Sm5-η, Al60Sm11-ε, Al5Sm-θ, Al5Sm-π and Al4Sm-γ, having basis stoichiometries from 9 to 20 at% Sm, a range over which the Al-fcc and Al3Sm phases are stable. Amongst the metastable phases examined, our findings indicate that the Al41Sm5-η and Al60Sm11-ε phases comprise the convex hull of minimum formation energies at absolute zero. Competitive crystallization processes were investigated through situ X-ray diffraction and differential scanning calorimetry and used to assess relative stability within the overall landscape. Asserting thermodynamic scenarios consistent with our measurements, temperature-dependent Gibbs free energies for the metastable phases are proposed along with the corresponding constrained phase diagrams, comprehensively showing metastable phases and associated invariant reactions. Assumptions and limitations of the proposed thermodynamic model are discussed with reference to available transport data.
1. Introduction Aluminum rare-earth alloys generally exhibit marginal glassforming tendency, which can be enhanced considerably by transition metal alloying [1–9]. Within this class of alloys, systems based on the Al-Sm binary are among the most extensively studied, and the number of metastable phases reported offer a rich landscape of structures accessible from the glassy state [2–7]. Indeed, transformation pathways involving the alloy glass as an intermediate state have been shown to give rise to several complex large-unit-cell phases and devitrification morphologies. The selection of these glass-enabled phases has been attributed to kinetic factors such as the limited atomic mobility and the presence of sub-crystalline precursors (a.k.a. crystal genes) inherent in the glass structure [10]. While recent experimental and theoretical investigations of complex intermetallic phases in the Al-Sm system have shed considerable light on the metastable phase landscape, recent findings [10–14] have not been reconciled with previously reported observations [2–9], and the comprehensive thermodynamic picture has not been substantially clarified. The Al-Sm alloys in the composition range of 8–16 at% Sm, nominally, can be rapidly solidified to the amorphous state [3,15], with alloys at the lower end of this range (∼8 at%) exhibiting Al(fcc) nanocrystals in the as-quenched state [16–19]. Upon devitrification, these
⁎
have been shown to promote primary crystallization of the Al(fcc) phase through growth of these quenched-in crystals, even though growth is limited by diffusive soft-impingement [6]. For alloys with higher Sm content, several metastable intermetallic phases have been observed to crystallize, as summarized in Table 1 [2,6–8]. Metastable intermetallics in Al-Sm, first reported by Battezzati et al. [2], were generically designated as MS1, MS2, MS3, and Al4Sm. Upon heating, the 10 at pct. Sm amorphous alloy was observed to crystallize fully to the MS1 phase, with no other product phases forming. Examining isothermal crystallization in melt-spun Al-Sm amorphous alloys with compositions ranging from 8 to 14 at. pct Sm, Guo et al. [7] observed three previously unidentified metastable crystalline phases, reporting them as M1 (hexagonal: lattice parameters a = 0.4597 nm and c = 0.6358 nm), M2 (cubic: lattice parameter a = 1.9154 nm) and S3 (orthorhombic: lattice parameters a = 1.3781 nm, b = 1.1019 nm and c = 0.7303 nm). A subsequent investigation by Rizzi et al. [8] confirmed that the MS1 and MS2 phases exhibit cubic and tetragonal structures, respectively, with MS2 having the Al4Sm stoichiometry (presently known as the high-temperature Al4Sm-β phase [2,20]. In addition, Rizzi et al. concluded that the previously reported Al4Sm phase [2] and S3 phase [7] are the same, an orthorhombic phase (Al4U prototype), presently termed Al4Sm-γ [13]. Recent work has further clarified this picture. The phases reported
Corresponding author at: Materials Science and Engineering, Iowa State University, 2220 Hoover Hall, 528 Bissell Road, Ames, IA 50014, USA. E-mail address: [email protected] (R.E. Napolitano).
https://doi.org/10.1016/j.mtcomm.2019.100673 Received 8 July 2019; Received in revised form 20 September 2019; Accepted 26 September 2019 Available online 30 September 2019 2352-4928/ © 2019 Elsevier Ltd. All rights reserved.
Materials Today Communications 21 (2019) 100673
S.H. Zhou, et al.
Table 1 Summary of reported crystallization sequences observed upon heating amorphous Al-Sm alloys in the composition range from 0.08 to 0.14 at% Sm. XSm
Observed phase sequence, as originally reported in the indicated reference
“Transition” Temps. (K)
Ref.
0.08
Am + Al(traces) > > Al + am > > Al + MS2 > > Al + Al4Sm Am > > Am + α-Al > > α-Al + Al4Sm > > α-Al + S3 (ortho) Am > > Am + Al > > Al + α- Al11Sm3 (tetra) > > Al + o-Al4Sm Am > > MS1 > > Al + MS2 > > Al + Al4Sm Am > > α-Al + Al4Sm + M1 (hexa) > > α-Al + Al4Sm + M1(hexa) > > αAl + S3 (ortho) Am > > MS1(cubic) > > Al+ α- Al11Sm3 (tetra) +M1(hexa) > > Al + o-Al4Sm Am + Al + M2 > > Am + Al + M2 > > Al+ α- Al11Sm3 (tetra) > > Al + o-Al4Sm Am > > fcc-Al + MS1(cubic) > > fcc-Al+ H1(hexa) > > fcc-Al + Al4Sm(ortho) Am + Al11Sm3 > > Al + Al11Sm3 +MS2 + MS3 > > Al + Al4Sm Am > > α-Al + Al4Sm + M1 (hexa) > > α-Al + Al4Sm + M1(hexa) > > αAl + S3 (ortho) Am + Al+ α- Al11Sm3 (tetra) +M1(hexa) > > MS1(cubic) +Al+ α- Al11Sm3 (tetra) + M1(hexa) > > Al + o-Al4Sm Am > > Al + Al11Sm3+MS3 > > Al + Al11Sm3 > > Al + Al4Sm Am > > α-Al + Al4Sm + M2(cubic) > > α-Al + Al4Sm + M1 (hexa) > > α-Al + S3 (ortho)
444 473 523 511 507
[2] [7] [8] [2] [7] [8] [8] [9,21]
0.10
0.12
0.14
/ / / / /
542 541 593 590 580
/ 673-736 / 594 /873 / 736 / 724
543 / 683 / 873 543 / 683 / 873 483 / 542 / 667 526 / 742 507 / 580 / 724 558 / 873 522 / 581 / 802 508 / 600 / 763
[2] [7] [8] [2] [7]
Note: The transition temperatures listed for Ref. [2] are estimated here from Fig.3 in that reference. Table 2 Summary of metastable phase nomenclature in relevant reports. Phase name used presently
Prototype
Al5Sm-π [22] Al61Sm11-ε [10] — Al4Sm-γ [13,23] Al4Sm-β [20,24] Al5Sm-θ [11] Al41Sm5-η [12]
Cu5Ca bcc — Al4U Al4Ba hcp tetragonal
Lattice Parameters (Å)
Phase names used in prior reports
a
b
c
Ref. [2]
Ref. [7]
Ref. [8]
Ref. [9]
4.597 13.904 — 4.44 4.28 5.451 13.284
— — — 6.38 — — —
6.356 — — 13.62 9.90 17.874 9.568
— MS1 MS3 Al4Sm MS2 — —
M1 M2 — S3 — — —
M1 MS1, M2 — S3 MS2 — —
H1 MS1 — Al4Sm — — —
as MS1 [2] and as M2 [7,8] were determined to be the same bodycentered cubic phase (Im 3¯ m, space group 229), presently designated as Al60Sm11-ε [10]. The phase previously reported as M1 [7] and as H1 [8,9] was confirmed to be hexagonal (P6/mmm, space group 191) and is presently designated as Al5Sm-π [22]. Recent work has further revealed two additional metastable phases that crystallize from the Al-Sm glass, including hexagonal Al5Sm-θ (P6322, space group 182) [11] and tetragonal Al41Sm5-η (I4/m, space group 87) [12]. These reports are summarized in Tables 1 and 2. The recently identified intermetallic phases, Al60Sm11-ε, Al41Sm5-η, Al5Sm-θ, and Al5Sm-π, constitute a rich low-temperature landscape in the Al-Sm system [10–12,22]. Owing to their metastable nature, however, thermodynamic description presents a significant challenge. Here, we address this challenge through first-principles calculations and experimental measurement of crystallization reactions upon heating of glassy alloys produced by melt spinning and DC magnetron sputtering. Differential scanning calorimetry (DSC) and in situ high-energy X-ray diffraction (HEXRD) are used to investigate phase transformations in the competitive low-temperature regime in which these metastable phases are observed to form. Calculations and experiments are used, with clearly stated assumptions, to incorporate these phases into a selfconsistent CALPHAD treatment of this system.
compositions of the MR and TF samples were measured using an x-ray fluorescence (XRF) spectrometer (Bruker M4 TORNADO Micro-XRF instrument) operated at 50 kV and 300 μA. with a Rh target and a 25 μm spot size. 2.2. Experiments Devitrification response and subsequent phase transformations occurring upon heating of amorphous MR and TF specimens were investigated using in-situ high-energy wide-angle X-ray scattering (WAXS). (Synchrotron X-ray diffraction was performed at the 1-ID-E beam line at the Advanced Photo Source, Argonne National Laboratory, USA.) Monochromatic X-rays of 71.77 keV (λ = 0.01728 nm) and 80.72 keV (λ = 0.01536 nm) were used to quantify the phase evolution during heating at 10 K/min. The X-ray imaging was performed in transmission mode using a 4-detector arrangement of amorphous silicon detectors (GE-RT41), each with 2048 × 2048 pixel array, situated down-beam of the furnace to collect the two-dimensional patterns. Samples were sealed in thin-walled SiO2 capillary tubes with inner diameter of 2 mm and heated using an infrared lamp. For direct comparison with X-ray data, corresponding differential scanning calorimetry (DSC) traces were obtained for each alloy using a heating rate of 10 K/min (Perkin Elmer Pyris DSC instrument).
2. Materials and methods
2.3. Calculation of phase stabilities through first principles
2.1. Preparation of amorphous alloys
To determine the relative stabilities of the η, ε, θ, π, and γ in comparison with the stable Al(fcc) and δ phases, the internal energy E is computed for each phase using the Vienna ab initio simulation package (VASP) code [27] using projector-augmented wave (PAW) potentials [28] with a high precision generalized gradient approximation (GGA) [29] and Monkhorst-Pack k-point sampling. The enthalpy of formation
Amorphous melt-spun ribbons (MR) of 9.7 and 10.9 at% Sm (20–30 μm thickness) were produced by arc-melting followed by singleroll melt-spinning. In addition, amorphous thin film specimens (TF) of Al-10.9 at% Sm were produced by sputter-deposition onto a silicon substrate. Both methods are described elsewhere [25,26]. The chemical 2
Materials Today Communications 21 (2019) 100673
S.H. Zhou, et al.
Table 3 Summary of the thermodynamic models used for the Al-Sm binary system. Phase
Prototype
Method (Formulation)
Free energy formulation (Gm =
Liquid
—
Association model (Al,Al2Sm,Sm)
ref
L
id L Gm L Gm
Cu α-Sm W
One-sublattice model (Al,Sm)1
Gm +
Gm =
xs
Al-fcc Sm-rho Sm-bcc
ref
id
xs
Gm )
Gm +
i = Al, Sm xi
0
Gi
L
=
RT 1 + 2y Al2 Sm
i = Al, Sm yi lnyi
=
1 1 + 2y Al2 Sm
i
j > i yi yj
0
L
0 Li, j + y Al2 Sm G Al 2 Sm
(i , j = Al, Al2 Sm , Sm ) ( yi = mole fraction of species i) ref
Gm =
id
i = Al, Sm xi
0
Gi
G m = RT
xs
Gm =
Two-sublattice model (Al,Sm)m (Al,Sm)n Al41Sm5-η tetragon-like (Al,Sm)0.891(Al,Sm)0.109 hcp-like (Al,Sm)0.833(Al,Sm)0.167 Al5Sm-θ Al5Sm-π Cu5Ca (Al,Sm)0.833(Al,Sm)0.167 Al4Sm-β Al4Ba (Al,Sm)0.8(Al,Sm)0.2 Al4Sm-γ Al4U (Al,Sm)0.8(Al,Sm)0.2
i = Al, Sm xi lnxi j n xAl xSm j = 1 LAl,Sm (xAl
ref
Gm =
0
Gi : j = Gi : j + m
id
G m = RT
I I Gm = yAl ySm II II yAl ySm
Four-sublattice model Al0.761(Al,Sm)0.084(Al,Sm)0.113Sm0.042 Al60Sm11-ε bcc-like (Al)0.761(Al,Sm)0.084 (Al,Sm)0.113(Sm)0.042
0
Giref
i = Al, Sm
xs
+
II 0 j = Al, Sm yj Gi : j
I i = Al, Sm yi
0
xSm ) j
+ n Gref ( Gi : j = ai : j + bi : j T ) j
(myiI lnyiI + nyiII lnyiII )
II i = Al, Sm yi
k =0
k
I L Al, Sm : i (yAl
k
I i = Al, Sm yi
II k = 0 Li, Al, Sm (yAl
I k ySm )
II k ySm )
( yiI = species i occupancy fraction on sublattice I) ref
Gm =
III 0 G Al : i : j : Sm l = Al, Sm, Va yj 0 fcc 0 GAl : i : j : Sm + 0.761 GAl + 0.084 Giref
II i = Al, Sm, Va yi
0
G Al : i : j : Sm =
0
0
rho + 0.113 Gref + 0.042 GSm j
( GAl : i : j : Sm = aAl : i : j : Sm + bAl : i : j : Sm T ) id
G m = RT
xs
i = Al, Sm, Va
II II G m = yAl ySm
(0.084yiII lnyiII + 0.113yiIII lnyiIII )
III i = Al, Sm, Va yi
for a given compound is calculated as the difference between the energy E of the compound and the linear combination of the pure element rho reference state energies, EAlfcc and ESm ,
Hf = E
xAl EAlfcc
rho xSm ESm .
k =0
k
II L Al: Al, Sm : i : Sm (yAl
II k III III ySm ) + yAl ySm
II i = Al, Sm, Va yi
k=0
k
III LAl: i : Al,Sm : Sm (yAl
III k ySm )
3. Results X-ray diffraction and calorimetry measurements are summarized in Figs. 1–3. In situ WAXS data and the corresponding DSC trace for the 9.7 at. pct Sm (MR) alloy are plotted in Fig. 1(a), revealing three distinct temperature intervals separated by two transition regimes, observed nominally at ∼490 K and ∼530-550 K, respectively. Rietveld analysis [33] of individual diffraction patterns was used to identify the phases present and their relative fractions as a function of temperature (time). The results, shown in Fig. 1(b, c), can be summarized by the following net transition sequence:
(4)
2.4. Thermodynamic modeling We have previously assessed the Al-Sm binary system and refer the reader to these reports for a description of the general formulation, where we apply a three-species (Al, Al2Sm, Sm) association model for the liquid and treat the fcc, bcc, and rhombohedral terminal solid solution phases as simple substitutional solutions [30,31]. Proceeding now to integrate the metastable intermetallic phases, Al41Sm5-η, Al60Sm11-ε, Al5Sm-θ, Al5Sm-π and Al4Sm-γ, we employ a two-sublattice model for all but the Al60Sm11-ε phase, for which we employ a foursublattice formulation, according to its reported structure [10]. For convenience, these phases will hereafter be referred to by symbol only. The Al-fcc phase will be referred to simply as fcc. The specific sublattice descriptions used presently are listed in Table 3, along with the overall free energy formulations for each phase. Given these formulations, sublattice end-members for the η, θ, π, β, and γ phases include four different stoichiometries, with formation free energies described as Gi :j = ai :j + bi :j T (i or j = Al and Sm).For the ε phase, we employ a different set of four end-members, with the formation free energy given as GAl : i : j : Sm = aAl :i :j :Sm + bAl : i :j : Sm T . Thermodynamic functions for the pure element states are taken from the Refs. [30,32] as listed in Table 4. Model parameters were evaluated through collective analysis of first-principles calculations and experimental measurements, as described briefly in the following sections.
Amorphous > > fcc + ε + η > > fcc + β + π
(1)
observed on heating. Similar experimental data for the 10.9 at. pct Sm (MR) alloy are shown in Fig. 2, revealing four distinct temperature intervals separated by three transition regimes, as summarized by the following sequence observed on heating: Amorphous > > ε > > fcc + β + π > > fcc + γ + β
(2)
where the three transition regimes were observed at 483 K, 520–570 K, and 670–780 K. For the 10.9 at% Sm (TF) alloy (See Fig. 3) experimental data revealing three distinct temperature intervals separated by two transition regimes, as summarized by following net sequence on heating: Amorphous > > fcc + θ > > fcc + β + π + γ
(3)
where the net reactions were observed at ∼525 K and 560–590 K respectively. For all three sequences described here, it should be noted that the net transitions indicated in Eqs. (1)–(3) simply state the observed change in phases present within each temperature interval and are not intended here to indicate any specific reaction or 3
Materials Today Communications 21 (2019) 100673
S.H. Zhou, et al.
Table 4 Coefficients for the standard Gibbs free energies of pure Al and Sm in the relevant phases [13,14,30]. Tmin Tmax 0G ref i
0G L Al
0G L Al
298 933.47
933.47 3200
0G fcc Al
0G fcc Al
0Gbcc Al
0G fcc Al
298 700
700 933.47
933.47 2900
298 3200 0G fcc Al
a0 a1 a2 a3/10−2 a4/10−6 a5 a6 a7/10−28 a8
11005.029 −11.841867 — — — 7.934 x10−20 — — 1
−795.996 177.430178 −31.748192 — — — — — —
7976.15 137.093038 −24.3671976 -0.1884662 −0.877664 — 74092 — —
−11276.24 223.048446 −38.5844296 1.8531982 −5.76422 — 74092 — —
−11278.37 188.68415 −31.74819 — — — — −1.2305 —
10083 −4.813 — — — — — — —
Tmin Tmax
298 3200
0Grho Al
0G L Sm 298 1190
1190 2100
0G bcc Sm 298 1190
1190 1345
1345 2100
0G ref i
0G fcc Al
3468.783 20.117456 −11.696828 −3.2418177 4.54427 — 23528
−11728.229 273.48707 −50.208 — — — —
−15957.862 253.121044 −46.9445 — — — —
111191.653 −624.680805 71.6856914 −0.4731496 3.32986 — −24870276
a0 a1 a2 a3/10−2 a4/10−6 a5 a6
2283.5 — — — — — — 0G rho Sm
−4368.72 55.972523 −16.929849 −2.544601 3.5795 94209
0G fcc Sm
Tmin Tmax
298 700
700 1190
1190 1345
1345 2100
298 2100
0G ref i a0 a1 a2 a3/10−2 a4/10−6 a5 a6
−3872.013 −32.10748 −1.6485 −5.0254 10.1035 — −82168
−50078.215 627.869894 −102.665 4.74522 -7.5384 — 3861770
289719.819 −2744.50976 381.41982 −25.4986338 27.51215 — −40102102
−23056.079 282.194375 −50.208 — — — —
890 — — — — — —
* Note: Each Gibbs free energy is described as: 0Gi = 0GiREF + a 0 + a1 T + a2 T ln T + a3 T 2 + a4 T 3 + a5 T 4 + a6 T
thermodynamic condition. Interpretation of the observed net reactions will be revisited in a later section. Before proceeding with the thermodynamic analysis, it is prudent to point out a few important features apparent in the data presented in Figs. 1–3, within the context of previously reported observations. In particular, we are compelled to make note of the difference between our observations and those which report a clearly discernable (in DSC) initial crystallization peak for the Al(fcc) phase, associated with the growth of quenched-in nanocrystals. For the 10.9 at% Sm sputtered thin film (TF) specimen (Fig. 3), it is not surprising that we have no initial Al (fcc) crystallization peak. The effective cooling rate here is much higher than that of the melt-spun ribbon, and it is certainly reasonable that the nucleation of Al(fcc) nanocrystals does not occur in this case, as it might during quenching from the melt. Looking at the data for the two meltspun ribbon specimens, we see evidence of Al(fcc) in the diffraction data for 9.7 at% Sm but no separate exothermic peak in the DSC trace (Fig. 1). This suggests that the multiphase structure is forming simultaneously, as indicated by a single primary crystallization peak in the DSC trace. Certainly, considering the high driving forces, it is possible that this crystallization includes one or more coupled-growth or co-operative nucleation scenarios involving the formation of ε, η, and Al (fcc) from the amorphous phase. In contrast, there is no discernable evidence of the Al(fcc) phase formation during the initial crystallization for the 10.9 at % Sm alloy. For this composition, the driving force for ε formation is very high while requirements for chemical partitioning are rather low, plausibly favoring crystallization of ε over the Al(fcc) phase. In addition, we have observed and reported on the ability of the ε phase
— —
0G rho Sm
1
+ a7 T
9
a8 RT ln(1 + e
— — — — — — — / RT )
(J/mol).
to accommodate site occupancy defects [10], so that it may crystallize in a partitionless (or nearly partitionless) manner over a rather large composition range. Of course, it would be driven to subsequently decompose, as we clearly see in Figs. 1–3. The relevance of these issues notwithstanding, we return to the primary intent of the present communication and to our stated focus of formulating a self-consistent thermodynamic description so that these dynamics can be more effectively investigated. Results from first principles calculations are summarized in Table 5 and Fig. 4, showing the relative stability of the η, ε, θ, π, and γ phases with respect to the stable fcc + δ two-phase state, represented in Fig. 4 by the dashed horizontal reference line. The metastable two-phase states of fcc + β and fcc + γ are also indicated by dashed lines in Fig. 4. Here, we see clearly that the complex intermetallic phases η, ε, θ, π, are all stable with respect to decomposition to fcc + β but unstable with respect to decomposition to both the metastable fcc + γ state and the stable fcc + δ state. 4. Discussion and parameter evaluation Employing the formulation described above and summarized in Table 3, the model parameters corresponding to the γ, π, ε, η, and θ phases were evaluated in a manner consistent with the computed formation energies and experimentally observed phase transition sequences. Parameters for the Al4Sm-β, Al11Sm3-α, Al3Sm-δ, Al2Sm-σ, AlSm-ψ, and AlSm2-χ phases were taken from our prior assessments [30,31]. All model parameters, including those determined in this 4
Materials Today Communications 21 (2019) 100673
S.H. Zhou, et al.
Fig. 1. (a) The high-energy X-ray scattered intensity with a superposed DSC trace for the 9.7 at% Sm MSR specimen, both collected during heating at 10 K/min; (b) corresponding phase fraction vs temperature determined through Reitveld analysis; (c) diffraction patterns indicating the phases present at selected temperatures.
work, are summarized in Table 6, and our evaluation methodology is detailed in the remainder of this section. The temperature-independent parameters in the end-member formation free energies, listed in Table 3 as ai :j (φ = γ, η, θ, or π) and aAl :i :j :Sm , were taken as the computed zero-Kelvin formation energies listed in Table 5. The coefficients for required temperature-dependent terms, bAl : Sm (φ = γ, η, θ, π) and bAl : Al :Sm :Sm , were determined by considering the experimental observations, as described below. The γ-β allotropic transition temperature (both phases metastable) was recently determined to be 896 K [14], and we use this value presently to determine the parameter bAl : Sm , as given in Table 6. The remaining parameters bi :j are taken as zero. The resulting constrained equilibrium phase diagram is plotted in Fig. 5, showing the γ-β transition and related invariant reactions in the Al-Sm binary. Examining first the HEXRD data shown in Fig. 2, we consider the constant-heating-rate phase evolution sequence (fcc + π + β > > fcc + γ + β) observed in the regime from 670 to 760 K. Upon closer examination of the temperature-dependent phase fractions ( f ) plotted in Fig. 2(b), it is apparent that this overall evolution sequence involves two distinguishable transformation stages. The first involves decomposition of the π phase, appearing as a relatively abrupt transition in the
range of 670–710 K, corresponding with dramatic increases in f fcc and f , along with a modest increase in f . This is followed by a second stage, observed from 710 to 760 K, involving a distinct decrease in f with a corresponding increase in f . We note that, while f is increasing with temperature during both stages, a clear change in df / dT delineates the two stages. To interpret this observation, we recognize three important points. First, we note that this entire range is below the metastable allotropic transition temperature of 896 K, such that the γ phase is stable throughout, relative to the β phase. Second, we note from the zero-Kelvin enthalpies (see Fig. 4) that the π phase is unstable with respect to fcc+γ even at absolute zero. Assuming that the relative stability of π decreases with increasing temperature (previously reported observations of fcc+β and fcc+γ cast structures support this hierarchy [14]), it follows that the π→fcc+γ decomposition reaction is driven for all temperatures and that no π-fcc-γ invariant is observable. Third, unlike the π→fcc+γ reaction, the π→fcc+β decomposition is not driven at absolute zero (Fig. 4). Furthermore, the fact that β exhibits a high-temperature range of stability suggests the existence of a metastable π-fcc-β invariant at some intermediate temperature. With these points recognized, we interpret the distinct first-stage onset (on 5
Materials Today Communications 21 (2019) 100673
S.H. Zhou, et al.
Fig. 2. (a) The high-energy X-ray scattered intensity with a superposed DSC trace for the 10.9 at% Sm MSR specimen, both collected during heating at 10 K/min; (b) corresponding phase fraction vs temperature determined through Reitveld analysis; (c) diffraction patterns indicating the phases present at selected temperatures.
heating) as an indication of such an invariant temperature and consider the abrupt initial transition stage (670–720 K) as an indication of the π→fcc+β decomposition reaction. We interpret the increase in fγ over this same temperature range as a consequence of simultaneous trans), which has formed well formation of the metastable β phase ( below the allotropic (γ−β) equilibrium temperature of 896 K. Thus, the T curve in Fig. 2b indicates the completion of slope change in the f the π→fcc+β decomposition, with further changes in phase fractions associated with continuation of the transition. Based on this interpretation of the data, we take the first-stage onset temperature (on heating), estimated as 674 K (see Fig. 2c), as an upper-bound estimate of the π→fcc+β invariant and use this to evaluate the parameter bAl :Sm . The remaining bi :j parameters are taken as zero. A corresponding constrained equilibrium phase diagram, including the liquid, fcc, γ, and π phases, is shown in Fig. 5c. Considering the lower temperature sequence in Fig. 2, involving the apparent decomposition of the ε phase and the net transition to fcc, β, and π at approximately 550 K, the possible reactions to consider are (i) ε→fcc+β and (ii) ε→fcc+π. Here, we make arguments similar to those described above for the higher temperature sequence. Because reaction (ii) is shown to be driven at 0 K (see Fig. 4), we assume that it is driven
at all temperatures such that no ε-fcc-π invariant is observable. On the other hand, Fig. 4 shows that reaction (i) is not driven at 0 K, and we assume that it becomes driven above some unknown invariant temperature. Accordingly, considering the abruptness of the observed transition, we take the onset temperature as an upper-bound estimate of the invariant temperature, estimated as 544 K (see Fig. 2c). Similar analysis and interpretation of HEXRD data for the Al-9.7 at pct Sm MR alloy yields a second estimate of 534 K for the of the ε→fcc+β invariant (Fig. 1c), and we take the mean value of 539 K as an estimate of this temperature. Base on previously reported experiments and computation, there is an additional condition that we employ for parameter evaluation for the ε phase. This phase has been shown to nucleate and grow with little or no chemical partitioning, enabled by variable site occupancies [2]. Accordingly, we assume that the observed ε crystallization temperatures (470 and 483 K) indicated in Figs. 1 and 2, are less than or equal to the T0 temperature for the two specific alloy compositions examined (9.7 and 10.9 at%, respectively). With this condition, along with an estimated temperature of 539 K for the ε→fcc+β invariant, we evaluate the four relevant model parameters (one bAl : Al :Sm :Sm parameter and three kL Al :Al : Al, Sm : Sm parameters, where k = 0, 1, 2), as listed in Table 6. 6
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Fig. 3. (a) The high-energy X-ray scattered intensity with a superposed DSC trace for the 10.9 at% Sm TF specimen, both collected during heating at 10 K/min; (b) corresponding phase fraction vs temperature, plotted over selected ranges; (c) diffraction patterns indicating the phases present at selected temperatures; (d) an expanded view of the DSC traces in the regime of the higher-temperature transition.
The corresponding constrained equilibrium phase diagram is shown in Fig. 6a and the relevant T0 curve is shown in Fig. 6(a,b). With similar arguments as employed above, we employ the HEXRD data in Fig. 1 to assess the η phase. Examining first the upper temperature overall transition, fcc+ε+η > > fcc+β+π, we consider the two possible decomposition reactions: (i) η→fcc+π and (ii) η→fcc+β. As described previously, we take the transition onset as a likely upperbound indicator of the η→fcc+β invariant and estimate this temperature as 530 K, as shown Fig. 1c. The parameter bAl : Sm was determined using this estimate, and other bi :j parameters were taken as zero, as listed in Table 6. The corresponding metastable phase diagram, showing only the liquid, fcc, Al41Sm5-η and Al4Sm-β phases, is plotted in Fig. 6c. Fig. 3 summarizes the overall sequence observed on constantheating-rate (10 K/min) treatment of the Al-10.9 at pct Sm (TF), with the overall phase evolution sequence given in Eq.(3). The initial crystallization involves both fcc and θ phase in the range of 520–530 K. Examining the subsequent portion of the net transition sequence in Eq. (3) (fcc+θ > > fcc+β+π +γ), which appears in the range of 550–600 K (Figs. 3(a–c)), we consider the possible reactions: (i) θ→π,
(ii) θ→fcc+γ, and (iii) θ→fcc+β. As shown in Fig. 4, reactions (i) and (ii) are driven at 0 K, while reaction (iii) is not. Attributing the formation of β to heating beyond an θ→fcc+β invariant, we take the onset as a reasonable estimate of the upper bound for this temperature. (While XRD measurements of phase fraction data are not available over the intermediate range from 568 to 585 K (Fig. 6c), the DSC trace indicates a smooth transition with no discontinuities.) This onset was estimated from the DSC data as 570 K, as shown in Fig. 3d, and the parameter bAl : Sm was evaluated, as listed in Table 6. The remaining bi :j parameters are taken as zero. The computed constrained equilibrium phase diagram, including liquid, θ, fcc, and β phases, is plotted in Fig. 6d. A brief comment is warranted here concerning the present interpretation of transformation sequences. In several cases, we assume that a transformation observed upon heating reflects a change in relative phase stability and, as such, serves as an upper bound to a specific invariant temperature, which we have stated clearly. We use these assumptions to enable a well-defined comprehensive thermodynamic description that is consistent with the observations at hand along with previously reported formulations. Of course, explicit confirmation that 7
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Table 5 Formation enthalpies at 0 K, computed from first-principles (Eq. (4)). Phase
Prototype
Formula
k points
Al-fcc Sm-rho Al41Sm5-η
Cu Sm tetragonal
Al Sm Al41Al 5 Al41Sm5 Sm41Al 5 Sm41Sm5 Al5Al Al5Sm Sm5Al Sm5Sm Al20Al4 Al20Sm4 Sm20Al4 Sm20Sm4 Al54Al6Al8Sm3 Al54Al6Sm8Sm3 Al54Sm6Al8Sm3 Al54Sm6Sm8Sm3 Al20Al4 Al20Sm4 Sm20Al4 Sm20Sm4 Al3Sm
12, 12, 12 8, 8, 12 8, 8, 12
Al5Sm-π
Cu5Ca
Al5Sm-θ
hcp
Al60Sm11-ε
bcc
Al4Sm-γ
Al4U
Al3Sm-δ
Ni3Sn
6, 6, 4
10, 10, 8
4, 4, 4
4, 6, 2
10, 19, 12
Table 6 Evaluated thermodynamic model parameters (in SI unit).
ΔHf (J/mol) 0 0 11512.1 −13647.2 10476.8 13847.3 22622.0 −27330.0 184334.0 153819.0 11201.8 −23378.1 21476.56 21409.8 −520.9 −22211.6 −1476.56 −19680.2 18610.0 −33324.5 20782.6 15117.7 −43421.1
Phase
Parameter
Value, J/mol
Ref.
Liquid
0Lliq Al, Sm 0Lliq Al, Al2 Sm1
−80524
[13,14,30]
bcc fcc Al41Sm5-η
Al60Sm11-ε
0Lliq Al2 Sm1, Sm 0 GAl GAl : Sm 2 Sm1 0Lbcc Al, Sm 1Lbcc Al, Sm 0L fcc Al, Sm
GAl : Al GAl : Sm GSm : Al GSm : Sm GAl : Al : Al : Sm GAl : Al : Sm : Sm GAl : Sm : Al : Sm GAl : Sm : Sm : Sm 0
L Al: Al : Al, Sm : Sm
Al4Sm-β
L Al : Al : Al, Sm : Sm GAl : Al
GSmSm GAl : Al GAl : Sm GSm : Al GSm : Sm GAl : Al
GSm : Sm
GAl: Al
GAl: Sm GSm : Al GSm : Sm
GAl : Al GAl : Sm
GSm : Al Al3Sm-δ
GSm : Sm GAl : Al GAl : Sm
Fig. 4. The enthalpies of formation (Eq. (4)) computed for the metastable phases listed in Table 5 showing the relative stabilities of the compounds at different compositions. The dashed-lines represent the corresponding 2-phase equilibrium states.
Al2Sm-σ
these invariants exist at the asserted temperature ranges and more precise determination of the specific transition temperatures remains as a point of ongoing research. In this manner, the overall picture of phase stability presented here may serve as a clear reference point for further refinement through experiment and/or computation. Certainly, an important component of this additional investigation involves quantification of the temperature dependence of diffusive relaxation processes over the relevant temperature ranges. To provide appropriate perspective with respect to this issue, a summary of relevant reports is provided in Fig. 7, showing the general temperature ranges associated with the sequences defined in Eqs. (1)–(3). Indeed, the figure shows that the observed transitions occur over a regime where the temperature dependence of diffusivity remains poorly understood. This further highlights the point that additional refinement of the metastable phase
11512.1 −13647.2–1.331T 10476.8 13847.3 −520.9 −22211.6+9.256T −1476.56 −19680.2 −13309.24
−27330+6.726T 184334 153819
11201.8 −23378.1+1.965T 21476.56 21409.8 18610 29451.8 25555.6 18610 −33324.5+5.186T
GAl : Sm
This work
20782.6 15117.7 21708
−34800+1.346T
[13,14,30]
31451.8 27555.6 17840
[13,14,30]
−48386+8.342T
14650
GAl : Sm
[13,14,30]
−23121-6.202T
GSm : Sm GAl : Al
GSm : Sm
This work
22622
−18922.5
GSm : Al AlSm-ψ AlSm2-χ
−7463
GSm : Al
GAl : Sm
[13,14,30]
18102
−11057.9
GSm : Al
Al11Sm3-α
−57431
14888.4
GAl : Sm
Al4Sm-γ
−144212+35.854T
2
GSm : Al Al5Sm-θ
−42022
1
L Al: Al : Al, Sm : Sm
Al5Sm-π
−26012
4855 −55000+7.382T
[13,14,30]
14202 8801
−49000+9.446T −37300+8.799T
[13,14,30]
thermodynamic landscape is intimately tied to the quantification of the temperature dependence of diffusive transport. 5. Conclusions High-energy XRD and DSC experiments were employed here in combination with first principles calculations of the corresponding zero-Kelvin energies to assess the relative phase stability of several intermetallic phases in the Al-Sm binary system. Moreover, a comprehensive self-consistent CALPHAD thermodynamic formulation is proposed to reconcile both recent and previously reported findings for this system. The present investigation focuses mainly on the Al41Sm5-η, 8
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Fig. 5. Constrained equilibrium phase diagram showing selected metastable phases and the corresponding invariants. In addition to liquid and Al(fcc) phases, the diagrams are constrained to include only (a) Al4Sm-γ and Al4Sm-β, (b) Al4Sm-γ and Al4Sm-π, (c) Al4Sm-β and Al4Sm-π.
Fig. 6. Constrained equilibrium phase diagram showing selected metastable phases and the corresponding invariants. In addition to liquid and Al(fcc) phases, diagrams (a, b, d) are constrained to include only (a) Al60Sm11-ε and Al4Sm-β, (b) Al41Sm5-η and Al4Sm-β, (d) Al4Sm-β and Al5Sm-θ. The diagram in (b) is further constrained, including only liquid and Al60Sm11-ε phases, showing also the corresponding T0 temperature in comparison with observed crystallization onset temperatures. 9
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Acknowledgements This work was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. The research was performed at the Ames Laboratory, which is operated for the U.S. DOE by Iowa State University under contract No. DE-AC02-07CH11358. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC0206CH11357. References [1] Y.X. Yao, R. Napolitano, C.Z. Wang, K.M. Ho, Thermodynamic limits of crystallization and the prediction of glass formation tendency, Phys. Rev. B 81 (2010). [2] L. Battezzati, M. Baricco, P. Schumacher, W.C. Shih, A.L. Greer, Crystallization behaviour of Al-Sm amorphous alloys, Mater. Sci. Eng., A 179–180 (1994) 600–604, https://doi.org/10.1016/0921-5093(94)90275-5. [3] A. Inoue, Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems, Prog. Mater. Sci. 43 (1998) 365–520, https://doi.org/10.1016/S00796425(98)00005-X. [4] G. Wilde, H. Sieber, J.H. Perepezko, Glass formation versus nanocrystallization in an Al92Sm8 alloy, Scr. Mater. 40 (1999) 779–783. [5] Y.E. Kalay, L.S. Chumbley, M.J. Kramer, I.E. Anderson, Local structure in marginal glass forming Al-Sm alloy, Intermetallics 18 (2010) 1676–1682, https://doi.org/10. 1016/j.intermet.2010.05.005. [6] J.H. Perepezko, R.J. Hebert, R.I. Wu, G. Wilde, Primary crystallization in amorphous Al-based alloys, J. Non. Solids 317 (2003) 52–61. [7] J.Q. Guo, K. Ohtera, K. Kita, J. Nagahora, N.S. Kazama, Crystallization behavior of Al100-xSmx (x=8-14 at. percent) amprphous alloys, Mater. Lett. 24 (1995) 133–138. [8] P. Rizzi, M. Baricco, S. Barace, L. Battezzati, Phase selection in Al-TM-RE alloys: nanocrystalline Al versus intermetallics, Mater. Sci. Eng. A 304–306 (2001) 574–578. [9] Y.E. Kalay, C. Yeager, L.S. Chumbley, M.J. Kramer, I.E. Anderson, Initial crystallization in a nanostructured Al-Sm rare earth alloy, J. Non. Solids 356 (2010) 1416–1424, https://doi.org/10.1016/j.jnoncrysol.2010.05.005. [10] Z. Ye, F. Zhang, Y. Sun, M.C. Nguyen, S.H. Zhou, F.Q. Meng, R.T. Ott, E. Park, M.F. Besser, M.J. Kramer, Z. Ding, M.I. Mendelev, C.-Z. Wang, R.E. Napolitano, K.M. Ho, Structural hierarchy as a key to complex phase selection in Al-Sm, Phys. Rev. Mater. 1 (2017) 55601, https://doi.org/10.1103/PhysRevMaterials.1.055601. [11] Z. Ye, F. Zhang, Y. Sun, M.I. Mendelev, R.T. Ott, E. Park, M.F. Besser, M.J. Kramer, Z. Ding, C.Z. Wang, K.M. Ho, Discovery of a metastable Al20Sm4 phase, Appl. Phys. Lett. 106 (2015). [12] Z. Ye, F.Q. Meng, F. Zhang, Y. Sun, L. Yang, S.H. Zhou, R.E. Napolitano, M.I. Mendelev, R.T. Ott, M.J. Kramer, C.-Z. Wang, K.-M. Ho, Observation of etaAl41Sm5 reveals motif-aware structural evolution in Al-Sm alloys, Sci. Rep. 9 (2019) 6692. [13] S.H. Zhou, R.E. Napolitano, The stability of Al11SM3 (Al4SM) phases in the Al-Sm binary system, Met. Mater. Trans. A 38A (2007) 1145–1151, https://doi.org/10. 1007/s11661-007-9148-z. [14] R.E. Napolitano, S.H. Zhou, X. Yang, F.Q. Meng, Experimental determination of the allotropic transition temperature between tetragonal and orthorhombic Al4Sm metastable phases, Metall. Mater. Trans. A (2019), https://doi.org/10.1007/ s11661-018-5064-7. [15] J.H. Perepezko, R.J. Hebert, R.I. Wu, G. Wilde, Primary crystallization in amorphous Al-based alloys, J. Non. Solids 317 (2003) 52–61. [16] J.C. Foley, D.J. Allen, J.H. Perepezko, Analysis of nanocrystal development in Al-YFe and Al-Sm glasses, Acta Metall. 35 (1996) 655–660. [17] D.R. Allen, J.C. Foley, J.H. Perepezko, Nanocrystal development during primary crystallization of amorphous alloys, Acta Mater. 46 (1998) 431–440. [18] J.C. Foley, D.R. Allen, J.H. Perepezko, Strategies for the development of nanocrystalline materials through devitrification, Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 226 (1997) 569–573, https://doi.org/10.1016/s09215093(97)80065-2. [19] J. Antonowicz, A.R. Yavari, W.J. Botta, P. Panine, Phase separation and nanocrystallization in Al92Sm8 metallic glass, Philos. Mag. 86 (2006) 4235–4242, https://doi.org/10.1080/14786430500375175. [20] A. Saccone, G. Cacciamani, D. Maccio, G. Borzone, R. Ferro, Contribution to the study of the alloys and intermetallic compounds of aluminium with the rare-earth metals, Intermetallics 6 (1998) 201–215. [21] Y.E. Kalay, L.S. Chumbley, I.E. Anderson, Characterization of a marginal glass former alloy solidified in gas atomized powders, Mater. Sci. Eng. A 490 (2008) 72–80, https://doi.org/10.1016/j.msea.2008.02.032. [22] F. Zhang, I. McBrearty, R.T. Ott, E. Park, M.I. Mendelev, M.J. Kramer, C.-Z. Wang, K.-M. Ho, Discovery of a meta-stable Al–Sm phase with unknown stoichiometry using a genetic algorithm, Scr. Mater. 81 (2014) 32–35, https://doi.org/10.1016/j. scriptamat.2014.02.019. [23] F. Casteels, D. P, A. Cools, An investigation of the aluminium-rich alloys in the aluminum-samarium-uranium and, J. Nucl. Mater. 24 (1967) 87–94.
Fig. 7. A summary of diffusivity in Al-Sm and other Al-rare-earth alloy liquids/ glasses as a function of aluminum homologous temperature. Values shown are based on available reports of experimental viscosity (η) measurements (a–g) and related models (h,i). The range of glass transition temperatures (Tg) for the included alloys is also shown. The curves labeled as VFT1 and VFT2 are simply provided here as an general indicator of the observed range of behaviors, computed using the Vogul-Fulcher-Tammann [34–36] and Stokes-Einstein relations [37], combined here as D = akBTexp(b/(c-T)), where a = 8.69 × 1012 Nm−1s−1, kB = Boltzmann’s constant, and where (b, c) are taken here as (2400 K, 280 K) and (8000 K, 300 K) for VFT1 and VFT2, respectively. The range of temperature associated with the transitions observed on heating are also shown for comparison, where diffusivity is changing rapidly but remains many orders of magnitude below that expected for T/Tm ∼ 0.8 and above. Notes on specific data: (a–d) based on oscillating viscometer measurements [38], (e–f) based on thermo-mechanical analyzer measurements [39], (g) each point shown is used here to represent a range of visocity measurements using a dynamic mechanical analyze under vibrational loading [40], (h) based on a reported semi-empirical viscosity-temperature relation reported for the range shown [41–43], (i) based on a reported semi-empirical viscosity-temperature relation obtained from solidification interface velocity measurements [44,45].
Al60Sm11-ε, Al5Sm-θ, Al5Sm-π and Al4Sm-γ metastable phases. Amongst these phases, our findings show that the Al41Sm5-η and Al60Sm11-ε phases comprise the convex hull of minimum formation energies at absolute zero. In addition, the data were interpreted to yield upperbound estimates of metastable invariant temperatures as follows: π→fcc +β at 674 K, ε→fcc+β at 539 K, η→fcc+β at 530 K, and θ→fcc+β at 570 K (arrow here indicates heating direction). The metastability of these phases necessitates various assumptions to be made in the interpretation of experimental data for the assessment of thermodynamic parameters describing temperature-dependent phase stability. While all assumptions are clearly stated to eliminate ambiguity in the proposed treatment, associated limitations of the model nevertheless remain. Accordingly, the comprehensive formulation and phase equilibria proposed here are intended to describe the current state of understanding, consistent with available experimental reports, while also providing a framework for additional investigation of the rich landscape of metastable intermetallic phases in the Al-Sm system. Data availability The raw data required to reproduce these findings are available to download from [link: https://doi.org/10.25380/iastate.9876455]. Declaration of Competing Interest None. 10
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S.H. Zhou, et al. [24] F. Casteels, The aluminium-rich parts of the aluminium-samarium and aluminiumdysprosium systems, J. Less Common Met. 12 (1967) 210–220. [25] H. Zhang, J. Geng, R.T. Ott, M.F. Besser, M.J. Kramer, Effect of temperature on the nano/microstructure and mechanical behavior of nanotwinned Ag films, Metall. Mater. Trans. A 46 (2015) 4078–4085, https://doi.org/10.1007/s11661-0153028-8. [26] M.J. Kramer, H. Mecco, K.W. Dennis, E. Vargonova, R.W. McCallum, R.E. Napolitano, Rapid solidification and metallic glass formation - experimental and theoretical limits, J. Non. Solids 353 (2007) 3633–3639. [27] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmentedwave method, Phys. Rev. B 59 (1999) 1758–1775. [28] D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41 (1990) 7892–7895. [29] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B 46 (1992) 6671–6687. [30] S.H. Zhou, R.E. Napolitano, Modeling of thermodynamic properties and phase equilibria for the Al-Sm binary system, Met. Mater. Trans. A 39A (2008) 502–512, https://doi.org/10.1007/s11661-007-9445-6. [31] S.H. Zhou, R.E. Napolitano, Energetics of nonequilibrium solidification in Al-Sm, Phys. Rev. B 78 (2008). [32] A.T. Dinsdale, No. 53–SGTE data for pure elements, CALPHAD 4 (1991) 317. [33] A.C. Larson, R.B. Von Dreele, General Structure Analysis System (GSAS), Los Alamos National Laboratory Report LAUR 86-748, (2004). [34] H. Vogul, The law of temperature dependence of the viscosity of fluids, Phys. Zeitschrift. 11 (1921) 645–646. [35] G. Tammann, G. Hesse, The dependence of viscosity on temperature for undercooled fluids, Zeitschrift Für Anorg, Und Allg. Chemie. 156 (1926) 245–257.
[36] G.S. Fulcher, Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8 (1925) 339–355. [37] C. Cruickshank Miller, The Stokes-Einstein law for diffusion in solution, Proc. R. Soc. London - Ser. A. 106 (1924) 724–749. [38] B. Sun, X. Bian, J. Hu, T. Mao, Y. Zhang, Fragility of superheated melts in Al-RE (Ce, Nd, Pr) alloy system, Mater. Charact. 59 (2008) 820–823, https://doi.org/10.1016/ j.matchar.2007.06.006. [39] W. Zhang, S. Chen, Z. Zhu, H. Wang, Y. Li, H. Kato, H. Zhang, Effect of substituting elements on thermal stability and glass-forming ability of an Al-based Al[sbnd]Ni [sbnd]Er metallic glass, J. Alloys. Compd. 707 (2017) 97–101, https://doi.org/10. 1016/j.jallcom.2016.11.423. [40] M. Gao, J. Perepezko, Al-based amorphous metallic plastics, Adv. Eng. Mat. 21 (2019) 1800930, , https://doi.org/10.1016/j.jallcom.2016.11.423. [41] L. Battezzati, Interplay of process kinetics in the undercooled melt in the proximity of the glass transition, Mater. Sci. Eng. A 375–377 (2004) 60–65, https://doi.org/ 10.1016/j.msea.2003.10.039. [42] R. Busch, E. Bakke, W. Johnson, Viscosity of the supercooled liquid and relaxation at the glass transition of the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulk metallic glass forming alloy, Acta Mater. 46 (1998) 4725–4732, https://doi.org/10.1016/S13596454(98)00122-0. [43] R. Busch, W. Liu, W.L. Johnson, Thermodynamics and kinetics of the Mg65Cu25Y10 bulk metallic glass forming liquid, J. Appl. Phys. 83 (1998) 4134–4141, https://doi.org/10.1063/1.367167. [44] N. Wang, Y.E. Kalay, R. Trivedi, Eutectic-to-metallic glass transition in the Al-Sm system, Acta Mater. 59 (2011) 6604–6619, https://doi.org/10.1016/j.actamat. 2011.07.015. [45] N. Wang, L. Ji, W.J. Yao, Y.P. Zheng, Correlation between fragility and eutectic instability and glass-forming ability in binary metallic glasses under growth controlled conditions, J. Appl. Phys. 111 (2012), https://doi.org/10.1063/1.4721405.
11
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Metastable intermetallic phases in the Al-Sm system a
a
S.H. Zhou , F.Q. Meng , M.J. Kramer a b
a,b
a
a
a
, R.T. Ott , F. Zhang , Z. Ye , S. Jain
a,b
a,b,⁎
, R.E. Napolitano
T
Division of Materials Science and Engineering, Ames Laboratory, DOE, USA Department of Materials Science and Engineering, Iowa State University, USA
ARTICLE INFO
ABSTRACT
Keywords: Intermetallic Metastability X-ray diffraction CALPHAD Devitrification
The thermodynamic landscape involving several metastable phases in the glass-forming Al-Sm system is assessed, integrating experimental measurements and first principles calculations into a comprehensive CALPHAD description. The phases examined here include Al41Sm5-η, Al60Sm11-ε, Al5Sm-θ, Al5Sm-π and Al4Sm-γ, having basis stoichiometries from 9 to 20 at% Sm, a range over which the Al-fcc and Al3Sm phases are stable. Amongst the metastable phases examined, our findings indicate that the Al41Sm5-η and Al60Sm11-ε phases comprise the convex hull of minimum formation energies at absolute zero. Competitive crystallization processes were investigated through situ X-ray diffraction and differential scanning calorimetry and used to assess relative stability within the overall landscape. Asserting thermodynamic scenarios consistent with our measurements, temperature-dependent Gibbs free energies for the metastable phases are proposed along with the corresponding constrained phase diagrams, comprehensively showing metastable phases and associated invariant reactions. Assumptions and limitations of the proposed thermodynamic model are discussed with reference to available transport data.
1. Introduction Aluminum rare-earth alloys generally exhibit marginal glassforming tendency, which can be enhanced considerably by transition metal alloying [1–9]. Within this class of alloys, systems based on the Al-Sm binary are among the most extensively studied, and the number of metastable phases reported offer a rich landscape of structures accessible from the glassy state [2–7]. Indeed, transformation pathways involving the alloy glass as an intermediate state have been shown to give rise to several complex large-unit-cell phases and devitrification morphologies. The selection of these glass-enabled phases has been attributed to kinetic factors such as the limited atomic mobility and the presence of sub-crystalline precursors (a.k.a. crystal genes) inherent in the glass structure [10]. While recent experimental and theoretical investigations of complex intermetallic phases in the Al-Sm system have shed considerable light on the metastable phase landscape, recent findings [10–14] have not been reconciled with previously reported observations [2–9], and the comprehensive thermodynamic picture has not been substantially clarified. The Al-Sm alloys in the composition range of 8–16 at% Sm, nominally, can be rapidly solidified to the amorphous state [3,15], with alloys at the lower end of this range (∼8 at%) exhibiting Al(fcc) nanocrystals in the as-quenched state [16–19]. Upon devitrification, these
⁎
have been shown to promote primary crystallization of the Al(fcc) phase through growth of these quenched-in crystals, even though growth is limited by diffusive soft-impingement [6]. For alloys with higher Sm content, several metastable intermetallic phases have been observed to crystallize, as summarized in Table 1 [2,6–8]. Metastable intermetallics in Al-Sm, first reported by Battezzati et al. [2], were generically designated as MS1, MS2, MS3, and Al4Sm. Upon heating, the 10 at pct. Sm amorphous alloy was observed to crystallize fully to the MS1 phase, with no other product phases forming. Examining isothermal crystallization in melt-spun Al-Sm amorphous alloys with compositions ranging from 8 to 14 at. pct Sm, Guo et al. [7] observed three previously unidentified metastable crystalline phases, reporting them as M1 (hexagonal: lattice parameters a = 0.4597 nm and c = 0.6358 nm), M2 (cubic: lattice parameter a = 1.9154 nm) and S3 (orthorhombic: lattice parameters a = 1.3781 nm, b = 1.1019 nm and c = 0.7303 nm). A subsequent investigation by Rizzi et al. [8] confirmed that the MS1 and MS2 phases exhibit cubic and tetragonal structures, respectively, with MS2 having the Al4Sm stoichiometry (presently known as the high-temperature Al4Sm-β phase [2,20]. In addition, Rizzi et al. concluded that the previously reported Al4Sm phase [2] and S3 phase [7] are the same, an orthorhombic phase (Al4U prototype), presently termed Al4Sm-γ [13]. Recent work has further clarified this picture. The phases reported
Corresponding author at: Materials Science and Engineering, Iowa State University, 2220 Hoover Hall, 528 Bissell Road, Ames, IA 50014, USA. E-mail address: [email protected] (R.E. Napolitano).
https://doi.org/10.1016/j.mtcomm.2019.100673 Received 8 July 2019; Received in revised form 20 September 2019; Accepted 26 September 2019 Available online 30 September 2019 2352-4928/ © 2019 Elsevier Ltd. All rights reserved.
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Table 1 Summary of reported crystallization sequences observed upon heating amorphous Al-Sm alloys in the composition range from 0.08 to 0.14 at% Sm. XSm
Observed phase sequence, as originally reported in the indicated reference
“Transition” Temps. (K)
Ref.
0.08
Am + Al(traces) > > Al + am > > Al + MS2 > > Al + Al4Sm Am > > Am + α-Al > > α-Al + Al4Sm > > α-Al + S3 (ortho) Am > > Am + Al > > Al + α- Al11Sm3 (tetra) > > Al + o-Al4Sm Am > > MS1 > > Al + MS2 > > Al + Al4Sm Am > > α-Al + Al4Sm + M1 (hexa) > > α-Al + Al4Sm + M1(hexa) > > αAl + S3 (ortho) Am > > MS1(cubic) > > Al+ α- Al11Sm3 (tetra) +M1(hexa) > > Al + o-Al4Sm Am + Al + M2 > > Am + Al + M2 > > Al+ α- Al11Sm3 (tetra) > > Al + o-Al4Sm Am > > fcc-Al + MS1(cubic) > > fcc-Al+ H1(hexa) > > fcc-Al + Al4Sm(ortho) Am + Al11Sm3 > > Al + Al11Sm3 +MS2 + MS3 > > Al + Al4Sm Am > > α-Al + Al4Sm + M1 (hexa) > > α-Al + Al4Sm + M1(hexa) > > αAl + S3 (ortho) Am + Al+ α- Al11Sm3 (tetra) +M1(hexa) > > MS1(cubic) +Al+ α- Al11Sm3 (tetra) + M1(hexa) > > Al + o-Al4Sm Am > > Al + Al11Sm3+MS3 > > Al + Al11Sm3 > > Al + Al4Sm Am > > α-Al + Al4Sm + M2(cubic) > > α-Al + Al4Sm + M1 (hexa) > > α-Al + S3 (ortho)
444 473 523 511 507
[2] [7] [8] [2] [7] [8] [8] [9,21]
0.10
0.12
0.14
/ / / / /
542 541 593 590 580
/ 673-736 / 594 /873 / 736 / 724
543 / 683 / 873 543 / 683 / 873 483 / 542 / 667 526 / 742 507 / 580 / 724 558 / 873 522 / 581 / 802 508 / 600 / 763
[2] [7] [8] [2] [7]
Note: The transition temperatures listed for Ref. [2] are estimated here from Fig.3 in that reference. Table 2 Summary of metastable phase nomenclature in relevant reports. Phase name used presently
Prototype
Al5Sm-π [22] Al61Sm11-ε [10] — Al4Sm-γ [13,23] Al4Sm-β [20,24] Al5Sm-θ [11] Al41Sm5-η [12]
Cu5Ca bcc — Al4U Al4Ba hcp tetragonal
Lattice Parameters (Å)
Phase names used in prior reports
a
b
c
Ref. [2]
Ref. [7]
Ref. [8]
Ref. [9]
4.597 13.904 — 4.44 4.28 5.451 13.284
— — — 6.38 — — —
6.356 — — 13.62 9.90 17.874 9.568
— MS1 MS3 Al4Sm MS2 — —
M1 M2 — S3 — — —
M1 MS1, M2 — S3 MS2 — —
H1 MS1 — Al4Sm — — —
as MS1 [2] and as M2 [7,8] were determined to be the same bodycentered cubic phase (Im 3¯ m, space group 229), presently designated as Al60Sm11-ε [10]. The phase previously reported as M1 [7] and as H1 [8,9] was confirmed to be hexagonal (P6/mmm, space group 191) and is presently designated as Al5Sm-π [22]. Recent work has further revealed two additional metastable phases that crystallize from the Al-Sm glass, including hexagonal Al5Sm-θ (P6322, space group 182) [11] and tetragonal Al41Sm5-η (I4/m, space group 87) [12]. These reports are summarized in Tables 1 and 2. The recently identified intermetallic phases, Al60Sm11-ε, Al41Sm5-η, Al5Sm-θ, and Al5Sm-π, constitute a rich low-temperature landscape in the Al-Sm system [10–12,22]. Owing to their metastable nature, however, thermodynamic description presents a significant challenge. Here, we address this challenge through first-principles calculations and experimental measurement of crystallization reactions upon heating of glassy alloys produced by melt spinning and DC magnetron sputtering. Differential scanning calorimetry (DSC) and in situ high-energy X-ray diffraction (HEXRD) are used to investigate phase transformations in the competitive low-temperature regime in which these metastable phases are observed to form. Calculations and experiments are used, with clearly stated assumptions, to incorporate these phases into a selfconsistent CALPHAD treatment of this system.
compositions of the MR and TF samples were measured using an x-ray fluorescence (XRF) spectrometer (Bruker M4 TORNADO Micro-XRF instrument) operated at 50 kV and 300 μA. with a Rh target and a 25 μm spot size. 2.2. Experiments Devitrification response and subsequent phase transformations occurring upon heating of amorphous MR and TF specimens were investigated using in-situ high-energy wide-angle X-ray scattering (WAXS). (Synchrotron X-ray diffraction was performed at the 1-ID-E beam line at the Advanced Photo Source, Argonne National Laboratory, USA.) Monochromatic X-rays of 71.77 keV (λ = 0.01728 nm) and 80.72 keV (λ = 0.01536 nm) were used to quantify the phase evolution during heating at 10 K/min. The X-ray imaging was performed in transmission mode using a 4-detector arrangement of amorphous silicon detectors (GE-RT41), each with 2048 × 2048 pixel array, situated down-beam of the furnace to collect the two-dimensional patterns. Samples were sealed in thin-walled SiO2 capillary tubes with inner diameter of 2 mm and heated using an infrared lamp. For direct comparison with X-ray data, corresponding differential scanning calorimetry (DSC) traces were obtained for each alloy using a heating rate of 10 K/min (Perkin Elmer Pyris DSC instrument).
2. Materials and methods
2.3. Calculation of phase stabilities through first principles
2.1. Preparation of amorphous alloys
To determine the relative stabilities of the η, ε, θ, π, and γ in comparison with the stable Al(fcc) and δ phases, the internal energy E is computed for each phase using the Vienna ab initio simulation package (VASP) code [27] using projector-augmented wave (PAW) potentials [28] with a high precision generalized gradient approximation (GGA) [29] and Monkhorst-Pack k-point sampling. The enthalpy of formation
Amorphous melt-spun ribbons (MR) of 9.7 and 10.9 at% Sm (20–30 μm thickness) were produced by arc-melting followed by singleroll melt-spinning. In addition, amorphous thin film specimens (TF) of Al-10.9 at% Sm were produced by sputter-deposition onto a silicon substrate. Both methods are described elsewhere [25,26]. The chemical 2
Materials Today Communications 21 (2019) 100673
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Table 3 Summary of the thermodynamic models used for the Al-Sm binary system. Phase
Prototype
Method (Formulation)
Free energy formulation (Gm =
Liquid
—
Association model (Al,Al2Sm,Sm)
ref
L
id L Gm L Gm
Cu α-Sm W
One-sublattice model (Al,Sm)1
Gm +
Gm =
xs
Al-fcc Sm-rho Sm-bcc
ref
id
xs
Gm )
Gm +
i = Al, Sm xi
0
Gi
L
=
RT 1 + 2y Al2 Sm
i = Al, Sm yi lnyi
=
1 1 + 2y Al2 Sm
i
j > i yi yj
0
L
0 Li, j + y Al2 Sm G Al 2 Sm
(i , j = Al, Al2 Sm , Sm ) ( yi = mole fraction of species i) ref
Gm =
id
i = Al, Sm xi
0
Gi
G m = RT
xs
Gm =
Two-sublattice model (Al,Sm)m (Al,Sm)n Al41Sm5-η tetragon-like (Al,Sm)0.891(Al,Sm)0.109 hcp-like (Al,Sm)0.833(Al,Sm)0.167 Al5Sm-θ Al5Sm-π Cu5Ca (Al,Sm)0.833(Al,Sm)0.167 Al4Sm-β Al4Ba (Al,Sm)0.8(Al,Sm)0.2 Al4Sm-γ Al4U (Al,Sm)0.8(Al,Sm)0.2
i = Al, Sm xi lnxi j n xAl xSm j = 1 LAl,Sm (xAl
ref
Gm =
0
Gi : j = Gi : j + m
id
G m = RT
I I Gm = yAl ySm II II yAl ySm
Four-sublattice model Al0.761(Al,Sm)0.084(Al,Sm)0.113Sm0.042 Al60Sm11-ε bcc-like (Al)0.761(Al,Sm)0.084 (Al,Sm)0.113(Sm)0.042
0
Giref
i = Al, Sm
xs
+
II 0 j = Al, Sm yj Gi : j
I i = Al, Sm yi
0
xSm ) j
+ n Gref ( Gi : j = ai : j + bi : j T ) j
(myiI lnyiI + nyiII lnyiII )
II i = Al, Sm yi
k =0
k
I L Al, Sm : i (yAl
k
I i = Al, Sm yi
II k = 0 Li, Al, Sm (yAl
I k ySm )
II k ySm )
( yiI = species i occupancy fraction on sublattice I) ref
Gm =
III 0 G Al : i : j : Sm l = Al, Sm, Va yj 0 fcc 0 GAl : i : j : Sm + 0.761 GAl + 0.084 Giref
II i = Al, Sm, Va yi
0
G Al : i : j : Sm =
0
0
rho + 0.113 Gref + 0.042 GSm j
( GAl : i : j : Sm = aAl : i : j : Sm + bAl : i : j : Sm T ) id
G m = RT
xs
i = Al, Sm, Va
II II G m = yAl ySm
(0.084yiII lnyiII + 0.113yiIII lnyiIII )
III i = Al, Sm, Va yi
for a given compound is calculated as the difference between the energy E of the compound and the linear combination of the pure element rho reference state energies, EAlfcc and ESm ,
Hf = E
xAl EAlfcc
rho xSm ESm .
k =0
k
II L Al: Al, Sm : i : Sm (yAl
II k III III ySm ) + yAl ySm
II i = Al, Sm, Va yi
k=0
k
III LAl: i : Al,Sm : Sm (yAl
III k ySm )
3. Results X-ray diffraction and calorimetry measurements are summarized in Figs. 1–3. In situ WAXS data and the corresponding DSC trace for the 9.7 at. pct Sm (MR) alloy are plotted in Fig. 1(a), revealing three distinct temperature intervals separated by two transition regimes, observed nominally at ∼490 K and ∼530-550 K, respectively. Rietveld analysis [33] of individual diffraction patterns was used to identify the phases present and their relative fractions as a function of temperature (time). The results, shown in Fig. 1(b, c), can be summarized by the following net transition sequence:
(4)
2.4. Thermodynamic modeling We have previously assessed the Al-Sm binary system and refer the reader to these reports for a description of the general formulation, where we apply a three-species (Al, Al2Sm, Sm) association model for the liquid and treat the fcc, bcc, and rhombohedral terminal solid solution phases as simple substitutional solutions [30,31]. Proceeding now to integrate the metastable intermetallic phases, Al41Sm5-η, Al60Sm11-ε, Al5Sm-θ, Al5Sm-π and Al4Sm-γ, we employ a two-sublattice model for all but the Al60Sm11-ε phase, for which we employ a foursublattice formulation, according to its reported structure [10]. For convenience, these phases will hereafter be referred to by symbol only. The Al-fcc phase will be referred to simply as fcc. The specific sublattice descriptions used presently are listed in Table 3, along with the overall free energy formulations for each phase. Given these formulations, sublattice end-members for the η, θ, π, β, and γ phases include four different stoichiometries, with formation free energies described as Gi :j = ai :j + bi :j T (i or j = Al and Sm).For the ε phase, we employ a different set of four end-members, with the formation free energy given as GAl : i : j : Sm = aAl :i :j :Sm + bAl : i :j : Sm T . Thermodynamic functions for the pure element states are taken from the Refs. [30,32] as listed in Table 4. Model parameters were evaluated through collective analysis of first-principles calculations and experimental measurements, as described briefly in the following sections.
Amorphous > > fcc + ε + η > > fcc + β + π
(1)
observed on heating. Similar experimental data for the 10.9 at. pct Sm (MR) alloy are shown in Fig. 2, revealing four distinct temperature intervals separated by three transition regimes, as summarized by the following sequence observed on heating: Amorphous > > ε > > fcc + β + π > > fcc + γ + β
(2)
where the three transition regimes were observed at 483 K, 520–570 K, and 670–780 K. For the 10.9 at% Sm (TF) alloy (See Fig. 3) experimental data revealing three distinct temperature intervals separated by two transition regimes, as summarized by following net sequence on heating: Amorphous > > fcc + θ > > fcc + β + π + γ
(3)
where the net reactions were observed at ∼525 K and 560–590 K respectively. For all three sequences described here, it should be noted that the net transitions indicated in Eqs. (1)–(3) simply state the observed change in phases present within each temperature interval and are not intended here to indicate any specific reaction or 3
Materials Today Communications 21 (2019) 100673
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Table 4 Coefficients for the standard Gibbs free energies of pure Al and Sm in the relevant phases [13,14,30]. Tmin Tmax 0G ref i
0G L Al
0G L Al
298 933.47
933.47 3200
0G fcc Al
0G fcc Al
0Gbcc Al
0G fcc Al
298 700
700 933.47
933.47 2900
298 3200 0G fcc Al
a0 a1 a2 a3/10−2 a4/10−6 a5 a6 a7/10−28 a8
11005.029 −11.841867 — — — 7.934 x10−20 — — 1
−795.996 177.430178 −31.748192 — — — — — —
7976.15 137.093038 −24.3671976 -0.1884662 −0.877664 — 74092 — —
−11276.24 223.048446 −38.5844296 1.8531982 −5.76422 — 74092 — —
−11278.37 188.68415 −31.74819 — — — — −1.2305 —
10083 −4.813 — — — — — — —
Tmin Tmax
298 3200
0Grho Al
0G L Sm 298 1190
1190 2100
0G bcc Sm 298 1190
1190 1345
1345 2100
0G ref i
0G fcc Al
3468.783 20.117456 −11.696828 −3.2418177 4.54427 — 23528
−11728.229 273.48707 −50.208 — — — —
−15957.862 253.121044 −46.9445 — — — —
111191.653 −624.680805 71.6856914 −0.4731496 3.32986 — −24870276
a0 a1 a2 a3/10−2 a4/10−6 a5 a6
2283.5 — — — — — — 0G rho Sm
−4368.72 55.972523 −16.929849 −2.544601 3.5795 94209
0G fcc Sm
Tmin Tmax
298 700
700 1190
1190 1345
1345 2100
298 2100
0G ref i a0 a1 a2 a3/10−2 a4/10−6 a5 a6
−3872.013 −32.10748 −1.6485 −5.0254 10.1035 — −82168
−50078.215 627.869894 −102.665 4.74522 -7.5384 — 3861770
289719.819 −2744.50976 381.41982 −25.4986338 27.51215 — −40102102
−23056.079 282.194375 −50.208 — — — —
890 — — — — — —
* Note: Each Gibbs free energy is described as: 0Gi = 0GiREF + a 0 + a1 T + a2 T ln T + a3 T 2 + a4 T 3 + a5 T 4 + a6 T
thermodynamic condition. Interpretation of the observed net reactions will be revisited in a later section. Before proceeding with the thermodynamic analysis, it is prudent to point out a few important features apparent in the data presented in Figs. 1–3, within the context of previously reported observations. In particular, we are compelled to make note of the difference between our observations and those which report a clearly discernable (in DSC) initial crystallization peak for the Al(fcc) phase, associated with the growth of quenched-in nanocrystals. For the 10.9 at% Sm sputtered thin film (TF) specimen (Fig. 3), it is not surprising that we have no initial Al (fcc) crystallization peak. The effective cooling rate here is much higher than that of the melt-spun ribbon, and it is certainly reasonable that the nucleation of Al(fcc) nanocrystals does not occur in this case, as it might during quenching from the melt. Looking at the data for the two meltspun ribbon specimens, we see evidence of Al(fcc) in the diffraction data for 9.7 at% Sm but no separate exothermic peak in the DSC trace (Fig. 1). This suggests that the multiphase structure is forming simultaneously, as indicated by a single primary crystallization peak in the DSC trace. Certainly, considering the high driving forces, it is possible that this crystallization includes one or more coupled-growth or co-operative nucleation scenarios involving the formation of ε, η, and Al (fcc) from the amorphous phase. In contrast, there is no discernable evidence of the Al(fcc) phase formation during the initial crystallization for the 10.9 at % Sm alloy. For this composition, the driving force for ε formation is very high while requirements for chemical partitioning are rather low, plausibly favoring crystallization of ε over the Al(fcc) phase. In addition, we have observed and reported on the ability of the ε phase
— —
0G rho Sm
1
+ a7 T
9
a8 RT ln(1 + e
— — — — — — — / RT )
(J/mol).
to accommodate site occupancy defects [10], so that it may crystallize in a partitionless (or nearly partitionless) manner over a rather large composition range. Of course, it would be driven to subsequently decompose, as we clearly see in Figs. 1–3. The relevance of these issues notwithstanding, we return to the primary intent of the present communication and to our stated focus of formulating a self-consistent thermodynamic description so that these dynamics can be more effectively investigated. Results from first principles calculations are summarized in Table 5 and Fig. 4, showing the relative stability of the η, ε, θ, π, and γ phases with respect to the stable fcc + δ two-phase state, represented in Fig. 4 by the dashed horizontal reference line. The metastable two-phase states of fcc + β and fcc + γ are also indicated by dashed lines in Fig. 4. Here, we see clearly that the complex intermetallic phases η, ε, θ, π, are all stable with respect to decomposition to fcc + β but unstable with respect to decomposition to both the metastable fcc + γ state and the stable fcc + δ state. 4. Discussion and parameter evaluation Employing the formulation described above and summarized in Table 3, the model parameters corresponding to the γ, π, ε, η, and θ phases were evaluated in a manner consistent with the computed formation energies and experimentally observed phase transition sequences. Parameters for the Al4Sm-β, Al11Sm3-α, Al3Sm-δ, Al2Sm-σ, AlSm-ψ, and AlSm2-χ phases were taken from our prior assessments [30,31]. All model parameters, including those determined in this 4
Materials Today Communications 21 (2019) 100673
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Fig. 1. (a) The high-energy X-ray scattered intensity with a superposed DSC trace for the 9.7 at% Sm MSR specimen, both collected during heating at 10 K/min; (b) corresponding phase fraction vs temperature determined through Reitveld analysis; (c) diffraction patterns indicating the phases present at selected temperatures.
work, are summarized in Table 6, and our evaluation methodology is detailed in the remainder of this section. The temperature-independent parameters in the end-member formation free energies, listed in Table 3 as ai :j (φ = γ, η, θ, or π) and aAl :i :j :Sm , were taken as the computed zero-Kelvin formation energies listed in Table 5. The coefficients for required temperature-dependent terms, bAl : Sm (φ = γ, η, θ, π) and bAl : Al :Sm :Sm , were determined by considering the experimental observations, as described below. The γ-β allotropic transition temperature (both phases metastable) was recently determined to be 896 K [14], and we use this value presently to determine the parameter bAl : Sm , as given in Table 6. The remaining parameters bi :j are taken as zero. The resulting constrained equilibrium phase diagram is plotted in Fig. 5, showing the γ-β transition and related invariant reactions in the Al-Sm binary. Examining first the HEXRD data shown in Fig. 2, we consider the constant-heating-rate phase evolution sequence (fcc + π + β > > fcc + γ + β) observed in the regime from 670 to 760 K. Upon closer examination of the temperature-dependent phase fractions ( f ) plotted in Fig. 2(b), it is apparent that this overall evolution sequence involves two distinguishable transformation stages. The first involves decomposition of the π phase, appearing as a relatively abrupt transition in the
range of 670–710 K, corresponding with dramatic increases in f fcc and f , along with a modest increase in f . This is followed by a second stage, observed from 710 to 760 K, involving a distinct decrease in f with a corresponding increase in f . We note that, while f is increasing with temperature during both stages, a clear change in df / dT delineates the two stages. To interpret this observation, we recognize three important points. First, we note that this entire range is below the metastable allotropic transition temperature of 896 K, such that the γ phase is stable throughout, relative to the β phase. Second, we note from the zero-Kelvin enthalpies (see Fig. 4) that the π phase is unstable with respect to fcc+γ even at absolute zero. Assuming that the relative stability of π decreases with increasing temperature (previously reported observations of fcc+β and fcc+γ cast structures support this hierarchy [14]), it follows that the π→fcc+γ decomposition reaction is driven for all temperatures and that no π-fcc-γ invariant is observable. Third, unlike the π→fcc+γ reaction, the π→fcc+β decomposition is not driven at absolute zero (Fig. 4). Furthermore, the fact that β exhibits a high-temperature range of stability suggests the existence of a metastable π-fcc-β invariant at some intermediate temperature. With these points recognized, we interpret the distinct first-stage onset (on 5
Materials Today Communications 21 (2019) 100673
S.H. Zhou, et al.
Fig. 2. (a) The high-energy X-ray scattered intensity with a superposed DSC trace for the 10.9 at% Sm MSR specimen, both collected during heating at 10 K/min; (b) corresponding phase fraction vs temperature determined through Reitveld analysis; (c) diffraction patterns indicating the phases present at selected temperatures.
heating) as an indication of such an invariant temperature and consider the abrupt initial transition stage (670–720 K) as an indication of the π→fcc+β decomposition reaction. We interpret the increase in fγ over this same temperature range as a consequence of simultaneous trans), which has formed well formation of the metastable β phase ( below the allotropic (γ−β) equilibrium temperature of 896 K. Thus, the T curve in Fig. 2b indicates the completion of slope change in the f the π→fcc+β decomposition, with further changes in phase fractions associated with continuation of the transition. Based on this interpretation of the data, we take the first-stage onset temperature (on heating), estimated as 674 K (see Fig. 2c), as an upper-bound estimate of the π→fcc+β invariant and use this to evaluate the parameter bAl :Sm . The remaining bi :j parameters are taken as zero. A corresponding constrained equilibrium phase diagram, including the liquid, fcc, γ, and π phases, is shown in Fig. 5c. Considering the lower temperature sequence in Fig. 2, involving the apparent decomposition of the ε phase and the net transition to fcc, β, and π at approximately 550 K, the possible reactions to consider are (i) ε→fcc+β and (ii) ε→fcc+π. Here, we make arguments similar to those described above for the higher temperature sequence. Because reaction (ii) is shown to be driven at 0 K (see Fig. 4), we assume that it is driven
at all temperatures such that no ε-fcc-π invariant is observable. On the other hand, Fig. 4 shows that reaction (i) is not driven at 0 K, and we assume that it becomes driven above some unknown invariant temperature. Accordingly, considering the abruptness of the observed transition, we take the onset temperature as an upper-bound estimate of the invariant temperature, estimated as 544 K (see Fig. 2c). Similar analysis and interpretation of HEXRD data for the Al-9.7 at pct Sm MR alloy yields a second estimate of 534 K for the of the ε→fcc+β invariant (Fig. 1c), and we take the mean value of 539 K as an estimate of this temperature. Base on previously reported experiments and computation, there is an additional condition that we employ for parameter evaluation for the ε phase. This phase has been shown to nucleate and grow with little or no chemical partitioning, enabled by variable site occupancies [2]. Accordingly, we assume that the observed ε crystallization temperatures (470 and 483 K) indicated in Figs. 1 and 2, are less than or equal to the T0 temperature for the two specific alloy compositions examined (9.7 and 10.9 at%, respectively). With this condition, along with an estimated temperature of 539 K for the ε→fcc+β invariant, we evaluate the four relevant model parameters (one bAl : Al :Sm :Sm parameter and three kL Al :Al : Al, Sm : Sm parameters, where k = 0, 1, 2), as listed in Table 6. 6
Materials Today Communications 21 (2019) 100673
S.H. Zhou, et al.
Fig. 3. (a) The high-energy X-ray scattered intensity with a superposed DSC trace for the 10.9 at% Sm TF specimen, both collected during heating at 10 K/min; (b) corresponding phase fraction vs temperature, plotted over selected ranges; (c) diffraction patterns indicating the phases present at selected temperatures; (d) an expanded view of the DSC traces in the regime of the higher-temperature transition.
The corresponding constrained equilibrium phase diagram is shown in Fig. 6a and the relevant T0 curve is shown in Fig. 6(a,b). With similar arguments as employed above, we employ the HEXRD data in Fig. 1 to assess the η phase. Examining first the upper temperature overall transition, fcc+ε+η > > fcc+β+π, we consider the two possible decomposition reactions: (i) η→fcc+π and (ii) η→fcc+β. As described previously, we take the transition onset as a likely upperbound indicator of the η→fcc+β invariant and estimate this temperature as 530 K, as shown Fig. 1c. The parameter bAl : Sm was determined using this estimate, and other bi :j parameters were taken as zero, as listed in Table 6. The corresponding metastable phase diagram, showing only the liquid, fcc, Al41Sm5-η and Al4Sm-β phases, is plotted in Fig. 6c. Fig. 3 summarizes the overall sequence observed on constantheating-rate (10 K/min) treatment of the Al-10.9 at pct Sm (TF), with the overall phase evolution sequence given in Eq.(3). The initial crystallization involves both fcc and θ phase in the range of 520–530 K. Examining the subsequent portion of the net transition sequence in Eq. (3) (fcc+θ > > fcc+β+π +γ), which appears in the range of 550–600 K (Figs. 3(a–c)), we consider the possible reactions: (i) θ→π,
(ii) θ→fcc+γ, and (iii) θ→fcc+β. As shown in Fig. 4, reactions (i) and (ii) are driven at 0 K, while reaction (iii) is not. Attributing the formation of β to heating beyond an θ→fcc+β invariant, we take the onset as a reasonable estimate of the upper bound for this temperature. (While XRD measurements of phase fraction data are not available over the intermediate range from 568 to 585 K (Fig. 6c), the DSC trace indicates a smooth transition with no discontinuities.) This onset was estimated from the DSC data as 570 K, as shown in Fig. 3d, and the parameter bAl : Sm was evaluated, as listed in Table 6. The remaining bi :j parameters are taken as zero. The computed constrained equilibrium phase diagram, including liquid, θ, fcc, and β phases, is plotted in Fig. 6d. A brief comment is warranted here concerning the present interpretation of transformation sequences. In several cases, we assume that a transformation observed upon heating reflects a change in relative phase stability and, as such, serves as an upper bound to a specific invariant temperature, which we have stated clearly. We use these assumptions to enable a well-defined comprehensive thermodynamic description that is consistent with the observations at hand along with previously reported formulations. Of course, explicit confirmation that 7
Materials Today Communications 21 (2019) 100673
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Table 5 Formation enthalpies at 0 K, computed from first-principles (Eq. (4)). Phase
Prototype
Formula
k points
Al-fcc Sm-rho Al41Sm5-η
Cu Sm tetragonal
Al Sm Al41Al 5 Al41Sm5 Sm41Al 5 Sm41Sm5 Al5Al Al5Sm Sm5Al Sm5Sm Al20Al4 Al20Sm4 Sm20Al4 Sm20Sm4 Al54Al6Al8Sm3 Al54Al6Sm8Sm3 Al54Sm6Al8Sm3 Al54Sm6Sm8Sm3 Al20Al4 Al20Sm4 Sm20Al4 Sm20Sm4 Al3Sm
12, 12, 12 8, 8, 12 8, 8, 12
Al5Sm-π
Cu5Ca
Al5Sm-θ
hcp
Al60Sm11-ε
bcc
Al4Sm-γ
Al4U
Al3Sm-δ
Ni3Sn
6, 6, 4
10, 10, 8
4, 4, 4
4, 6, 2
10, 19, 12
Table 6 Evaluated thermodynamic model parameters (in SI unit).
ΔHf (J/mol) 0 0 11512.1 −13647.2 10476.8 13847.3 22622.0 −27330.0 184334.0 153819.0 11201.8 −23378.1 21476.56 21409.8 −520.9 −22211.6 −1476.56 −19680.2 18610.0 −33324.5 20782.6 15117.7 −43421.1
Phase
Parameter
Value, J/mol
Ref.
Liquid
0Lliq Al, Sm 0Lliq Al, Al2 Sm1
−80524
[13,14,30]
bcc fcc Al41Sm5-η
Al60Sm11-ε
0Lliq Al2 Sm1, Sm 0 GAl GAl : Sm 2 Sm1 0Lbcc Al, Sm 1Lbcc Al, Sm 0L fcc Al, Sm
GAl : Al GAl : Sm GSm : Al GSm : Sm GAl : Al : Al : Sm GAl : Al : Sm : Sm GAl : Sm : Al : Sm GAl : Sm : Sm : Sm 0
L Al: Al : Al, Sm : Sm
Al4Sm-β
L Al : Al : Al, Sm : Sm GAl : Al
GSmSm GAl : Al GAl : Sm GSm : Al GSm : Sm GAl : Al
GSm : Sm
GAl: Al
GAl: Sm GSm : Al GSm : Sm
GAl : Al GAl : Sm
GSm : Al Al3Sm-δ
GSm : Sm GAl : Al GAl : Sm
Fig. 4. The enthalpies of formation (Eq. (4)) computed for the metastable phases listed in Table 5 showing the relative stabilities of the compounds at different compositions. The dashed-lines represent the corresponding 2-phase equilibrium states.
Al2Sm-σ
these invariants exist at the asserted temperature ranges and more precise determination of the specific transition temperatures remains as a point of ongoing research. In this manner, the overall picture of phase stability presented here may serve as a clear reference point for further refinement through experiment and/or computation. Certainly, an important component of this additional investigation involves quantification of the temperature dependence of diffusive relaxation processes over the relevant temperature ranges. To provide appropriate perspective with respect to this issue, a summary of relevant reports is provided in Fig. 7, showing the general temperature ranges associated with the sequences defined in Eqs. (1)–(3). Indeed, the figure shows that the observed transitions occur over a regime where the temperature dependence of diffusivity remains poorly understood. This further highlights the point that additional refinement of the metastable phase
11512.1 −13647.2–1.331T 10476.8 13847.3 −520.9 −22211.6+9.256T −1476.56 −19680.2 −13309.24
−27330+6.726T 184334 153819
11201.8 −23378.1+1.965T 21476.56 21409.8 18610 29451.8 25555.6 18610 −33324.5+5.186T
GAl : Sm
This work
20782.6 15117.7 21708
−34800+1.346T
[13,14,30]
31451.8 27555.6 17840
[13,14,30]
−48386+8.342T
14650
GAl : Sm
[13,14,30]
−23121-6.202T
GSm : Sm GAl : Al
GSm : Sm
This work
22622
−18922.5
GSm : Al AlSm-ψ AlSm2-χ
−7463
GSm : Al
GAl : Sm
[13,14,30]
18102
−11057.9
GSm : Al
Al11Sm3-α
−57431
14888.4
GAl : Sm
Al4Sm-γ
−144212+35.854T
2
GSm : Al Al5Sm-θ
−42022
1
L Al: Al : Al, Sm : Sm
Al5Sm-π
−26012
4855 −55000+7.382T
[13,14,30]
14202 8801
−49000+9.446T −37300+8.799T
[13,14,30]
thermodynamic landscape is intimately tied to the quantification of the temperature dependence of diffusive transport. 5. Conclusions High-energy XRD and DSC experiments were employed here in combination with first principles calculations of the corresponding zero-Kelvin energies to assess the relative phase stability of several intermetallic phases in the Al-Sm binary system. Moreover, a comprehensive self-consistent CALPHAD thermodynamic formulation is proposed to reconcile both recent and previously reported findings for this system. The present investigation focuses mainly on the Al41Sm5-η, 8
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Fig. 5. Constrained equilibrium phase diagram showing selected metastable phases and the corresponding invariants. In addition to liquid and Al(fcc) phases, the diagrams are constrained to include only (a) Al4Sm-γ and Al4Sm-β, (b) Al4Sm-γ and Al4Sm-π, (c) Al4Sm-β and Al4Sm-π.
Fig. 6. Constrained equilibrium phase diagram showing selected metastable phases and the corresponding invariants. In addition to liquid and Al(fcc) phases, diagrams (a, b, d) are constrained to include only (a) Al60Sm11-ε and Al4Sm-β, (b) Al41Sm5-η and Al4Sm-β, (d) Al4Sm-β and Al5Sm-θ. The diagram in (b) is further constrained, including only liquid and Al60Sm11-ε phases, showing also the corresponding T0 temperature in comparison with observed crystallization onset temperatures. 9
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Acknowledgements This work was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. The research was performed at the Ames Laboratory, which is operated for the U.S. DOE by Iowa State University under contract No. DE-AC02-07CH11358. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC0206CH11357. References [1] Y.X. Yao, R. Napolitano, C.Z. Wang, K.M. Ho, Thermodynamic limits of crystallization and the prediction of glass formation tendency, Phys. Rev. B 81 (2010). [2] L. Battezzati, M. Baricco, P. Schumacher, W.C. Shih, A.L. Greer, Crystallization behaviour of Al-Sm amorphous alloys, Mater. Sci. Eng., A 179–180 (1994) 600–604, https://doi.org/10.1016/0921-5093(94)90275-5. [3] A. 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Fig. 7. A summary of diffusivity in Al-Sm and other Al-rare-earth alloy liquids/ glasses as a function of aluminum homologous temperature. Values shown are based on available reports of experimental viscosity (η) measurements (a–g) and related models (h,i). The range of glass transition temperatures (Tg) for the included alloys is also shown. The curves labeled as VFT1 and VFT2 are simply provided here as an general indicator of the observed range of behaviors, computed using the Vogul-Fulcher-Tammann [34–36] and Stokes-Einstein relations [37], combined here as D = akBTexp(b/(c-T)), where a = 8.69 × 1012 Nm−1s−1, kB = Boltzmann’s constant, and where (b, c) are taken here as (2400 K, 280 K) and (8000 K, 300 K) for VFT1 and VFT2, respectively. The range of temperature associated with the transitions observed on heating are also shown for comparison, where diffusivity is changing rapidly but remains many orders of magnitude below that expected for T/Tm ∼ 0.8 and above. Notes on specific data: (a–d) based on oscillating viscometer measurements [38], (e–f) based on thermo-mechanical analyzer measurements [39], (g) each point shown is used here to represent a range of visocity measurements using a dynamic mechanical analyze under vibrational loading [40], (h) based on a reported semi-empirical viscosity-temperature relation reported for the range shown [41–43], (i) based on a reported semi-empirical viscosity-temperature relation obtained from solidification interface velocity measurements [44,45].
Al60Sm11-ε, Al5Sm-θ, Al5Sm-π and Al4Sm-γ metastable phases. Amongst these phases, our findings show that the Al41Sm5-η and Al60Sm11-ε phases comprise the convex hull of minimum formation energies at absolute zero. In addition, the data were interpreted to yield upperbound estimates of metastable invariant temperatures as follows: π→fcc +β at 674 K, ε→fcc+β at 539 K, η→fcc+β at 530 K, and θ→fcc+β at 570 K (arrow here indicates heating direction). The metastability of these phases necessitates various assumptions to be made in the interpretation of experimental data for the assessment of thermodynamic parameters describing temperature-dependent phase stability. While all assumptions are clearly stated to eliminate ambiguity in the proposed treatment, associated limitations of the model nevertheless remain. Accordingly, the comprehensive formulation and phase equilibria proposed here are intended to describe the current state of understanding, consistent with available experimental reports, while also providing a framework for additional investigation of the rich landscape of metastable intermetallic phases in the Al-Sm system. Data availability The raw data required to reproduce these findings are available to download from [link: https://doi.org/10.25380/iastate.9876455]. Declaration of Competing Interest None. 10
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