Frédéric Soisson
email: frederic.soisson@cea.fr

Yimi Wang
email: yimi.wang@cea.fr

Kangming Li
email: kangming.li@cea.fr

Charlotte S Becquart
email: charlotte.becquart@univ-lille.fr

Combining DFT and CALPHAD for the development of on-lattice interaction models: the case of Fe-Ni system

published or not. The documents may come

Combining DFT and CALPHAD for the development of on-lattice interaction models: The case of Fe-Ni system

Yimi Wang, Kangming Li,

I. INTRODUCTION

Atomistic Monte Carlo simulations of phase transformation kinetics in metallic alloys (precipitation, ordering, etc. [START_REF] Pareige | Ordering and phase separation in Ni-Cr-Al: Monte carlo simulations vs three-dimensional atom probe[END_REF][START_REF] Clouet | Nucleation of Al 3 Zr and Al 3 Sc in aluminum alloys: From kinetic monte carlo simulations to classical theory[END_REF][START_REF] Vincent | Solute interaction with point defects in α-Fe during thermal ageing: A combined ab initio and atomic kinetic Monte Carlo approach[END_REF][START_REF] Lavrentiev | Monte Carlo study of thermodynamic properties and clustering in the bcc Fe-Cr system[END_REF][START_REF] Soisson | Cu-precipitation kinetics in α-Fe from atomistic simulations: Vacancytrapping effects and Cu-cluster mobility[END_REF][START_REF] Becquart | Introducing chemistry in atomistic kinetic Monte Carlo simulations of fe alloys under irradiation[END_REF][START_REF] Ngayam-Happy | Formation and evolution of MnNi clusters in neutron irradiated dilute fe alloys modelled by a first principle-based AKMC method[END_REF][START_REF] Martínez | Decomposition kinetics of Fe-Cr solid solutions during thermal aging[END_REF][START_REF] Senninger | Atomistic simulations of the decomposition kinetics in Fe-Cr alloys: Influence of magnetism[END_REF][START_REF] Liebscher | A hierarchical microstructure due to chemical ordering in the bcc lattice: Early stages of formation in a ferritic Fe-Al-Cr-Ni-Ti alloy[END_REF][START_REF] Senninger | Modeling radiation induced segregation in iron-chromium alloys[END_REF][START_REF] Soisson | Atomistic modeling of precipitation in fe-cr alloys under charged particles and neutron irradiations: Effects of ballistic mixing and sink densities[END_REF][START_REF] Becquart | Monte carlo simulations of precipitation under irradiation[END_REF]) require interaction models that allow a precise description of the thermodynamic and kinetic properties of the materials, while remaining simple enough to model systems of a few million atoms over long periods of time (their evolution being controlled by thermally activated diffusion mechanisms). Models using effective interactions on rigid lattices -although limited to coherent problems -are among the most widely used and have become more reliable since they are systematically fitted to ab initio calculations of materials properties at 0 K (such as the formation energies of ordered phases or special quasi-random structures, point defect formation and migration energies, etc.) [START_REF] Soisson | Cu-precipitation kinetics in α-Fe from atomistic simulations: Vacancytrapping effects and Cu-cluster mobility[END_REF][START_REF] Ngayam-Happy | Formation and evolution of MnNi clusters in neutron irradiated dilute fe alloys modelled by a first principle-based AKMC method[END_REF][START_REF] Becquart | Monte carlo simulations of precipitation under irradiation[END_REF].

Evaluating non-zero temperature effects from ab initio methods is more difficult: calculations of vibration entropy, for example, are in principle possible but are computationally expensive and are usually limited to simple systems (e.g. pure metals, perfectly ordered phases, or dilute alloys). Modeling the effect of magnetic transitions and magnetic disorder -especially important in iron based alloys -is also very challenging. Alternatively, the temperature dependence of pair interactions can be adjusted on experimental data, for example on phase diagrams, but these adjustments are often made on a case-by-case basis. We propose here a new approach to systematically fit a pair interaction model both on ab initio calculations at 0 K and, for high temperatures, on a CALPHAD-type model. CALPHAD models provide an accurate description of the Gibbs free energies of the different phases of an alloy, based on empirical thermodynamic models fitted (mainly) on large numbers of experimental measurements. They also provide a specific description of some important contributions (e.g. magnetic contributions in iron-based alloys). The objective of this paper is to show how to establish a term-to-term correspondence between the empirical models used in CALPHAD and the effective interactions of a lattice model; to show the improvements that this brings to the description of a particular alloy; but also to discuss the limits of such a correspondence.

FIG. 1. The phase diagram of the Fe-Ni system (from [START_REF] Vernyhora | Thermodynamics of f.c.c. Ni-Fe Alloys in a Static Applied Magnetic Field[END_REF] and [START_REF] Yang | A revision of the Fe-Ni phase diagram at low temperatures (< 400 • c)[END_REF])

We apply this approach to Fe-Ni alloys with a face-centered cubic structure (FCC).

Recent ab initio [START_REF] Mishin | Phase stability in the Fe-Ni system: Investigation by first-principles calculations and atomistic simulations[END_REF][START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF] and CALPHAD [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF][START_REF] Ohnuma | Experimental determination and thermodynamic evaluation of low-temperature phase equilibria in the Fe-Ni binary system[END_REF] studies are available for this system. The thermodynamic properties of Fe-Ni alloys have been much studied, because of their industrial interest and because they still raise unresolved questions. The phase diagram of the Fe-Ni system (Fig. 1) is well known at temperatures above 400 • C [START_REF] Swartzendruber | The Fe-Ni (iron-nickel) system[END_REF]: the FCC solid solution γ is stable over the whole composition range and over a wide temperature range. The body centered cubic (BCC) solid solution α is stable below 912 • C, and only with nickel contents below approximately 10%. A two-phase domain α -γ is observed in iron-rich alloys, and an ordered FeNi 3 phase (with the L1 2 structure) is formed below 516 • C. At lower temperatures, the phase diagram is -as usual -more difficult to establish, because of slow diffusion processes. However, irradiation experiments [START_REF] Paulevé | Une nouvelle transition ordre-désordre dans Fe-Ni (50-50 )[END_REF][START_REF] Chamberod | Electron irradiation effects on iron-nickel invar alloys[END_REF][START_REF] Reuter | Ordering in the Fe-Ni system under electron irradiation[END_REF], observations of meteorites [START_REF] Yang | A revision of the Fe-Ni phase diagram at low temperatures (< 400 • c)[END_REF][START_REF] Reuter | Determination of the Fe-Ni phase diagram below 400 • C[END_REF], and ab initio studies [START_REF] Mishin | Phase stability in the Fe-Ni system: Investigation by first-principles calculations and atomistic simulations[END_REF][START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF] suggest that other ordered FCC phases may be stable or metastable (notably the FeNi phase of L1 0 structure and the Fe 3 Ni phase of L1 2 structure). Many CALPHAD studies have sought to complement the Fe-Ni phase diagram by extrapolating at low temperatures the empirical thermodynamic models fitted to experiments at high temperatures. This is especially difficult in the case of Fe-Ni, and as a result, the proposed phase diagrams show significant differences [START_REF] Yang | A revision of the Fe-Ni phase diagram at low temperatures (< 400 • c)[END_REF][START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF][START_REF] Swartzendruber | The Fe-Ni (iron-nickel) system[END_REF][START_REF] Xiong | Magnetic phase diagram of the Fe-Ni system[END_REF]. A particular difficulty of this system is that the experimental data are obtained essentially in paramagnetic phases, whereas the ordered phases are ferromagnetic. Magnetic contributions are indeed taken into account in CALPHAD approaches, but again by empirical models using experimental data and still under discussion [START_REF] Xiong | Magnetic phase diagram of the Fe-Ni system[END_REF].

Atomistic models combining the information from experiments and first principle methods may provide additional insight on these issues. A few rigid lattice interaction models, fitted to ab initio calculations, have been developed for Fe-Ni alloys: Mohri et al. [START_REF] Mohri | First-principles calculation of L1 0 -disorder phase equilibria for Fe-Ni system[END_REF] proposed a cluster expansion to study the stability of the ordered compound FeNi-L1 0 in the framework of a CVM approximation: they found an ordering temperature of 483 K (taking into account the vibration entropy, which lowers it by about 40 K). But they did not study the FeNi 3 phase, nor the effect of the ferro-to-paramagnetic transition. Effective interactions models including an explicit description of the magnetic moments have been proposed for Fe-Ni alloys, using Ising [START_REF] Lawrence | Chemical and magnetic interactions in FCC Fe-Ni alloys using the cluster variation method[END_REF][START_REF] Taylor | Magnetic and compositional order in nickel-rich Ni c Fe 1-c alloys[END_REF][START_REF] Dang | Simultaneous magnetic and chemical order-disorder phenomena in Fe 3 Ni, FeNi, and FeNi 3[END_REF][START_REF] Vernyhora | Monte carlo investigation of the correlation between magnetic and chemical ordering in nife alloys[END_REF] or Heisenberg [START_REF] Vernyhora | Monte carlo investigation of the correlation between magnetic and chemical ordering in nife alloys[END_REF][START_REF] Taylor | Monte carlo simulations of an fcc Ni c Fe 1-c alloy with vector magnetic freedom[END_REF] models for the magnetic interactions and parameters fitted to the experimental transition temperatures. Similar magnetic models have been also used in phase-field simulations of ordering and precipitation of the FeNi 3 phase [START_REF] Vernyhora | Atomic density function modeling of microstructure evolution in Ni 3-x Fe x alloys[END_REF].

More recently Lavrentiev, Wrobel et al. [START_REF] Lavrentiev | Magnetic and thermodynamic properties of face-centered cubic fe-ni alloys[END_REF][START_REF] Wróbel | Phase stability of ternary fcc and bcc Fe-Cr-Ni alloys[END_REF] developed a Magnetic Cluster Expansion (MCE), based on a Heisenberg-Landau Hamiltonian, fitted to ab initio calculations. Its properties have been studied by Monte Carlo methods, but the combined equilibration of the chemical and magnetic configurations is very costly in computational time, and the complete phase diagram of the MCE model of Fe-Ni remains to be established.

In the present paper, we propose a pair interaction model (PIM) based on a rigid lattice approximation, aiming at modelling the Fe-Ni system. The model does not describe explicitly the magnetic moments, nor the lattice relaxations, which makes it faster to process in Monte Carlo simulations. It only involves pair interactions between atoms that depends both on the local composition and temperature. Finite temperature effects of magnetic transitions or of lattice vibrations (harmonic and non-harmonic), on the energetic proprieties are taken into account through these dependencies.

The outline of this article is as follows: section II is devoted to the thermodynamic models of FCC phases in the Fe-Ni system. We briefly recall the Gibbs free energy models used in the CALPHAD approaches, focusing on the recent study of Cacciamani et al. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF] (II A); then the available ab initio results on the properties of Fe-Ni alloys (in particular those of K. Li and C.-C. Fu [START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF]) (II B). We then show how to reproduce these results with the PIM in section (II C). In section III, we use Monte Carlo simulations in the semi-canonical grand ensemble, to measure the Gibbs free energies of the FCC alloys, and to build the FCC phase diagram.

II. THERMODYNAMIC MODELS

Our PIM is built using both a CALPHAD study and ab initio calculations. We therefore recall the main information provided by these two approaches before to explain how it can be reproduced with effective interactions on a rigid lattice.

A. CALPHAD Models

Several CALPHAD-type studies have been proposed for the Fe-Ni system: the most recent are those of Cacciamani et al. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF] and Ohnuma et al. [START_REF] Ohnuma | Experimental determination and thermodynamic evaluation of low-temperature phase equilibria in the Fe-Ni binary system[END_REF] (for older ones, see the reviews in refs. [START_REF] Yang | A revision of the Fe-Ni phase diagram at low temperatures (< 400 • c)[END_REF][START_REF] Swartzendruber | The Fe-Ni (iron-nickel) system[END_REF]). Within the CALPHAD framework, a Gibbs free energy model can be defined for each of the phases to be considered (e.g. in the Fe-Ni system, the α and γ solid solutions and the different ordered phases). This gives great flexibility to fit the parameters to the experimental data. We will fit our PIM parameters to the study by Cacciamani et al. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF] (which will be hereafter simply referred to as the "CALPHAD model" or even as "CALPHAD"), but the following presentation and procedure could easily be adapted to other CALPHAD studies.

The γ solid solution

The Gibbs free energy per atom of the solid solution γ (FCC) Fe 1-x Ni x is:

G γ = G γ ref + G γ ex + G γ mag + G γ id (1)
This is the total Gibbs free energy, including the entropy of configuration. (Note that in CALPHAD one rather uses molar energies, in J.mol -1 . We convert them in energies per atom, in eV).

G γ ref is the non-magnetic contribution of pure metals:

G γ ref = (1 -x)G γ F e -xG γ N i (2)
where G γ F e and G γ N i are the Gibbs free energy of pure Fe and pure Ni. G γ ex is the excess Gibbs free energy, written as a sum of Redlich-Kister polynomials:

G γ ex = x(1 -x) i L γ i (T )(1 -2x) i (3)
(from i = 0 to 2 in [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF]) G γ mag is the magnetic contribution:

G γ mag = -k B T f (τ ) ln(β(x) + 1) (4)
τ = T /T c (x), where T c (x) is the Curie temperature, β(x) the average magnetic moment of the γ solid solution and f (τ ) is a polynomial function of the reduced temperature. T c (x) and β(x)

are also given by Redlich-Kister polynomials of the composition x, fitted to experimental measurements. Different expressions and values have been proposed [START_REF] Xiong | Magnetic phase diagram of the Fe-Ni system[END_REF], those used by Cacciamani et al. are given in [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF].

G γ id corresponds to an ideal entropy of configuration:

G γ id = -T S γ id = k B T [x ln x + (1 -x) ln(1 -x)] (5)
i.e. to the configuration entropy of a perfectly disordered solid solution with no short-range order. Note that the excess term (eq. 3) may include a non-ideal configurational part, but it is not identified as such.

Finally, the Gibbs free energy of mixing is:

G γ mix = G γ -(1 -x)G γ F e -xG γ N i (6)
where

G γ F e = G γ F e + G γ mag (x = 0) and G γ N i = G γ N i + G γ mag (x = 1
) are the total Gibbs free energies of the pure metals, including the magnetic part.

Ordered Phases

In the study by Cacciamani et al. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF], the ordered phases FeNi 3 (L1 2 ), Fe 3 Ni (L1 2 ) and FeNi (L1 0 ) are modeled within the framework of the Compound energy formalism (CEF) with 4 sublattices. An additional term is added to the Gibbs free energy of the γ phase, which depends on the distribution of species on the different sublattices and on interaction energies (limited to the first nearest neighbors) fitted to ab initio calculations of the formation enthalpy of the perfectly ordered phase.

In the present work, we will use more detailed ab initio studies, involving both ordered and disordered configurations and summarized in the following section.

B. Ab initio calculations

Density functional theory method

In this work, the 0 K formation enthalpies of Fe-Ni ordered and disodered phases are fitted to those computed in the ab initio study of Ref. [START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF]. The essential computational points are presented in the following.

The ab initio calculations were performed using density functional theory (DFT) with the projector augmented wave method [START_REF] Blöchl | Projector augmented-wave method[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] as implemented in the VASP (Vienna Ab-initio Simulation Package) [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF]. The generalized gradient approximation for the exchangecorrelation functional in the Perdew-Burke-Ernzerhof parametrization [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] was employed.

All the calculations are spin-polarized. 3d and 4s electrons were considered as valence electrons. The plane-wave basis cutoff was set to 400 eV. The Methfessel-Paxton broadening scheme with a smearing width of 0.1 eV was used [START_REF] Methfessel | High-precision sampling for Brillouin-zone integration in metals[END_REF]. The k-point grids were generated according to the cell size to achieve a k-sampling equivalent to a cubic unit cell with a 16 × 16 × 16 shifted grid following the Monkhorst-Pack scheme [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF]. The zero-point energies, which can be significant for light elements, have been calculated in the ordered phases. Their contribution to the mixing enthalpies is very small (typically 0.001 to 0.003 eV) and has been neglected in the following. FCC solid solutions were represented by Special Quasirandom Structures (SQS) [START_REF] Zunger | Special quasirandom structures[END_REF] minimizing Warren-Cowley short-range order parameters [START_REF] Cowley | An approximate theory of order in alloys[END_REF][START_REF] Martinez | Simulations of Decomposition Kinetics of Fe-Cr Solid Solutions during Thermal Aging[END_REF], with 128-atom and 108-atom supercells for anti-ferromagnetic-double-layer and ferromagnetic phases, respectively.

Ordered Phases

TABLE I. Formation enthalpies of FCC ordered phases in Fe-Ni (DFT calculations from [17]).

Ordered phase H f or (eV/atom)

Fe 7 Ni-cI32 0.039273 Fe 3 Ni-L1 2 -0.01636 Fe 3 Ni-Z1 -0.04414 Fe 2 Ni-C11 f -0.06991 FeNi-L1 1 -0.04040 FeNi-L1 0 -0.10797 Fe 2 Ni-C11 f -0.08064 FeNi 2 -L1 2 -0.10879 FeNi 7 -cI32 -0.04541
The formation enthalpies of nine ordered structures on the FCC lattice, calculated by Kangming et al. [START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF] using the DFT method presented in the previous section, are given in Table I and Fig. 2. The ordered structures are ferromagnetic, except for Fe 7 Ni-cI32 which is ferrimagnetic. The formation enthalpies are defined with the anti-ferromagnetic FCC iron and the ferromagnetic FCC nickel as reference states. The trends are the same as in a previous study by Mishin et al. [START_REF] Mishin | Phase stability in the Fe-Ni system: Investigation by first-principles calculations and atomistic simulations[END_REF]: only the FeNi-L1 0 and FeNi 3 -L1 2 phases are located on the convex hull (Fig. 2) and must therefore be stable at low temperature on the FCC lattice. However the FeNi 7 -cI32 and Fe 2 Ni-C11 f phases are close to the stability limit.

Special Quasi-Random Structures

The formation enthalpies H f or of special quasi-random structures (SQS) of different compositions have also been calculated in the same study with different magnetic states. These structures are representative of random solid solutions. They were generated by standard methods, with a minimization of Warren-Cowley short-range order parameters. They are described in Ref. [START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF], with a detailed analysis of their volume and magnetic moments. We just recall here the energetic results used for the PIM parametrization.

The most stable SQS are found to be double-layered anti-ferromagnetic for x < 0.184 and ferromagnetic for x > 0.184 (red circles in Fig. 3). One observes an asymmetrical evolution of H f or with the composition, as already predicted in the study by Cacciamani et al., with mainly negative values (i.e. a tendency to order) and a minimum in the vicinity of the composition of the FeNi 3 phase. However, the SQS values are significantly larger than the CALPHAD ones (Fig. 3), and are even slightly positive for x < 0.20 (as already obtained by Sansa et al. [START_REF] Sansa | Tight-binding modelling of ferromagnetic metals and alloys[END_REF], using a tight-binding approach).

C. Pair interaction model

We propose to reproduce the properties of Fe-Ni alloys with a model of concentrationand temperature-dependent pair interactions on a perfect FCC lattice. FIG. 3. Formations enthalpies at 0 K of quasi-random FCC structures (DFT calculations [START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF]) and FCC solid solutions (CALPHAD [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF], with separate magnetic and excess contributions).

alloys [START_REF] Senninger | Atomistic simulations of the decomposition kinetics in Fe-Cr alloys: Influence of magnetism[END_REF][START_REF] Levesque | Simple concentrationdependent pair interaction model for large-scale simulations of fe-cr alloys[END_REF], which had however not been fitted systematically on a CALPHAD model, and did not explicitly distinguish a magnetic contribution.

The essential assumption of the PIM is that the Gibbs free energy (per atom) of a given configuration, i.e. a given distribution of n F e Fe atoms and

n N i Ni atoms (N = n F e + n N i )
on the FCC lattice, can be written as a sum of interactions g

(n) ij (x, T
) between pairs of i and j atoms on n th neighboring sites:

G conf = 1 N ij g (n) ij (x, T ) (7)
The pair interactions depend on the temperature, T , and the Ni concentration, x (we will omit these dependencies in the following, to simplify the notations). The dependence on concentration is required to reproduce an asymmetric evolution of formation enthalpies, as observed in Fig. 2 and Fig. 3. The dependence on temperature describes the entropic contributions (electronic, vibrational and magnetic) other than the configuration entropy, so the g

(n)
ij are indeed "pair Gibbs free energies" and can be written as: g

(n) ij = h (n) ij -T s (n) ij [48].
To facilitate the comparison with CALPHAD models, each interaction g

(n)
ij is written as a sum of a non-magnetic (nm) and a magnetic term (mag). G conf is therefore the sum of:

G nm conf = 1 N ij g nm(n) ij (8)
which accounts for the chemical and vibrational contributions, and of:

G mag conf = 1 N ij g mag(n) ij (9)
The total Gibbs free energy of the alloy is:

G = G conf -T S conf (10)
where S conf is the entropy of configuration, which will be evaluated from Monte Carlo simulations.

The Gibbs free energy of mixing G mix is:

G mix = G -(1 -x)G F e -xG N i (11)
G F e is the Gibbs free energy of pure iron, on the same FCC lattice:

G F e = G nm F e + G mag F e (12)
= n z n 2 (g nm(n) F eF e + g mag(n) F eF e ) (13)
= n z n 2 g (n) F eF e (14)
where z n is the coordination number for the nearest neighbors n. The same expressions apply to pure nickel.

High temperatures: fitting of the pair interactions to CALPHAD

In the PIM, the Gibbs free energy of mixing of a perfectly disordered solid solution is:

G mix (x, T ) = x(1 -x) n v n (x, T ) -T S id (15)
where the ordering parameters v n are defined as:

v n (x, T ) = g (n) F eN i - 1 2 g (n) F eF e + g (n) N iN i (16)
To reproduce the properties of the CALPHAD model, we identify the non-magnetic part of the ordering parameters (in eq. 15) to the excess Gibbs free energy of CALPHAD (eq. 3):

n v nm n (x, T ) = G γ ex x(1 -x) (17)
and their magnetic part to the magnetic Gibbs free energy of CALPHAD (eq. 4):

n v mag n (x, T ) = G γ mag x(1 -x) (18)
The fitting of the PIM parameters on CALPHAD can be summarized to the equations 16-18. It is worth to notice that it is based on an approximation: eq. 15 is exact only for a disordered solid solution, i.e. at sufficiently high temperatures. In the real solid solution, a short-range order may exist, and the configuration entropy does not reduced to an ideal term.

Low temperatures: fitting of the pair interactions to ab initio calculations

To reproduce the properties of a solid solution at 0 K, the same method can be used by fitting v n (x, T ) on the formation enthalpies of SQS calculated by DFT. The magnetic part remains fitted to the magnetic model of CALPHAD (eq. 18) and the non-magnetic part is fitted so that the sum of the magnetic and non-magnetic contributions of the PIM reproduces the DFT formation enthalpies. A good agreement is obtained with a Redlich-Kister polynomial of order 5 (instead of 2 for G γ ex in ref. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF]), as shown in Fig. 4 (with respectively the magnetic part, the non-magnetic part and the total mixing enthalpies of the PIM). The fitting coefficients L DF T j of the polynomial are given in Table II, corresponding to the orange curve in Fig. 4. As mentioned above, this gives mixing enthalpies above those predicted by CALPHAD at 0 K. This fit of pair interactions (using eq. 15) to the CALPHAD model or to the formation enthalpies of SQS, only involves the sum of v n and can be done with any range n of interac- tions. However, it is well known that in FCC ordered structures, the phase diagram and in particular the order-disorder temperatures, depend strongly on the ratio = v 2 /v 1 [START_REF] Gahn | Ordering in face-centered cubic binary crystals confined to nearest-neighbour interactions-monte carlo calculations[END_REF]. The fit is also independent of the choice of the composition x (local or global) in eq. 18 and 17.

Therefore, it does not provide a very accurate description of the interatomic interactions in Fe-Ni alloys.

To get a better description of the thermodynamic properties, the range of interactions and the ratio between the interactions at different distances is fitted to the DFT calculations of the formation enthalpies of the ordered phases (Table I).

With only first nearest neighbors (nn) interactions (Fig. 5

Transition between parameters at high and low temperatures

The final PIM will therefore use first and second neighbor pair interactions with a constant α = v 2 /v 1 = -0.7 ratio:

-At 0 K the variations of v 2 and v 1 with the composition are fitted to the formation enthalpies of SQS and ordered structures calculated by Li and Fu [START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF] using DFT methods, ). The final parameters are obtained by using coefficients

8 3 v 1 + 2 3 v 2 FeNi-L1 1 1 2 1 2 3v 1 + 3v 2 FeNi-L1 0 1 2 0 4v 1 FeNi 2 -C11 f 11 17 11 17 8 3 v 1 + 2 3 v 2 FeNi 3 -L1 2 25 34 1 3v 1 FeNi 7 -cI32
L P IM i (T )
which evolves gradually from one to the other according to:

L P IM j (T ) = exp - T T j L DF T j + 1 -exp - T T j L CALP HAD j (T ) (19)
with T j = 400 K for j = 0, 1, 2 and T j = 80 K for j = 3, 4, 5. The example of coefficient

L P IM 2
is given in fig. 6. The temperatures T j have been chosen so as to give the Gibbs free energy of CALPHAD for T > 1000 K, at temperatures where it is derived from numerous and reliable experimental data. The influence of these transition temperatures on the phase diagram will be discussed later.

Let us note finally that the Gibbs free energy of mixing of the solid solution, the formation enthalpies of of SQS or ordered structures and the FCC phase diagram, depend only on the parameters v n . We have chosen to take g (n)

F eF e and g (n)

N iN i interactions independent of the concentration, but dependent on the temperature and adjusted to the free enthalpies of the pure metals (eq. 12). Only the g (n)

F eN i interactions are dependent on local concentration. This choice does not affect the results of the present study, but it allows a better description of the properties of point and diffusion defects [START_REF] Senninger | Atomistic simulations of the decomposition kinetics in Fe-Cr alloys: Influence of magnetism[END_REF], which we will address in future work. It also makes the Monte Carlo simulations slightly less time consuming.

III. MONTE CARLO SIMULATIONS

We will now use Monte Carlo simulations to measure of Gibbs free energies of the PIM (including the configuration entropy) at different compositions and temperatures and build the FCC phase diagram.

A. Semi-grand canonical isotherms

The equilibrium properties of the PIM are determined by Monte Carlo simulations carried out in the semi-grand canonical ensemble. In general, we use a system of N = 4 × 16 3 atoms, with periodic boundary conditions. Exchanges are tried between a randomly chosen atom of the system and an atom taken in a reservoir, with a given difference of chemical potential ∆µ = µ N i -µ F e . By changing ∆µ, one modifies the equilibrium concentration (Fig. 8 and9). A total of 500 increments for a interval of 1 eV in ∆µ are used to go from pure iron to pure nickel, and then 500 increments to go the other way. For each value of ∆µ, 5 × 10 6 attempts of atomic exchange (or Monte Carlo steps, MCS) are performed before measuring the equilibrium composition and order parameters. For building the phase diagram of Fig. 16, a larger system of N = 4 × 24 3 atoms and much smaller increments of ∆µ are used, in order to get a better precision (up to 100 increments for a interval of 0.04 in ∆µ).

To identify the different ordered phases, the FCC lattice is divided into 4 simple cubic sublattices, shifted by a distance a/2 in the x, y, z directions [START_REF] Inden | Atomic ordering[END_REF]. We measure the Ni concentration on each sublattice, and the long range order parameter defined as:

η = 1 4 4 i=1 x i x -1 (20)
where x i is the Ni concentration on the sublattice i. With this definition, η = 1 in the perfect FeNi-L1 0 structure and η = 0.5 in the perfect FeNi 3 -L1 2 structure.

The short range order is characterized by the Warren-Cowley parameters for the first and second nearest neighbors:

σ i = 1 - f (i) N i x (21)
where

f (i)
N i is the average fraction of Ni atoms among the i th nn of the Fe atoms. For a perfect L1 2 ordered phase, σ 1 = -0.33 and σ 2 = +1. The evolution of the long-range η (eq. 20), and of the short range order parameters σ 1 and σ 2 (eq. [START_REF] Paulevé | Une nouvelle transition ordre-désordre dans Fe-Ni (50-50 )[END_REF], in an alloy of composition FeNi 3 as a function of the temperature, is shown in Fig. 7. The L1 2 ordered phase is found to be stable up to 765 K (instead of 790 K for CALPHAD [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF]). The evolution of η is in good agreement with the experiments of Kozlov et al. [START_REF] Kozlov | Order-discharge transition in ni 3 fe alloy[END_REF] (which gives a slightly higher ordering temperature: 807 K). The discontinuity at the order/disorder temperature indicates a first-order transition. A significant short range order remains well above the disordering temperature, especially between the first nearest neighbors.

Two examples of isotherms x = f (∆µ), at T = 1000 K and T = 600 K are shown in

B. Gibbs free energy of mixing

Using the definition of chemical potentials: µ i = (∂G/∂n i ) T,P,n j and integrating the ∆µ(x) curve, we obtain the Gibbs free energy of mixing G mix . The results obtained at different temperatures can be directly compared with the G mix of the CALPHAD study [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF]. In each case, one can also compare separately, the enthalpy H mix and entropy S mix of mixing, as well as the magnetic, excess and configuration contributions.

∆µ = µ N i -µ F e .
worth to notice that the excess contribution is slightly lower in the PIM, with a minimum of -0.038 eV at x = 0.69 instead of -0.033 eV in CALPHAD. The difference is due to the fact that in the PIM, some short range order remains in the γ solid solution, even at this high temperature (Fig. 7). The effect is clearer if one separates the enthalpic and entropic contributions of G mix = H mix -T S mix . The enthalpy of mixing (Fig. 11) is dominated by the excess term. Due to the remaining short range order (σ 1 = -0.066 and σ 2 = 0.048), the PIM gives a minimum of H mix = -0.054 eV at x = 0.67 instead of -0.047 eV in CALPHAD. This discrepancy on H mix only disappear at very high temperature. At 3000 K (i.e. above the liquidus), the maximum difference between the PIM and CALPHAD is still ∆H mix = 0.0022 eV (for σ 1 = 0.06 and σ 2 = 0.013). It becomes negligible only above 5000 K.

The entropy of mixing of the the PIM (Fig. 12) is dominated by the entropy of configuration, which is very close to the ideal S id of CALPHAD. In the PIM as in CALPHAD, the excess and magnetic contributions to the entropy of mixing are less important, and negative (except below x 0.1). At x = 0.67, the discrepancy due to the short range order is only S conf -S id = 0.15 × 10 -5 eV/(atom•K), which corresponds to a difference of T (S conf -S id ) = -0.00225 eV/atom. The difference on S mix partly compensate the one on H mix , which explain the good agreement on G mix between the PIM and CALPHAD, even below 1500 K, when the short range order increases. The G mix of the PIM and CALPHAD are therefore in very good agreement in the whole range of composition and temperature where the γ solid solution is stable (Fig. 13). The difference between the Gibbs free energy of mixing of the PIM and CALPHAD [Fig. 14(a)] slightly increases at lower temperatures, when the ordered phase L1 2 stabilizes, i.e. when the long-range order parameter η is close to 0.5, between x 0.6 and x 0.82 [Fig. 14(b)]. This is not surprising since the PIM parameters at low temperatures are not fitted on CALPHAD, but on DFT calculations which give a different energetic landscape, especially for the disordered phase (section II C). In spite of this difference, the G mix (x) curve of the PIM is still in good agreement with CALPHAD at T = 700 K.

At 650 K, the agreement between the Gibbs free energy of mixing of the PIM and CAL-PHAD is still quite good for the compositions where the γ solid solution and the L1 2 phase ordered for the stoichiometric composition FeNi 3 (η 0.5 for x = 0.75)). However, the PIM predicts that the FeNi-L1 0 phase is stable between x 0.52 and 0.63, while it only appears at lower temperature (below 316 K) according to the CALPHAD model [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF]. Note that it is not perfectly ordered (η 0.6 instead of 1 for the perfect order), because it is slightly non-stoichiometric (x > 0.5) and because 650 K is close to its order disorder-temperature (680 K).

C. FCC phase diagram

The FCC phase diagram of the Fe-Ni system predicted by the PIM is shown in Fig. 16 and compared with experimental data [START_REF] Josso | Equilibrium Diagram for the Order to Disorder Transformation of Iron-Nickels near Ni 3 Fe[END_REF][START_REF] Heumann | Karbonylverfahren und aufdampfverfahren zur bestimmung von phasengleichgewichten im temperaturbereich geringer beweglichkeit am beispiel der eisennickel-legierungen[END_REF][START_REF] Van Deen | Phase diagram of the order-disorder transition in ni3fe[END_REF][START_REF] Woude | Phase diagram of the order-disorder transition in ni3fe[END_REF]. It can be also compared to the FCC diagram of Cacciamani et al. (Fig. 8 in [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF]).

The ordering temperatures of the FeNi 3 -L1 2 phase are slightly different: the PIM gives 765 K, a little lower than 790 K for the CALPHAD study of Cacciamani et al. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF] (which is adjusted to the experimental value). As in CALPHAD, the limits of the two-phase domain FeNi 3 +γ for x > 0.75, are slightly shifted towards lower values (∆x -0.04 at 571 K) by comparison with the experiments by Heumann et al. [START_REF] Heumann | Karbonylverfahren und aufdampfverfahren zur bestimmung von phasengleichgewichten im temperaturbereich geringer beweglichkeit am beispiel der eisennickel-legierungen[END_REF]. And as in CALPHAD, the width of the two-phase domain γ+FeNi 3 at x < 0.75 is smaller than the one of the two-phase domain at x > 0.75 (earlier CALPHAD studies predicted a larger two-phase field, as in Fig. 1). Here it should be noted that, except in the vicinity of the ordering temperature at x = 0.75, the experimental data for these two-phase fields are going back to 1963 [START_REF] Heumann | Karbonylverfahren und aufdampfverfahren zur bestimmung von phasengleichgewichten im temperaturbereich geringer beweglichkeit am beispiel der eisennickel-legierungen[END_REF] and are only available for one temperature.

The discrepancy is more important for the FeNi-L1 0 phase: the PIM predicts an ordering temperature of 680 K instead of 316 K for CALPHAD. The CVM study of Mohri et al. [START_REF] Mohri | First-principles calculation of L1 0 -disorder phase equilibria for Fe-Ni system[END_REF] predicts an intermediate ordering temperature (483 K). A direct estimation by DFT calculations (taking into account the vibrational entropy, but not the configurational entropy of the FeNi-L1 0 phase) gives 640 K. There is no precise experimental measurement available for the evolution of the degree of order as a function of the temperature (as for the FeNi 3 phase, in Fig. 7), but the experimental observations under electron irradiation by Reuter et al. [START_REF] Reuter | Ordering in the Fe-Ni system under electron irradiation[END_REF] suggest an ordering temperature of approx. 593 K.

As in CALPHAD, the FCC phase diagram of the PIM also displays a two-phase field with an equilibrium between a ferromagnetic (γ f ) and a paramagnetic (γ p ) solid solution, at x = 0.4 and below T = 660 K. This phase separation has been first predicted by Chuang et al. [START_REF] Chuang | Magnetic contributions to the thermodynamic functions of alloys and the phase equilibria of Fe-Ni system below 1200 K[END_REF], but it has not been confirmed experimentally. The PIM is able to reproduce this two-phase field because it includes the magnetic contribution of the CALPHAD model. It is however more limited in temperatures than in ref. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF], because of the higher stability of the FeNi-L1 0 phase in the PIM, which limits its extension below 680 K.

The phase diagram of the PIM without the magnetic contribution is shown in Fig. 17.

As in the study by Cacciamani et al., the non-magnetic phase diagram reduces the critical temperature of L1 2 by approx. 118 K and shows no γ f -γ p two-phase field.

Finally, let us recall that the parameters of the PIM and the results of section III have been obtained with parameters fitted to DFT calculations at 0 K, the CALPHAD data of ref. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF] at high temperatures, and a transition between the high and low temperature regimes controlled by the exponential interpolation of Eq. 17. With the chosen T j temperatures, the Redlich-Kister coefficients of the PIM are almost identical to those of CALPHAD above approximately 1000 K. To assess the effect of this choice on the phase diagram, we have performed some simulations with a different set of paramaters: T j = 50 K for j = 0, 1, 2 and T j = 10 K for j = 3, 4, 5 (using the same notation as in II C 3). With these parameters, the Redlich-Kister coefficients of the PIM becomes almost identical to those of CALPHAD at a lower temperature (approx. 315 K). The resulting phase diagram is shown in Fig. 18.

It is not very different from the previous one (Fig. 16(a)), except from a moderate increase of the ordering temperatures of the L1 0 and L1 2 phases. The reason is that with the new parameters, the ordering tendency is a little more pronounced below 1000 K (Fig. 4). As a consequence, the γ p -γ f two-phase domain almost completely disappears.

IV. DISCUSSIONS AND CONCLUSIONS

We have presented in this study a method for developing a pair interaction model for Fe-Ni alloys, fitted at 0 K on the enthalpies of formation of ordered and disordered structures (computed by first-principle methods) and at high temperatures on the Gibbs free energy of the γ solid solution (as given by a CALPHAD study and its underlying experimental data).

Thanks to the temperature and concentration dependence of the pair interactions, the PIM is able to reproduce precisely these two types of energetic properties, and to distinguish between excess, magnetic and configurational entropic contributions. The identification between CALPHAD and the PIM is not perfect, because the configurational entropy and short-range order in the solid solution is described more approximately in CALPHAD methods than in the Monte Carlo simulations used to determine the equilibrium properties of the PIM. The CALPHAD method is more flexible than an atomistic model: the properties of each phase can be adjusted very precisely and independently on the experiments. The PIM imposes some constraints but, combined with Monte Carlo simulations, it ensures a consistent description of the short-and long-range order and of the entropy of configuration. Despite these differences, the Gibbs free enthalpies of mixing of the γ solid solution, as given by CALPHAD, are very well reproduced by the PIM, throughout the composition and temperature range of stability of the phase. The Gibbs free enthalpy of the FeNi 3 -L1 2 phase is also well reproduce, although the parameters of the PIM and CALPHAD for that phase are not fitted on the same DFT calculations. At high temperatures, the FCC phase diagram involves only these two phases, and both methods give similar results (especially for the order-disorder transition in the vicinity of FeNi 3 , and for the γ p -γ f phase separation).

On the other hand, both models predict that the FeNi-L1 0 phase is stable at low temperature, but with different ordering temperatures. Taking the electron irradiation experiments [START_REF] Reuter | Ordering in the Fe-Ni system under electron irradiation[END_REF] as a reference, it seems that CALPHAD underestimates the ordering temperature, while the PIM overestimates it. It should be noted here that alloys under irradiation may be not fully at equilibrium, so that no real experimental thermodynamic data are available for this phase; and that both the CALPHAD model and the PIM are only fitted to DFT calculations of enthalpies of formation at 0 K. The PIM and CALPHAD should therefore be both improved to properly describe this phase. One possibility is to use DFT methods to compute finite temperature contributions. These methods are computationally expansive, but can separate each energetic contribution and provide results at intermediate temperature (say, between 0 and 400 • C), where experimental results are rarer and perhaps less accurate. An example is given in the study of K. Li and C.-C. Fu [START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF], which shows that the vibrational entropy decreases the ordering temperatures of the L1 0 and L1 2 phases by respectively 280 and 200 K.

In spite of this limitation, the PIM model gives a satisfactory description of the γ solid solution and of the L1 2 phase. Of course, such a model is necessarily dependent on the CALPHAD data it uses. For the magnetic contribution for example, we rely on the recent study by Cacciamani et al., which is itself based on a large experimental database (with measurements of specific heats, Curie temperatures, magnetic moments, etc. of γ solid solutions with various compositions, described in ref. [START_REF] Cacciamani | The Fe-Ni system: Thermodynamic modelling assisted by atomistic calculations[END_REF][START_REF] Cacciamani | Critical evaluation of the fe-ni, fe-ti and fe-ni-ti alloy systems[END_REF]). For the same reason, our model takes into account, but cannot distinguish between energetic contributions that are not identified separately in CALPHAD (for example, harmonic and non-harmonic vibrational contributions -which are both gathered in the excess Gibbs free energy, together with the non-ideal part of the configurational entropy). However it could easily be updated to take into account future improvement on that points. It could also be easily extended to Fe-Ni-Cr ternary alloys or to other binary or ternary systems. Finally the PIM is simple enough to be used as a basis for Atomistic Kinetic Monte Carlo methods to simulate the kinetics of homogeneous ordering or of heterogeneous precipitation of the L1 2 phase; or to model the interdiffusion properties in the γ solid solution at high temperature. It is indeed not more numerically expensive than the PIM for BCC Fe-Cr alloys described in Ref. [START_REF] Levesque | Simple concentrationdependent pair interaction model for large-scale simulations of fe-cr alloys[END_REF],

which has been used for the simulations of precipitation kinetics [START_REF] Martínez | Decomposition kinetics of Fe-Cr solid solutions during thermal aging[END_REF][START_REF] Senninger | Atomistic simulations of the decomposition kinetics in Fe-Cr alloys: Influence of magnetism[END_REF] or irradiation effects [START_REF] Senninger | Modeling radiation induced segregation in iron-chromium alloys[END_REF][START_REF] Soisson | Atomistic modeling of precipitation in fe-cr alloys under charged particles and neutron irradiations: Effects of ballistic mixing and sink densities[END_REF]. As in these studies, the modeling of kinetics will require the extension of the PIM to describe the formation and migration properties of point defects.

FIG. 2 .

 2 FIG.2. Formations enthalpies of ordered FCC structures at 0 K (DFT calculations from[START_REF] Li | Ground-state properties and lattice-vibration effects of disordered Fe-Ni systems for phase stability predictions[END_REF]).

FIG. 4 .

 4 FIG. 4. Formations enthalpies of quasi-random FCC Structures at 0 K: ab initio calculations (DFT) and pair interaction model (PIM, with the excess and magnetic contributions). The formations enthalpy of the γ solid solution of CALPHAD is also shown for comparison.

5 - 0 .

 50 03696 0.09631 -0.04722 0.21141 -0.04752 -0.18389

FIG. 5 .

 5 FIG. 5. Formations enthalpies of FCC ordered phases at 0 K: ab initio calculations (DFT, full circles) and pair interaction model (PIM, open circles) with (a) only first nn interactions, (b) first and second nn interactions, α = v 2 /v 1 = -0.7

2 as summarized in fig. 5 and 4 ;-

 24 At high temperatures the variations of v 2 and v 1 with the composition are fitted to the Gibbs free energies of the γ solid solution, from the CALPHAD study of Cacciamani et al. [18]; These two sets of parameters differ only in the non-magnetic part of parameters v 2 and v 1 , which is described by Redlich-Kister polynomials having different order and coefficients (respectively L DF T i and L CALP HAD i

FIG. 6 . 2 (

 62 FIG. 6. The evolution of the coefficient L P IM2

FIG. 7 . 2 in

 72 FIG. 7. Evolution the long-range parameter η and of the short-range order parameters σ 1 and σ 2 in FeNi 3 as a function of T (Monte Carlo simulations and experiments by Kozlov et al. [51]).

Fig. 8 and 9 .FIG. 8 .

 98 Fig. 8 and 9. At 1000 K, x(∆µ) evolves continuously, with η 0: the disordered solid solution is stable in the whole composition range. At 600 K, η 0.76 to 0.53 between ∆µ = -0.188 and -0.068 eV, which corresponds to an over stoichiometric L1 0 phase; and η 0.49 between ∆µ = -0.05 and +0.3 eV, which corresponds to an almost stoichiometric L1 2 phase. Discontinuities and hysteresis on the x(∆µ) curve indicate first order transitions and the limits of two-phase domains.

Fig. 10 FIG. 9 .

 109 Fig. 10 for example, gives the Gibbs free energy of mixing of the Fe-Ni solid solution at T = 1500 K. The PIM is in very good agreement with the CALPHAD study. At this high temperature (well above T c ), the magnetic contribution is negligible. However it is

FIG. 10 .

 10 FIG.10. Gibbs free energy of mixing of the Fe-Ni solid solutions at 1500 K: PIM (dotted lines) vs CALPHAD (full lines), with the separate magnetic, excess and configurational entropic contributions.

FIG. 11 .

 11 FIG. 11. Enthaply of mixing of the Fe-Ni solid solutions at 1500 K: PIM (dotted lines) vs CALPHAD (full lines), with separate magnetic and excess contributions.

FIG. 12 .FIG. 13 .

 1213 FIG.12. Entropy of mixing of the Fe-Ni solid solutions at 1500 K: PIM (dotted lines) vs CALPHAD (full lines), with separate magnetic, excess and configurational contributions.

  are stable [Fig.15(a)]. However the evolution of the long-range parameter η as a function of the nickel concentration x now displays two bumps [Fig.15(b)]. The second one (between x 0.63 and x 0.85) still corresponds to the L1 2 phase. The phase is almost perfectly

FIG. 14

 14 FIG. 14. (a) Gibbs free energy of mixing of Calphad and the PIM and (b) long range order parameter of the PIM, for Fe-Ni alloys at 700 K.

FIG. 15 .

 15 FIG. 15. (a) Gibbs free energy of mixing of Calphad and the PIM and (b) long range order parameter of the PIM, for Fe-Ni alloys at 650 K.

FIG. 16 .

 16 FIG. 16. (a) The Fe-Ni FCC phase diagram: comparison between the PIM and experiments (1950 Jos = [52], 1963 Heu = [53], 1980 Van = [54, 55]., (b) zoom in the region of the L1 2 ordering temperature.

FIG. 17 .FIG. 18 .

 1718 FIG. 17. The Fe-Ni FCC phase diagram of the PIM without magnetic contribution

TABLE II .

 II The coefficients L DF T j of the Redlich-Kister polynomial for the excess enthalpy of mixing of the γ solid solution of the PIM (in eV).

TABLE III .

 III Formation enthalpies of FCC ordered phases in a pair interaction model with first and secong nearest neighbor interactions.

	Ordered phases x 1 x 2 H P IM f or
	Fe 7 Ni-cI32	1 34	5 34	3 2 v 1 + 3 4 v 2
	Fe 3 Ni-L1 2	9 34 0 3v 1
	Fe 3 Ni-Z1	11 34	9 34 2v 1 + 1 2 v 2
	Fe 2 Ni-C11 f	6 17	6 17

ACKNOWLEDGMENTS

We thank our colleagues Chu-Chun Fu and Maylise Nastar for many fruitful discussions.

The research leading to these results has been carried out in the frame of EERA Joint Program for Nuclear Materials and is partly funded by the European Commission HORIZON 2020 Framework Programme under grant agreement No. 755269.


Johannes Karges

Kai Xiong

Olivier Blacque

Hui Chao

Gilles Gasser
email: gilles.gasser@chimieparistech.psl.eu

Highly Cytotoxic Copper(II) Terpyridine Complexes as Anticancer Drug Candidates

Keywords: Anticancer, Antineoplastic Agents, Medicinal Inorganic Chemistry, Metals in Medicine, Toxicity

Cancer is one of the deadliest diseases worldwide. Chemotherapy remains one of the frequently applied treatment modalities in the clinics. However, as the currently applied agents are associated with severe side effects, scientists are searching for novel chemotherapeutic drugs.

Within the last decades, Cu(II) polypyridine complexes have received increasing attention as potential anticancer drug candidates. Herein, the biological activity of terminally functionalised mono-and bis-coordinated Cu(II)-2,2´:6´,2´´-terpyridine complexes have been investigated.

The bis-coordinated compounds were found to have a cytotoxic effect in the nanomolar range in human adenocarcinomic alveolar basal epithelial cells. Promisingly, the complexes were equally active in the corresponding cisplatin resistant cell line, indicating that they could potentially be useful for the treatment of drug resistant tumours.

HIGHLIGHTS

-Synthesis of terminally functionalised Cu(II) polypyridine of the type [Cu(2,2´:6´,2´´terpyridine)(Cl)2] and [Cu(2,2´:6´,2´´-terpyridine)2][NO3]2.

-Single crystal X-ray analysis of metal complexes.

-Biological evaluation revealed cytotoxicity of lead compounds in the nanomolar range against human adenocarcinomic alveolar basal epithelial cells.

-Effective in drug resistant cancer cell line.

INTRODUCTION

Cancer remains one of leading causes of death worldwide as demonstrated by the alarming numbers published by World Health Organisation (WHO) over the last decades. [1] As treatment modalities, chemotherapy is commonly applied in the clinics in combination with radiotherapy, immunotherapy and surgery to circumvent the limitations of each treatment and overall improve the chances of eradication of the tumour and therefore survival of the patient. [2] To date, the platinum based agents cisplatin, oxaliplatin and carboplatin are clinically applied in more than 50% of chemotherapeutic treatments worldwide. [3,4] Despite their enormous success, these compounds are not ideal and associated with numerous side effects including nerve and kidney damage, nausea, vomiting, and bone marrow suppression. More worryingly, the number of resistant cancers is increasing, limiting the application of these compounds. [START_REF] Pil | Cisplatin and Related Drugs[END_REF][START_REF] Johnstone | [END_REF][7][8] To tackle this issue, scientists from all over the world are searching for novel chemotherapeutic agents. While the majority of investigated metal complexes are based on rare transition metals, it would be very interesting to develop compounds based on cheap and abundant metals. [9][10][11][12][13][14][15][16] Among other investigated metals, copper containing compounds are receiving increasing attention due their bioavailability and biocompatibility. The possibility of the reversible change of the oxidation state of the Cu(I)/Cu(II) couple under physiological conditions is appealing and has promoted the development of metal complexes with an active redox chemistry within cancerous cells. While Cu(II) polypyridine complexes have shown to interact with DNA, they were found to oxidatively cleave the phosphodiester bond through the generation of reactive oxygen species. These effects can cause DNA strand breaks and ultimately trigger cell death. [17][18][19] The first example of such compounds was the [Cu(1,10-phenanthroline)2] 2+ complex, which was found to cleave DNA of Escherichia coli bacteria. [20] Based on these attractive properties, Cu(II) polypyridine complexes are receiving increasing attention as artificial nucleases as well as potential anticancer candidates. [21][22][23][24][25][26] It is important to note, that two of such compounds, referred to as Casiopeinas ® , are currently investigated in clinical trials. [27,28] Further the complex diacetylbis(4-methylthiosemicarbazonato)copper(II), also abbreviated as copper-ATSM, is under investigation in clinical trials for the treatment of motor neurone disease. [29,30] As a class of compounds with particular interest, complexes of the type [Cu(2,2´:6´,2´´terpyridine)(Cl)2] have been studied. The terminal extension of the ligand with piperidine, bis(2-pyridylmethyl)amine [31,32], naphthalene [33], anthracene [34] as well as diverse substituted phenyl groups [35] including their multinuclear complexes have generated cytotoxic agents against various cancer cell lines. Worthy of note, the naphthalene derivative with a labile nitrate and water molecule instead of chloride ligands, was also found to be cytotoxic against cancerous cells. [36] The vast majority of these complexes demonstrated to strongly bind to DNA through an intercalative mode. While being able to efficiently cleave DNA, the compounds were found to be cytotoxic in the low micromolar to nanomolar range, making this class of compounds interesting candidates as anticancer agents. were synthesised and their cytotoxicity towards cancer cells investigated. We note that during the writing-up of this article, compounds 2 and 8 (with perchlorate as counter ions) were reported as cytotoxic agents against ovarian carcinoma cells by Gamez and co-workers. This study indicated that these compounds strongly interact with DNA and trigger cell death by apoptosis. [33] The compounds reported in our work were synthesised by complexation of the functionalised 2,2´:6´,2´´-terpyridine derivative with CuCl2 or CuNO3 . xH2O. Several complexes were also characterised by single crystal X-ray crystallography. The bis-coordinated complexes were found to be cytotoxic in the nanomolar range in adenocarcinomic human alveolar basal epithelial (A549) cells. Promisingly, the Cu(II) complexes were found to be toxic in the corresponding cisplatin resistant cell line, making them potentially interesting as anticancer agents against drug resistant tumours.

EXPERIMENTAL SECTION

Materials

All chemicals were obtained from commercial sources and used without further purification.

Solvents were dried over molecular sieves if necessary. The substituted 2,2':6',2"-terpyridine ligands (terpy-X): 4'-chloro-2,2':6',2"-terpyridine (terpy-Cl) [37], 4'-bromo-2,2':6',2"terpyridine (terpy-Br) [38], 4'-methoxy-2,2':6',2"-terpyridine (terpy-OMe) [39], 4'-carboxy-2,2':6',2"-terpyridine (terpy-COOH) [40], 4'-dimethylamino-2,2':6',2"-terpyridine (terpy-NMe2) [41] were synthesised as previously reported.

Instrumentation and methods

ESI-MS experiments were carried out using a LTQ-Orbitrap XL from Thermo Scientific (Thermo Fisher Scientific) and operated in positive ionization mode, with a spray voltage at 3.6 kV. No Sheath and auxiliary gas was used. Applied voltages were 40 and 100 V for the ion transfer capillary and the tube lens, respectively. The ion transfer capillary was held at 275 °C.

Detection was achieved in the Orbitrap with a resolution set to 100,000 (at m/z 400) and a m/z range between 150-2000 in profile mode. Spectrum was analyzed using the acquisition software XCalibur 2.1 (Thermo Fisher Scientific). The automatic gain control (AGC) allowed accumulation of up to 2 . 10 5 ions for FTMS scans, maximum injection time was set to 300 ms and 1 µscan was acquired. 10 µL was injected using a Thermo Finnigan Surveyor HPLC system (Thermo Fisher Scientific) with a continuous infusion of methanol at 100 µL . min -1 . Infrared (IR) spectra (w= weak, m=medium, s=strong, br=broad) were measured with a Nicolet 6700 FTIR spectrometer (Thermo Scientific). Elemental microanalyses were performed on a Thermo Flash 2000 elemental analyser.

Synthesis

General procedure for the synthesis of [Cu(terpy-X)(Cl) 2 ]:

CuCl2 (40 mg, 0.30 mmol) was dissolved in 20 mL of dry methanol under N2 atmosphere. A solution of the terpy-X ligand (70-83 mg, 0.30 mmol) in dry methanol/dichloromethane (1:1, 20 mL) was added dropwise. The mixture was stirred vigorously for 24 h at room temperature.

The generated precipitate was isolated by filtration and washed with diethyl ether (10 mL) and dichloromethane (10 mL). The crude product was purified by recrystallisation from methanol.

General procedure for the synthesis of [Cu(terpy-X) 2 ][NO 3 ] 2 :

A solution of the terpy-X ligand (70-83 mg, 0.30 mmol) was dissolved in dry methanol/dichloromethane (1:1, 20 mL) under N2 atmosphere. A solution of Cu(NO3)2 . xH2O (56 mg, 0.15 mmol) was dissolved in 20 mL of dry methanol was added dropwise. The mixture was stirred vigorously for 24 h at room temperature. The generated precipitate was isolated by filtration and washed with diethyl ether (10 mL) and dichloromethane (10 mL). The crude product was purified by recrystallisation from methanol.

Single crystal X-ray diffraction

All single crystal X-ray diffraction analyses were performed on Rigaku Oxford Diffraction instruments: the XtaLAB Synergy diffractometer (Pilatus 200 K detector) for 3 and 5, and the SuperNova diffractometer (Atlas CCD detector) for 6, 7 and 11. Both instruments are dual microfocus X-ray diffractometers (two possible wavelengths Mo and Cu) equipped with Oxford liquid-nitrogen cryostream coolers. The selected single crystals were mounted using polybutene oil on a flexible loop fixed on a goniometer head and transferred to the diffractometer. Preexperiments, data collections, data reductions and analytical absorption corrections [42] were performed with the program suite CrysAlisPro. [START_REF] Rigaku | Rigaku Oxford Diffraction[END_REF] Using Olex2, [START_REF] Dolomanov | [END_REF] the structures were solved with the SHELXT [45] small molecule structure solution program and refined with the SHELXL2018/3 program package [46] by full-matrix least-squares minimization on F 2 . All nonhydrogen atoms were refined anisotropically and hydrogen atoms were placed in calculated positions and refined as riding with C-H = 0.95 Å, Uiso(H) = 1.2Ueq(C) (for aromatic), C-H = 0.98 Å, Uiso(H) = 1.5Ueq(C) (for methyl) and O-H = 0.85 Å, Uiso(H) = 1.5Ueq(O) (for water).

The crystal data collections and structure refinement parameters are shown in Tables S1 -S3 .

CCDC 2034245 (for 3), 2034246 (for 5), 2034247 (for 6), 2034248 (for 7), and 2034249 (for 11) contain the supplementary crystallographic data for these compounds, and can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

Cell culture

All the cells lines were obtained from the animal experimental Centre of Sun Yat-Sen University (Guangzhou, China). The cell lines human adenocarcinomic alveolar basal epithelial (A549), cisplatin resistant human adenocarcinomic alveolar basal epithelial (A549R) and human liver (LO2) were maintained in DMEM media supplemented with fetal bovine serum (10%), penicillin (100 units/mL), streptomycin (50 units/mL) at 37 °C in a humidified atmosphere with 5% CO2. The cisplatin resistance of A549R was maintained by cisplatin treatment (1µM) for one week every month. Before an experiment, the cells were passaged three times.

Cytotoxicity assay

The cytotoxicity of a sample was accessed using a 3-(4,5-dimethylthiazol-2-yl)-2,5diphenyltetrazolium bromide (MTT) assay. Cells were seeded in 96 well plates and allowed to adhere upon incubation for 24 h. The cells were treated with increasing concentrations of the compounds diluted in cell media achieving a total volume of 200 μL. All cells were incubated in the dark for 44 h. After this time, the media was replaced with fresh media containing MTT (20 μL, 5mg/ mL). After 4 h incubation, the absorption at 595 nm in each well was determined with a SpectraMax CMax Plus (Molecular Devices) absorbance microplate reader. The viability of the cells in each well was obtained by subtracting the average absorbance of the blank group.

RESULTS AND DISCUSSION

Synthesis

The terminally functionalised 2,2´:6´,2´´-terpyridine ligands were prepared according to previously published synthetic procedures (Scheme S1). [37][38][39][40][41]47] The synthesis of the

X-ray crystallography

Perspective views of the molecular structures of 3, 5, 6, 7 and 11 are shown in Figure 2. In the crystal structures of 5 and 6, the asymmetric units contain two crystallographically independent Cu(II) molecules and isolated molecule(s) of water (one for 5, and two for 6). In the crystal structure of 7, the Cu(II) molecule lies on several special positions, a two fold axis and a rotoinversion four-fold axis. Only one fourth of the molecule had to be refined, the other positions were obtained by symmetry operations. The nitrate anions and water molecules are severely disordered around symmetry elements. Restraints had to be used to correct the geometry of the counterions and the thermal parameters of the corresponding atoms. In the crystal structure of 11, the asymmetric unit contains one Cu(II) molecule for two nitrate counterions and two isolated water molecules.

As revealed by the X-ray diffraction studies, the copper (II) atom in the terminally functionalised complexes of the type Cu(2,2´:6´,2´´-terpyridine)(Cl)2 3 (Br), 5 (OMe) and 6 (NMe2) is pentacoordinated in a distorted square-pyramidal geometry by one terpyridyl ligand atoms and two chlorido ligands. The terpyridyl ligand is coordinated in an usual manner acting as a tridentate N 3 chelating ligand while one chlorine atom is in an apical position and the second one is in the so-called "basal plane" formed by the latter and the three nitrogen atoms.

As expected, these four atoms are nearly coplanar in our crystal structures as confirmed by the calculated r.m.s. deviations (Table 1) of 0.1110 (3), 0.0795 and 0.0937 (5), and 0.0602 and 0.0655 [START_REF] Johnstone | [END_REF]. The metal center and the apical Cl ion are located on the same side of the basal plane, the former deviates from the basal plane by about 0.2 -0.3 Å while the latter is at about 2.8 Å (the exact values are reported in Table 1). Concerning the bond distances and angles, the Cu-N bond of the central pyridine is shorter by about 0.1 Å than those of the external rings, and the Cu-Cl basal bond length is much shorter than the Cu-Cl apical bond length by more than 0.2 Å (Table 1). Such a difference between the Cu-Cl distances is attributed to the wellknown Jahn Teller effect. In the crystal structures of the complexes of the type [Cu(2,2´:6´,2´´terpyridine)2][NO3]2 7 (H) and 11 (OMe) the metal center is hexacoordinated and exhibits a distorted octahedral coordination geometry. The two N 3 coordinated terpyridyl ligands are nearly planar and perpendicular to each other in 7 (due to the Cu atom located on special positions) or nearly perpendicular in 11 since the dihedral angle between the mean plane is 87.24(3)°. Like in the dichloro complexes, the Cu-N bond distance of the central pyridine is significantly smaller than those of the external rings (by 0.15 -0.25 Å, Table 2). Despite the large number of aromatic rings in all our complexes, there are no strong π … π interactions in the crystal structures. These interactions correspond to slipped face-to-face π stacking with the shortest centroid -centroid distances of 3.573 (3), 3.493 (5), 3.594 (6), 3.634 (7) and 4.106 Å (11) and slipped distances in the range 0.925 -1.175 Å (Tables 1 and2).

Biological Evaluation

The mono-coordinated dichloro complexes 1-6 were found to be poorly soluble in water and showed limited solubility even upon the addition of DMSO. For this reason, their cytotoxicity was not investigated. On the contrary, the bis-coordinated complexes 7-12 were highly water soluble. For this reason, the cytotoxicity of only 7-12 towards cancerous human adenocarcinomic alveolar basal epithelial (A549), the corresponding cisplatin resistant version (A549R) and non-cancerous human liver (LO2) cells was investigated using a 3-(4,5dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay (Table 3). Previous studies have shown that the toxicity of Cu(II) 2,2´:6´,2´´-terpyridine complexes within a cellular model is highly increased upon incubation for several days. [33] Therefore, the complexes were incubated for 44 h and, after this time, the cell viability assessed. The complexes 7-9, 11-12

were found to be cytotoxic in the nanomolar range (IC50 = 150-1030 nM) in A549 cells. As an exception, the carboxylic acid functionalized compound 10 was significantly less toxic (IC50 = 38.92±4.50 μM). As the Cu complexes showed a similar cytotoxic effect in the non-cancerous cell line LO2, no selectivity for cancerous cells was observed. Promisingly, all complexes showed a comparable effect in the cisplatin resistant cell line A549R, indicating that these compounds could potentially be useful to overcome drug resistance. As the lead structure of this study, complex 7 was identified with a cytotoxicity in the nanomolar range (IC50 = 80-180 nM). These results are very encouraging as this compound is 82-times more cytotoxic in A549 The complexes, except for the carboxylic acid functionalised derivative, were found to have a cytotoxicity in the nanomolar range, an order of magnitude more toxic than the clinically applied anticancer agent cisplatin. Promisingly, the compounds had an equal effect in the corresponding cisplatin resistant cancer cell line, making them potentially useful for applications to overcome drug resistant cancers.

  Considering these promising results, herein, a series of terminally functionalised complexes of the type [Cu(2,2´:6´,2´´-terpyridine)(Cl)2] 1-6 and [Cu(2,2´:6´,2´´-terpyridine)2][NO3]2 7-12

[

  Cu(terpy-H)(Cl) 2 ] (1): Yield: 73%, ESI-HRMS (pos. detection mode): calcd for C15H11Cl1CuN3 m/z [M-Cl] + 330.9932; found: 330.9932, FT-IR: 3014 (brw), 1597 (m), 1578 (w), 1475 (m), 1448 (s), 1329 (w), 1304 (w), 1255 (w), 1167 (w), 1034 (w), 1020 (m), 791 (m), 769 (s), 748 (m), 729 (m) cm -1 , Elemental analysis calcd for C15H11Cl2CuN3 (%): C 48.97, H 3.02, N 11.43; found: C 49.15, H 3.24, N 11.27. [Cu(terpy-Cl)(Cl) 2 ] (2):Yield: 82%, FT-IR: 3012 (brw), 1597 (m), 1578 (w), 1473 (m), 1446 (s), 1324 (w), 1301 (w), 1255 (w), 1167 (w), 1033 (w), 1020 (m), 791 (m), 770 (s), 748 (m), 730 (m) cm -1 , ESI-HRMS (pos. detection mode): calcd for C15H10Cl2CuN3 m/z [M-Cl] + 364.9542; found: 364.9541, Elemental analysis calcd for C15H10Cl3CuN3 (%): C 44.78, H 2.51, N 10.45; found: C 44.97, H 2.63, N 10.28. [Cu(terpy-Br)(Cl) 2 ] (3): Yield: 68%, FT-IR: 3043 (brw), 1585 (m), 1556 (m), 1471 (m), 1414 (s), 1246 (w), 1109 (w), 1020 (m), 891 (m), 787 (s), 748 (m), 729 (m) cm -1 , ESI-HRMS (pos. detection mode): calcd for C15H10BrClCuN3 m/z [M-Cl] + 408.9037; found: 408.9037, Elemental analysis calcd for C15H10BrCl2CuN3 (%): C 40.32, H 2.26, N 9.41; found: C 40.60, H 2.07, N 9.39. [Cu(terpy-COOH)(Cl) 2 ] (4): Yield: 41%, FT-IR: 3012 (brw), 1709 (m), 1603 (m), 1570 (m), 1471 (m), 1417 (s), 1387 (m), 1301 (m), 1190 (s), 1151 (m), 1109 (w), 1018 (m), 874 (m), 799 (m), 766 (s), 723 (m), 706 (m), 729 (m), 671 (s) cm -1 , ESI-HRMS (pos. detection mode): calcd for C16H11ClCuN3O2 m/z [M-Cl] + 374.9830; found: 374.9831, Elemental analysis calcd for C16H11Cl2CuN3O2 (%): C 46.65, H 2.69, N 10.21; found: C 46.83, H 2.88, N 10.34. [Cu(terpy-OMe)(Cl) 2 ] (5): Yield: 56%, FT-IR: 3012 (brw), 1600 (m), 1572 (w), 1479 (m), 1436 (m), 1416 (m), 1373 (m), 1228 (s), 1161 (w), 1059 (m), 1036 (s), 1018 (m), 874 (w), 796 (s), 750 (m), 729 (m) cm -1 , ESI-HRMS (pos. detection mode): calcd for C16H13ClCuN3O m/z [M-Cl] + 361.0038; found: 361.0040, Elemental analysis calcd for C16H13Cl2CuN3O (%): C 48.29, H 3.30, N 10.57; found: C 48.53, H 3.47, N 10.34. [Cu(terpy-NMe 2 )(Cl) 2 ] (6): Yield: 74%, FT-IR: 3475 (w), 3404 (w), 3028 (brw), 1616 (s), 1570 (w), 1541 (m), 1475 (m), 1432 (m), 1416 (m), 1391 (w), 1303 (w), 1153 (w), 1051 (w), 1026 (s), 849 (m), 795 (s), 750 (w), 721 (w), 692 (w) cm -1 , ESI-HRMS (pos. detection mode): calcd for C17H16ClCuN4 m/z [M

[

  Cu(terpy-COOH) 2 ][NO 3 ] 2 (10): Yield: 57%, FT-IR: 3531 (brw), 3463 (brw), 3064 (brw), 1706 (m), 1625 (m), 1606 (w), 1562 (w), 1475 (w), 1388 (s), 1317 (s), 1295 (s), 1284 (s), 1236 (m), 1022 (m), 1008 (m), 827 (m), 798 (s), 752 (w), 728 (w) cm -1 , ESI-HRMS (pos. detection mode): calcd for C32H22CuN6O4 m/z [M] 2+ 308.5494; found: 308.5482, Elemental analysis calcd for C32H22CuN8O10 (%): C 51.79, H 2.99, N 15.10; found: C 52.09, H 3.16, N 15.04. [Cu(terpy-OMe) 2 ][NO 3 ] 2 (11): Yield: 88%, FT-IR: 3511 (brw), 3442 (brw), 3076 (brw), 1616 (m), 1603 (w), 1574 (w), 1562 (w), 1481 (m), 1438 (m), 1417 (m), 1346 (s), 1309 (s), 1228 (s), 1157 (m), 1037 (m), 1008 (m), 829 (w), 776 (s), 734 (w) cm -1 , ESI-HRMS (pos. detection mode): calcd for C32H26CuN6O2 m/z [M] 2+ 294.5701; found: 294.5698, Elemental analysis calcd for C32H26CuN8O8 (%): C 53.82, H 3.67, N 15.69; found: C 53.71, H 3.50, N 15.47. [Cu(terpy-NMe 2 ) 2 ][NO 3 ] 2 (12): Yield: 74%, FT-IR: 3519 (brw), 3436 (brw), 3089 (brw), 1622 (m), 1604 (w), 1571 (w), 1556 (m), 1537 (m), 1469 (m), 1438 (m), 1432 (m), 1392 (m), 1344 (s), 1301 (w), 1157 (w), 1028 (m), 1006 (m), 998 (m), 848 (m), 815 (w), 789 (s), 744 (w), 731 (w) cm -1 , ESI-HRMS (pos. detection mode): calcd for C34H32CuN8 m/z [M] 2+ 307.6017; found: 307.6010, Elemental analysis calcd for C34H32CuN10O6 (%): C 55.17, H 4.36, N 18.92; found: C 54.93, H 4.54, N 18.68.

complexes 1 [Figure 1 .

 11 Figure 1. Chemical structures of the terminally-functionalised complexes of the type [Cu(2,2´:6´,2´´-terpyridine)(Cl)2] 1-6 and [Cu(2,2´:6´,2´´-terpyridine)2][NO3]2 7-12. The biscoordinated complexes were isolated as nitrate salts.

Figure 2 .

 2 Figure 2. The molecular structure of 3, 5, 6, 7 and 11. Solvent molecules and hydrogen atoms are excluded for clarity. For 5 and 6, only one of the two crystallographically independent Cu(II) molecules is presented.

33

 33

  In this study, we report on the synthesis, characterisation and biological evaluation of Cu(II) 2,2´:6´,2´´-terpyridine complexes as potential anticancer agents. Terminally functionalised metal complexes of the type [Cu(2,2´:6´,2´´-terpyridine)(Cl)2] and [Cu(2,2´:6´,2´´terpyridine)2][NO3]2 were synthesised and characterized by HR-MS and IR spectroscopy.Several compounds were further characterised by single crystal X-ray diffraction studies. Due to poor water solubility of the mono-coordinated complexes, only the bis-coordinated complexes were investigated in a human adenocarcinomic alveolar basal epithelial cell model.

terpy-H) 2 ][NO 3 ] 2 (7):

  -Cl] + 374.0354; found: 374.0354, Elemental analysis calcd for C17H16Cl2CuN4 (%): C 49.68, H 3.93, N 13.64; found: C 49.96, H 4.13, N 13.35. Yield: 67%, FT-IR: 3489 (brw), 3079 (brw), 1600 (w), 1575 (w), (m), 775 (s), 735 (m) cm -1 , ESI-HRMS (pos. detection mode): calcd for C30H22CuN6 m/z [M] 2+ 264.5595; found: 264.5596, Elemental analysis calcd for C30H22CuN8O6 (%): C 55.09, H 3.39, N 17.13; found: C 55.30, H 3.42, N 16.97. 2+ 343.4690; found: 343.4679, Elemental analysis calcd for C30H20Br2CuN8O6 (%): C 44.38, H 2.48, N 13.80; found: C 44.31, H 2.62, N 13.74.

	[Cu(terpy-Cl) 2 ][NO 3 ] 2 (8): Yield: 88%, FT-IR: 3529 (brw), 3464 (brw), 3070 (brw), 1594 (m),
	1574 (w), 1560 (w), 1475 (w), 1419 (s), 1342 (s), 1305 (s), 1274 (s), 1241 (m), 1112 (w), 1018
	(s), 827 (s), 798 (s), 752 (w), 729 (w) cm -1 , ESI-HRMS (pos. detection mode): calcd for
	C30H20Cl2CuN6 m/z [M] 2+ 298.5206; found: 298.5202, Elemental analysis calcd for
	C30H20Cl2CuN8O6 (%): C 49.84, H 2.79, N 15.50; found: C 50.15, H 2.84, N 15.73.
	[Cu(terpy-Br) 2 ][NO 3 ] 2 (9): Yield: 82%, FT-IR: 3457 (brw), 3068 (brw), 1587 (m), 1571 (w),
	1558 (m), 1473 (m), 1417 (s), 1338 (s), 1308 (s), 1280 (s), 1245 (m), 1113 (w), 1018 (m), 1008
	(m), 875 (w), 829 (w), 791 (s), 748 (w), 727 (w) cm -1 , ESI-HRMS (pos. detection mode): calcd
	for C30H20Br2CuN6 m/z [M]

[Cu(

Table 1 .

 1 Selected geometrical parameters for 3, 5 and 6. two crystallographically independent copper(II) molecules per asymmetric unit b basal plane formed by the three nitrogen atoms and the basal chlorine atom c deviation from the basal plane

		3		5 a		6 a
	Cu-N central (Å)	1.9718(16)	1.9484(12)	1.9503(12) 1.9349(18) 1.9356(19)
	Cu-N lateral (Å)	2.0428(16)	2.0413(13)	2.0497(13)	2.0407(19)	2.0448(15)
		2.0442(17)	2.0604(13)	2.0538(13)	2.0503(19)	2.0490(19)
	Cu-Cl basal (Å)	2.2534(5)	2.2362(4)	2.2493(4)	2.2337(6)	2.2302(6)
	Cu-Cl apical (Å)	2.4642(5)	2.4921(4)	2.4939(4)	2.5678(6)	2.5501(7)
	Cl-Cu-Cl (deg.)	104.532(19)	104.514(16) 105.314(15)	98.75(2)	99.00(2)
	r.m.s. deviation b Cu (Å) c Cl apical (Å) c	0.1110 0.3479(8) 2.8049(9)	0.0795 0.2930(6) 2.7735(7)	0.0937 0.3314(6) 2.8104(7)	0.0655 0.2748(9) 2.8405(10)	0.0602 0.2724(9) 2.8201(10)
	shortest	3.573	3.493	3.634
	centroid…centroid (Å)
	slippage (Å)	1.083	0.925	1.175

a

Table 2 .

 2 Selected geometrical parameters for 7 and 11.

		7a	11
	Cu-N1 (Å) Cu-N2 (Å)	2.1876(19) a 1.990(3) a	2.2474(14) 2.0059(14)
	Cu-N3 (Å)		2.2843(14)
	Cu-N4 (Å)		2.0999(14)
	Cu-N5 (Å)		1.9486(14)
	Cu-N6 (Å)		2.0907(13)
	dihedral angle (deg.)	90	87.24(3)
	shortest centroid…centroid	3.634	4.106
	(Å)
	slippage (Å)	1.175	-

a the Cu atom lies on several special positions: a two fold axis and a rotoinversion four-fold axis b between the mean planes of the terpyridyl ligands

Table 3 .

 3 cells and 242-times more cytotoxic in its drug resistant version A549R than the clinically approved drug cisplatin. Recent studies have demonstrated that structurally related Cu(II) 2,2´:6´,2´´-terpyridine complexes trigger cell death by necrosis or apoptosis.[33] IC50 values (μM) of the bis-coordinated Cu(II) complexes 7-12 against cancerous human adenocarcinomic alveolar basal epithelial (A549), cisplatin resistant human adenocarcinomic alveolar basal epithelial (A549R) and non-cancerous human liver (LO2) cells.

	Compound	A549	A549R	LO2
	7	0.15 ± 0.01	0.18 ± 0.07	0.08 ± 0.01
	8	0.59 ± 0.05	0.64 ± 0.04	0.23 ± 0.02
	9	1.03 ± 0.07	0.93 ± 0.11	0.52 ± 0.06
	10	38.92 ± 4.50	40.02 ± 3.56	21.35 ± 0.95
	11	0.73 ± 0.03	0.60 ± 0.08	0.37 ± 0.01
	12	0.87 ± 0.09	0.95 ± 0.16	0.35 ± 0.04
	cisplatin	12.35 ± 1.23	43.5 ± 3.93	16.75 ± 2.

ACKNOWLEDGEMENTS

This work was financially supported by an ERC Consolidator Grant PhotoMedMet to G.G. (GA 681679), has received support under the program Investissements d' Avenir launched by the French Government and implemented by the ANR with the reference ANR-10-IDEX-0001-02 PSL (G.G.), the National Science Foundation of China (Nos. 21525105 and 21778079 for H.C.) and the 973 Program (No. 2015CB856301 for H.C.).