The role of Ni in modifying the order of the phase transition of La(Fe,Ni,Si)(13)

Repositorio Institucional de la Universidad Autónoma de Madrid https://repositorio.uam.es Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in: Acta Materialia 160 (2018): 137-146 DOI: https://doi.org/10.1016/j.actamat.2018.08.054 Copyright: © 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. El acceso a la versión del editor puede requerir la suscripción del recurso Access to the published version may require subscription © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 1 The role of Ni in modifying the order of the phase transition of La(Fe,Ni,Si)13 L.M. Moreno-Ramírez 1 , C. Romero-Muñiz 2 , J.Y. Law 1 , V. Franco 1 , A. Conde 1 , I. Radulov 3 , F. Maccari 3 , K. P. Skokov 3 , O. Gutfleisch 3 1 Dpto. Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065, 41080-Sevilla, Spain 2 Dpto. de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain 3 Institut für Materialwissenschaft, TU Darmstadt, 64287 Darmstadt, Germany Abstract In this work, we study the effect of Ni substitution on the magnetocaloric properties of La(Fe,Si) 13 compounds. Sample quality has been optimized by a combination of induction melting and suction casting techniques, which allowed to shorten the annealing time by an order of magnitude and expand the existing range of LaFe 11.6-x Ni x Si 1.4 phase with cubic NaZn 13 -type structure up to x=0.4. According to our Density Functional Theory calculations, Ni addition does not significantly alter the crystal structure (finding that Ni atoms occupy preferably 96i positions) as well as the total magnetic moment; both predictions are in agreement with experimental results. With increasing of Ni concentration, the transition temperature increases and the order of the phase transition changes from first to second-order type. In addition, we show that the magnetic field dependence of magnetocaloric effect enable a clear analysis of the order of phase transition even for compositions near the critical point, surpassing the accuracy of conventionally used techniques for determining the order of magnetic phase transitions (e.g. Banerjee’s criterion). © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 2 1. Introduction Magnetic refrigeration is a new technology aiming to replace the conventional chillers exploiting the gas expansion/compression cycles, which are dominating the market since 1927 when first commercial devices appeared. Most of the traditional refrigerators operate in a closed circuit, in which the condensation/evaporation of gas leads to wasted heating/cooling of a load. For magnetic refrigeration, a solid magnetic material substitutes those gas refrigerants and the expansion/compression is replaced by the application/removal of a magnetic field 1-4 . Hence, the use of non-environmental-friendly gases, such as CFC, NH 3 , HCFC or HCF, responsible for greenhouse effect and ozone depletion is eliminated. Furthermore, magnetocaloric prototypes show a larger energy efficiency (60 % of the theoretical limit versus 40 % in typical refrigerator), which is another significant advantage of magnetic refrigeration 5 . This emerging magnetic refrigeration technology is based on the magnetocaloric (MC) effect. This effect, discovered and explained by P. Weiss in 1917 6 , is defined as the thermal response of a magnetic material upon subjected to a varying magnetic field 7-10 and is conventionally ascribed to the interactions between the magnetic and lattice subsystems. With the application of an alternating magnetic field, the entropy of the magnetic subsystem changes due to the alignment/misalignment of the magnetic moments along the direction of the magnetic field while the lattice entropy is only affected by temperature variations. Under isothermal conditions, the system undergoes a change in the total entropy (∆ST) that equates to the variation in the magnetic subsystem (no lattice contribution to the entropy). When the magnetic field is changed adiabatically, a variation of the material temperature (∆TS) results from the change in lattice © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 3 entropy that compensates for the magnetic entropy change, as the total entropy is maintained constant. A significant MC effect (i.e. large values of ∆ST and ∆TS at moderate magnetic field change of 1- 2 T, which are used in real devices) occurs in the vicinity of a magnetic phase transition. Phase transitions are mainly classified as first (FOPT) and second-order (SOPT) phase transitions according to the Ehrenfest´s classification 11 . A FOPT is characterized by a discontinuity in the first derivative of the free energy associated to a thermodynamic parameter (leading to the existence of a latent heat, coexistence of the two phases during the transition and hysteresis phenomena 12 ). A SOPT is characterized by a discontinuity in the second derivative of the free energy (leading to a continuous phase transformation). With this, MC materials are categorized with the same classification. Typically, SOPT MC materials present lower MC effect than FOPT MC materials, nevertheless exhibiting a broader temperature width of MC maximum and a reversible character of the transition. The FOPT MC materials show a large MC effect but in a narrow temperature range accompanied by thermal/field hysteresis. Nowadays, one of the most promising family of MC materials are La(Fe,Si) 13 compounds 13,14 . These compounds are compositionally based on abundant, non-critical and non-contaminant elements. From the different binary systems consisting of a rare earth element and one of the Fe, Co or Ni transition metals, only the La-Co system presents an intermetallic compound with the NaZn 13 -type structure 15,16 . The large saturation magnetization and high Curie temperature of LaCo 13 made it attractive for its possible application as a permanent magnet (with limited success, as the cubic structure has no anisotropy) or as a high temperature soft magnetic material 17,18 . It is possible to obtain the NaZn 13 -type structure in the LaFe 13 system by incorporating Si 19 . The cubic La(Fe,Si) 13 phase shows a temperature-induced FOPT ferro-paramagnetic transition © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 4 (as well as field-induced para-ferromagnetic transition) around 200 K. The temperature and type of the transition are strongly depended on Si content 20,21 . The corresponding transition leads to an MC effect with moderate thermal hysteresis (compared to other FOPT MC materials, such as FeRh or Heusler alloys) and with associated volume change of around 1% though the crystal symmetry remains unaltered (magneto-elastic transition). Hydrogenation of the La(Fe,Si) 13 compounds produce an expansion of the NaZn 13 -type unit cell that shifts the transition temperature (Ttrans) close to room temperature (around 340 K) without decreasing the MC effect, which facilitates their application in room temperature devices 22,23 . However, it entails issues to be solved before commercialization of La(Fe,Si) 13 , for example the material degradation under cycling or reducing the thermal hysteresis 24 . Its MC effect is tunable by the additions of different dopants (mainly, rare earths substitution to La or transition metals to Fe). It has been reported that elements on the left side of Fe in the periodic table, which exhibit similar atomic radius as Fe (e.g. Mn 25 , Cr 26 ), shift Ttrans to lower temperatures (antiferromagnetic coupling) 27 . Conversely, those on the right side (e.g. Co 28 , Ni 26 ) shift Ttrans to higher temperatures (ferromagnetic coupling) 27 . For Ni additions, the MC effect can be tuned in the same way as Co additions but the former avoids using critical raw materials and at the same time reducing material cost (Co is a critical element), which contributes to enabling commercial magnetocaloric devices. With the aim of studying the influence of Fe substitution by Ni on the properties of La(Fe,Si) 13 magnetocaloric materials, a series of LaFe 11.6-x Ni x Si 1.4 compounds were developed and characterized. The studied samples, produced by induction melting and suction casting, exhibit an extended compositional critical point of SOPT of x critical =0.21 (leading to a 2.6-fold extension compared to previously reported similar alloys 26 ) together with high sample homogeneity and © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 5 amount of NaZn 13 phase. Density Functional Theory (DFT) calculations show that the NaZn 13 - type crystal structure is retained with Ni substitutions, in agreement with experiments. The order of the phase transition is also studied using the Banerjee´s criterion and two other methods based on field dependence of MC effect (one based on the Bean and Rodbell model 29 and a recent proposed quantitative criterion using the field exponent 30 ). The latter two techniques are shown to successfully determine the order of phase transitions for all compositions and even address for compositions near the compositional critical point of SOPT, which is challenging for such materials exhibiting a gradual crossover from FOPT to SOPT. 2. Experimental and methods LaFe 11.6 Si 1.4 compound, which was demonstrated that it underwent a FOPT 31 , was chosen as the parent composition. In order to investigate influence of Ni on the MC effect of this compound, 20 g of material, each with nominal compositions of LaFe 11.6-x Ni x Si 1.4 (x=0, 0.1, 0.2, 0.3 and 0.4) were produced by induction melting from pure elements. To remove possible oxide phases in the elements, La was initially cleaned by arc melting prior to being induction melted with other elements. It was reported that the shape and cooling rate influence the annealing time for La(Fe,Si) 13 compounds, which consequently affect the amount of the NaZn 13 -type structure phase (denoted as 1:13 phase) 32 . To ensure homogeneity, the samples, encapsulated in quartz tubes under Ar atmosphere, were subsequently annealed at 1050 ºC for 3 h. The annealed ingot was then further segmented into different pieces for subsequent suction casting (using a rectangular mold of 10×4×0.5 mm 3 ). A 9 wt. % excess of La was also added to compensate its vaporization during the melts. Suction casted samples were then annealed (wrapped in Mo foil © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 6 and sealed in quartz tubes) in a resistance tube furnace at 1100 °C for 24 h to obtain high amount of the desired 1:13 phase. Microstructural characterization and average bulk compositional quantification of the samples were performed using a Philips XL30 FEG scanning electron microscope equipped with energydispersive X ray system (SEM/EDX). The X-ray diffraction (XRD) of the pulverized samples were collected at room temperature using a Stoe Stadi P instrument in transmission mode with Molybdenum Kα 1 source radiation (λ=0.70930 Å). Rietveld refinement of the XRD patterns was performed using TOPAS Version 6.0 software. Magnetization measurements were performed with a vibrating sample magnetometer (standard option of a Quantum Design Physical Properties Measurement System, PPMS). The magnetic field was applied along the length of the suction casted plates to minimize contributions from the demagnetizing factor (further details in Results and discussion section). From isothermal magnetization (M) curves measured at different temperatures, the isothermal entropy change (∆ST) was calculated numerically indirectly using the Maxwell relation according to 33 : ∆     ,   =         ´ d  ´   , (1) where the initial magnetic field is fixed as 0. The adiabatic temperature change (∆TS) was directly measured in a home-built experimental set-up whereby the sample was thermally isolated to ensure adiabatic conditions during the variation of the magnetic field (more information can be found in Ref. 34 ). As FOPT MC materials can exhibit thermal hysteresis, a special characterization protocol for erasing the thermal and magnetic history of the samples has been applied in order to appropriately measure their isothermal magnetization curves and © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 7 correctly apply the Maxwell relation for ∆ST calculations 24,35 . A power law for the field dependence of ∆ST (in the form of ∆ST∝Hn(T,∆H)) is assumed 36,37 . The local field dependence exponent n was calculated from ∆ST data as:    ,   = d   ∆    d      . (2) In addition, Density Functional Theory (DFT) calculations were performed to unveil at atomic level the structural, electronic and magnetic properties of LaFe 11.5-x Ni x Si 1.5 compound series, using a plane-wave basis set as implemented in the VASP package 38 . This composition is one of the closest that can be generated using the selected unit cell for the NaZn 13 -type crystal. Although the Si content slightly deviates from the experimental compound investigated in this work, LaFe 11.5 Si 1.5 also shows a FOPT and the effects of Ni additions should be similar for both cases. An energy cutoff of 335 eV was considered to build the plane-wave basis set, which was proved to accurately describe such compounds 39,40 . The projected augmented wave method 41,42 was employed for the pseudopotentials of all species involved and the Perdew-Burke-Ernzerhof (PBE) functional 43 was chosen to reproduce the exchange and correlation electronic interactions. The four constituent metals were separately tested by calculating simple bulk structures to ensure a good agreement of the obtained lattice parameters. Following a conjugate gradient algorithm, to study their equilibrium configurations all the structures subjected to ionic relaxations were considered, starting from the same parent unit cell (NaZn 13 -type) with a lattice parameter of 11.488 Å (see Results and Discussion section for further details about the cell). Although no restrictions in the cell volume were imposed during © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 8 these relaxations, no significant distortions from the initial cubic symmetry are observed in the final structures. The convergence criterion to complete the structural minimization process was using a force upon atoms of less than 0.005 eV/Å while a cutoff of 10 -6 eV was established to achieve electronic self-consistency. Due to the large size of the cell, the reciprocal space was sampled using a 3x3x3 Monkhorst-Pack grid 44 . To explore magnetic and electronic properties, collinear spin polarization was required for all calculations and the Vosko-Wilk-Nusair interpolation 45 was used to resolve the on-site magnetism at atomic level. Due to the strong ferromagnetism of this material, it is necessary to start from an initial high magnetic moment configuration, which in our case was 3.5 Bohr magnetons per Fe atom. Both magnetic and electronic features were evaluated using a thinner k-point grid of 4x4x4 and a Gaussian broadening of 0.1 eV, starting from the converged structures. 3. Results and Discussion Fig. 1 shows the BSE images for the Ni-containing LaFe 11.6-x Ni x Si 1.4 samples. Bright spots correspond to La 1 Fe 1 Si 1 phase (P4/nmm), dark ones to α-Fe phase (Im-3m) and the grey ones to the desired 1:13 phase (NaZn 13 -type, Fm-3c). For all studied compositions, BSE images show a homogenous structure with the main phase of the desired 1:13 stoichiometry. Almost negligible α-Fe impurities were observed for samples with low Ni contents of x=0.1 and 0.2 (while some minor amounts of α-Fe was reported for similar alloys in the literature 46 ). Some bright spots of La 1 Fe 1 Si 1 phase can be noticed, which could be due to the excess La added for suction casting. The dark spots corresponding to α-Fe phase become more noticeable with increasing Ni concentration for higher Ni contents (x=0.3 and 0.4), although the high amount of the obtained 1:13 phase with compositions close to the nominal shows an extension of the solid solubility limit previously ascribed to Ni 47 . In addition, the compositional analysis by EDX (Table 1) © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 15 dependence of ∆ST adopts a power law expression as ∆ST∝, and its exponent n at the transition temperature is correlated to the critical exponents of the material in the form of n(Ttrans)=1+(1-β-1)δ-1 (where the critical exponents β and δ give the temperature dependence of M at zero field and the field dependence of M at Ttrans, respectively) 37 . For SOPT materials with long range interactions, the values of n(Ttrans) are typically similar to those determined using critical exponents for mean field model (n(Ttrans)=0.67). On the other hand, for short range interactions, the typical values are close to Heisenberg or 3D-Ising models (0.63 and 0.57, respectively). For the n(Ttrans) of SOPT, there exists a lower compositional limit corresponding to the case where the material transits from SOPT to FOPT and this point is called the compositional critical point of SOPT (denoted as “tricritical point” by some authors). According to theoretical considerations, the values of the critical exponents at this critical point yield n(Ttrans)=0.4 59 . For FOPT, although the material does not exhibit a critical region, the ∆ST in high fields lead to n(Ttrans)<0.4 when using the Bean and Rodbell model 60 . This is also experimentally observed for other La(Fe,Si) 13 series 21 . Therefore, there is a clear criterion to identify SOPT and FOPT MC materials based on the values of n(TTrans) when materials can be described with the Bean and Rodbell model (e.g. La(Fe,Si) 13 compounds). To clearly distinguish the order of the phase transition and also to find the compositional critical point of SOPT, the field dependence exponent n of the studied LaFe 11.6-x Ni x Si 1.4 series is plotted as a function of temperature for µ 0 ∆H=1.9 T (main panel of Fig 8). The n(TTrans) as a function of Ni content is presented in the inset of Fig 7. Although the demagnetizing effect on ∆ST curves has been earlier shown to be negligible in this study, it is being considered for exponent n as it was reported to affect n more significantly than the former 61-63 . It can be observed that samples with x=0, 0.1 and 0.2 show n(Ttrans)<0.4 values, indicating they undergo FOPT. On the other © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 16 hand, larger n(Ttrans) values (above 0.4) are observed for x=0.3 and 0.4, indicating they undergo SOPT. Also, the compositional critical point of SOPT corresponding to a Ni content is predicted as x=0.21 (where it is assumed a linear interpolation between the different points). The presence of α-Fe could contribute to increasing the values of n(T trans ) for higher Ni-containing samples 64 though this effect is relatively small as the transition temperature of α-Fe is well above of that of La(Fe,Si) 13 phase. For samples with a Si content of 1.5 (LaFe 11.5-x Ni x Si 1.5 ), it was reported that their order of phase transition altered from FOPT to SOPT for alloys with a Ni content of x=0.08 26 , which is a smaller limit compared to our case. Furthermore, a higher amount of 1:13 phase is attained for all samples studied in the present work. The next method to determine the order of the phase transition using the field and temperature dependence of exponent n is model independent, unlike the previous technique 30 . It shows that a quantitative criterion of n>2 near the transition indicates a FOPT and was successfully applied to different MC materials, such as La(Fe,Si) 13 and Heusler alloys, composites etc. From Fig. 8, overshoots of n>2 near the phase transition for LaFe 11.6 Si 1.4 , LaFe 11.5 Ni 0.1 Si 1.4 and LaFe 11.4 Ni 0.2 Si 1.4 are observed, which indicate that they undergo FOPT. On the other hand, higher Ni-containing samples show a gradual increase from the minimum towards a maximum value of 2 (paramagnetic region), indicating SOPT behavior. This is in agreement with the previous observations in n(TTrans) values. In addition, the applicability of Banerjee’s criterion to determine the order of phase transition 65 was also studied. This criterion establishes that the negative slopes of isothermal  vs H/M curves (Arrott plots) indicate FOPT, while positive slopes point to SOPT. Furthermore, it implies that the material follows a mean field model. The Arrott plots of the studied samples are plotted in Fig. 9 (magnetic fields lower than 500 Oe are not considered). They show good agreement © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 17 with the former analyses (from the exponent n) except for LaFe 11.4 Ni 0.2 Si 1.4 alloy, which shows positive slopes in the Arrott plot (instead of negative). One should note that this compound exhibits a composition very near to the compositional critical point of SOPT for this series (x=0.21). The imposition of a mean field model in this method leads to values of the critical exponents rather different from those of the critical point of SOPT, which attributes to its failure for this composition (LaFe 11.4 Ni 0.2 Si 1.4 ). These were also reported for other magnetocaloric materials, wherein the results from Banerjee’s criterion contradict to calorimetric data 66 . 4. Conclusions In this work, we studied the influence of Fe substitution by Ni on the structure, magnetic behavior and magnetocaloric effect of La(Fe,Si) 13 compounds. Using induction melting combined with suction casting, the required annealing duration was reduced by an order of magnitude as compared to that for the former counterparts. On top of that, the solid solubility of Ni in the desired 1:13 phase was extended. DFT calculations show that the NaZn 13 -type structure was retained (Ni occupies the 96i sites) and only slight decrease in the overall magnetic moment was predicted (ascribed to the lower moment of Ni atoms); both theoretical predictions are in agreement with experimental results. Magnetocaloric studies show that the first order phase transition was transformed into a second order type with increasing Ni concentration. We show that using the field dependence of magnetocaloric effect, the order of the phase transition can be unambiguously determined using a quantitative criterion even for compositions near the compositional critical point of SOPT (for which FOPT → SOPT). This critical point was © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 18 determined as x=0.21 in this work, leading to a 2.6-fold extension compared to previously reported similar alloys (x=0.08) 26 . Acknowledgements This work was supported by AEI/FEDER-UE (project MAT-2016-77265-R), the PAI of the Regional Government of Andalucía. L.M.R acknowledges a FPU fellowship from the Spanish MECD. C.R.M thanks Prof. Rubén Pérez and Dr. Pablo Pou for useful discussions. O.G., I.R., and K.S. acknowledge funding by the DFG in the framework of the priority program “Ferroic Cooling” (SPP1599). © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 19 Tables Sample 1:13 phase composition LaFe 11.6 Si 1.4 La 1.00(3) Fe 11.2(4) Si 1.45(12) LaFe 11.5 Ni 0.1 Si 1.4 La 1.00(3) Fe 11.2(2) Ni 0.10(2) Si 1.42(12) LaFe 11.4 Ni 0.2 Si 1.4 La 1.00(2) Fe 11.1(2) Ni 0.18(3) Si 1.44(12) LaFe 11.3 Ni 0.3 Si 1.4 La 1.00(3) Fe 10.9(2) Ni 0.26(3) Si 1.50(12) LaFe 11.2 Ni 0.4 Si 1.4 La 1.00(3) Fe 10.9(2) Ni 0.33(3) Si 1.54(12) Table 1. Compositional EDX analysis for the 1:13 phase in the different samples. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 20 Sample a [ LaFe 13 ] ( Å ) 1:13 (wt.%) α-Fe (wt.%) LaFeSi (wt.%) GoF LaFe 11.6 Si 1.4 11.49043(13) 97.9 0.2 1.9 1.35 LaFe 11.5 Ni 0.1 Si 1.4 11.49179(16) 96.9 0.9 2.3 1.17 LaFe 11.4 Ni 0.2 Si 1.4 11.48836(15) 96.2 3.8 0 1.26 LaFe 11.3 Ni 0.3 Si 1.4 11.4884(3) 84.9 14.2 0.9 1.01 LaFe 11.2 Ni 0.4 Si 1.4 11.4857(5) 77.6 21.3 1.1 1.10 Table 2. Lattice parameters of NaZn 13 -type phase, phase proportions and goodness of fit (GoF) obtained for the LaFe 11.6-x Ni x Si 1.4 series determined from Rietveld refinement. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 21 Alloy a ( Å ) Density (g cm - 3 ) µ (µ B ) M S (emu g - 1 ) LaFe 11.5 Si 1.5 11.4473 7.291 24.61 166.9 LaFe 11.375 Ni 0.125 Si 1.5 11.4457 7.297 24.40 165.4 LaFe 11.25 Ni 0.25 Si 1.5 11.4431 7.305 24.16 163.8 LaFe 11.125 Ni 0.375 Si 1.5 11.4429 7.309 24.04 162.8 LaFe 11 Ni 0.5 Si 1.5 11.4419 7.314 23.85 161.5 Table 3. Lattice parameters, mass densities, magnetic moment per formula unit and saturation magnetization obtained with DFT calculations for the LaFe 11.5-x Ni x Si 1.5 alloys. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 22 Figure captions Fig 1. BSE images for the set of LaFe 11.6-x Ni x Si 1.4 series. Fig 2. XRD spectra for the LaFe 11.6-x Ni x Si 1.4 series. Fig. 3: a) Lattice parameter obtained from Rietveld refinement and DFT calculations for different Ni concentrations. b) Side view along de the (100) face of the unit cell of LaFe 11.5 Si 1.5 crystal structure (space group Fm-3c) represented with a ball-and-stick model. La atoms (blue) occupy 8a positions, Fe-I (orange) 8b sites while Fe-II and Si atoms (depicted with red or gray bonds) distribute randomly on 96i sites. Fig 4. Normalized magnetization (with respect magnetization at 150 K) at 0.05 T and calculated transition temperature (inset) for the for the LaFe 11.6-x Ni x Si 1.4 series. Fig 5. Left) Atomic on-site resolved magnetic moment obtained with spin-polarized DFT for the 112 atoms of the unit cell in the LaFe 11.5-x Ni x Si 1.5 compound as a function of Ni content. Right) Mean values of the moments per species in the different compounds Fig 6. Evolution of the Projected Density of States per species in the LaFe 11.5-x Ni x Si 1.5 alloys. Notice that Si contribution is only shown for x=0 and it remains unaltered in the other compositions. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 23 Fig 7. a) Temperature dependence of the isothermal entropy change (∆ST) and b) adiabatic temperature change (∆TS) while heating for the LaFe 11.6-x Ni x Si 1.4 series (at µ 0 ∆H=1.9 T). Fig 8. Temperature dependence of the field dependence exponent n of ∆ST (at µ 0 ∆H=1.9 T) for the LaFe 11.6-x Ni x Si 1.4 series. Inset: n values at the transition temperature as a function of the Ni content. Fig 9. Arrott plots for the LaFe 11.6-x Ni x Si 1.4 series at selected temperatures close to their transitions. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 24 References 1 G. V. 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Huang, W. E. Wallace, R. T. Obermyer, S. Simizu, M. McHenry, and S. G. Sankar, “Magnetic characteristics of RCo13−xSix alloys (R=La, Pr, Nd, Gd, and Dy)”, Journal of Applied Physics 79, 5949 (1996). 19 P. I. Krypiakewytsch, O. S. Zaretschniuk, E. I. Hladyschewskyj, and O. I. Bodak, “Ternre Verbindungen vom NaZn13-Typ”, Zeitschrift fur anorganische und allgemeine Chemie 358, 90 (1968). © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT © 2018. 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