Materials Today: Proceedings xxx (xxxx) xxx Contents lists available at ScienceDirect Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results Said Kardellass a,b,⇑, Colette Servant c, Isabelle Drouelle c, Fatima Zahra Chrifi-Alaoui a, Mohamed Idbenali d, Alyen Abahazem f, Aissam Hidoussi e, Amine Bendarma b, Najim Selhaoui a a Laboratoire de Thermodynamique et Energétique, LTE, Université Ibn-Zohr, B.P.8106, Agadir, Morocco Sustainable Innovation and Applied Research Laboratory, Polytechnic School, International University of Agadir, Agadir, Morocco Laboratoire de Physicochimie de l’Etat Solide, ICMMO, Université Paris-Sud, 91405 Orsay Cedex, France d Laboratoire de Mécanique, Procédés de l’Energie et de L’Environnement (LMP2E), ENSA, Agadir, Morocco e Laboratoire d’étude Physico-Chimique des Matériaux, Université de Batna 1, Rue Chahid Boukhlouf, 05000 Batna, Algeria f Laboratoire Matériaux et Energies Renouvelables (LMER), Faculté des Sciences, Université Ibn Zohr, Agadir, Morocco b c a r t i c l e i n f o Article history: Received 1 June 2019 Received in revised form 11 August 2019 Accepted 20 August 2019 Available online xxxx Keywords: Thermodynamic description Pd-Yb phase diagram Pd-based alloys First-principles calculations Kaptay and Redlich-Kister models a b s t r a c t In the present paper, the thermodynamic properties of the Palladium-Ytterbium binary system were optimized using the CALPHAD approach. The liquid phase and the terminal solid solutions: body-centered cubic for cYb and face-centered cubic for bYb, and (Pd) are described by the substitutional solution model with the exponential (Kaptay model) and linear (Redlich-Kister polynomials) models for the temperature dependence of the excess Gibbs energy. The other intermetallic compounds, PdYb3, a-Pd2Yb5, b-Pd2Yb5, Pd4Yb3, Pd2Yb, a-Pd21Yb10, b-Pd21Yb10, and Pd7Yb are treated as stoichiometric compounds. The thermodynamic properties of the intermetallic compounds at 0 K are predicted using the first-principles approach. Two sets of self consistent thermodynamic parameters for the Palladium-Ytterbium binary system are obtained. With the present thermodynamic descriptions, the thermochemical properties and the phase equilibria are well reproduced. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Plasma and Energy Materials ICPEM2019. 1. Introduction Widely used in different sectors viz. nuclear energy, metallurgy, chemical engineering, electronics, computer manufacturing and numerous medical devices [1,2], REEs fall into two categories, viz. light rare earths (La to Sm) with varying levels of uses and demand and heavy rare earths (Eu to Lu, Y) which are less common and more valuable [3]. The overall chemical and metallurgical properties of the REEs are due to their outer electrons 5d6s (3d4s for Sc and 4d5s for Y). For the lanthanides, the normal configuration for the metallic state is 4fn(5d6s)3, that is, trivalent, with only Eu and Yb having the divalent 4f(n+1)(5d6s)2 configuration. Recovery of REEs is interesting due to its high market prices along with various industrial applications. Biosorption represents a biotechnological innovation as well as a cost effective excellent tool for ⇑ Corresponding author. E-mail address: said.kardellass@edu.uiz.ac.ma (S. Kardellass). the recovery of rare earth metals from aqueous solutions [4]. Alloying with platinum group metals PGMs especially Palladium, which is used as catalyst in a number of important chemical processes, they have an significant influence on the structures and properties. For instance, the palladium-rich RE solid solution alloys are of interest due to their own physical and metallurgical properties, and their potential applications as hydrogen diffusion membranes for purification and isotope separation but also as redox catalysis and hydrogen absorption (e.g.: hydrogen storage materials in batteries or fuel cells) [5–6]. Moreover, compounds of the PalladiumRE systems were found to exhibit unique optical properties. The most pronounced optical properties were found just for LuPd3 and LuPd compounds, which are blue (similar to silicon) and golden, respectively [7]. The purposes of the present work are (1) to evaluate the measured phase diagram data and thermodynamic data available in the literature (2), to compute the enthalpies of formation (DHf) for all the intermetallic compounds in this binary system via https://doi.org/10.1016/j.matpr.2019.08.196 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Plasma and Energy Materials ICPEM2019. Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 Phases Thermodynamic model Liquid (Pd,Yb)1 2 Thermodynamic parametersb Redlich-Kister model [17] bcc_A2 (Pd,Yb)1(Va)*3 fcc_A1 (Pd,Yb)1(Va)*1 PdYb3 (Pd)0.25(Yb)0.75 aPd2Yb5 (Pd)0.285(Yb)0.714 bPd2Yb5 (Pd)0.285(Yb)0.714 aPdYb (Pd,Yb)0.50(Pd)0.50 Kaptay model [18–20] 0 Liq LPd:Yb ¼ - 269657:509 þ 7:929 T 1 Liq LPd:Yb ¼ - 92217:234 þ 16:714 T 2 Liq LPd:Yb ¼ þ46141:615 - 21:085 T 0 BCC A2 LPd:Yb ¼ þ5010 0 FCC A1 LPd:Yb ¼ - 228337:332 1:315 T 1 FCC A1 LPd:Yb ¼ - 95731:401 þ 8:478 T A1 A1 0 PdYb3 GPd:Yb 0:250 298:15 Hfcc 0:750 298:15 Hfcc ¼ Pd Yb A1 0 fcc A1 þ 0:750 G ¼ 52718:199 þ 10:843 þ0:250 0 Gfcc Pd Yb A1 A1 0 aPd2 Yb5 GPd:Yb 0:285 298:15 Hfcc 0:714 298:15 Hfcc ¼ Pd Yb A1 0 fcc A1 þ 0:714 G ¼ þ0:285 0 Gfcc Pd Yb 0 Liq LPd:Yb 1 Liq LPd:Yb 2 Liq LPd:Yb ¼ - 255693:94 EXPð- 5:628E - 05 TÞ ¼ - 97449:687 EXPð- 4:135E - 04 TÞ ¼ þ 22699:94 EXPð- 5:822E - 04 TÞ No excess term optimized T - 48250:046 þ 0:0501 T bPdYb (Pd,Yb)0.50(Pd)0.50 A1 2 Yb5 GbPd 0:285 298:15 Hfcc 0:714 Pd Pd:Yb A1 0 fcc A1 þ 0:714 G ¼ þ0:285 0 Gfcc Pd Yb - 56723:003 þ 8:859 T 0 aPdM GPd:Pd ¼ þ183254:857 0 aPdM GPd:Yb 0:500 298:15 Hfcc Pd A1 þ 0:500 þ0:500 0 Gfcc Pd 0 aPdM LPd;Yb:Pd ¼ - 219378:233 (Pd)0.571(Yb)0.428 aPd5Yb3 (Pd,Yb)0.625(Yb)0.375 0 0 fcc HYb A1 ¼ A1 0:500 298:15 Hfcc ¼ Yb A1 Gfcc ¼ 80832:267 þ 2:56371 T Yb GbPdM ¼ 129496:642 - 4:989 T Pd:Pd A1 0 bPdM GPd:Yb 0:500 298:15 Hfcc 0:500 Pd A1 þ 0:500 þ0:500 0 Gfcc Pd 0 bPdM LPd;Yb:Pd ¼ - 157086:906 Pd4Yb3 A1 298:15 Gfcc Yb A1 298:15 Hfcc Yb A1 ¼ - 80831:963 þ 2:56353 T A1 A1 0 Pd4 Yb3 GPd:Yb 0:571 298:15 Hfcc 0:428 298:15 Hfcc ¼ Pd Yb A1 A1 þ 0:428 0 Gfcc ¼ - 77228:898 þ 0:650 T þ0:571 0 Gfcc Pd Yb Pd5 Yb3 GaYb:Yb ¼ 164644:571 - 2:044 T fcc A1 A1 Pd5 Yb3 GaPd:Yb 0:625 298:15 HPd 0:375 298:15 Hfcc ¼ Yb A1 0 fcc A1 þ0:625 0 Gfcc þ 0:375 G ¼ 74419:861 þ 0:650 T Pd Yb 0 aPd5 Yb3 LPd;Yb:Yb ¼ - 219975:471 (Pd,Yb)0.625(Yb)0.375 5 Yb3 GbPd ¼ 134825:227 - 3:005 T Yb:Yb A1 A1 5 Yb3 GbPd 0:625 298:15 Hfcc 0:375 298:15 Hfcc ¼ Pd Yb Pd:Yb A1 0 fcc A1 þ 0:375 G ¼ 72679:697 0:521 T þ0:625 0 Gfcc Pd Yb 0 bPd5 Yb3 LPd;Yb:Yb ¼ - 203743:952 0 Pd2Yb (Pd)0.667(Yb)0.333 aPd21Yb10 (Pd)0.667(Yb)0.322 bPd21Yb10 (Pd)0.667(Yb)0.322 fcc 0 Pd2 Yb GPd:Yb 0:667 298:15 HPd A1 þ 0:333 þ0:667 0 Gfcc Pd (Pd)0.750(Pd,Yb)0.250 0 A1 0:333 298:15 Hfcc ¼ Yb A1 Gfcc ¼ 72047:889 þ 0:806 T Yb fcc A1 A1 0 aPd21 Yb10 GPd:Yb 0:677 298:15 HPd 0:322 298:15 Hfcc ¼ Yb A1 0 fcc A1 þ 0:322 G ¼ 71444:09 þ 0:895 T þ0:677 0 Gfcc Pd Yb 0 21 Yb10 GbPd 0:677 Pd:Yb þ0:677 Pd3Yb A1 0 A1 Gfcc Pd 298:15 Hfcc Pd þ 0:322 0 A1 0:322 A1 Gfcc Yb 298:15 fcc HYb A1 ¼ ¼ - 71283:910 þ 0:787 T Pd7Yb (Pd)0.875(Yb)0.125 A1 0 bPd2 Yb5 GPd:Yb 0:285 298:15 Hfcc 0:714 Pd A1 0 fcc A1 þ 0:714 GYb ¼ þ0:285 0 Gfcc Pd - 45302:168 - 0:179 T aPdM GPd:Pd ¼ þ183254:857 0 aPdM GPd:Yb 0:500 298:15 Hfcc Pd A1 þ 0:500 þ0:500 0 Gfcc Pd 0 aPdM LPd;Yb:Pd ¼ - 219421:652 A1 þ 0:500 þ0:500 0 Gfcc Pd 0 bPdM LPd;Yb:Pd ¼ - 156874:725 Units in J/mol atom and J/mol atom/K. Reference states are fcc_A1for both elements Pd andYbatTa, a Since the Neumann–Kopp Rule has been invoked, the formation properties are independent of temperature, b Note that the enthalpies and entropies of formation of the intermetallic compounds are listed per mole of atoms, *(Va) for Vacancy. A1 ¼ A1 0:500 298:15 Hfcc ¼ Yb A1 Gfcc ¼ 75645:441 þ 3:076 T Yb Gfcc Yb A1 298:15 Hfcc Yb A1 ¼ ¼ - 75602:902 þ 3:051 T A1 fcc A1 0 aPd5 Yb3 GPd:Yb 0:625 298:15 Hfcc 0:375 298:15 HYb ¼ Pd A1 0 fcc A1 þ0:625 0 Gfcc þ 0:375 G ¼ 68646:217 þ 0:972 T Pd Yb 0 aPd5 Yb3 LPd;Yb:Yb ¼ - 219280:03 5 Yb3 GbPd ¼ þ 138070:331 - 3:005 T Yb:Yb fcc A1 A1 0 bPd5 Yb3 GPd:Yb 0:625 298:15 HPd 0:375 298:15 Hfcc ¼ Yb A1 0 fcc A1 þ 0:375 G ¼ 68242:869 þ 0:705 T þ0:625 0 Gfcc Pd Yb 0 bPd5 Yb3 LPd;Yb:Yb ¼ - 196686:219 fcc 0 Pd2 Yb GPd:Yb 0:667 298:15 HPd A1 þ 0:333 þ0:667 0 Gfcc Pd A1 0 A1 0:333 298:15 Hfcc ¼ Yb fcc A1 GYb ¼ - 65717 þ 0:679 T A1 A1 0 aPd21 Yb10 GPd:Yb 0:677 298:15 Hfcc 0:322 298:15 Hfcc ¼ Pd Yb A1 0 fcc A1 þ 0:322 G ¼ 65094:386 þ 0:738 T þ0:677 0 Gfcc Pd Yb 0 21 Yb10 GbPd 0:677 Pd:Yb þ0:677 0 A1 Gfcc Pd 298:15 Hfcc Pd þ 0:322 fcc 0 Pd7 Yb GPd:Yb 0:875 298:15 HPd A1 þ0:875 0 Gfcc þ 0:125 Pd A1 0:125 298:15 Hfcc ¼ Yb A1 Gfcc ¼ - 40179:490 þ 7:518 T Yb Hfcc Yb Pd5 Yb3 GaYb:Yb ¼ þ165041:895 - 2:044 T fcc 0 Pd7 Yb GPd:Yb 0:875 298:15 HPd A1 þ0:875 0 Gfcc þ 0:125 Pd 0 0 298:15 A1 fcc A1 0 Pd4 Yb3 GPd:Yb 0:571 298:15 Hfcc 0:428 298:15 HYb ¼ Pd A1 fcc A1 þ 0:428 0 GYb ¼ - 71589:817 þ 1:065 T þ0:571 0 Gfcc Pd Pd3 Yb GPd:Pd ¼ 6013:804 0 Pd3 Yb GPd:Yb 0:750 298:15 Hfcc Pd A1 þ 0:250 þ0:750 0 Gfcc Pd 0 Pd3 Yb LPd:Pd;Yb ¼ - 8001:508 A1 A1 0 Pd3 Yb GPd:Pd ¼ 2601:005 A1 fcc A1 Pd3 Yb GPd:Yb 0:750 298:15 Hfcc 0:250 298:15 HYb ¼ Pd A1 0 fcc A1 þ 0:250 G ¼ 60717:520 - 2:336 T þ0:750 0 Gfcc Pd Yb 0 Pd3 Yb LPd:Pd;Yb ¼ - 157086:906 0 T - 60466:957 þ 15:703 T GbPdM ¼ þ129496:642 - 4:989 T Pd:Pd A1 0 bPdM GPd:Yb 0:500 298:15 Hfcc 0:500 Pd ¼ 0 bPd5Yb3 0 FCC A1 LPd:Yb ¼ - 207603:954E þ 05 EXPð-9:017E - 06 TÞ 1 FCC A1 LPd:Yb ¼ - 63182:40 A1 A1 0 PdYb3 GPd:Yb 0:250 298:15 Hfcc 0:750 298:15 Hfcc ¼ Pd Yb A1 0 fcc A1 þ 0:750 G ¼ 52992:667 þ 13:275 þ0:250 0 Gfcc Pd Yb A1 A1 0 aPd2 Yb5 GPd:Yb 0:285 298:15 Hfcc 0:714 298:15 Hfcc ¼ Pd Yb A1 0 fcc A1 þ 0:714 G ¼ þ0:285 0 Gfcc Pd Yb 0 A1 0 A1 0 A1 0:322 fcc A1 GYb 298:15 Hfcc Yb A1 ¼ ¼ - 64013:243 þ 1:46E - 03 T A1 0:250 298:15 Hfcc ¼ Yb A1 Gfcc ¼ 60144:816 þ 0:574 T Yb A1 0:125 298:15 Hfcc ¼ Yb fcc A1 GYb ¼ - 32239:586 þ 1:315 T S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 Table 1 Thermodynamic parameters in the Palladium-Ytterbium binary systema. S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx Fig. 1a. Calculated Palladium-Ytterbium phase diagram (continuous line) using the thermodynamic parameters optimized in the present work used Redlich-Kister model [17] along with the experimental data from literature, [11–13] and [14]. Fig. 1b. Calculated Palladium-Ytterbium phase diagram (continuous line) using the thermodynamic parameters optimized in the present work used Kaptay model [18– 20] along with the experimental data from literature, [11–13] and [14]. first-principles calculations to supply the experimental information, and (3) to obtain a set of self-consistent thermodynamic parameters for the Pd-Yb binary system by means of the CALPHAD approach. 2. Assessment procedure Although there are a large number of thermodynamic assessments published, there is a rather small number of publications discussing the process of assessment. Recently, in the hope to help researchers in Calphad modelling field, Tang [8] published very important work in which he discussed the assessment procedure 3 Fig. 2a. Enlarged part of the calculated Pd-Yb phase diagram using the thermodynamic parameters optimized with Redlich-Kister model showing the congruent melting of the b-Pd5Yb3, Pd4Yb3 and b-PdYb phases. Fig. 2b. Enlarged part of the calculated Pd-Yb phase diagram using the thermodynamic parameters optimized with Kaptay model showing the congruent melting of the b-Pd5Yb3, Pd4Yb3 and b-PdYb phases. and described how to use the PARROT module in Thermo-Calc [9,10] to optimize thermodynamic parameters. Most of the above experimental information was selected for the evaluation of the thermodynamic model parameters. In the present work, the phase relation and transformation temperatures are based on recent version of phase diagram of Pd-Yb system determined by [11–14]. An assessed value of the parameters in the Gibbs free energy expressions was carried out by means of the computer optimization program: the PARROT module of the Thermo-Calc software. The stability constraint was enforced by requiring that the Gibbs energy of the liquid phase had positive curvature, 2 2 i.e.d GLiq =dxi 0, at all compositions and temperatures up to Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 4 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx 10,000 K. The program allows simultaneous treatment of all the various types of experimental data. Each piece of information is given a certain weight, chosen by personal judgment, which is a measure of its probable accuracy. This was done in order to reproduce the phase diagram correctly. The detailed description of the assessment procedure can refer the book written by Lukas et al. [15]. The optimization strategy is to start with the liquid phase when we have enough data to fix its variables. Part of other phases will depend on the liquid. Subsequently, intermetallic compounds and the other solution phases were introduced into the modeling one by one. Parameters ai and bi mentioned in i a LPd;Yb ¼ ai þ bi T (i = 0, 1, 2) were adjusted to describe the enthalpies of formation, liquidus and invariant reactions. Afterwards, parameters for the solution phases were introduced to describe the solubility ranges according to the measured terminal solubilities and the invariant reactions in which they are involved. When the calculated invariant temperatures were adjusted within the claimed error ranges, sublattice models were introduced to describe the composition ranges of three phases exist in the PdYb system. In the light of the discussion envisaged in stoichiometric compounds with homogeneity range part, we note here that the parameters obtained from the first treatment were used as the starting values for the second treatment. An optimization with all variables selected may lead to (i) errors, (ii) local minima, (iii) inconsistencies. To have a self-consistent set, the last optimizevariable in PARROT is done over all variables (generally without those related to Cp). Fortunately, in the present assessment all parameters for different phases were optimized simultaneously allowing to achieve a globally self-consistent thermodynamic description. 3. Results and discussion In the Table 1, the thermodynamic parameters optimized in the present work using two formalisms are listed. The calculated phase diagram using the presently obtained parameters with RedlichKister and Kaptay formalisms are depicted in Figs. 1a and b, respectively, along with reported experimental data published by [11–14]. Enlarged parts at high temperature are shown in Figs. 2a and b to bring to light the congruent meltings. As shown in the figures, a satisfactory agreement between the calculated phase diagrams and the experimental data has been achieved except for the PdYb HT $ Liq and Pd2 Yb $ Pd21 Yb10 LT þ Pd5 Yb3 HT reactions which are calculated at temperature too low, 1445 °C (with Redlich-Kister formalism) and 1438 °C (with Kaptay formalism) instead of 1460 °C [11,12], and 1150 °C (with Redlich-Kister formalism) and 1141 °C (with Kaptay formalism) instead of 1195 °C [11,12], respectively. In fact, these discrepancies between the experiment and calculation are due to the different weights given to the experimental data during the optimization. In both cases, small visible deviation from experimental data can be detected on the range of liquidus extends from 0.30 to 0.60 at.Yb. Our result makes the liquidus around the most stable compound more symmetric. Furthermore, the Kaptay model gives a better account of the eutectic reaction Pd5 Yb3 HT þ Pd4 Yb3 $ Liq than the RedlichKister model. For both diagrams, the catatectic reaction bYb $ Liq þ cYb is well reproduced. However, on the Yb rich side, the bYb domain calculated is too extended while [11,12] reported no extension. We have tried to eliminate this extension by adding fcc A1 . However, we have not succeeded in a positive term to 0 GYb:VA reproducing the eutectic bYb þ PdYb3 $ Liqin a satisfying way. The Yb-rich eutectic was usually difficult to reproduce. We think it may be caused by probable contamination with other lanthanides, or inaccuracies in SGTE description of Yb. We usually neglected these discrepancies. The calculated phase boundaries by using both descriptions of liquid phase and solid solutions are in good agreement with all measured data. Especially, no liquid miscibility gap was observed within the defined temperature range of the SGTE database (PURE5) (298.15–104 K) [16]. The invariant equilibria in the Pd-Yb binary system are displayed in Table 2. As shown in this table, satisfactory agreement is obtained between the calculations by using two models and experiments, where the largest uncertainty in the temperature of all invariant reactions is about 15 K. In view of the estimated experimental errors (about 1–2 at.% Pd), 20 of 22 experimental invariant reaction compositions in the Palladium-Ytterbium binary system are well reproduced. The present optimization result is the compromise Table 2 Invariant reactions of the Palladium-Ytterbium binary system.Comparison between the experimental data by [11–14] and the calculated values after the current optimization with. Reactions Reaction Type Literature [11–14] T/°C bYb $ aYb þ Liq bYb þ PdYb3 $ Liq PdYb3 $ Pd2 Yb5 LT þ Liq Pd2 Yb5 HT $ PdYb LT þ Liq Pd2 Yb5 LT $ Pd2 Yb5 HT PdYb HT $ Liq PdYb LT $ PdYb HT þ Liq PdYb HT $ PdYb LT þ Liq PdYb LT þ Pd4 Yb3 $ Liq Pd4 Yb3 $ Liq Pd5 Yb3 HT þ Pd4 Yb3 $ Liq Pd5 Yb3 HT $ Liq Pd5 Yb3 LT $ Pd4 Yb3 þ Pd5 Yb3 LT Pd5 Yb3 HT $ Pd2 Yb þ Pd5 Yb3 LT Pd5 Yb3 HT þ Pd21 Yb10 HT $ Liq Pd2 Yb $ Pd21 Yb10 LT þ Pd5 Yb3 HT Pd21 Yb10 LT $ Pd21 Yb10 HT Pd21 Yb10 HT $ Pd3 Yb þ Liq Pd3 Yb $ Liq Pd3 Yb þ fcc A1 $ Liq Pd7 Yb $ Pd3 Yb þ fcc A1 Liq $ ðPdÞ Peritectoid Eutectic Peritectic Peritectic Transition Congruent Transition Transition Eutectic Congruent Eutectic Congruent Transition Transition Eutectic Peritectoid Transition Peritectic Congruent Eutectic Peritectoid Melting 765 615 670 695 685 1460 1435 1390 1390 1415 1345 1360 1155 1185 1340 1195 1195 1380 1700 1350 449 1555 Composition at.%Yb 95.00 85.10 77.80 73.60 71.40 50.00 49.20 45.20 45.40 42.80 39.30 37.50 37.20 37.50 36.90 33.30 32.20 35.20 25.00 13.40 12.50 0 to 12.2 Current work Redlich-Kister Formalism [17] Kaptay Formalism [18–20] T/°C Composition, at.%Yb T/°C Composition, at.%Yb 775 633 656 699 689 1445 1437 1394 1394 1401 1360 1361 1161 1185 1348 1150 1196 1365 1697 1346 451 1555 94.72 83.33 79.24 72.00 71.40 50.00 51.85 44.83 44.84 42.80 38.87 37.50 37.20 37.50 35.70 33.30 32.20 34.29 25.0 14.68 11.48 0 760 621 667 693 682 1438 1432 1392 1392 1402 1348 1343 1154 1185 1348 1141 1195 1376 1702 1352 433 1555 95.08 85.11 77.66 72.21 71.40 50.00 51.20 44 44.74 42.80 38.35 37.50 37.20 37.50 36.70 33.30 32.20 35.32 25.0 14.05 21.04 0 Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 5 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx Table 3 Comparison between the enthalpies, entropies, and the Gibbs energies of formation of the intermetallic compounds in the Palladium-REE binary systems derived from the present optimization and taken from literature. Intermetallic compounds Enthalpies of formation, J. mol1. at1 Pd3RE Sc Y Eu Gd Dy Er Yb Pd2RE5 Y Eu Dy Yb PdRE Sc Y Eu Gd Dy Er Yb Pd4RE3 Y Gd Dy Er Yb Pd21RE10 Er Yb Pd5RE3 Pd2RE Yb Sc Y Eu Gd Dy Yb 82174 96080 95334 78078 79821 94070 60717.52 60144.82 64755.16 68000 ± 2000 21084 68548 44766 63190 48250.046 56723 60466.96 45302.17 56818.93 60350 89250 90583 78545 85265 80946 90231 80832.26 80831.96 75645.44 75602.902 54000 90954 66000 ± 3000 83450 92300 82523 81371 92573 77228.89 71589.82 92562.04 73000 ± 3000 81181 94070 71283.91 71444.09 64013.24 65094.38 80776.67 75000 ± 4000 75630 72679.697 74419.861 68242.869 68646.217 88681.57 75000 ± 3000 81703 84788 94330 104630 80498 81376 72047.88 65717 80776.67 T(K) Entropies of formation, J. mol1. at1. K1 Gibbs free Energies, J. mol1. at1 Technique Used References 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 819– 1240 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 819– 1240 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 819– 1240 298.15 298.15 298.15 298.15 298.15 298.15 298.15 819– 1240 298.15 298.15 298.15 298.15 298.15 298.15 819– 1240 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 18.13 12.51 10.83 7.63 7.11 5.723 2.336 0.574 – – 87579.45 99809.85 98562.96 80352.88 81940.84 95776.31 60021.04 60315.96 – – Optimization Optimization Optimization Optimization Optimization Optimization OptimizationR-K OptimizationK Prediction KEML/KEMS* [29] [28] [24] [25] [26] [27] Current work Current work [22] [12] – 13.686 13.95 11.72 0.0501 8.859 15.703 0.179 – – 13.61 4.145 8.461 8.684 3.500 0.862 2.5637 2.5635 3.076 3.051 – – – – 72628.48 40606.80 66684.31 48264.98 59364.31 65148.81 45248.80 – – 93307.82 91818.83 81067.64 87854.13 81989.52 89973.99 81596.627 81596.267 76562.549 76512.557 – – – Ab-initio Optimization Optimization Optimization OptimizationR-K Current work [28] [24] [26] Current work OptimizationK Current work Prediction Ab-initio Optimization Optimization Optimization Optimization Optimization Optimization OptimizationR-K [22] Current work [29] [28] [24] [25] [26] [27] Current work OptimizationK Current work Prediction Prediction KEML/KEMS* [21] [22] [12] – 4.396 5.790 2.966 0.549 0.650 1.065 – – – 93610.66 84249.28 82255.31 92409.31 77422.68 71907.35 – – Ab-initio Optimization Optimization Optimization Optimization OptimizationR-K OptimizationK Prediction KEML/KEMS* Current work [28] [25] [26] [27] Current work Current work [22] [12] – 5.723 0.787 0.896 0.00146 0.738 – – – 95776.31 71518.55 71711.23 64013.675 65314.415 – – Ab-initio Optimization OptimizationR-K Current work [27] Current work OptimizationK Current work Prediction KEML/KEMS* [22] [12] – 0.522 0.650 0.705 0.972 – – – 72835.33 74613.65 68453.06 68936.018 – – Ab-initio OptimizationR-K Current work Current work OptimizationK Current work Prediction KEML/KEMS* [22] [12] – 16.175 8.189 9.236 6.446 5.200 0.806 0.679 – – 89610.576 96771.550 107383.713 82419.875 82926.38 72288.189 65919.443 – Ab-initio Optimization Optimization Optimization Optimization Optimization OptimizationR-K OptimizationK Prediction Current work [29] [28] [24] [25] [26] Current work Current work [22] (continued on next page) Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 6 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx Table 3 (continued) Intermetallic compounds Enthalpies of formation, J. mol1. at1 PdRE3 Y Yb Pd7RE Y Eu Gd Dy Er Yb 62254 52718.199 52992.667 49609.80 52818 58188 51176 48335 48326 55755 40179.49 32239.586 32071.91 T(K) Entropies of formation, J. mol1. at1. K1 Gibbs free Energies, J. mol1. at1 Technique Used References 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 13.89 10.843 13.275 – – 12.943 6.200 9.402 8.268 7.360 7.518 1.315 – 66395.30 55951.03 56950.608 – – 62046.95 53024.53 51138.20 50791.10 57949.38 42420.981 32631.653 – Optimization OptimizationR-K OptimizationK Prediction Ab-initio Optimization Optimization Optimization Optimization Optimization OptimizationR-K OptimizationK Prediction [28] Current work Current work [22] Current work [28] [24] [25] [26] [27] Current work Current work [22] *KEML: Knudsen Effusion Mass Loss, KEMS: Knudsen Effusion Mass Spectrometry. between phase diagram and thermodynamic data. The calculated standard enthalpies, entropies and Gibbs free energies of formation of the intermetallic compounds according to the present description along with reported measurements (at various T), ab-initio, and theoretically predicted values for comparison are summarized in Table 3 and presented in Fig. 3a. Error bars are plotted according to the reported experimental uncertainties for each piece of experimental data. This figure shows that the computed values are in the range of experimental data. The enthalpy variation vs. composition is correctly reproduced. The present optimization of the thermodynamic parameters by using the Kaptay and Redlich-Kister models was based on the assumption that the enthalpy and entropy of formation (the reference state are solid: fcc_A1 for Pd and fcc_A1 for Yb) are independent of the temperature and, hence, the parameters obtained from fits to high-temperature data are used for calculating standard enthalpies at 298.15 K. Compared with experimental values measured by Ciccioli et al. [12] and our obtained ab-initio data, overall agreement is achieved for Pd3Yb, a- and b-Pd21Yb10, Fig 3a. Comparison of the calculated enthalpies J. mol1. at1 (HMR) of the intermetallic compounds in the Pd-Yb binary system with the experimental data in J. mol1. at1. HMR calculated with the present database: using Redlich-Kister model [17] ( , ), using Kaptay model ( , ) [18–20], theoretically predicted [22] ( ), experimental measured by [12] ( with is Error bars), and ab-initio data (This work). Pd2Yb, a- and b-Pd5Yb3, Pd4Yb3, a- and b-Pd2Yb5, PdYb3, and Pd7Yb phases. The agreement is less satisfactory for a- and b-PdYb equiatomic compound. For that phase, we pointed out that the enthalpy of formation given by [21] is less negative than optimized in the present study. The calculated values of the enthalpies of formation by using Kaptay model are more negative than the ones calculated by using Redlich-Kister model (see Table 3). In addition, in both cases, these calculated values are less negative than the predicted ones by [22]. This later, generally predict more exothermic values of DHf than are indicated by experiment and their values differ more from experimental results than the other predictions. Our calculated formation enthalpies from CALPHAD approach are in good agreement with our DFT GGA-PBE calculations, especially for Kaptay model, only a minor difference (several kJ) which can be attributed to the fact that CALPHAD enthalpies are given at 298.15 K, and DFT calculations are done at 0 K, in addition to the convergence accuracy in our DFT calculations (±1 kJ/mol. at.). We mention that GGA-PBE doesn’t take into account the correlation of the 4f states of Yb element, which can be enhanced using Hubbard-DFT methods (GGA + U). Unfortunately, Pd-Yb compounds are conductors without a band gap, and it is very difficult to keep a physical meaning by fitting the appropriate value for the Hubbard parameter U to other properties rather than the band gap. Although these discrepancies, DFT (GGA-PBE) calculations without employing the Hubbard parameter U still provide an accurate results with the experimental methods, and more accurate than the semi-empirical values for similar systems. The Redlich-Kister model’s minimum formation enthalpy is at a,bPdYb, while the experiment’s minimum [12] is at Pd5Yb3Pd21Yb10 (xPd = 0.625–0.677). Our results for this phase are in the range of the values reported in [23] for the equimolar phases PdRE, from 76 to 95 kJ/mol at., much more exothermic than one estimated by [12]. As it is rather difficult to assess the actual accuracy of such values, the agreement is considered satisfactory. The calculated Gibbs’ energy change during the intermetallic formation from the solid compounds at 298 K (dotted line with + for Kaptay model and r for Redlich-Kister model) and at 1000 K (dashed line with + for Kaptay model and r for Redlich-Kister model) are also shown in Fig. 3b. Moreover, the enthalpies of formation and the Gibbs free energies of the PdpREq compounds extracted from the literature [12,24–29] next to the experimental data, the values obtained from thermodynamic optimization, and theoretical models are compared in Table 3. We note that the variation with uncertainty of those enthalpies increase with the atomic number. It will be apparent from these figures that while there is reasonable agreement in the order of magnitude between experimental and predicted values, there are also some significant differences. Our optimized values agree well with the noted variation of the (Sc, Y, La-Lu) with Pd Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx 7 Fig. 3b. Calculated Gibbs free energies of the intermetallic compounds in the Pd-Yb binary system at T = 298 K, using Redlich-Kister model ( ), using Kaptay model ( ) and at T = 1000 K, using Redlich-Kister model ( ), using Kaptay model ( ). The reference states for the elements are fcc_A1 for Pd and fcc_A1 for Yb. Fig. 4a. Calculated integral (HMR) and partial (HPd and HYb) enthalpies of mixing of liquid phase at temperatures of 1000 K (continous and dashed lines), 2000 K (dash dotted line), and 3000 K (dotted line) using two models Redlich-Kister (R-K) and Kaptay (K) along with experimental data of Ivanov et al. [21] in 0.63 < xYb < 1 range at T = 1300 K. enthalpy of formation. As mentioned above, no experimental thermodynamic property of liquid has been reported in the literature. In order to provide a reasonable prediction of the properties of liquid, we have plotted on the liquidus of the REEs–Pd binary systems. Moreover, the calculated enthalpies and entropies of mixing of liquid phase are plotted, respectively. The calculated integral and partial enthalpies of mixing of the Pd-Yb binary system at T = 1300 K, compared with those found by Ivanov et al. [30] using calorimetry for Pd-Eu melts are shown in Fig. 4a. We noticed a good agreement in the Eu rich corner for both calculated properties by applying two models with those measured in [30]. The value calculated by Entall Miedema Calculator developed by De˛bski et al. [22] is in good agreement with our calculated values in both cases. We have plotted the excess Gibbs energies of mixing Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 8 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx of the liquid phase at xYb = 0.1, 0.2, 0.3, and 0.4 as function of temperature from 0 to 4.104 K for 0L by applying the two models as follows: Redlich Kister model : DGExYb ¼ xYb ð1 xYb Þ ð269657:509 þ 7:929 TÞ Kaptay model : DGExYb ¼ xYb ð1 xYb Þ ð255693:94 EXPð- 5:628E - 05 TÞÞ As can be seen in the Fig. 4b, at high temperatures interval: For Kaptay model: in accordance with the rule of Lupis and Elliott proposed for the first time in 1966 [31] and recenly reformulated by Kaptay [98] as,‘‘Real solid, liquid and gaseous solutions (and pure gases) gradually approach the state of an ideal solution (perfect gas) as temperature increases at any fixed pressure and composition.’’, the excess Gibbs energy function tends towards zero. However, for Redlich-Kister model: this function changes its sign from negative to positive and goes to more and more positive values which is probably unphysical [32]. Moreover, at low-T interval, the Redlich-Kister polynomial provides more negative excess Gibbs energy compared to the Kaptay formalism. This behavior changes at middle-T interval, the Kaptay formalism provides more negative excess Gibbs energy compared to the Redlich-Kister polynomial. With our optimization, in both cases, the evolutions of Gibbs free energy of mixing for the liquid phase as a function of temperature T, show that when T is increasing up to 104 K, the Gibbs free energy for the liquid phase increases in absolute value. The single liquid phase is stable at very high temperatures (if gas phase is suspended). As we can see, no spinodal points were detected until a temperature of 104 K, and no formation of an inverted miscibility gap was detected during the optimization in the region of validity of parameters. Theoretically, as explained by [19,33], the appearance of the high-T artefact Fig. 5a. Calculated heat contents (green continous line) for PdYb along with the experimental values ( ) [34] and least-squares fitted to the experimental data ( ) [34].(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 34 Fig. 5b. Calculated heat capacity in J.(mol K)–1 (continous line) of the PdYb intermetallic compounds along with least-squares fitted to the experimental data ( ) [34]. Calculated heat capacity in J.(mol K) –1(dashed line) of the Pd ( ) and Yb ( ), respectively. U U ( b0 T >> aU 0 ) if the linear model is applied is a0 < 0 and U b0 > 2 R Fig. 4b. Calculated excess Gibbs energies of the liquid phase in different temperature (0 – 40,000 K) and concentrations (xYb = 0.1, 0.2, 0.3, and 0.4) for Pd-Yb system using Redlich-Kister (continous line) [17] and Kaptay formalisms (dashed line) [18–20]. (sU 0 < 16:629). In the case of our sys- U temaU 0 ¼ - 269657:509 J/mol.at. and b0 ¼ - 7:929 J/mol.at.K (the reader is referred to the Table 1), thus no miscibility gaps arises using the linear model. Heat contents growth of the intermediate valence compound YbPd as a function of T are displayed in Fig. 5a. The calculated heat contents increased continuously together with the experimentally determined data and least squared fitted ones by [34] in the range 400 to 1200 K. Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx 9 Fig. 6a. Calculated partial pressure lnpYb using two Redlich-Kister (dotted line) and Kaptay (dashed dotted line) formalisms along with experimental ones determined by Ciccioli et al. [12] (continous line). Fig. 6b. Calculated chemical activities of the Palladium and Ytterbium at different temperature T = 1000, 1500, 2000 and 3000 K by using Kaptay model [18–20]. A satisfactory agreement is noted. The calculated temperature dependencies of specific heat for PdYb are shown in Fig. 5b together with least squared fitted values [34]. As we can see the transition temperature calculated in this study was 553 K. Furthermore, our calculated heat capacities are approximately higher and they are slowly increasing when the amount of Yb increases in the PdYb compound. A discrepancy is not higher. Ciccioli et al. [12] described Yb gas properties by a simple formula log10pYb (bar) = 5 – 7340 / T (K). In Fig. 6a the lnpYb are plotted versus the tempera- tures. The experimental values are also reported. In the temperature range and within the error margins, the variation of the partial pressures be approximated by a linear function of the temperatures. A satisfactory agreement was achieved for exponential model. The calculated evolution of the activities of Yb and Pd with Kaptay formalism at different temperatures T = 1000, 1500, 2000, and 3000 K are shown in Fig. 6b. The activities of palladium in the ytterbium alloys are found to have a negative deviation from Raoultian behavior over most of the composition range. Same Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 10 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx Fig. 7a. Gibbs energies of the liquid phase and solid phases in the Pd-Yb binary system at T = 298.15 K using Redlich-Kister formalism. Fig. 7b. Gibbs energies of the liquid phase and solid phases in the Pd-Yb binary system at T = 298.15 K using Kaptay formalism. behevior was observed for the activities of ytterbium in palladium alloys. Although the exponential model is proven to be an efficient tool to avoid high-T artifacts (artificial inverted miscibility gap), Schmid-Fetzer [33] claimed that it can lead to a low-T artefact, i.e. to the artificial low-T re-stabilization of the liquid solution. The results are shown in Figs. 7a, and b, respectively. As we can see the exponential and linear models for the solid phases provides much more negative Gibbs energy values compared to the Gibbs energies of the liquid solution. Hence we can conclude that our optimisation does not lead to any low-T artefact. The Gibbs energy values of the liquid solution and solid phases are close in palladium rich corner in the case of exponential model. 4. Summary The phase relations and thermodynamic description of the Palladium-Ytterbium binary system were critically evaluated from the experimental information available in the literature for the first time. A good agreement is obtained between experiments and Please cite this article as: S. Kardellass, C. Servant, I. Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196 S. Kardellass et al. / Materials Today: Proceedings xxx (xxxx) xxx calculations. It is suggested that new and more reliable thermodynamic measurements are necessary and would help to refine the present thermodynamic description. Acknowledgements The author of this work wants to thank M. A. 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Drouelle et al., Calphad-type assessment of the Pd-Yb binary system supported by first-principles calculations – Part II: Results, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.08.196