shell nanoparticle

Chemical Physics Letters 718 (2019) 46–53

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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett

Research paper

Electro-elastic modeling of thermal and mechanical properties of a spin crossover core/shell nanoparticle

T

⁎

Karim Affesa, Ahmed Slimania,b, , Ahmed Maaleja, Kamel Boukheddadenc a

Laboratoire des Matériaux Multifonctionnels et Applications, Université de Sfax, Faculté des Sciences de Sfax, Route de la Soukra km 3.5, 3000 Sfax, Tunisia Sciences and Engineering Department, Sorbonne University Abu Dhabi, Al Reem Island, Abu Dhabi, PO Box 38044, United Arab Emirates c GEMaC, CNRS – Université de Versailles Saint Quentin en Yvelines, 45 Avenue des Etats Unis, F-78035 Versailles Cedex, France b

A R T I C LE I N FO

A B S T R A C T

Keywords: Molecular materials Core/Shell nanoparticle Electro-elastic modelling Monte-Carlo simulation

We investigated theoretically the thermo-induced spin transition of a nanostructure made of an active spin crossover core surrounded by an inert shell with a misfit of lattice parameters between the two constituents. We demonstrated that (i) the structural and magnetic features of the SCO core are very sensitive to the structural properties of the surrounding environment. (ii) The misfit of lattice parameters influences the nature of the spin transition from gradual to abrupt one with an important shift of the transition temperature. (iii) The structural heterogeneity of the nanoparticle affects as well the spatiotemporal kinetics of the thermo-induced spin transition. The mechanical properties of the nanoparticle were as well studied and correlated with the magnetic behaviour of the nanoparticle.

1. Introduction The spin crossover compounds SCO [1] are switchable molecular materials between high spin (HS) and low spin states (LS) under external stimuli, such as pressure [2,3], light [4], temperature [5], magnetic [6] and electric [7] fields. The most frequent spin crossover systems are based on Fe (II), where the HS state corresponds to a total spin S = 2, while the LS state has a total spin S = 0. The HS to LS transition induces a change in the metal to ligand bondslengths of approximately 0.2 Ȧ (≈10%) , and the “ligand-metal-ligand” bond angle by 0.5–80° [8,9], as well as in the optical properties; for example the absorption peak of the SCO compound [Fe(Htrz)2,95 (NH2 trz)0.05] centered at 530 nm in the LS state is shifted towards 800 nm in the HS state [10]. As a result, optical, magnetic and X-rays diffraction [11] measurements [12–14] are the most used experimental techniques to study the spin transition phenomenon. In SCO systems, the interactions between molecules, play a crucial role and may lead to different behaviors: (i) first-order thermally-induced spin transition (cooperative behavior), accompanied with a thermal hysteresis [15], (ii) gradual spin transitions. [16] for less cooperative systems and many exotic behaviors, (iii) like multistep [17] or incomplete [16] spin transitions. These properties have been considered as the foundation for promising technological applications as memory devices and sensors [2,18–22]. For example, Matsuda and al, [23] demonstrated that [Fe(dpp)2](BF4)2(dpp = 2,6-di(pyrazol-1-yl) ⁎

pyridine) and chlorophyll a may introduce on-off switching of the light emission from the electroluminescent device containing spin crossover complex. In order to integrate the SCO materials in the technological devices, many experimental investigations focused on SCO nanoparticles [24–40]. From a theoretical point of view, some attempts have been committed to describe the bistability of spin crossover materials at the nanoscale, where different models were introduced as the Ising-like model with constrained high-spin (HS) molecules at the surface [41], atom-phonon model [42,43], and mechano-elastic description [44–65]. The theoretical investigations allowed to clarify some of the experimental observations of SCO nanoparticles, but a lot remains to discover such as the interplay between the spin crossover properties of the nanoparticles and those of the surrounding environment. The SCO core/ shell nanoparticles display a variety of complex phenomena [29] as a marginal change in the thermal properties of the core accompanied by a significant lattice change, which induces strain on the matrix and feedbacks. In this paper, we use the microscopic electro elastic model [49–51], to simulate a spin crossover core surrounded by a shell having different lattice parameter. The electro-elastic model has proven its capability where it was used in our prior studies of the spin crossover systems to investigate the spatio-temporal aspects of the spin transition of single crystals and nanoparticles, [66–70]. This paper is organized as follows: in Section 2, we define the electro elastic model and we describe the simulation technique. In

Corresponding author. E-mail addresses: [email protected] (A. Slimani), [email protected] (K. Boukheddaden).

https://doi.org/10.1016/j.cplett.2019.01.034 Received 20 December 2018; Received in revised form 12 January 2019; Accepted 15 January 2019 Available online 29 January 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. (a) Schematic view of the SCO nanoparticle. Green and red dots are the shell and the core atoms, respectively, belonging to different constituents. (b) The configuration of the elastic interactions in two dimensional square model considered in this study. Here Nc , Ns and N are the core size, shell thickness and nanoparticle size, respectively. [71]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the equilibrium lattice parameter distances for nn and the nnn which depend on the spin states as well. According to the spin states of the linked sites, the nn bond length R 0 (Si , Sj) may have the following R 0 (+1, −1) = R 0 (−1, +1) = R HL valuesR 0 (−1, −1) = R LL R0 0 ,and 0 , (+1, +1) = R HH , for the LS-LS, HS-LS, and the LS-LS site configurations, 0 respectively. It is easy to demonstrate that,

Section 3, we study the structural, magnetic and mechanical properties of the core-shell nanoparticle. In Section 4, we conclude and outline some possible extension of this work. 2. Theoretical details We studied a distortable 2D square lattice with a fixed topology and open boundary conditions. The nanoparticle is constituted by an inner spin crossover core and an outer shell (see Fig. 1). The core size is 15 × 15 placed in the center and surrounded with 13 shell layers. Each node of the SCO core may have two states, LS or HS, described by an associated fictitious spin Si , whose eigenvalues are Si = −1for LS and Si = +1for HS. The shell sites do not have any electronic contribution. The sites of the lattice are allowed to move only in the plane. We recall here the electro-elastic model was used in several prior works to investigate the spin transition of core-shell nanoparticle. [29,49–50,67–69,71] The total Hamiltonian of this nanostructure taking into account for the spin states and lattice positions writes

R 0 (Si , Sj) =

where Hc , Hs and Hc − s are respectively, the core, the shell and coreshell contributions to the total Hamiltonian (1). Their expressions are given as follows,

Hc =

∑ i∈c

+

(Δ − kBTlng)Si + 2

∑

∑

A c [rij − R 0 (Si , Sj )]2

i,j ∈ c

Bc [rik − d 0 (Si , Sk )]2 (2)

i,k ∈ c

∑

Hs =

A s [rij − R s]2 +

i,j ∈ shell

∑

Bs [rik − d s ]2 (3)

i,k ∈ shell

and

Hc − s =

involved

∑ i,j ∈ interface

A c − s [rij − R c − s]2 +

in

the

R s + R HH 0

∑ Bc−s [rik − dc−s ]2 i,k

(5)

LL where δR = R HH 0 − R 0 is the lattice parameter misfit between LS and HS phases. rij and (resp. rik ) represents the instantaneous distance between two nn (resp. nnn) sites, i − j (resp. i − k ).A c (rij) and Bc (rik) are the local bond stiffness of nn and nnn bonds, respectively. To take into account far the difference of rigidity of LS and HS states [72,73], we adopted the following form for the elastic constants 2 2 Bc (rik) = B0 + B1 (rij − 2 R HH A c (rij) = A 0 + A1 (rij − R HH and 0 ) ; 0 ) where A 0 (resp. B0 ) and A1 (resp. B1) are, respectively, the harmonic and anaharmonic contributions to the elastic interaction energy between nn (resp. nnn). The shell’s Hamiltonian, Hs (given in Eq. (3)), contains only elastic contributions where R s and d s = 2 R s are the equilibrium lattice parameter distances of nn and nnn sites and corresponding elastic constant A s and Bs . The core-shell contribution, given in Eq. (4), describes the atoms located at the core/shell interface. The position of these atoms as well as the interactions with their neighbors may have a spin state dependence or not, according to their positions in the shell or in the core. Indeed, the elastic interactions at the interface are defined as Ac-s and Bc-s, for nn and nnn interactions, respectively. To seek simplicity, the elastic interactions at the interface were introduced as the average value of the elastic interactions of the core and the shell, B +B A +A Ac − s = c 2 s and Bc − s = c 2 s . The nn (resp. nnn) equilibrium bond length at the interface may have two values according to the spin state

(1)

H = H c + Hs + H c − s

LL R HH δ 0 + R0 + R (Si + Sj) 2 4

interaction, R s + R LL 0

so

as

R c−s =

R s + R HH 0

2 R s + R LL 0

(resp.

dc−s = 2 ) or R c − s = (resp. d c − s = 2 2 ). 2 2 Next, the following model parameter values are used: the degeneracy ratio g = 150 [74,75] and the ligand field energy Δ = 700 K , leading to ΔH = 9.96 kJ/mol and ΔS = 41, 63 JK−1 mol−1and a tranΔH Δ sition temperature Teq = ΔS = k lng = 140 K . These values are in good B agreement with the experimental data whose ΔH and ΔS are in the ranges 5 − 20 kJ/mol and 35 − 80 JK−1 mol−1 [76], respectively. The bond lengths in the HS and LS states are, respectively, taken as R 0 (+1, +1) = 1.2 nm and R 0 (−1, −1) = 1 nm, whereas in the HL state we have considered the average value,

(4)

The term in Eq. (2) contains the electronic contribution Δ = EHS − ELS (ligand field energy) corresponding to the energy difference between the HS and LS states at 0 K and the entropic effects (kBTlng) arising from the degeneracy ratio, g, between the HS and LS states. The second and third contributions contain the elastic interaction between the nearest (nn) and the next nearest neighbors (nnn) core SCO units, respectively. The quantities R 0 (Si , Sj) and d 0 (Si , Sk ) = 2 R 0 (Si , Sk ) are respective 47

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K. Affes et al. R (+1, +1) + R (−1, −1)

0 R 0 (+1, −1) = 0 = 1, 1 nm. According to the square 2 symmetry of the lattice, the lattice parameter between LS (resp. HS) 2 R 0 (−1, −1) ≈ 1, 4 nm (resp. nnn atoms are given by 2 R 0 (+1, +1)≈1, 7 nm) . In this paper, we report a systematic study of the thermal and elastic properties of different shell’s lattice parameter, R s , ranging between, 0, 9 and 1, 3nm . The values of the nn elastic constants were fixed to A c = 10000 K/nm2 = 10 meV/Ȧ 2 for the core, while those of nnn, are Bc = 0.28A c . For seek of simplicity, we use the same elastic constants for core and shell constituents. The Monte-Carlo Metropolis method was used to solve the electroelastic Hamiltonian (1). We used an iterative strategy based on two steps: (i) a site is randomly selected, where an eventual spin switching is performed based on the variation of the energy of the system and (ii) site displacements is performed by a Metropolis Monte Carlo update. During the step (i) the position of the sites is frozen, while during step (ii) the spins are frozen. The step (i) is equivalent to a Franck-Condon process. During the step (ii) a sufficient number of Monte Carlo cycles are called in order to reach the mechanical equilibrium. At low temperatures, the energy barrier is sufficiently large (ΔELH ≫ kB T ), the LS → HS process is neglected. The transition rate is determined by calculating the probability of transition from a vibrational level of one state to another for a molecule in contact with a thermal bath at temperature T and a bath of intermolecular phonons corresponding to the vibrations of the network. It is well known that many of the existing processes in the spin crossover compounds, such as thermal relaxation without the tunnel regime, are thermally activated processes, linked to the crossing of energy barriers, in a purely classical view of the phenomenon. This vision was adapted the Monte-Carlo procedure developed in this work. At each temperature, for a core site i randomly se→ lected, with spin (Si = ± 1) located at a position ri , a new value (Si = −Si) will be set without position change. This spin change is rejected or accepted by the usual Metropolis criterion, which is based on the comparison of the final and initial energies. Once the spin change is accepted, the whole lattice positions (core + shell) are relaxed mechanically by a slight motion of each node selected randomly with a → → quantity ∥δ ri ∥ ≪ ∥ ri ∥. When all the nodes of the core are inspected for the spin change, we specify such a step as the Monte Carlo step (MCS). At each temperature, 500 MCS were used to evaluate the HS fraction, nHS,and the average lattice parameter < r >, defined respec1+ < S > , where < S> is the average value of the spin and tively as: nHS = 2

= <

∑ij (xi − xj)2 + (yi − yj)2 nb 2

core. Thus, the latter shrinks to keep the mechanical equilibrium of the lattice. More the misfit of lattice parameters between the core and the shell is important more the shrinkage of the SCO core is significant as we can easily see in the inset of Fig. 2(a). The snapshots of the final structure of the nanoparticle shown in Fig. 3(a) and 3(b) clearly reveals significant deformations of the whole lattice, which amplify for outer layers due to surface effects. The meticulous inspection of the spatial bond length profiles along horizontal lines given in Fig. 3(c) and (d), shows a compressive (resp. tensile) strain along lines crossing the core (at coordinate Y = 20 and26) for R s = 0.9 nm (respR s = 1.3 nm ) while an opposite behavior is found for outer lines (Y = 32 ). This behavior is general and remains valid for vertical lines. The relaxed bond length distances for the different equilibrium lattice parameters, R s , reported in Fig. 3 (e), reveal a significant difference between the core and the shell especially when R s > R HH 0 . As stated above, the free border of the shell eases the mechanical relaxation, unlike the LS core placed in the center. The latter is slightly disturbed from its initial state, for example, when R s = 1.3 nm , < r >shell changes by 9% compared to 1% of the core. Starting from the relaxed structure of the nanoparticle, we sweep the temperature from 1 K towards 400 K and then cool-down till 1 K with a thermal step of 1 K . During the MC procedure, at each temperature, each spin site is visited 2 × 500 times, while each node position is updated 2 × N × 500 . The thermo-induced spin transitions for the different shell’s lattice parameters, R s , are shown in Fig. 4(a). ForR s ≤ 1 nm , the thermal spin transition is gradual, whereas for R s = 1.3 nm , the transition becomes abrupt with a shift of the equiliT +T brium temperature, Teq = HS → LS 2 LS → HS , towards lower temperatures, T T where HS → LS (resp. LS → HS ) is the HS → LS (resp. LS → HS ) transition temperature. Indeed, Teq shows a linear behavior as a function of R s (Fig. 4(b)). We notice that uncoated core (green curve) and core-shell R +R with R s = LL 2 HH = 1.1 nm give the same transition temperature. According to the initial misfit of lattice parameters between the core and the shell, when it is compressive (R s ≤ 1 nm ), the shell promotes the LS state, due to the consistency of lattice parameters, consequently the transition towards HS state is gradual and the equilibrium temperature is shifted towards higher values (∼250 K). However, when the tensile field is important (R s≥1.2 nm) the life time of the LS state is considerably reduced and thus the transition becomes of 1st order and starts at lower temperatures (∼70 K) (Fig. 4(b)). We should here state that such a result recalls an experimental one where the Fe(pyrazine)Pt(CN)4 nanoparticles coated with a silica film have exhibited gradual transition at higher temperatures when surrounded with thick silica film and as the thickness of the shell decreases the transition becomes abrupt and the transition temperature shifts towards lower values. Indeed, such a fact confirms that the compressible surrounding environment significantly weakens the cooperativity between the SCO molecules of the inner core. [16] To understand the structural synergy between the shell and the core, we presented the lattice parameters of the core and the shell through the thermo-induced spin transition in Fig. 5(a) and (b), respectively, for the differentR s . By monitoring the variation of lattice parameters of the core, Δrcore , between the lower and higher temperatures (Fig. 5(c)), one can easily notice that Δrcore remains quasi-constant 0.15 nm when R s is ranging between [0.9, 1.1] nm. However, for R s > 1.1 nm, Δrcore decreases, due to the residual amount of HS lattice parameter introduced by the surrounding environment so as the volume dilatation, accompanying the LS → HS transition, is damped. In Fig. 5(b), one can easily notice that the lattice parameter of the shell is slightly disturbed through the thermal loop. Such a fact is confirmed by the small value ofΔrshell , which is the difference of lattice parameters of the shell at high and low temperatures. Indeed, Δrshell is one order of magnitude lower than Δrcore . Such a feature can be explained by the free border of the surrounding environment. Furthermore, at higher temperatures, corresponding to the HS state

>, where nb is the number of neighboring

bonds between molecules i and j of coordinates (xi, yi) and (xj, yj) . Here, < r > is calculated either for shell, core and whole system. 3. Results and discussion We considered a squared core-shell nanoparticle (L × L = 40 × 40 nm) whose an L c × L c = 15 × 15 nm SCO core surrounded by 25 nm thick shell. In these simulations, the core and the shell have two different lattice parameters, R c and R s , respectively. Initially at0K , we construct the nanoparticle with uniform bond lengths equal to those of the LS core, i.e.rs = R c = R LL 0 . In such situation, we should state that, the SCO core is in its equilibrium state unlike the shell since its equilibrium lattice parameter, R s , may have a value different from R LL 0 . Thus, to satisfy, from the structural point of view, whole the nanoparticle (core + shell), the system undergoes a mechanical relaxation with 100,000 MCS. In Fig. 2(a&b), we reported the mechanical relaxation performed on nanoparticles whose shells have equilibrium lattice parameters R s = 0.9 nm and R s = 1.3 nm , respectively. The temporal evolution of the mechanical relaxation of core and shell is presented in terms of average nn bond length < r > in both constituents. The most remarkable fact in Fig. 2(a) is at the beginning of the relaxation process < r >core decreases then increases. Such a behavior could be explained by the quick relaxation of the shell that disturbs the 48

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Fig. 2. (a) and (b) Time dependence of average bond lengths of core, < r >core , and shell, < r >shell , for different values of the shell lattice parameters, during the mechanical relaxation. Inset: Zoom on < r >core at the beginning of the relaxation process.

Fig. 3. Final configurations of the lattice after mechanical relaxation for the shell equilibrium bond lengths Rs = 0.9 nm (a) and Rs = 1.3 nm (b). The corresponding lattice parameter profiles along the red arrow crossing the lattice at different Y coordinates at mechanical equilibrium for Rs = 0.9 nm (c) and Rs = 1.3 nm (d). relax o Y = 20 corresponds to the middle of the lattice. (e) The average relaxed bond lengths of the core and the shell < r >relax core and < r >shell as function of R s showing a linear behavior. Simulation performed of a nanoparticle of 40 × 40 whose core’s size is15 × 15. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 4. (a) Thermal dependence of the HS fraction for the different lattice parameters of the shell. (b) The equilibrium temperature as a function of the equilibrium shell’s lattice parameter, R s .

Fig. 5. Thermal dependence of lattice parameter of the core, < rcore >(a) and the shel l < rshell > (b) for different initial values of shell’s lattice parameters . (c) Difference of lattice parameters between high and low temperatures for the core, Δrcore , (black) and the shell, Δrs (blue). (d) Linear variation of < rcHS > and < rshell > as a function of Rs at high temperature. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. Distributions of local pressures at T = 0 K inside the core/shell nanoparticle for Rs = 0.9 nm (a) and Rs = 1.3 nm (b).

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Fig. 7. Snapshots of the nanoparticle during the thermo-induced spin transition (heating and cooling process) corresponding to Rs = 0.9 nm(a) and Rs = 1.3 nm (b). The red (blue) dots are associated with HS (LS) sites and green for the shell. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the HS state. It is expected that, in a such situation, the shell hinders the volume expansion of the SCO core accompanying the LS → HS transition. Indeed, such a fact justifies the relatively higher value of Teq 320K compared to the other values. We investigated the mechanical features of the lattice via the estimation of the pressure density, DP , defined as : DP = < ∑i Pi >, where Pi is the local pressure of the site (i).

of the core, we verified the linear relationship between the lattice parameters (core and shell) as a function of R s (see Fig. 5(d)), as reported above in Fig. 3 (e). Indeed, we should here state that the lattice parameter of the LS core is less sensitive to the structural misfit between the shell and the core than in its HS state, where in the latter case the slope of < rcore> VS. R s was estimated around 0, 4 compared to 0,2 in the LS state. While, the slope of shell’s lattice parameter as a function of Rs remains the same ∼0.9 at high and low temperatures. The most interesting result arising from Fig. 5 (c) is the lattice parameters of the HS core forR s = 0.9 nm . Remarkably, although the core is decorated with a very compressive shell, it succeeds to switch to

Pij = − ∑ A c (rij)(rij − R(Si , Sj)) − j

∑ Bc (rik )(rik − k

2 R(Si , Sk )) (6)

where j and k run over the nearest and next nearest neighbors to the site i , respectively. The distributions of the local pressure over the 51

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Conflict of interest

relaxed nanoparticle, at 0 K, are illustrated in Fig. 6(a) and (b) for R s = 0.9 and 1.3 nm, respectively. For lower shell’s lattice parameter, the SCO core undergoes a positive pressure that hinders the volume expansion and thus the LS → HS transition. However, the situation is reversed with higher R shell . For example, forR s = 1.3 nm , on-cooling branch the elastic barrier corresponding to the HS → LS transition is very high due to the important mismatch of lattice parameter when compared to that of the LS state, R LL 0 . Consequently, the HS state is promoted and the spin transition is remarkably delayed when compared to the case R s = 0.9 nm . In the latter situation, the HS state quickly switches to the LS one due to the compressive behavior of the shell. We have as well analyzed the effect of the shell’s lattice parameter on the spatio-temporal aspects of the thermo-induced spin transition. These results are summarized in Fig. 7(a) and (b), where we depicted the snapshots of the lattice, through the thermal loop forR s = 0.9 and 1.3 nm , respectively. Fig. 7(a) reveals that, upon heating process (nHS=0.25), the HS sites growth mainly in the core's center, unlike R s = 1.3 nm , where nucleation of HS sites starts from the core/shell interface (Fig. 7(b)). To explain such a fact, we refer to the elastic profiles reported in Fig. 3(c) and (d). When the SCO core is surrounded with a shell, whose R s = 0.9 nm , the bond lengths around the core/shell interface are very close to R s , thus, the elastic barrier corresponding to the switch from the LS to HS is higher when compared to the core’s center, where the lattice parameter remains close to R LL 0 . However, the latter configuration is reversed when the lattice parameter of the surrounding environment is R s = 1.3 nm . In the latter case, the elastic barrier is pushed down around the core/shell interface, where the HS sites nucleate easily. The spatio-temporal aspects of the HS → LS transition (on-cooling branch), for R s = 0.9 nm , are similar to those observed on heating. In fact, the lattice parameter of the HS core estimated as 1.05 nm is very close to R LL 0 . We can easily imagine that the nucleation of the LS sites occurs mainly in the center of the HS core than in the interface between the core and the shell, where the lattice parameter of the core is close to R s = 0.9 nm . However, for R s = 1.3 nm , the situation is different. Where, the elastic barrier corresponding to the HS → LS transition is lower in the center (the misfit between R c and R LL 0 is at its minimum) when compared to the core/shell interface.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors acknowledge the support received from the Tunisian ministry of higher education and scientific research, CNRS (Centre National de la Recherche Scientifique) and the University of Versailles, member of the University Paris-Saclay. References [1] P. Gutlich, H.A. Goodwin (Ed.), Topics in Current Chemistry, Spin Crossover in Transition Metal Compounds I-III, Springer, Heidelberg, 2004, pp. 233–235. [2] J. Linares, E. Codjovi, Y. Garcia, Sensors 12 (2012) 4479. [3] G. Molnar, V. Niel, J.A. Real, L. Dubrovinsky, A. Bousseksou, J. Mc-Garvey, J. Phys. Chem. B 107 (2003) 3149. [4] S. Decurtins, P. Gutlich, K.M. Hasselbach, A. Hauser, H. Spiering, Inorg. Chem. 24 (1985) 2174. [5] P. Gutlich, Struct. Bonding 44 (1981) 83. [6] A. Bousseksou, K. Boukheddaden, M. Goiran, C. Consejo, M.L. Boillot, J.P. Tuchagues, Phys. Rev. B 65 (2002) 172412. [7] F. Prins, M. Monrabal-Capilla, E.A. Osorio, E. Coronado, H.S.J. van der Zant, Adv. Mater. 23 (2011) 1545. [8] P. Gutlich, A. Hausser, H. Spiering, Angew. Chem., Int. Ed. Engl. 33 (1994) 2024. [9] B. Gallois, J.A. Real, C. Hauw, J. Zarembowitch, Inorg. Chem. 29 (1990) 1152. [10] D. Tanaka, N. Aketa, H. Tanaka, T. Tamaki, T. Inose, T. Akai, H. Toyama, O. Sakata, H. Tajiri, T. Ogawa, Chem. Commun. 50 (2014) 10074. [11] L. Wiehl, H. Spiering, P. Gütlich, K. Knorr, J. Appl. Crystallogr. 23 (1990) 151. [12] S. Decurtins, P. G¨utlich, C.P. Ko hler, H. Spiering, A. Hauser, Chem. Phys. Lett. 105 (1984) 1. [13] E.W. Muller, J. Ensling, H. Spiering, P. Gutlich, Inorg. Chem. 22 (1983) 2074. [14] G. Vos, R.A. Le Fèbre, R.A.G. de Graff, J.G. Haasnoot, J. Reedijk, J. Am. Chem. Soc. 105 (1983) 1682. [15] O. Kahn, Molecular Magnetism, VCH, New York, 1993. [16] Y. Raza, F. Volatron, S. Moldovan, O. Ersen, V. Huc, C. Martini, F. Brisset, A. Gloter, O. Stéphan, A. Bousseksou, L. Catala, T. Mallah, Chem. Commun. 47 (2011) 11501. [17] K. Boukheddaden, J. Linares, E. Codjovi, F. Varret, V. Niel, J.A. Real, J. Appl. Phys. 93 (2003) 7103. [18] C. Lefter, V. Davesne, L. Salmon, G. Molnar, P. Demont, A. Rotaru, A. Bousseksou, Magnetochemistry 2 (2016) 18. [19] C. Lefter, S. Rat, J.S. Costa, M.D. Manrique-Juarez, C.M. Quintero, L. Salmon, I. Séguy, T. Leichle, L. Nicu, P. Demont, A. Rotaru, G. Molnar, A. Bousseksou, Adv. Mater. 28 (2016) 7508. [20] J. Dugay, M. Giménez-Marqués, T. Kozlova, H.W. Zandbergen, E. Coronado, H.S.J. van der Zant, Adv. Mater. 27 (2015) 1288. [21] A. Holovchenko, J. Dugay, M. Giménez-Marqués, R. Torres- Cavanillas, E. Coronado, H.S.J. van der Zant, Adv. Mater. 28 (2016) 7228. [22] C. Lochenie, K. Schötz, F. Panzer, H. Kurz, B. Maier, F. Puchtler, S. Agarwal, A. Köhler, B. Weber, Spin-crossover iron(II) coordination polymer with fluorescent properties: correlation between emission properties and spin state, J. Am. Chem. Soc. 140 (2) (2018) 700–709. [23] M. Matsuda, H. Isozaki, H. Tajima, Thin Solid Films 517 (2008) 1465. [24] A. Rotaru, F. Varret, A. Gindulescu, J. Linares, A. Stancu, J.F. Létard, T. Forestier, C. Etrillard, Eur. Phys. J. B 84 (2011) 439. [25] T. Forestier, S. Mornet, N. Daro, T. Nishihara, S. Mouri, K. Tanaka, O. Fouche, E. Freysz, J.-F. Létard, Chem. Commun. 4327 (2008). [26] T. Forestier, A. Kaiba, S. Pechev, D. Denux, P. Guionneau, C. Etrillard, N. Daro, E. Freysz, J.-F. Létard, Chem. Eur. J. 15 (2009) 6122. [27] E. Coronado, J.R. Galán-Mascarós, M. Monrabal-Capilla, J. García-Martínez, P. Pardo-Ibáñez, Adv. Mater. 19 (2007) 1359. [28] A.C. Felts, M.J. Andrus, E.S. Knowles, P.A. Quintero, A.R. Ahir, O.N. Risset, C.H. Li, I. Maurin, G.J. Halder, K.A. Abboud, M.W. Meisel, D.R. Talham, Evidence for interface induced strain and its influence on photo magnetism in Prussian blue analogue core–shell heterostructures, RbaCob[Fe(CN)6]c.mH20@KjNik[Cr(CN)6] l.nH2O, J. Phys. Chem. C 120 (2016) 5420. [29] A.C. Felts, A. Slimani, J.M. Cain, M.J. Andrus, A.R. Ahir, K.A. Abboud, M.W. Meisel, K. Boukheddaden, D.R. Talham, Control of the speed of a light-induced spin transition through mesoscale core–shell architecture, J. Am. Chem. Soc. 140 (17) (2018) 5814. [30] A. Tissot, C. Enachescu, M.L. Boillot, Control of the thermal hysteresis of the prototypal spin-transition Fe- II(phen)(2)(NCS)(2) compound via the microcrystallites environment: experiments and mechanoelastic model, J. Mater. Chem. 22 (2012) 20451. [31] Y. Chen, J.-G. Ma, J.-J. Zhang, W. Shi, P. Cheng, D.-Z. Liao, S.-P. Yan, Spin crossover-macromolecule composite nano film material, Chem. Commun. 46 (2010) 5073. [32] S.-W. Lee, J.-W. Lee, S.-H. Jeong, I.-W. Park, Y.-M. Kim, J.-I. Jin, Processable

4. Conclusion We investigated the thermo-induced spin transition of a spin crossover nanoparticle in a core-shell structure through the electroelastic model. We demonstrated that the thermal and mechanical properties of the spin crossover core are highly dependent on the structural and mechanical features of the shell. The increase of shell’s lattice parameter, R shell,leads to an important change in the thermoinduced spin transition of the core: from gradual to an abrupt with a shift towards lower temperatures. By varying the misfit of the lattice parameters between the core and the shell, the cooperativity, the thermal, and even the mechanical properties are changed through the extra amount of pressure. For a spin crossover core surrounded by an expanded shell, the nucleation of HS sites, on-heating process, takes place at the interface core/shell. However, compressive shells lead to the appearance of HS sites in the center of the nanoparticle. Such behaviors underline the crucial role of the shell in the magnetic and mechanical properties of the core; our results are in good agreement with the experimental results [16] where the authors observed a restoration of hysteresis loop due to an important cooperativity when Fe(pyrazine)Pt(CN)4 coated with a thin film silica, however, softer matrices destroy the cooperativity. It is interesting to mention that the reasoning developed here could be extended to the case of a spin crossover nanoparticle embedded in a matrix.

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K. Affes et al.

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

[41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53]

[54]

[55]

magnetic plastics composites—spin crossover of PMMA/Fe(II)-complexes composites, Synth. Met. 142 (2004) 243. V. Martinez, I. Boldog, A.B. Gaspar, V. Ksenofontov, A. Bhattacharjee, P. Gütlich, J.A. Real, Spin crossover phenomenon in nanocrystals and nanoparticles of [Fe(3Fpy)2MCN)4MII=Ni, Pd, Pt two-dimensional coordination polymers, Chem. Mater. 22 (2010) 4271. M. Rubio, R. Hernández, A. Nogales, A. Roig, D. López, Structure of a spin-crossover Fe(II)—1,2,4-triazole polymer complex dispersed in an isotactic polystyrene matrix, Eur. Polym. J. 47 (2011) 52. J. Larionova, L. Salmon, Y. Guari, A. Tokarev, K. Molvinger, G. Molnar, A. Bousseksou, Towards the ultimate size limit of the memory effect in spincrossover solids, Angew. Chem. Int. Ed. 47 (2008) 8236. P. Durand, S. Pillet, E.E. Bendeif, C. Carteret, M. Bouazaoui, H. El Hamzaoui, B. Capoen, L. Salmon, S. Hebert, J. Ghanbaja, L. Aranda, D. Schaniel, Room temperature bistability with wide thermal hysteresis in a spin crossover silica nanocomposite, J. Mater. Chem. C 1 (2013) 1933. A. Tissot, J.-F. Bardeau, E. Rivière, F. Brisset, M.-L. Boillot, Thermo- and photoswitchable spin-crossover nanoparticles of an iron(II) complex trapped in transparent silica thin films, Dalton Trans. 39 (2010) 7806. S. Titos-Padilla, J.M. Herrera, X.-W. Chen, J.J. Delgado, E. Colacio, Bifunctional hybrid SiO2 nanoparticles showing synergy between core spin crossover and shell luminescence properties, Angew. Chem. Int. Ed. Engl. 50 (2011) 3290. C. Faulmann, J. Chahine, I. Malfant, D. de Caro, B. Cormary, L. Valade, A facile route for the preparation of nanoparticles of the spin-crossover complex [Fe(Htrz) 2(trz)](BF4) in xerogel transparent composite films, Dalton Trans. 40 (2011) 2480. A. Adam, M. Poggi, E. Larquet, R. Cortès, L. Martinelli, P.E. Coulon, E. Lahera, O. Proux, D. Chernyshov, K. Boukheddaden, T. Gacoin, I. Maurin, Nanoscale 10 (2018) 16030. A. Muraoka, K. Boukheddaden, J. Linares, F. Varret, Phys. Rev. B 84 (2011) 054119. J.A. Nasser, Eur. Phys. J. B 21 (1) (2001) 3. J.A. Nasser, K. Boukheddaden, J. Linares, Two-step spin conversion and other effects in the atom-phonon coupling model, Eur. Phys. J. B 39 (2004) 219. L. Stoleriu, P. Chakraborty, A. Hauser, A. Stancu, C. Enachescu, Phys. Rev. B 84 (2011) 134102. S. Miyashita, Y. Konishi, M. Nishino, H. Tokoro, P.A. Rikvold, Phys. Rev. B 77 (2008) 014105. M. Nishino, K. Boukheddaden, Y. Konishi, S. Miyashita, Phys. Rev. Lett. 98 (2007) 247203. C. Enachescu, L. Stoleriu, A. Stancu, A. Hauser, Phys. Rev. Lett. 102 (2009) 257204. W. Nicolazzi, S. Pillet, Phys. Rev. B 85 (2012) 094101. A. Slimani, H. Khemakhem, K. Boukheddaden, Phys. Rev. B 95 (2017) 174104. A. Slimani, K. Boukheddaden, F. Varret, H. Oubouchou, M. Nishino, S. Miyashita, Phys. Rev. B 87 (2013) 014111. A. Slimani, K. Boukheddaden, K. Yamashita, Phys. Rev. B 92 (2015) 014111. H. Oubouchou, Y. Singh, K. Boukheddaden, Magnetoelastic modeling of core-shell spin-crossover nanocomposites, Phys. Rev. B 98 (2018) 014106. C. Enachescu, L. Stoleriu, A. Stancu, A. Hauser, Model for elastic relaxation phenomena in finite 2D hexagonal molecular lattices, Phys. Rev. Lett. 102 (2009) 257204. C. Enachescu, R. Tanasa, A. Stancu, A. Tissot, J. Laisney, M.-L. Boillot, Matrix-assisted relaxation in Fe(phen)2(NCS)2 spin-crossover microparticles, experimental and theoretical investigations, Appl. Phys. Lett. 109 (2016) 031908. L. Stoleriu, A. Stancu, P. Chakraborty, A. Hauser, C. Enachescu, Analysis of first

[56]

[57] [58] [59] [60] [61]

[62]

[63]

[64]

[65]

[66] [67]

[68]

[69]

[70]

[71]

[72] [73] [74] [75] [76]

53

order reversal curves in the thermal hysteresis of spin-crossover nanoparticles within the mechanoelastic model, J. Appl. Phys. 117 (2015) 17B307. G. Félix, W. Nicolazzi, L. Salmon, G. Molnár, M. Perrier, G. Maurin, J. Larionova, J. Long, Y. Guari, A. Bousseksou, Enhanced cooperative interactions at the nanoscale in spin- crossover materials with a first-order phase transition, Phys. Rev. Lett. 110 (2013) 235701. H.J. Shepherd, G. Molnar, W. Nicolazzi, L. Salmon, A. Bousseksou, Spin crossover at the nanometre scale, Eur. J. Inorg. Chem. 2013 (2013) 653. A. Bousseksou, G. Molnar, L. Salmon, W. Nicolazzi, Molecular spin crossover phenomenon: recent achievements and prospects, Chem. Soc. Rev. 40 (2011) 3313. W. Nicolazzi, S. Pillet, C. Lecomte, Two-variable anharmonic model for spincrossover solids: a like-spin domains interpretation, Phys. Rev. B 78 (2008) 174401. M. Mikolasek, W. Nicolazzi, F. Terki, G. Molnár, A. Bousseksou, Surface transition in spin crossover nanoparticles, Chem. Phys. Lett. 678 (2017) 107. M. Mikolasek, W. Nicolazzi, F. Terki, G. Molnár, A. Bousseksou, Investigation of surface energies in spin crossover nanomaterials: the role of surface relaxations, Phys. Chem. Chem. Phys. 19 (2017) 12276. G. Félix, W. Nicolazzi, M. Mikolasek, G. Molnár, A. Bousseksou, Non-extensivity of thermodynamics at the nanoscale in molecular spin crossover materials: a balance between surface and volume, Phys. Chem. Chem. Phys. 16 (2014) 7358. G. Félix, M. Mikolasek, G. Molnár, W. Nicolazzi, A. Bousseksou, Tuning the spin crossover in nano-objects: from hollow to core-shell particles, Chem. Phys. Lett. 607 (2014) 10. M. Mikolasek, G. Félix, G. Molnár, F. Terki, W. Nicolazzi, A. Bousseksou, Role of surface vibrational properties on cooperative phenomena in spin-crossover nanomaterials, Phys. Rev. B 90 (2014) 075402. G. Félix, M. Mikolasek, G. Molnár, W. Nicolazzi, A. Bousseksou, Control of the phase stability in spin-crossover core-shell nanoparticles through the elastic interface energy, Eur. J. Inorg. Chem. 2018 (2018) 435. R. Traiche, M. Sy, H. Oubouchou, G. Bouchez, F. Varret, K. Boukheddaden, J. Phys. Chem. C 121 (2017) 11700. A. Slimani, K. Boukheddaden, K. Yamashita, Thermal spin transition of circularly shaped nanoparticles in a core-shell structure investigated with an electroelastic model, Phys. Rev. B 89 (2014) 214109. H. Oubouchou, A. Slimani, K. Boukheddaden, Interplay between elastic interactions in a core-shell model for spin crossover nanoparticles, Phys. Rev. B 87 (2013) 104104. K. Boukheddaden, A. Slimani, M. Sy, F. Varret, O. Hassane, T. Rachid, Physical Properties of 2D Spin-Crossover Solids from an Electro-Elastic Description: Effect of Shape, Size, and Spin-Distortion Interactions, Pan Stanford, New York, 2016. R. Traiche, M. Sy, K. Boukheddaden, Elastic frustration in 1D spin-crossover chains: evidence of multi-step transitions and self-organizations of the spin states, J. Phys. Chem. C 122 (2018) 4083. A. Slimani, K. Boukheddaden, An electro elastic theory for the mechanically-assisted phot-induced spin transition in core-shell spin crossover nanoparticles, Phys. Chem. Chem. Phys. (2018), https://doi.org/10.1039/c8cp05578e. J. Jung, F. Bruchhäuser, R. Feile, H. Spiering, P. Gütlich, Z. Phys, Rev. B 100 (1996) 517. H. Spiering, K. Boukheddaden, J. Linares, F. Varret, Phys. Rev. B 70 (2004) 184106. K. Boukheddaden, I. Shteto, B. Hoo, F. Varret, Phys. Rev. B 62 (2000) 14796. A. Bousseksou, J. Nasser, J. Linares, K. Boukheddaden, F. Varret, J. Phys. I France 2 (1992) 1381. M. Sorai, Top. Curr. Chem. 235 (2004) 153.