Terminal Solid Solutions Research Articles

Solidus surface of the Al–Ti–Pd system in the Al–AlPd–TiPd–Ti region

The Al–Ti–Pd system has been studied by microstructural analysis, electron microprobe analysis, x-ray diffraction, and differential temperature analysis in the composition range 0–50 at.% Pd (Al–AlPd–TiPd–Ti partial system) at subsolidus temperatures. The solidus surface of the system is constructed for the first time. At subsolidus temperatures, there are two ternary compounds, τ1 (Al61Ti26Pd13, AuCu3 type) and τ3 (Al44Ti35Pd21, MgZn2 type), a continuous solid solution (β0 phase) between isostructural (CsCl type) high-temperature modifications of AlPd and TiPd equiatomic phases, and terminal solid solutions based on β-Ti and α-Ti and TiAl, Ti2Al5, TiAl3, and Al3Pd2 binary compounds and e phase. The above-mentioned phases participate in 11 four-phase invariant equilibria involving the liquid phase and are represented by isothermal tie-line triangles in the temperature range between 630 and 1205°C.

Phase equilibria in the Lu-Pd system in the composition range 0–50 at % Lu

X-ray diffraction, differential thermal analysis, and electron microscopy are used to study the crystal structures and formation sequence of intermetallics in the Lu-Pd system in a composition range of Pd-(0–50 at %) Lu. The alloys are synthesized using high-purity lutetium. Within the composition range under study, the system is characterized by terminal Pd-based solid solutions with a lutetium content up to 10 at % Lu (at 1000°C) and a number of intermetallics (Lu3Pd4, Lu2Pd3, LuPd, LuPd3, Lu10Pd21). A nonequilibrium bertholide phase is found to form in the composition range from 30 to 45 at % Lu. The phase diagram is given in the composition range Pd-(0–50 at %) Lu.

Ordering and magnetostriction in Fe alloy single crystals

Short-range and long-range ordering in α-Fe terminal solid solution phase (A2 phase with bcc structure) influences its physical, mechanical, magnetic and magnetostrictive behavior. Single crystal sample forms are ideal for examining order in these alloys using X-ray and neutron scattering techniques. Limited structural information available suggests that the lattice of A2 phase at room temperature contains a mixture of regions with local atomic environments similar to those expected in the long-range ordered structures in stable/metastable equilibrium with the A2 phase. The nature and extent of these regions are sensitive to alloy composition and the thermal history. The lattice strain modulations result from the nature of solute atom distribution (short-range ordering) in each region and impact the physical, mechanical, corrosion and magnetic behaviors. A need for a fundamental understanding of ordering in Fe and other alloys through structural evaluations of local atomic environments in alloy single crystals is suggested in this review.

First Phase Selection in Solid Ti/Al Diffusion Couple

Abstract Ti/Al diffusion couples fabricated by hot pressing were annealed at 525, 550, 575 and 600 °C. TiAl3 was the only observed phase at the Ti/Al interface when the unreacted Al foils remained. TiAl3 grew towards Al foil side. Few Al atoms were detected in Ti foils. The first formation of TiAl3 is explained on the basis of solubility limits of terminal solid solution, lattice mismatch among Al, Ti and TiAl3, and the increasing interfacial energy caused by newly formed interface. The first saturation of Al (Ti) solid solution due to the little solubility of Ti in Al, and the slight misfit among the close-packed planes of Al, Ti and TiAl3, advance the nucleation of TiAl3. TiAl3, rather than other compounds, has the lowest increasing interfacial energy, indicating its preferential formation. The formation of other titanium aluminides is suppressed due to their growth which is kinetically unstable.

Thermodynamic assessment of the Nb–Ge system

The Nb–Ge binary system has been thermodynamically assessed using the CALPHAD (Calculation of Phase Diagrams) approach on the basis of the experimental data of both the phase equilibria and the thermochemical properties. The reasonable models were constructed for all the phases of the system. The liquid and the terminal solid solution phases, Bcc-(Nb) and Diamond-(Ge), were described as the substitutional solutions with Redlich–Kister polynomials for the expressions of the excess Gibbs free energies. The intermediate phases (Nb 3Ge), (Nb 5Ge 3), (Nb 3Ge 2) and (NbGe 2) with homogeneity ranges were treated as the sublattice models Nb 0.75(Ge,Nb,Va) 0.25, Nb 0.5(Nb,Ge) 0.125(Ge,Va) 0.375, (Nb,Ge) 0.222(Nb,Ge) 0.333Nb 0.333(Ge,Va) 0.111 and (Nb,Ge) 0.333(Nb,Ge) 0.667 respectively based on their structure features of atom arrangements. A set of self-consistent thermodynamic parameters for the Nb–Ge system was obtained. Using the present thermodynamic data, the calculation results can reproduce the experimental data well.

Microstructures and liquidus projection of the ternary Ag–Sb–Te system

Ag–Sb–Te alloys are important for thermoelectric applications. Fifty-one Ag–Sb–Te ternary alloys were prepared, and their primary solidification phases were analyzed. The liquidus troughs of the liquidus projection of the ternary Ag–Sb–Te system are determined based on the experimental results and the phase diagrams of the three binary constituent systems. There are 13 primary solidification phase regions. In addition to the three terminal solid solution phases and nine binary compounds, there is one ternary compound, AgSbTe 2. A unique microstructure with bright spherical phases uniformly dispersed in a matrix caused by a miscibility gap in the liquid phase is found in the γ-Ag 2Te primary solidification phase regime. A very fine microstructure with nanometer size Ag 2Te is also observed, resulting from the class I reaction, liquid = δ + Ag 2Te + AgSbTe 2, at 496.5 °C, and the liquid composition of Ag–40.0 at%Sb–36.0 at%Te.

The Co-Sn-Zr (Cobalt-Tin-Zircoium) System

The Co-Sn binary system [1983Nis, Massalski2] (Fig. 1) has three intermediate phases: Co3Sn2 in two allotropic forms Co3Sn2 (g) above 500 C and Co3Sn2 (g1) below 500 C, CoSn (p) and CoSn2 (f). The g phase melts congruently at 1170 C and the other two phases form through peritectic reactions: L +gM p at 936 C and L + pM f at 525 C. Two eutectic reactions LM c + g and LM f + b occur at 1112 C and 229 C, respectively. The c and b phases are the terminal solid solutions of fcc aCo and of tetragonal bSn, respectively. The cM e transformation possibly occurs through a eutectoid type reaction at 420 C where e is the terminal solid solution of close packed hexagonal (cph) eCo. The Co-Zr system [Massalski2] (Fig. 2) shows the presence of five intermediate phases Co11Zr2 (w), Co4Zr ðiÞ, Co2Zr (k2), CoZr (b1), and CoZr2 (n). The probable presence of another phase CoZr3 (m) was reported but requires further confirmation. With the Co2Zr phase being an exception, all other phases are stoichiometric compounds. The Co2Zr, CoZr, and CoZr2 phase are believed to melt congruently at approximately 1620, 1420, and 1125 C, respectively. The w and i phases form through peritectic reactions: L + k2ML at 1452 C and Lþ i $ w at 1272 C. Four eutectic reactions occur in the Co-Zr system: LM c + w at 1222 C, LM k2 + b1 at 1312 C, LM b1 + n at 1061 C, and LM n + a at 981 C where a is the body centered cubic (bcc) terminal solid solution of bZr. A eutectoid reaction aM n + e2 occurs at 834 C where e2 is the cph terminal solid solution of aZr. In the Co-rich region possibly a eutectoid reaction cMw + e1 occurs at 422 C. The Sn-Zr system [Massalski2] (Fig. 3) has three intermediate phases, SnZr4 (h), Sn3Zr5 (x), and Sn2Zr (/) of which the x phase melts congruently at 1988 C. The probable existence of another phase Sn4Zr5 (T) has been suggested in the SnZr system. The h and / phases form through peritectoid and peritectic reactions: x + aM h at 1327 C and L + xM/ at 1142 C. The reaction through which the T phase forms is not known. Two eutectic reactions LM a + x and LM/ + b occur at 1592 and 232 C, respectively. The cph e2 phase forms through a peritectoid reaction a + hM e2 at 982 C where e2 is the cph terminal solid solution aZr.

Phase equilibria in the systems AgInSe2-HgIn2Se4 and AgInSe2-HgSe

The equilibrium phase diagrams along the AgInSe2-HgIn2Se4 and AgInSe2-HgSe joins of the ternary system Ag2Se-HgSe-In2Se3 have been constructed using X-ray diffraction and differential thermal analysis. Both joins are pseudobinary, with eutectic phase diagrams (type V in Roseboom’s classification). The eutectics are located at ≃30 mol % HgIn2Se4 (melting point of 1000 K) and ≃54 mol % HgSe (993 K), respectively. Both systems have considerable terminal solid-solution ranges.

Thermodynamic assessment of the U–Mo–Al system

Thermodynamic assessment of the U–Mo–Al ternary system has been performed by CALPHAD method. Firstly, the U–Mo binary system has been thermodynamically optimized. The reported five solution phases, liquid, orthorhombic_A20 (αU), tetragonal_U (βU), BCC_A2 (γU) and terminal Mo solid solution are treated as substitutional solution phases. The BCC_A2 takes the same structure as Mo thus they are described with the same model. And the only intermetallic compound, MoU 2, is treated as stoichiometric compound. Secondly, by using the available thermodynamic parameters of the Al–U and Al–Mo binary systems reported in literatures, the U–Mo–Al ternary system was thermodynamically assessed. A set of self-consistent thermodynamic parameters has been obtained, which can satisfactorily reproduce most of the thermodynamic and phase diagram data.

The Ni-Re-Ti (Nickel-Rhenium-Titanium) System

The Ni-Re system [Massalski 2] is a simple peritectic system (Fig. 1). At the Ni side of the Ni-Re system face centered cubic (fcc) solid solution c forms through a peritectic reaction L + e1M c at 17.4 at.% Re, the peritectic reaction temperature being 1620 C. e1 is the close packed hexagonal (cph) terminal solid solution of Re. The Ni-Ti system [Massalski 2] has three intermediate phases Ni3Ti(h), NiTi(u) and NiTi2(p) of which the h and u phases melt congruently at 1380 and 1310 C, respectively (Fig. 2). The p phase forms through a peritectic reaction L + uM p at 984 C. Three eutectic reactions L M c + h, L M h + u and L M a + p, where a is the body centered cubic (bcc) terminal solid solution of bTi, occur at 1304, 1118, and 942 C, respectively. Two eutectoid reactions a M p + e2 where e2 is the cph terminal solid solution of aTi, and uM h + p occur at 765 and 630 C, respectively. The Re-Ti system [Massalski 2] has only one intermediate phase Re24Ti5(v), which forms through a peritectic reaction L + e1M v at 2750 C. A peritectic reaction L + vM a occurs at 2025 C. The a phase transforms to e2 phase at temperatures £882 C (Fig. 3).

The Ni-Re-V (Nickel-Rhenium-Vanadium) System

The Ni-Re system [Massalski 2] (Fig. 1) is a simple peritectic system, the peritectic reaction L + eM c occurs at 1620 C where e and c are the terminal solid solutions (Re) and (Ni), respectively. The Ni-V system [Massalski 2] (Fig. 2) has five intermediate phases: Ni8V(f), Ni3V(p), Ni2V(q), r, and NiV3(d). The f, p, and q phases form from the solid solution c through congruent transformations at 405, 1045, and 922 C, respectively. The r phase appears to have two polymorphic forms r¢ and r. The r¢ phase forms through a peritectic reaction L + aMr¢ at 1280 C, where a is the terminal solid solution (V). The r phase occurs below 790 C, the probable reaction at the high Ni side is a peritectoid reaction r¢ + qM r at 790 C and a eutectoid reaction r¢Mr + d probably occurs at the high V end. The d phase forms through a peritectoid reaction L + aM d at 900 C. A eutectoid reaction LM c + r¢ occurs at 1202 C and two eutectoid reactions cM p + q and cM q + r¢ occur at 908 and 890 C. The Re-V system [Massalski 2] has two intermediate phases r and d. The r phase forms through a pertiectic reaction L + eMr at 2460 C. The d phase forms through a peritectoid reaction r + aM d at 2280 C. The a phase extends from V to 56 at.% Re and has a congruent melting temperature of 2400 C at 47 at.% V. A eutectic reaction LMr + a occurs at 2380 C. The r and d phases exist only at high temperatures and undergo eutectoid transformations rM e + d at 1970 C and dM e + a at 1470 C.

The Mo-Ni-Re (Molybdenum-Nickel-Rhenium) System

The Mo-Ni system [1990Nas] (Fig. 1) shows the existence of three intermediate phased MoNi (d), MoNi3 (q) and MoNi4(t). The d phase forms through a peritectic reaction L + aM d at 1362 C, where a is the body centered cubic (bcc) terminal solid solution (Mo). The q phase forms through a peritectoid reaction d + cM q at 910 C where c is the face centered cubic (fcc) terminal solid solution (Ni). The t phase forms through a peritectoid reaction q + cM t at 870 C. A eutectic reaction LM d + c occurs at 1317 C. The Mo-Re system [Massalski 2] (Fig. 2) has two intermediate phases r and v. The r phase forms through a peritectic reaction L + eM r at 2645 C, where e represents the close packed hexagonal (cph) terminal soid solution (Re). The v phase forms through a peritectoid reaction r + eM v at 2000 C. The r phase exists only at temperatures higher than 1125 C and transforms through a eutectoid reaction rM a + v at 1125 C. A eutectic reaction LM a + r occurs at 2505 C. The Ni-Re system [Massalski 2] (Fig 3) is a simple peritectic system, the peritectic reaction L + eM c occurs at 1620 C.

The Cr-Ni-Hf (Chromium-Nickel-Hafnium) System

The Cr-Ni-Hf system was reviewed by [2001Gup]. For development of high temperature resistant brazing alloys, the Cr-Ni-Hf system was studied at the Ni-corner. The results are reported here. In order to discuss the results it is necessary to recapitulate the binary systems. The Cr-Hf system [Massalski2] (Fig. 1) has only one intermediate phase Cr2Hf which exists in two polymorphic forms in high temperature Cr2Hf (Y) phase and a low temperature Cr2Hf (Y1) phase. The Y phase melts congruently at 1825 C and the polymorphic transformation temperature for the Cr2Hf phase is 1335 C. Two eutectics, LM a + Y and LM Y + a1, occur at 1665 and 1500 C, respectively. The a and a1 phases are the two body centered cubic (bcc) terminal solid solutions (Cr) and (bHf), respectively. A eutectoid reaction a1MY + x occurs at 1370 C; x is the close packed hexagonal (cph) terminal solid solution (aHf). The Cr-Ni system [1991Nas] (Fig. 2) is a simple eutectic system. The eutectic reaction LM c + a occurs at 1345 C, where c is the face centered cubic (fcc) terminal solid solution (Ni). The c phase extends to 50 at.% Cr and the bcc a phase extends to 32 at.% Ni. An ordered CrNi2 phase forms from the c phase at T < 600 C. The Hf-Ni system [1991Nas] (Fig. 3) has nine intermediate phases: HfNi5 (e), Hf2Ni7 (p), high temperature HfNi3 (k1) and a low temperature HfNi3 (k), Hf8Ni21 (h), Hf3Ni7 (w), Hf7Ni10 (b), Hf9Ni11 (m), HfNi (/1) phase at high temperature and HfNi (/) at low temperature, and Hf2Ni (n). The polymorphic transformation temperatures for the HfNi3 and HfNi phases are 1200 and 1175 C, respectively. The p and /1 phases melt congruently at 1460 and 1530 C, respectively. All other phases form through peritectic reactions: L + pM e at 1240 C, L + pM k1 at 1340 C, L + k1M h at 1300 C, L + hM w at 1350 C, L + /1 M m at 1340 C, L + m M b at 1290 C, and L + /1 M n at 1200 C. Three eutectic reactions LM c + e, LMw + b, and LM n + x occur at 1190, 1190, and 1150 C, respectively. The h and w phases exist at high temperature and transforms through eutectoid reactions hM k + w at 1177 C and wM k + b at 1020 C. The binary phases and their structure data are given in the review by [2001Gup]. No ternary phase exists in the Cr-Hf-Ni system. The Cr-Hf-Ni system has been reinvestigated at the Ni-Corner of the Cr-Hf-Ni system by [1999Kho]. Twenty two alloys were prepared using 99.98 mass% Cr, 99.9 mass% Hf, and 99.95 mass% Ni. The alloys were arc melted

The Co-Nb-Si (Cobalt-Niobium-Silicon) System

The Co-Nb system [Massalski2] shows the presence of three intermediate phases Co3Nb (k3), Co2Nb, and Co6Nb7 (l), of which the Co6Nb7 and Co2Nb phases melt congruently at 1402 and 1480 C, respectively. The Co2Nb phase is known to have two polymorphic forms, Co2Nb (k2), a Cu2Mg type Laves phase and Co2Nb (k1), a MgZn2 type Laves phase, the latter phase has been reported to exist above 1225 C [1964Kuz2]. The k3 phase, a MgNi2 type Laves phase, forms through a peritectic reaction L + Co2Nb $ k3 at 1247 C. Three eutectic reactions L $ a þ l;L $ l þ Co2Nb and L $ c þ k3 occur at 1374, 1378, and 1237 C, respectively. The a and c phases are the terminal solid solutions (Nb) and (aCo), respectively. The Co-Si system [Massalski2] has five intermediate phases, Co3Si (/), aCo2Si (q1), bCo2Si (q2), CoSi (f), and CoSi2 (p) of which the bCo2Si, CoSi, and CoSi2 phases melt congruently at 1334, 1460, and 1326 C, respectively. The Co3Si and aCo2Si phases form through peritectic reactions Lþ aCo2Si $ Co3Si at 1214 C and Lþ bCo2Si $ aCo2Si at 1320 C. The cph (eCo) phase is stabilized to higher temperatures with addition of Si to Co and at 1250 C a peritectic reaction Lþ ðaCoÞ $ ðeCoÞ occurs. The Co3Si and the bCo2Si phases exist only at higher temperatures and decompose through eutectoid reactions Co3Si $ ðeCoÞ þ aCo2Si at 1193 C and bCo2Si $

The Ni-Re-Zr (Nickel-Rhenium-Zirconium) System

The Ni-Re system [Massalski2] (Fig. 1) is a simple peritectic system. The peritectic reaction e + LM c occurs at 1670 C where e and c are the terminal solid solutions (Re) and (Ni), respectively. The Ni-Zr system [1991Nas] (Fig. 2) shows the presence of eight intermediate phases: Ni5Zr(e), Ni7Zr2(p), Ni3Zr(j), Ni21Zr8(h), Ni10Zr7(b), Ni11Zr9(m), NiZr(/), and NiZr2(n), of which the p, /, and n phases melt congruently at 1440, 1260, and 1120 C, respectively. All the other phases form through peritectic or peritectoid reactions: L + pM e at 1300 C, L + p M h at 1180 C, L + m M b at 1160 C, L + /M m at 1170 C, and p + h M j at 920 C. Two eutectoid reactions m +/ + b and (bZr) M (aZr) + n occur at 978 and 843 C, respectively. The p, h, m, /, and n phases are of invariant compositions. The Re-Zr system [Massalski2] (Fig. 3) has three intermediate phases. Re24Zr5(v), Re2Zr(k1) and ReZr2(f), of which the k1 phase melts congruently at 2750 C. The v phase and the f form through peritectic reactions L + k1M v at 2500 C and L + k1M f at 1640 C. Two eutectic reactions LM (Re) + v and L M f + bZr occur at 2400 and 1593 C, respectively. A eutectoid reaction bZr M f + aZr occurs between 550 and 600 C. The f phase is of invariant composition.

The Co-Ni-Y (Cobalt-Nickel-Yttrium) System

The Co-Ni system [Massalski2] (Fig. 1) is a simple isomorphous system with solidus and liquidus lines very close to each other. The solid solution, face centered cubic (fcc) c phase, extends from fcc aCo to Ni. At the Co-end, at temperatures 1300 C and p¢ at <1300 C), Co5Y (x), Co7Y2 (q), Co3Y (m), Co2Y (k2), Co3Y2 (f), Co 7Y 6 (s), CoY (h¢), Co3Y4 (d), Co5Y8 (i), CoY3 (g). A metastable phase Co2Y3 (/¢) has been reported in the Co-Y system. The p and x phases melt congruently at 1357 and 1345 C, respectively. All other phases form through peritectic or peritectoid reactions: Lþ x $ q at 1320 C, Lþ q $ m at 1308 C, Lþ m $ k2 at 1154 C Lþ k2 $ f at 866 C, Lþ f $ h0 at 798 C, Lþ h0 $ i at 740 C, Lþ e0 $ g at 889 C, h0 þ f $ s at 775 C, and i þ h0 $ d at 732 C. Three eutectic reactions L $ c þ p, L $ p þ x, and L $ i þ g occur at 1340, 1300, and 738 C. The Ni-Y system [Massalski2] (Fig. 3) has nine intermediate phases, Ni17Y2 (p), Ni5Y (x), Ni4Y (w), Ni7Y2 (q), Ni3Y (m), Ni2Y (k2), NiY (h), Ni2Y3 (/), and NiY3 (g), of which the x and h phases melt congruently at 1430 and 1070 C, respectively. All other phases form through peritectic reactions: Lþ x $ p at 1330 C, Lþ x $ w at 1340 C, Lþ w $ q at 1298 C, Lþ q $ m at 1237 C, Lþ m $ k2 at 1106 C, Lþ h $ / at 820 C, and Lþ e0 $ g at 902 C. Three eutectic reactions, L $ c þ p; L $ k2 þ h, and L $ / þ g occur at 1285, 950, and 805 C, respectively. e¢ is the cph terminal solid solution of ac.

The Cu-Ni-Y (Copper-Nickel-Yttrium) System

The Cu-Ni system [Massalski2] (Fig. 1) is a simple isomorphous system with a continuous liquid solution separated by a narrow two-phase region from a continuous solid solution. The face centered cubic (fcc) solid solution of Cu and Ni (c), however, undergoes a short range order transformation at temperatures less than 300 C. The Cu-Y system [Massalski2] (Fig. 2) has five intermediate phases, Cu6YðgÞ;Cu4YðdÞ;Cu7Y2ðhÞ;Cu2YðiÞ; and CuYðt1Þ; of which the d; i; and t1 phases melt congruently at 975, 935, and 935 C, respectively. The g and h phases form through peritectic reactions L + dM g at 910 C and L + dM h at 920 C. Four eutectic reactions: L $ c þ g; L $ h þ i;L $ i þ t1; and L M c + e occur at 860, 840, 830, and 770 C, respectively. e is the terminal solid solution (aY). A metastable phase of composition Cu5Y was found to form through rapid quenching of a liquid alloy. The h; i; and t1 phases are of invariant compositions. The Ni-Y system [1991Nas] (Fig. 3) has nine intermediate phases: Ni17Y2(f), Ni5Y(x), Ni4Y(j), Ni7Y2(q), Ni3Y(p), Ni2Y(k), NiY(s), Ni2Y3(w), and NiY3(n). The Ni5Y(x) and NiY(s) phases melt congruently at 1430 and 1070 C, respectively. All the other phases form through peritectic reactions: L + x M f at 1350 C, L + x M j at 1340 C, L + j M q at 1298 C, L + q M p at 1237 C, L + p M k at 1106 C, L + s M w at 820 C, and L + e M n at 902 C, where e is the terminal solid solution (Y). All the intermediate phases are of invariant compositions. Three eutectic reactions L M f + c, L M k + s, and L M w + n occur at 1085, 950, and 805 C, respectively.

Thermodynamic description of the Cr–Ge system

The Cr–Ge binary system was thermodynamically optimized using the CALPHAD method. The liquid phase was described by means of an associate solution model. The BCC terminal solid solution was described by the substitutional solution model. The two-sublattice model was used to describe the non-stoichiometric compounds Cr 3Ge, αCr 5Ge 3 and βCr 5Ge 3. The Cr 11Ge 8, CrGe and Cr 11Ge 19 phases were modeled as stoichiometric compounds. A set of thermodynamic parameters for the Cr–Ge system was obtained via thermodynamic optimization using assessed experimental data. The calculated phase diagram and thermodynamic properties agree well with most of the experimental data.

Thermodynamic modeling of the germanium–nickel system

A thermodynamic optimization of the Ge–Ni system was carried out and a set of thermodynamic parameters were obtained. The substitutional solution model was used to describe the liquid and FCC (Ni) terminal solid solution phases. The two-sublattice model was used to describe the non-stoichiometric compounds βNi3Ge, ɛNi5Ge3, Ni19Ge12 and Ni3Ge2. The γNi3Ge, δNi5Ge2, Ni2Ge, ɛ′Ni5Ge3 and NiGe phases were modeled as stoichiometric compounds. The calculated phase diagram and thermodynamic properties agree well with most of the experimental data.

Thermodynamic modeling of the Si–Sr system

Thermodynamic modeling of the Si–Sr system was carried out using the CALPHAD method. In this system, three of the intermetallic compounds, Sr 2Si,Sr 5Si 3,SrSi, were considered to be stoichiometric and SrSi 2 was modeled as a non-stoichiometric phase. For the liquid phase, two different models were used. In one case, Sr and Si were assumed to constitute a random solution, with its excess Gibbs energy being described through the Redlich–Kister polynomial. In the second case, the liquid phase was described through the associate model, considering the species Si, Sr and SrSi. The terminal solid solutions, ( β Sr ), ( α Sr ) and (Si), are treated with negligible solubilities. A set of self-consistent thermodynamic parameters is obtained by considering experimental phase equilibria, measurements of the mixing enthalpy in the liquid phase, as well as measured and calculated–via first-principles methods based on density functional theory–formation enthalpies of the intermetallic compounds.