M Kassem

I Alekseev

M Bokova

D Le Coq

E Bychkov

Ionic-to-Electronic Conductivity Crossover in CdTe-AgI-As 2 Te 3 Glasses: An 110m Ag Tracer Diffusion Study

Conductivity isotherms of (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses (0.0 ≤ x ≤ 0.15) reveal a non-monotonic behavior with increasing CdTe content reminiscent of mixed cation effect in oxide and chalcogenide glasses. Nevertheless, the apparent similarity appears to be partly incorrect. Using 110m Ag tracer diffusion measurements, we show that semiconducting CdTe additions produce a dual effect: (i) decreasing the Ag + ion transport by a factor of ≈200 with a simultaneous increase of the diffusion activation energy, and (ii) increasing the electronic conductivity by 1.5 orders of magnitude. Consequently, the conductivity minimum at x = 0.05 reflects an ionic-to-electronic transport crossover; the silver ion transport number decreases by three orders of magnitude with increasing x.

INTRODUCTION

Tracer diffusion experiments have been widely used in the past to study ion transport in oxide glasses. [START_REF] Terai | Ionic Diffusion in Glasses[END_REF][START_REF] Frischat | Ionic Diffusion in Oxide Glasses[END_REF][START_REF] Natrup | Cation Diffusion and Ionic Conductivity in Soda-Lime Silicate Glasses[END_REF][START_REF] Mehrer | Diffusion and Ionic Conduction in Oxide Glasses[END_REF] Among the most important results found previously, we should note: (i) the diffusion coefficients of alkali cations are significantly higher than those of alkalineearth ions, oxygen species, or glass-forming elements (Si, Al ...); (ii) a diffusivity crossover in the mixed alkali glasses; (iii) the Haven ratio HR varies systematically, 0.2 ≤ HR ≤ 1, depending on the mobile ion content. Nevertheless, until recently, diffusion measurements in chalcogenide glasses were rather scarce. [START_REF] Kawamoto | Silver Diffusion in As2S3-Ag2S, GeS2-GeS-Ag2S and P2S5-Ag2S Glasses[END_REF][START_REF] Kazakova | A Study of Silver-Containing Chalcogenide Glasses[END_REF][START_REF] Thomas | Tracer Diffusion and Electrical Conductivity in Sodium-Rubidium Silicon Sulfide Glasses[END_REF] However, during the last decade, several diffusion studies combining both electrical conductivity and radioactive tracer diffusion D* were presented; thus highlighting phenomena that could not be reached by electrical measurements alone. [START_REF] Bychkov | Percolation Transition in Ag-Doped Germanium Chalcogenide-Based Glasses: Conductivity and Silver Diffusion Results[END_REF][START_REF] Bychkov | Percolation Transition in Ag-Doped Chalcogenide Glasses: Comparison of Classical Percolation and Dynamic Structure Models[END_REF][START_REF] Drugov | Ag Tracer Diffusion Study of Percolation Transition in Ag2S-As2S3 Glasses[END_REF][START_REF] Bychkov | 64 Cu Tracer Diffusion in Copper Chalcogenide Glasses[END_REF][START_REF] Bychkov | Ionic Diffusion and Local Hopping in Copper Chalcohalide Glasses Measured Using 64 Cu Tracer and 129 I-Mössbauer Spectroscopy[END_REF][START_REF] Bychkov | EXAFS Studies of Cu + Ion Conducting and Semiconducting Copper Chalcogenide and Chalcohalide Glasses[END_REF][START_REF] Bolotov | Degenerated Mixed Cation Effect in CuI-AgI-As2Se3 Glasses: 64 Cu and 110 Ag Tracer Diffusion Studies[END_REF] Recently, chalcogenide glasses in the ternary system CdTe-AgI-As2Te3 [START_REF] Kassem | New Chalcogenide Glasses in the CdTe-AgI-As2Te3 System[END_REF] were synthesized, and the effect of CdTe semiconductor additives on transport and physical properties of binary AgI-As2Te3 glasses has been investigated. [START_REF] Bobylev | Electrical Properties of Glasses in the AgI-As2Te3 System[END_REF][START_REF] Alekseev | Ionic and Electronic Transport in AgI-As2Te3 Glasses[END_REF] The glass-forming range for (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 compositions was found to be limited to x ≤ 0.15. The glass transition temperature Tg decreases in the range 0.0 ≤ x ≤ 0.1 and remains constant with further increasing x. More importantly, the electrical properties of cadmium telluride glasses exhibit a non-monotonic behavior with (i) diminished (x ≤ 0.05) and (ii) enhanced total conductivity σdc (x > 0.05), reminiscent of mixed cation effect in oxide and chalcogenide glasses. Semiconducting CdTe additions were assumed to produce two distinct phenomena: (i) a decrease of the ionic conductivity by blocking the Ag + ion transport within the preferential conduction pathways, and (ii) an increase of the electronic conductivity caused by Te 5p lone-pair electronic states in the top of the valence band.

The present paper deals with 110m Ag tracer diffusion measurements in the ternary (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses, which would allow to obtain a detailed information on the ionic and electronic components of the charge transport.

EXPERIMENTAL DETAILS

Glass Preparation

(CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 samples (x = 0, 0.01, 0.025, 0.05, 0.075, 0.10, 0.125, 0.15, 0.17, 0.20) were prepared using the appropriate proportions of CdTe, AgI and As2Te3. The starting materials were sealed under vacuum (10 -6 mbar) in a cleaned silica tube (8 mm ID and 1 mm wall thickness), heated slowly in a rocking furnace to 850 °C at 5 K min -1 heating rate, maintained at this temperature for 24 hours, then cooled down to 650 °C before quenching in cold salt/water mixture. Several three-gram samples were obtained for each composition. Further synthesis details and properties characteristic to this telluride system are published elsewhere. [START_REF] Kassem | New Chalcogenide Glasses in the CdTe-AgI-As2Te3 System[END_REF]

Conductivity Measurements

Total electrical conductivity of the samples was measured using a Hewlett Packard 4194A impedance meter. The impedance modulus Z and the phase angle θ were obtained in the frequency range from 100 Hz to 15 MHz at temperatures between 293 and 378 K, the maximum temperature was below Tg for the glass samples. [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] The quenched samples, prepared as rectangular plates, were polished using SiC powder (9.3 µ grain size). The sample sides were ground parallel and gold was deposited on opposite sides to form electrodes for conductivity experiment, i.e., the electrochemical cell for conductivity measurements was Au|glass|Au. Typical thickness and area of the samples were in the range of 0.7-1.5 mm and 6-8 mm 2 , respectively. Further details of conductivity measurements are published previously. [START_REF] Kassem | New Chalcogenide Glasses in the CdTe-AgI-As2Te3 System[END_REF][START_REF] Bobylev | Electrical Properties of Glasses in the AgI-As2Te3 System[END_REF][START_REF] Alekseev | Ionic and Electronic Transport in AgI-As2Te3 Glasses[END_REF][START_REF] Kassem | Chemical and Structural Origin of Conductivity Changes in CdSe-AgI-As2Se3 Glasses[END_REF]

110m Ag Tracer Experiments

The 110m Ag tracer (the half-life t½ = 249.76 d) was produced by the 109 Ag(n,γ) 110m Ag nuclear reaction in a research reactor of St. Petersburg Nuclear Physics Institute using thermal neutrons with an average flux of 8.0(2) × 10 13 n cm -2 s -1 . For each composition, samples having the same conductivity parameters within the experimental uncertainty were used in diffusion experiments. Measurements were carried out using thin-layer geometry. A drop of radioactive 110m AgN03 solution was deposited onto one face of the sample, kept there for 2 h, wiped with a filter paper, washed with distilled water and ethyl alcohol, and then dried. The sample was wrapped in aluminium foil and encapsulated in a Pyrex tube. The samples were annealed in a furnace at 20 to 115 °C for a period of several hours to 60 days. The diffusion anneals were terminated by quenching the samples in air. The sides of the sample parallel to the diffusion direction were ground to eliminate surface diffusion effects. The sample was then sectioned on a parallel grinder. The thickness of each section was determined either from the density, cross-sectional area and weight change of the sample, or by direct thickness measurements. In the latter case, the thickness uncertainty was ± 5 µm. Further details on tracer diffusion measurements were published elsewhere. [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF]

RESULTS AND DISCUSSION

Tracer Diffusion Results

Penetration profiles for 110m Ag tracer diffusion in the CdTe-AgI-As2Te3 glasses obey the usual solution of Fick's law for an infinitesimally thin deposit of radioactive isotope on a semi-infinite specimen 2 :

) erf( ) , ( 1 0 q A t y A = - , (1)
where

t D y q Ag 2 = , (2)
A(y,t) is the residual activity of the sample after a thickness y was removed, t is the diffusion anneal time, A0 is the initial residual activity, DAg is the tracer diffusion coefficient, and erf(q) is the Gauss error function. Experimentally determined values of A(y,t) and A0 yield q values which, when plotted vs. y, produce a straight line passing through the origin, Figure 1.

The silver tracer diffusion coefficients DAg, determined from the slope of the penetration profiles, are given in Figure 2, plotted as log DAg versus T -1 . Figure 2 shows that the temperature dependences of the tracer diffusion coefficient are in good agreement with Arrhenius-type activation dependence

) exp( d 0 kT E D D - = , ( 3
)
where D0 is the diffusion pre-exponential factor, Ed the diffusion activation energy, k and T have their usual meaning. The derived diffusion parameters D298, Ed and D0 were calculated from a least-square fit of the data to Equation (3). D298 corresponds to roomtemperature silver tracer diffusion coefficient DAg. The results are listed in Table 1 and shown in Figure 3.

The 110m Ag tracer diffusion coefficient decreases monotonically by 2.3 orders of magnitude with increasing x from 6.8 × 10 -11 cm 2 s -1 (x = 0) to 3.8 × 10 -13 cm 2 s -1 (x = 0.15) at room temperature (Table 1). Fig. 3a shows that the conductivity and tracer diffusion isotherms for the ternary CdTe-AgI-As2Te3 glasses are significantly different, especially at x ≥ 0.05. These results are consistent with our previous assumption [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] that the ternary glasses, depending on x, are either mixed or predominantly electronic conductors. Fig. 3b shows that the diffusion activation energy Ed increases simultaneously from 0.47 eV to 0.68 eV. Meanwhile, the pre-exponential factor D0 increases by a factor of 15 with increasing x, Fig. 3c. Similar increase of D0 was also observed in the (CdSe)x(AgI)0.5-x/2(As2Se3)0.5-x/2 system. [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] The diffusion pre-exponential factor is proportional to the attempt frequency ߥ , the jump distance ℓ, and the activation entropy for the jump of a mobile ion

Δܵ # ܦ ∝ ߥ ℓ ଶ exp (∆ܵ # /݇), ( 4
)
where ݇ is the Boltzmann constant. Neglecting the entropy term, the ܦ increase may be related either to higher ߥ , or to longer ℓ. Taking into account the proposed immobilization of some Ag + cations by cadmium species within the preferential conduction pathways in the CdSe-AgI-As2Se3 glasses [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] , the effective jump distance is expected to increase with x, thus increasing ܦ .

Apparent Haven Ratio

The Haven ratio HR is a simple experimental parameter easily accessible from a combined (tracer diffusion coefficient D and ionic conductivity σi) experiment or from a single electro-diffusion or Chemla measurement. Since the total conductivity σdc, measured using impedance spectroscopy, is not purely ionic, i.e., the silver ion transport number tAg + < 1, we cannot calculate the Haven ratio HR 20

σ D D H Ag R = , ( 5
)
where σ D is the conductivity diffusion coefficient calculated from the ionic conductivity i σ using the Nernst-Einstein relation

2 ) (ze N kT D i σ σ = , ( 6
)
where N is the concentration of the mobile species, ze is the electric charge of the carrier ion, and k and T have their usual meaning. However, we have calculated the apparent Haven ratio tAg + HR using the usual definition of the ion transport number

dc i Ag t σ σ + = (7)
By combining the equations 5, 6 and 7, the apparent Haven ratio tAg + HR can be expressed as:

σ kT ze N D H t Ag R Ag 2 ) ( = + (8)
The calculated tAg + HR are presented in Figure 4 as a function of temperature and their average values are also given in Table 1. The apparent Haven ratio decreases significantly with x from tAg + HR = 0.16±0.02 for the x = 0 glassy host, (AgI)0.5(As2Te3)0.5, to tAg + HR = (3.7±0.8)×10 -4 for the x = 0.15 glass at the limit of the glass-forming range. Since the overall changes of the Haven ratio in glasses and crystals are limited, 0.2 ≤ HR ≤ 1 (see for example, references [START_REF] Terai | Ionic Diffusion in Glasses[END_REF][START_REF] Frischat | Ionic Diffusion in Oxide Glasses[END_REF][START_REF] Bychkov | Percolation Transition in Ag-Doped Germanium Chalcogenide-Based Glasses: Conductivity and Silver Diffusion Results[END_REF][START_REF] Alekseev | Ionic and Electronic Transport in AgI-As2Te3 Glasses[END_REF][START_REF] Murch | The Haven Ratio in Fast Ionic Conductors[END_REF] and references therein), doping with CdTe results in a remarkable decrease of tAg + , at least by two or three orders of magnitude, discussed in details in the next section.

Ionic versus Electronic Transport

Analysis of the total conductivity σdc and 110m Ag tracer diffusion DAg allows the ionic and electronic transport to be distinguished. Figure 5a shows the room-temperature conductivity σdc and its ionic counterpart HRσAg + , calculated from DAg using Equations ( 5)

and (6). The two activation energies and pre-exponential factors are compared in Fig. 5b and Fig. 5c.

A non-monotonic change in σdc accompanied by a shallow maximum in the conductivity activation energy E σ seems to be related to a crossover from the mixed conducting glasses with a significant contribution of the Ag + ion transport to the CdTe-rich vitreous alloys having predominantly electronic conductivity. Similar phenomenon was observed in the binary (AgI)z(As2Te3)1-z glassy system with variable silver iodide content z. [START_REF] Bobylev | Electrical Properties of Glasses in the AgI-As2Te3 System[END_REF][START_REF] Alekseev | Ionic and Electronic Transport in AgI-As2Te3 Glasses[END_REF] The AgI-poor glasses are essentially electronic conductors but the Ag + ion transport becomes predominant at z ≥ 0.4. The most concentrated (AgI)0.6(As2Te3)0.4 and (AgI)0.8(As2Te3)0.2 glasses appear to be nearly pure ionic conductors with tAg + ≅ 1 and tAg + >> te, where te = tn + tp is the electron transport number of n-and/or p-type. [START_REF] Alekseev | Ionic and Electronic Transport in AgI-As2Te3 Glasses[END_REF] Using the apparent Haven ratio tAg + HR for the ternary glasses, we can estimate the silver ion transport numbers tAg + in this system. The Haven ratio for the ion-conducting glass (AgI)0.6(As2Te3)0.4, HR = 0.44±0.08, is very similar to those for AgI-rich superionic (AgI)z(As2Se3)1-z vitreous alloys, HR = 0.40±0.04 at z ≥ 0.4. [START_REF] Alekseev | Ionic and Electronic Transport in AgI-As2Te3 Glasses[END_REF][START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] Assuming that the (AgI)0.5(As2Te3)0.5 glass also has HR = 0.44, the calculated tAg + values vary between 0.8 and 0.2 for this particular composition, Figure 6.

The observed decrease of tAg + with increasing temperature is expected since the diffusion activation energy Ed is lower than E σ , Fig. 5b. In other words, the electronic conductivity increases faster with increasing temperature than the ionic transport, resulting in a tAg + decrease, ݐ߲ శ ߲ܶ ൗ < 0. In addition, we have observed earlier that the mixed conducting silver selenide and silver telluride glasses are characterized by higher values of the activation energy and pre-exponential factor related to electronic or hole transport. [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF][START_REF] Vlasov | Compositional Dependence of Ionic Conductivity and Diffusion in Mixed Chalcogen Ag-Containing Glasses[END_REF][START_REF] Vlasov | Ionic and Electronic Conductivity in the Copper-Silver-Arsenic-Selenium Glasses[END_REF] In ion-conducting (CdSe)x(AgI)0.5-x/2(As2Se3)0.5-x/2 glasses, the Haven ratio increases with x from HR = 0.4 to 0.7. [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] Assuming similar trend for the ternary telluride system, we have calculated the silver ion transport numbers. The room temperature tAg + values, shown in Figure 7, decrease exponentially with x from 0.67±0.15 (x = 0) to (6.6±1.8)×10 -4 (x = 0.15), i.e., by 3 orders of magnitude. The calculated tAg + was used to divide the total conductivity σdc into ionic σAg + and electronic σe parts, Figure 8.

The binary x = 0 glassy host, (AgI)0.5(As2Te3)0.5, is a mixed conductor with a significant contribution of the Ag + ion conductivity, tAg + = 0.67±0.15. Semiconducting CdTe additions induce two opposite processes: (1) a remarkable exponential decrease of the ion transport by a factor of ≈200; and (2) a monotonic increase of the electronic conductivity by ≈1.5 orders of magnitude. The crossover between the two regimes is reflected by a non-monotonic change in σdc. The electronic conductivity increase with x is caused by Te 5p lone-pair electronic states in the top of the valence band. [START_REF] Mott | Electronic Processes in Non-Crystalline Materials[END_REF]

Suppression of the Ion Transport

We have already reported similar decrease of the ionic conductivity σi and 110m Ag tracer diffusion DAg with increasing x in the ternary selenide system (CdSe)x(AgI)0.5-

x/2(As2Se3)0.5-x/2. 18,19 Comparing the ion transport parameters with those for the binary superionic AgI-As2Se3 glasses, it was found that the ternary glasses with the same silver concentration exhibit much lower σi and DAg. A comparable effect is observed for the binary AgI-As2Te3 and ternary CdTe-AgI-As2Te3 glasses, Figure 9. The diffusion coefficient at 25 °C, D298, for the ternary CdTe-rich glass (x = 0.15) appears to be lower by ≈2 orders of magnitude in comparison with its binary counterpart, Fig. 9a. The respective diffusion activation energy is higher by 0.2 eV, Fig. 9b.

The remarkable suppression of the Ag + ion transport with increasing CdTe content can also have chemical and structural origin similar to that in the selenide system. [START_REF] Kassem | Chemical and Structural Origin of Conductivity Changes in CdSe-AgI-As2Se3 Glasses[END_REF][START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] The exchange reaction CdTe + 2AgI ⇄ CdI2 + Ag2Te in the glass-forming melt may lead to a mixed silver environment. As a result, the Ag + ion mobility within the mixed iodide/telluride conduction pathways decreases. Nevertheless, the quantitative analysis of the chemical effect does not reproduce the observed ion transport changes in the ternary selenide glasses. [START_REF] Kassem | Chemical and Structural Origin of Conductivity Changes in CdSe-AgI-As2Se3 Glasses[END_REF] At x < 0.2, a significant difference still exists between the simulated and experimental conductivity. A non-random mixing of cadmium and silver species in the ternary glass network appears to be the basis of an additional and/or alternative structural interpretation. Cd-related structural units do not form separate domains but are positioning within the preferential conduction pathways built-up by Ag-related polyhedra. Immobile or slow Cd 2+ ions will affect the Ag + ion dynamics by restricting the number of accessible empty sites thus reducing the ionic conductivity. The observed increase of the Haven ratio in the selenide system with increasing x is consistent with the non-random mixing but implies immobilisation of some neighboring Ag + cations by a Cd 2+ ion. [START_REF] Alekseev | 110 Ag Tracer Diffusion Studies of CdSe-AgI-As2Se3 Glasses[END_REF] Both chemical and structural reasons of the Ag + ion transport suppression need further experimental verification in the ternary telluride system. The experimental conductivity and diffusion data alone do not allow any reliable evidence in favor of either hypothesis to be provided. High-energy x-ray diffraction results could provide a clue for solving the problem.

Transport Properties in the Telluride and Selenide Ternary Systems

The two ternary (CdX)x(AgI)0.5-x/2(As2X3)0.5-x/2 systems, where X = Se or Te, exhibit many similarities and characteristic differences in transport properties, Figure 10. First, the telluride glasses, as the vast majority of vitreous tellurides [START_REF] Mott | Electronic Processes in Non-Crystalline Materials[END_REF][START_REF] Zhang | Chalcogenide Glasses: Preparation, properties and applications[END_REF] , have a significantly higher electronic conductivity compared to their selenide counterparts, ≈2 orders of magnitude at 25 °C, Fig. 10a. The observed difference is caused by Te 5p lone-pair electron states forming the top of the valence band in telluride alloys compared to lower lying Se 4p lone pairs. [START_REF] Mott | Electronic Processes in Non-Crystalline Materials[END_REF][START_REF] Kolobov | Metastability and Phase Change Phenomena[END_REF] On the contrary, the ionic conductivity and silver tracer diffusion coefficient are by a factor of 100 to 300 higher in the selenide ternaries, Fig. 10b, accompanied also by lower activation energy. Similar decrease of DAg was reported earlier for mixed chalcogen Ag-As-Se-Te glasses [START_REF] Vlasov | Compositional Dependence of Ionic Conductivity and Diffusion in Mixed Chalcogen Ag-Containing Glasses[END_REF] , when Se was progressively replaced by Te. Only the intermediate compositions with Te fraction r = Te/(Se+Te) in the range of 0.05 ≤ r ≤ 0.35, have shown a non-monotonic change in DAg, attributed to a mixed anion effect. The reason of the observed difference in the magnitude of σi and DAg between telluride and selenide systems is not yet clear. Detailed structural studies are needed to compare the connectivity of Ag-related sub-network in the two families. Finally, the effect of CdX (X = Se or Te) additions is identical for the two systems. Semiconducting cadmium chalcogenides increase the electronic conductivity and decrease the ionic one. Even quantitatively, the observed changes are similar: DAg decreases of 2-2.5 orders of magnitude and σe increases by a factor of 10-30.

CONCLUSIONS

The 110m Ag tracer diffusion coefficient in the (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses (0.0 ≤ x ≤ 0.15) decreases by a factor of ≈200 with increasing x from 6.8×10 -11 cm 2 s -1 (x = 0.0) to 3.8×10 -13 cm 2 s -1 (x = 0.15) at room temperature. The DAg decrease is accompanied by a simultaneous increase of the diffusion activation energy from 0.47 eV to 0.68 eV and the diffusion pre-exponential factor by a factor of 15. The combined analysis of diffusion and conductivity data shows a significant decrease of the silver ion transport number by three orders of magnitude with increasing x. The suppression of the Ag + ion transport accompanied by a simultaneous increase of the electronic conductivity causes an ionic-to-electronic transport crossover in cadmium telluride glasses; the CdTe-rich vitreous alloys become nearly pure electronic conductors.

List of Figures

        - = - 0 1 ) , ( 1 A t y A erf q .
2. Temperature dependences of the silver tracer diffusion coefficient for glasses in the ternary system (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2. The solid lines represent a least-square fit of the data to Equation (3). 6. Silver ion transport number tAg + plotted as a function of temperature for selected (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses, x = 0 and 0.05.

7.

Room temperature silver ion transport number tAg + for the ternary (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses plotted as a function of CdTe content.

8. Room temperature total conductivity σdc as well as its ionic σAg + and electronic σe components for the ternary CdTe-AgI-As2Te3 glasses. List of Tables Uncertainties in the last digit(s) of the parameter are given in parentheses.

The apparent Haven ratio tAg + HR averaged over the temperature range of diffusion measurements.

3 . 4 . 5 .

 345 Composition dependences of both (•) diffusion and (•) conductivity parameters for the ternary (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses: (a) room-temperature silver tracer diffusion coefficient DAg and conductivity diffusion coefficient D σ calculated using the Nernst-Einstein relation; (b) diffusion activation energy Ed; (c) diffusion pre-exponential factor D0. All solid lines are drawn as a guide to the eye. Apparent Haven ratio tAg + HR for the CdTe-AgI-As2Te3 glasses plotted as a function of temperature. Total conductivity σdc and ionic transport parameters for the ternary CdTe-AgI-As2Te3 glasses: (a) room-temperature σdc and HRσAg + ; (b) the conductivity E σ and diffusion Ed activation energies, and (c) the conductivity σ0 and recalculated diffusion HRσ0(Ag + ) pre-exponential factors. All solid lines are a guide to the eye.

9 .

 9 (a) Room temperature diffusion coefficient DAg, and (b) diffusion activation energy Ed for the binary AgI-As2Te3 17 and ternary CdTe-AgI-As2Te3 glasses plotted as a function of the silver content. The solid lines are drawn as a guide to the eye. 10. Room-temperature transport characteristics of the ternary (CdX)x(AgI)0.5x/2(As2X3)0.5-x/2 glasses, where X = Se or Te: (a) electronic conductivity; (b) 110m Ag tracer diffusion coefficient.

Fig. 1 .

 1 Fig. 1. Typical 110m Ag tracer diffusion profile for a (CdTe)0.05(AgI)0.475(As2Te3)0.475 glass annealed at 45 °C for 17 days. The penetration depth was calculated using (a) weight changes (filled circles) and (b) direct thickness measurements (open circles). The solid line shows a least-square fit of all experimental data points (open and filled circles) to Equation (2) where         -= -

Fig. 2 .

 2 Fig. 2. Temperature dependences of the silver tracer diffusion coefficient for glasses in the ternary system (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2. The solid lines represent a leastsquare fit of the data to Equation (3).

Fig. 3 .

 3 Fig. 3. Composition dependences of both (•) diffusion and (•) conductivity parameters for the ternary (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses: (a) room-temperature silver tracer diffusion coefficient DAg and conductivity diffusion coefficient calculated using the Nernst-Einstein relation; (b) diffusion activation energy Ed; (c) diffusion pre-exponential factor D0. All solid lines are drawn as a guide to the eye.

Fig. 4 .

 4 Fig. 4. Apparent Haven ratio tAg + HR for the CdTe-AgI-As2Te3 glasses plotted as a function of temperature.

Fig. 5 .

 5 Fig. 5. Total conductivity σdc and ionic transport parameters for the ternary CdTe-AgI-As2Te3 glasses: (a) room-temperature σdc and HRσAg + ; (b) the conductivity E σ and diffusion Ed activation energies, and (c) the conductivity σ0 and recalculated diffusion HRσ0(Ag + ) pre-exponential factors. All solid lines are a guide to the eye.

Fig. 6 .

 6 Fig. 6. Silver ion transport number tAg + plotted as a function of temperature for selected (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses, x = 0 and 0.05.

Fig. 7 .

 7 Fig. 7. Room temperature silver ion transport number tAg + for the ternary (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses plotted as a function of CdTe content.

Fig. 8 .

 8 Fig.8. Room temperature total conductivity σdc as well as its ionic σAg + and electronic σe components for the ternary CdTe-AgI-As2Te3 glasses.

Fig. 9 .

 9 Fig. 9. (a) Room temperature diffusion coefficient DAg, and (b) diffusion activation energy Ed for the binary AgI-As2Te3 17 and ternary CdTe-AgI-As2Te3 glasses plotted as a function of the silver content. The solid lines are drawn as a guide to the eye.

Fig. 10 .

 10 Fig. 10. Room-temperature transport characteristics of the ternary (CdX)x(AgI)0.5x/2(As2X3)0.5-x/2 glasses, where X = Se or Te: (a) electronic conductivity; (b) 110m Ag tracer diffusion coefficient.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Typical 110m Ag tracer diffusion profile for a (CdTe)0.05(AgI)0.475(As2Te3)0.475 glass annealed at 45 °C for 17 days. The penetration depth was calculated using (a) weight changes (filled circles) and (b) direct thickness measurements (open circles). The solid line shows a least-square fit of all experimental data points (open and filled circles) to Equation (2) where q = erf -1 (1-A(y,t)/A0).241x179mm (300 x 300 DPI)

Figure 4 .

 4 Figure 4. Apparent Haven ratio tAg + HR for the CdTe-AgI-As2Te3 glasses plotted as a function of temperature. 234x180mm (300 x 300 DPI)

Figure 5 .

 5 Figure 5. Total conductivity σdc and ionic transport parameters for the ternary CdTe-AgI-As2Te3 glasses: (a) room-temperature σdc and HRσAg + ; (b) the conductivity Eσ and diffusion Ed activation energies, and (c) the conductivity σ0 and recalculated diffusion HRσ0(Ag+) pre-exponential factors. All solid lines are a guide to the eye. 230x152mm (150 x 150 DPI)

Figure 6 .

 6 Figure 6. Silver ion transport number tAg + plotted as a function of temperature for selected (CdTe)x(AgI)0.5x/2(As2Te3)0.5-x/2 glasses, x = 0 and 0.05. 183x250mm (300 x 300 DPI)

Figure 7 .

 7 Figure 7. Room temperature silver ion transport number tAg + for the ternary (CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2 glasses plotted as a function of CdTe content. 174x239mm (300 x 300 DPI)

Figure 8 .

 8 Figure 8. Room temperature total conductivity σdc as well as its ionic σAg + and electronic σe components for the ternary CdTe-AgI-As2Te3 glasses. 97x129mm (220 x 220 DPI)

Figure 9 .

 9 Figure 9. (a) Room temperature diffusion coefficient DAg, and (b) diffusion activation energy Ed for the binary AgI-As2Te3 17 and ternary CdTe-AgI-As2Te3 glasses plotted as a function of the silver content. The solid lines are drawn as a guide to the eye. 410x306mm (300 x 300 DPI)

Figure 10 .

 10 Figure 10. Room-temperature transport characteristics of the ternary (CdX)x(AgI)0.5-x/2(As2X3)0.5-x/2 glasses, where X = Se or Te: (a) electronic conductivity; (b) 110m Ag tracer diffusion coefficient. 407x304mm (300 x 300 DPI)

Table 1 110m

 1 1. 110m Ag tracer diffusion parameters for the CdTe-AgI-As2Te3 glasses: the roomdiffusion coefficient D298, the diffusion activation energy Ed, the pre-exponential factor D0, and the apparent Haven ratio tAg + HR Ag tracer diffusion parameters for the CdTe-AgI-As2Te3 glasses: the room-diffusion coefficient D298, the diffusion activation energy Ed, the pre-exponential factor D0, and the apparent Haven ratio tAg + HR

	Composition	D298 (cm 2 s -1 )	Ed (eV)	D0 (cm 2 s -1 )	tAg + HR
			(CdTe)x(AgI)0.5-x/2(As2Te3)0.5-x/2
	x	[Ag] (at.%)
	0.00	14.28	6.8×10 -11	0.471(13)	6.0×10 -3	1.6(2)×10 -1
	0.05	13.87	1.3×10 -11	0.560(31)	3.6×10 -2	9.4(7)×10 -2
	0.10	13.43	2.1×10 -12	0.582(45)	1.3×10 -2	4.6(7)×10 -3
	0.15	12.98	3.8 ×10 -13	0.675(46)	9.1×10 -2	3.7(8)×10 -4

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ACKNOWLEDGMENTS

This work was supported by the European Commission within the Interreg IIIA (CTMM project) and Interreg IVA (CleanTech project) programmes and by Agence Nationale de la Recherche (ANR, France) under Grant No. ANR-15-ASTR-0016-01.

AUTHOR INFORMATION

Corresponding Author *E-mail: Mohamad.Kassem@univ-littoral.fr. Phone: +33-328-658270.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.


B Mehdaoui
email: boubker.mehdaoui@gmail.com

R Moubah

B Orayech

M Bahout

O Peña

M Jáuregui

D Saurel

A El Bouari

Structural and magnetic properties of frustrated Ga x Mn (3-x) O(1.2 ≤ x ≤ 1.6) spinels

Keywords: Spinel, Cation distribution, Ferrimagnetism, Magnetic frustration, Spin wave Stiffness parameter

We report a systematic study of the structural and magnetic properties of frustrated compounds of Ga x Mn (3-x) O 4 (1.2 ≤ x ≤ 1.6) prepared by solid-state reaction. Using Rietveld refinement of X-ray diffraction patterns and O'Neill-Navrotsky model, we demonstrate that the system Ga x Mn (3-x) O 4 (1.2 ≤ x ≤ 1.6) is an inverse spinel with low inversion parameter, in which Ga 3+ replaces Mn 3+ cations located in B-sites. The inverse magnetic susceptibility, the shape of ZFC/FC magnetization curves at low temperatures, the existence of hysteresis in all compounds, the frustration parameter and the spontaneous magnetization analysis show that the compounds with x = 1.2-1.4 exhibit a non-collinear ferrimagnetic order and the compounds with x = 1.5-1.6 exhibit a frustrated non-collinear ferrimagnetic order. Spin wave stiffness parameters were determined for each composition using the fitting results of spontaneous magnetization curves. It is demonstrated that for the compounds x = 1.2 -1.4 with a non-frustrated ferrimagnetic order, the change of spontaneous magnetization Ms(T) obeys to Bloch's law (T 3/2 ). For x = 1.5 -1.6, the compounds exhibit a frustrated ferrimagnetic order, and the Ms(T) shows a deviation from Bloch's law.

Introduction

Magnetic spinels with general formula AB 2 O 4 are a large class of oxides with remarkable magnetic properties which make them interesting for both the fundamental and technological

M A N U S C R I P T A C C E P T E D

ACCEPTED MANUSCRIPT 2 levels. They are promising in a wide range of applications such as multiferroic devices 1 , spintronics 2 , cathode materials with high energy densities 3 , microwaves 4 , sensors for ac and dc magnetic fields 5 , magnetic hyperthermia 6 , and magnetic refrigeration 7 . The diversity of their magnetic properties is associated with the complexity of their magnetic structure which leads to peculiar effects, such as magnetic frustration or multiferroicity. In spinel structure AB 2 O 4 , the A ions occupy tetrahedral sites and B ions occupy octahedral sites. The B sites form a pyrochlore network of tetrahedrons linked by their vertices; the antiferromagnetic interactions between the first neighbors B lead to strong magnetic frustration 8 . The diamondlike network A has an antiferromagnetic collinear order with long-range magnetic frustration; this frustration is due to a competition between the interactions of the first, second and third neighbors 9 , 10 . The frustration could also be originated from the chemical disorder or competition of J AA , J AB and J BB interactions, as in spin glasses 11,12 . As a consequence, the substitution in two sublattices A and B, occupied by magnetic ions, by different magnetic or diamagnetic ions, lifts a part of the degeneration and leads to magnetic states which can break the inversion symmetry and allow the appearance of fascinating physical effects 13 . In this perspective, the Mn 3 O 4 is an interesting compound to investigate the influence of ion substitution on its magnetic properties. Mn 3 O 4 crystallizes in the I4 1 /amd space group, it is a normal spinel with Mn 2+ divalent ions in tetrahedral sites (A) and Mn 3+ trivalent ions in octahedral sites (B). It shows a non-collinear magnetic order below Tc ≈ 42K 14 , while below 33K the magnetic structure is non-collinear of the Yafet-Kittel type. The moments of Mn 2+ ions (A) are directed along the [010] axis and the Mn 3+ ones (B), located in the plane (100), are divided into two sublattices, each forming an angle of 69° with the [010] axis so that the resulting B moment is antiparallel to that of the A site. Between 33 and 39K the B magnetic moments form a spiral with a propagation of the magnetic moment along the [010] axis, and between 39 and 42 K, the structure is collinear with Néel type 15 . In addition, using neutron diffraction, it was shown a complex magnetic structure with a diffuse scattering component characteristic of a short order distance which persists at room temperature due to the geometric frustration imposed by the pyrochlore network B 16 . Therefore, it is interesting to study the magnetic behavior of the Ga x Mn 3-x O 4 system (1.2 ≤ x ≤ 1.6), where the substitution takes place in the pyrochlore network, the sublattice A being occupied by a magnetic ion Mn 2+ . The synthesis and structural properties of Ga x Mn 3-x O 4 were recently studied 17 .

However, no study concerning the magnetic properties was reported on the Ga x Mn 3-x O 4 system. It is known that in spinels, the cation distribution in octahedral and tetrahedral sites strongly influences the structural and magnetic properties; the cation distribution in these two

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

sites are subjected to many factors, such as the preparation method, temperature and eventual impurities 18 . So, it is important to determine the cation distribution for each system. Several studies were made to characterize the cation distribution in spinels and related their thermodynamic properties to structural information 19 , 20 , 21 , 22 , 23 . O'Neill and Navrotsky 24 , 25 developed a thermodynamic model, widely used to calculate the cation distribution from thermodynamic constants 26 , 27 , 28 , 29 , 30 , 31 . In this work we present the synthesis of the solid solution Ga x Mn (3-x) O 4 (x = 1.2-1.6), we discuss the structural properties according to the structural parameters (cell parameters and cationic distribution), we use different models for Rietveld refinement, and O'Neill and Navrotsky's model to calculate the cationic distribution in different sites from the thermodynamic constants. We also present a study of the magnetic properties using magnetization measurements; the detailed relationship between the structural and magnetic properties was also investigated.

Experimental

Polycrystalline Ga x Mn (3-x) O 4 (0 ≤ x ≤ 2) compounds were synthesized using solid-state reaction method. Stoichiometric amounts of Mn 2 O 3 and Ga 2 O 3 (purity 99%) were mixed, grounded and annealed at 1000°C during 48h. The obtained powder was then pressed into 13 mm-diameter pellets at 377 MPa, annealed in air at 1100°C for 48h and heated at 1350°C for 24h. The cooling rate was set at 1°C/min. X-ray diffraction (XRD) measurements were performed at room temperature for all samples using Panalytical X'Pert Pro diffractometer.

The recording was carried out with a wavelength λ = 1.5405Å, in the angular range 16°< 2θ < 130° with a counting step of 0.0083°. The data were analysed using Rietveld method as implemented in the Fullprof program 32 . The changes of magnetization as function of temperature under a fixed value of applied magnetic field were performed in two temperature ranges using Quantum Design MPMS-XL5 SQUID magnetometer, from 5 -300K under an applied magnetic field of 0.1T and through zero-field cooling (ZFC) and field cooling (FC) procedures on the temperature range 2 -50K at an applied magnetic field of 0.005 T.

Magnetization measurements as function of applied magnetic field were carried out in two magnetic field ranges, i) hysteresis loops were recorded at 2K from -5T up to +5T; and ii) first

Results and discussion

3.1.Structural properties

According to the XRD patterns of the Ga x Mn 3-x O 4 samples (0 ≤ x ≤ 2) obtained after annealing at 1350°C for 24h, four regions can be deduced. For 0 ≤ x ≤ 0.2, the patterns show characteristic peaks of a single tetragonal spinel phase typical of Mn 3 O 4 . When 0.3 ≤ x ≤ 1.1, the patterns indicate the coexistence of two phases: cubic and tetragonal. For 1.2 ≤ x ≤ 1.6, only one phase is observed which corresponds to cubic spinel with Fd-3m space group. For x ≥ 1.7, the XRD data suggest the presence of a cubic spinel phase and Ga 2 O 3 as a secondary phase (see Fig. SI-1).

In the following, we only investigate the single-phase Ga x Mn 3-x O 4 (1.2 ≤ x ≤ 1.6) system. The analysis of XRD patterns for 1.2 ≤ x ≤ 1.6 shows a solid solution domain, characterized by a single phase indexed in cubic spinel structure. As can be seen from Figure 1(a), all the phases show the same peaks distribution. A shift of the Bragg peak towards higher Bragg angles with the increase of Ga content, which means that the unit cell gets smaller, and the variation of the peak intensities with increasing x(Ga 3+ ), as evident from Figure (SI-2), is a manifestation of the substitution effect in the system.

The structural refinements were carried out by Rietveld method using the FullProf program.

The cubic MgAl 2 O 4 with Fd-3m space group was the starting structural model used in our refinements 33 . The oxygen ions are located in the 32e position; the tetrahedral sites A are in 8a positions, while the octahedral sites B are in the 16d positions. The refined parameters were the lattice parameter (a), the oxygen atomic coordinates (u), the occupancy of the tetrahedral and octahedral sites and the atomic displacement parameters of all atoms. The peak shapes were described using a pseudo-Voigt function. The first step of refinement was to determine the correct cell parameters using a cubic cell. For structural refinement, several models were tested. The quality of the refinements was judged based on the reliability factors (R P , R wp , R Bragg , R F -factor, and Chi 2 ).

The Ga x Mn 3-x O 4 (1.2 ≤ x ≤ 1.6) system consists of two different types of atoms that are distributed over the tetrahedral (A) and the octahedral (B) sites. The atomic scattering factors of Ga and Mn for X-rays are shown in Figure (SI-3). The significant difference in atomic scattering is favorable for the precise determination of the atomic occupancies. The four test models for the Ga The results show that a3 and a4 models give the best reliability factors with R p = 10.7% and 10.2% for models a3 and a4, respectively. The a3 model is a normal spinel (Mn) A [Ga 1.2 Mn 0.8 ] B O 4 . Based on this model, the Mn and Ga located at the octahedral site have an oxidation state of +3 while the Mn located at the tetrahedral site has a +2 oxidation state. The cation distribution for a3 model is then given by (Mn 2+ ) A [Ga 3+ 1.2 Mn 3+ 0.8 ] B O 4 . Model a4 is an inverse spinel with low inversion parameter; 0.2 Ga 3+ occupies the tetrahedral site and an equivalent amount of Mn 2+ occupies the octahedral site. The cation distribution for the a4 model is in agreement with that obtained recently by Venediktova et al. 17 .

The a3 and a4 models have similar reliability factors. In order to confirm the a4 model, we calculated the cation distribution in A and B sites according to the O'Neill and Navrotsky's model 24,25 . It is known that the cation distribution in spinels is explained by the cation site preference. Based on literature data 31 , the Mn 3+ cations strongly prefer the octahedral sites, whereas Mn 2+ et Ga 3+ are randomly distributed over both tetrahedral and octahedral sites. The cation distribution in that case is given by (Mn 2+ 1-y Ga 3+ y ) A [Mn 2+ y Ga 3+

x-y Mn +3 2-x ] B O 4 , where (x) is the mole number of Ga introduced into the system and (y) represents the inversion parameter. The O'Neill-Navrotsky model consists in minimizing the free energy. The disordering enthalpy has a quadratic form with the inversion parameter and the disordering entropy is related to the configurational entropy 24,25 . The configuration entropy ∆S C of the system is given by:

∆ܵ = -ܴ ቂሺ1 -ݕሻ lnሺ1 -ݕሻ + ݕ݈݊ݕ + ݈݊ݕ ݕ 2 + ሺ2ݔ -ݕሻ ln ቀ ݔ -ݕ 2 ቁ + ሺ2 -ݔሻ ln ቀ1 - ݔ 2 ቁቃ ሺ1ሻ
A change in the cation distribution is accompanied by a change in the free energy of disorder ∆G cd which is given by:

ܩ∆ ௗ ሺݕሻ = ߙݕ ெ మశ ିீ యశ + ݕߚ ଶ -ߪܶݕ ெ మశ ିீ యశ -ܶ∆ܵ ሺ2ሻ
α and β are the interchange enthalpy parameters. It was found that for 2-3 spinels, β takes values between -15 and -25 kJ mol -1 and an average value of β = -20 kJ mol -1 can be used 27 .

The parameters α Mn2+-Ga3+ and σ Mn2+-Ga3+ are calculated from the values given in reference [25] for Mn 2+ and Ga 3+ cations; the values used in the calculation are α Mn2+-Ga3+ = 49kJ mol -1 and σ Mn2+-Ga3+ = 0 kJmol -1 . At the equilibrium of the cation arrangement, the free energy will be minimum with respect to any change in the inversion parameter y, that is

డሺ∆ீ ሺ௬ሻ డ௬ = 0, hence: M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 6 -ܴ݈ܶ݊ሺ ݕ ଶ ሺ1 -ݕሻሺݔ -ݕሻ ሻ = ߙ ெ మశ ିீ యశ + ݕߚ2 -ܶߪ ெ మశ ିீ యశ ሺ3ሻ
Solving equation ( 3) allows us to calculate the inversion parameter y for each value of x at T = 1350 ° C (the synthesis temperature). Results are shown in Table 1. We find that the inversion parameter y increases slightly as a function of x (Ga 3+ ), varying between 0.16 and 0.20 for x = 1.2-1.6.

This result shows that our solid solution is an inverse spinel with a low inversion parameter, in agreement with the a4 model. Recent results on the same system showed an inversion parameter of approximately 0.20 17 .

Once the a4 model was confirmed, a Rietveld refinement was performed on the Ga x Mn 3-x O 4

system with x = 1.2-1.6. Figure 1 (b) shows, as an example, the refined pattern for x = 1.2 with good agreement between the observed and calculated profiles. Table 1 displays details of the crystal structures, cell parameters, oxygen atomic coordinates, cation distribution and reliability factors for all compounds.

The obtained cell parameters are plotted versus Ga content in Figure 1 (c). These results fit perfectly well with the observed peak shift (Fig. SI-2) and confirm that the lattice parameter a decreases linearly with increasing Ga 3+ content. decreases with the increase of x(Ga 3+ ) in the octahedral site due to its progressive substitution by Ga 3+ which increases in the same site. The octahedral site is also occupied by a small amount (y) of Mn 2+ , while the tetrahedral site remains occupied by a fraction (1-y) of Mn 2+ and (y) of Ga 3+ cations. The inversion parameter (y) shows a small variation depending on the substitution, it increases from y = 0.20 to y = 0.24 for the compounds x = 1.2-1.4, and then it decreases to reach y = 0.16 for the compound x = 1.6. As said above, the cationic distribution in the octahedral and tetrahedral sites is given by (Mn 2+ (1-y) Ga 3+ y ) A [Mn 2+ y Ga 3+ (x-y) Mn 3+

(2-

x) ] B O 4 . This result is consistent with that calculated using O'Neill's model which shows an inversion parameter y = 0.16-0.20.

Therefore, the decrease of lattice parameter can be attributed to the slightly smaller Ga 3+ radius at the octahedral site compared to Mn 3+ . In addition, in cubic spinel structures, the relationship between the lattice parameter and the distances d A-O and d B-O is given by the following equation 34 :

ܽ = 2.09 + ඥ5.81݀ ଶ -1.41݀ ଶ ሺ4ሻ.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

The theoretical tetrahedral and octahedral cation-anion distances d A-O and d B-O were calculated using Shannon ionic radii 35

: d A (Ga 3+ -O) = 1.85Å, d B (Ga 3+ -O) =2.00 Å ; d A (Mn 2+ -O)=2.04 Å, d B (Mn 2+ -O)=2.22 Å, d B (Mn 3+ -O) = 2.045Å
. Since more than one type atom occupies the same site, the mean distances for each site were calculated, on one hand, using Shannon ionic radii and the chemical occupancy determined from the Rietveld refinements, and on the other hand the cation distribution obtained from O'Neill's model. The calculated lattice parameters are compared in Table 1 with those obtained from the experimental data refinements. The good agreement between the lattice parameters obtained experimentally and those calculated, confirms that the substitution proceeds in the octahedral sites according to the formula Above the magnetic ordering temperature T C , the shape of curves is not linear, but follows a hyperbolic form typical of a ferrimagnetic system with two sublattices in antiferromagnetic interaction. These curves can be analyzed using the following equation 36 :

(Mn 2+ (1-y) Ga 3+ y ) A [Mn 2+ y Ga 3+ x-y Mn 3+ (2-x) ] B O 4 .

3.2.Magnetic Properties

Paramagnetic regime

1 ߯ = 1 ߯ + ܶ ܥ - ߪ ܶ -ߠ ሺ5ሻ
If T >>θ, the third term becomes negligible and the hyperbolic form reduces to a linear form at high temperature; therefore the Curie-Weiss linear law can be applied [Fig. 2 (b)]. Table 2 lists the fitting parameters obtained using Curie-Weiss linear equation in the temperature range from 150 to 300K. The theoretical magnetic moments were calculated using the following formula:

ߤ ௧ = ඥߤሺ݊ܯ ଶା ሻ ଶ + ሺ2 -ݔሻߤሺ݊ܯ ଷା ሻ ଶ ሺ6ሻ
Here x is the Ga 3+ content with values given by the XRD refinement. The theoretical moments of Mn 2+ and Mn 3+ can be expressed as ߤ = ݃ඥܵሺܵ + 1ሻ, where g is the Landé factor (g = 2), and S(Mn 2+ ) = 5/2 and S(Mn 3+ ) = 2. In the case of x = 1.2, 1.5 and 1.6, the deduced theoretical moments µ theo are in good agreement with the experimental effective magnetic moments µ eff , with a difference ∆µ = |µ eff -µ theo | < 1.7% (see Table 2). For the compound with x = 1.3, a small difference ∆µ = 3% was observed. The compound x = 1.4 has a

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

difference of ∆µ = 4.8%. In general, the effective moments show a nice agreement with the theoretical moments with a difference ∆µ <5 %. This small difference could be attributed to the presence of impurities non-detectable by XRD such as Mn 3 O 4 .

By increasing x(Ga 3+ ), the effective magnetic moment decreases due to the substitution of Mn 3+ by non-magnetic Ga 3+ ions. The large and negative Curie-Weiss temperature θ indicates the existence of strong antiferromagnetic coupling between two sublattices. The absolute value of θ decreases with increasing Ga 3+ content, highlighting that the insertion of nonmagnetic ions into the B sites reduces the interactions between A and B networks. The magnetic ordering temperature T C was determined from the minimum of the magnetization derivative as a function of temperature, as it will be discussed later; T C shows a gradual decrease with increasing x. For x = 1.2 and 1.3, the magnetic frustration parameter f = θ/T C is less than 10, indicating that the magnetic order in both compounds is a long-range order 37 .

With further increasing x (Ga 3+ ), the f parameter increases, suggesting the appearance of a short-range order due to disorder of magnetic interactions introduced by the non-magnetic Ga 3+ ions.

Ordered regime

To have further information on the magnetic interactions in the ferrimagnetic state, we have performed ZFC/FC measurements at 5mT and hysteresis loops M(H) at 2K, for the five compositions. Figure 3 (a) displays the ZFC/FC curves of Ga x Mn 3-x O 4 (1.2 ≤ x ≤ 1.6). We note the existence of irreversibility T irrev at the approach of the maximum value of ZFC magnetization. Below T irrev , the ZFC magnetization decreases rapidly, a behavior typical of antiferromagnetic interactions. For x = 1.2-1.3, the ZFC magnetization becomes negative below a certain compensation temperature, confirming the existence of antiferromagnetic interactions between two sublattices. This behavior has already been observed in similar compounds based on Ni, Co and Mn, and shows a global ferrimagnetic behavior at low temperature 38,39,40 . The FC curves superpose the ZFC curves in the temperature range from 300 K to T irrev . Below T irrev , the FC magnetization increases to reach a maximum followed by a saturation at lower temperatures. This behavior is more pronounced for compositions x = 1.2, 1.3 and 1.4. This is characteristic of a P-type ferrimagnetic structure [START_REF] Herpin | Théorie du magnétisme[END_REF] .The shape of the FC magnetization curve can be explained by a competition between the J AA , J BB and J AB interactions. For x = 1.5 and 1.6, the shape of magnetization curves ZFC/FC indicates the existence of magnetic frustration in agreement with the frustration parameter (see Table 2).

The transition temperature T C decreases with magnetic dilution [Inset, Fig. 3

(a)], highlighting

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

an evolution towards a complex magnetic structure due to a magnetic frustration which becomes more important with dilution. The magnetization curves show a hysteresis typical of a ferrimagnetic system with an unsaturated character up to 5T, for all compounds. With increasing Ga 3+ content, the hysteresis cycles become increasingly closer, the coercive field (Hc) and the magnetization decrease with increasing x(Ga 3+ ), indicating an evolution towards a complex magnetic structure.

To see the possibility of reaching saturation under a magnetic field, we have performed first magnetization curve measurements as a function of magnetic field up to 9T at different temperatures (Fig. 4). For T < T C , the magnetization rapidly increases for low magnetic fields, followed by a linear increase as a function of the applied magnetic field without saturation, which indicates that the magnetic structure is canted. The spontaneous magnetizations Ms (T)

were deduced by extrapolating to H = 0T the linear part of the magnetization curves. The values of the spontaneous magnetization Ms (2K) determined at 2 K are listed in Table 3. The results show that Ms(2K) decreases with increasing x(Ga 3+ ). Quantitative information on the cation distribution in Ga x Mn (3-x) O 4 , obtained by refinement of the XRD data using Rietveld methods, is very helpful in the interpretation of the observed magnetization degradation. In the system Ga x Mn (3-x) O 4 , the Mn 2+ (S = 5/2) cations occupy both sites A and B, and the Mn 3+ (S = 2) cations occupy only the B sites. Under the assumption of collinear spin arrangement, the values of the spontaneous magnetization Ms can be calculated by the Néel model, expressed by Ms = M A (Mn +2 ) + M B (Mn +2 )-M B (Mn +3 ), where M A and M B are the effective magnetic moments of A and B sublattices, respectively. The values of Ms obtained using the collinear model are presented in Table 3. The Ms values were found to be larger than the experimental values. This indicates that the compounds have a non-collinear ferrimagnetic structure, with the Mn 3+ and Mn 2+ magnetic moments in B sites being linear and antiferromagnetic, and those of Mn 2+ in A sites making an angle φ with the direction of the total magnetization. The φ angle of each composition (Table 3) was calculated as a function of magnetic field from the first magnetization curves M(H) measured at 2K, using the following formula: Ms(H) = M A (Mn +2 )cos(φ(H)) + M B (Mn +2 ) -M B (Mn +3 ).

Figure 5(a) displays, the corresponding φ(H) curve. It is found that the angle φ(H) decreases with increasing magnetic field according to an exponential function for all compounds:

߮ሺܪሻ = ߮ + ߮ ଵ ݁ షಹ ಹ బ

ሺ7ሻ

The fitting by this equation allows to determine the canting angle φ 0 at strong magnetic field (H tends to infinity), and also determines the (φ 0 + φ 1 ) canting angle at zero magnetic field (H = 0T). The term H 0 is a mean field that represents the magnetic interactions; it includes the exchange interaction between the magnetic moments and the magnetic anisotropy. The results of the fit are shown in Figure 5(a), and in Table 3 we present the obtained fit parameters φ 0 , φ 1 and H 0 .

The (φ 0+ φ 1 ) values which represent the canting angle at zero magnetic field were found to increase with increasing x(Ga 3+ ) (Figure 5 (b)) showing an evolution towards an antiferromagnetic structure in the A sites with the substitution of Mn 3+ ions by non-magnetic Ga 3+ ions in B sites. At zero magnetic field and at T = 2K, the compounds stabilize in a noncollinear ferrimagnetic structure, in which the magnetic moments of Mn 3+ and Mn 2+ ions are collinear in the B sites and those of Mn 2+ ions in A sites form an angle (φ 0 + φ1)with the direction of total magnetization.

Under a strong magnetic field, the magnetic structure remains non-collinear with an angle of φ 0 smaller than that observed at zero magnetic field (Fig. 5 (b)).

The H 0 parameter, which represents the effects of magnetic interactions, shows a decrease between the compounds x = 1.2-1.4, due to the introduction of non-magnetic ions into the system. For compounds x = 1.5-1.6, the observed increase may be related to the effects of magnetic frustration (See Table 3).

In summary, the shape of the inverse magnetic susceptibility, the shape of the ZFC/FC magnetization curves at low temperatures, the existence of hysteresis in all compounds, the frustration parameter and the spontaneous magnetization analyses show that the compounds present a non-collinear ferrimagnetic order, and with further increasing x(Ga 3+ ), the frustration parameter f increases, suggesting the appearance of a short-range order, which coexists with a non-collinear ferrimagnetic state.

Determination of spin wave stiffness parameters

Using spin waves theory [START_REF] Van Kranendonk | [END_REF] , we determine the spin wave stiffness parameter D from the temperature dependence of magnetization. For systems with two magnetic sublattices, A (tetrahedral sites) and B (octahedral sites), the dispersion relation for acoustic magnons to order k 2 can be expressed as 43,44 :

ℎ ഥ ߱ = ݇ܦ ଶ , M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
ω is the frequency, k is the spin wave momentum. The temperature dependence of magnetization M(T) follows Bloch's law (T 3/2 ) which is associated to the thermal excitation of spin waves. The M (T) curves can be expressed as 45,46 :

ܯ ௦ ሺܶሻ ܯ ௌ ሺ0ܭሻ = 1 - 0.0568 4ሺܵ -2ܵ ሻ ሺ ܽ ଶ ݇ ܦ ሻ ଷ/ଶ ܶ ଷ/ଶ = 1 -ܶܤ ଷ/ଶ ሺ8ሻ
Spin-wave stiffness parameter with the notation D is given by the following formula:

ܦ = ሺ 0.0568 8ሺߤ/ܯ ሻ ሻ మ య ܽ ଶ ݇ ܤ మ య ሺ9ሻ
Here a is the unit cell parameter, M is the spontaneous magnetization, k B is the Boltzman constant and B is the Bloch constant.

In order to determine the spin wave stiffness parameters D from the temperature dependence of magnetization below T C using the results of spin wave theory, we have plotted in Fig. 6, the change of Ms (T) as a function of temperature for the different samples. We note that Ms (T) decreases with increasing temperature due to the spin-wave excitations.

The Ms(T) curves were fitted using equation ( 8) (Bloch's law). The results of fits are presented in Fig. 7.

We find that for samples with x = 1.2 and 1.4, the change of the spontaneous magnetization with temperature is in line with Bloch's law. However, for the samples x = 1.5 and 1.6, the experimental Ms(T) deviates from T 3/2 law. The Ms(T) change can then be modeled using Dyson approximation [START_REF] Yu | Magnetic Neutron Diffraction[END_REF] :

ܯ ௦ ሺܶሻ ܯ ௦ ሺ0ܭሻ = 1 -ܶܤ ଷ/ଶ -ܶܥ ହ/ଶ ሺ10ሻ
Bloch's constants B and D parameters calculated using equation ( 9) are listed in Table 3.

These results indicate that we have two sets of compounds with two different magnetic behaviors, the samples x = 1.2-1.4 and the compounds x = 1.5-1.6. These observations are in line with the results reported by Efimova and Kufterina on the magnetic properties of dilute frustrated ferromagnetic spinels Li 0.5 Fe (2.5-x) Ga x O 4 [START_REF] Efimova | [END_REF] . They have shown that the Ms(T) curves for the frustrated ferrimagnets do not obey Bloch T 3/2 law, which is satisfied in the absence of frustrations. If the collinear ferrimagnetic ordering is restored by applying an external magnetic field, the Ms(T) curves could be described using Dyson approximation (Eq. 10).

Thus, we conclude that our samples x = 1.2-1.4 present a non frustrated ferrimagnetic order,

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

and that samples x = 1.5-1.6 present a frustrated ferrimagnetic order. This frustration is attributed to chemical disorder caused by the introduction of non-magnetic ions into the octahedral sites. In these compounds, frustration can also be caused by a competition between the interactions of the first, second and third neighbors as in spin glasses.

Spin wave stiffness parameters D are shown in Table 3 for four compounds. For nonfrustrated compounds x = 1.2-1.4, D decreases with the introduction of a non-magnetic cation into B sites, D = 53 -40meV Å 2 , D calculated from Bloch equation (8). These D values are five times smaller than those obtained in the ferrimagnetic Mg x Fe 3-x O 4 compounds (296 -202 meV Å 2 ) 49 , due to the stronger J AB interactions in the ferrites.

For the frustrated compounds (x = 1.5-1.6), we note that D increases as a function of x (D = 82 -135meV Å 2 ), D calculated using Dyson equation (10). The evaluated D values are close to those for ferromagnetic glasses (≈100 meVÅ 2 ) 50 . In perspective, an accurate determination of the spin wave stiffness parameters D requires measurements of the magnon-dispersion relations performed by magnetic elastic neutrons scattering or Brillouin light scattering.

Conclusions

By analyzing the XRD data refined using Rietveld methods, we have shown that the system

Ga x Mn (3-x) O 4 (1.2 ≤ x ≤ 1.6
) is an inverse spinel with low inversion parameter, in which Ga 3+ ions replace the Mn 3+ cations located in B-sites, in agreement with the O'Neill-Navrotsky model. The cation distribution is given by (Mn 2+ 1-y Ga 3+ y ) A [Mn 2+ y Ga 3+

x-y Mn +3 2-x ] B O 4 . Magnetic information was extracted from the curves of the inverse magnetic susceptibility, the ZFC/FC magnetization, the first magnetization and hysteresis curves. The shape of inverse magnetic susceptibility is a hyperbolic form typical of a ferrimagnetic system. The calculated moments µ theo are in agreement with the experimental effective magnetic moments µ eff , and confirm the cation distribution. For x = 1.2 and 1.3, the magnetic frustration parameter f = θ/T C is less than 10, indicating that the magnetic order in both compounds is a long-range order. With further increasing x(Ga 3+ ), the f parameter increases, suggesting the appearance of a short-range order. The shape of the ZFC/FC magnetization curves at low temperatures, the existence of hysteresis in all compounds, and the spontaneous magnetization analyses show that the compounds x = 1.2-1.4 have a non-collinear ferrimagnetic order and the compounds x = 1.5-1.6 have a frustrated non-collinear ferrimagnetic order. It has been established that for compounds with x = 1.2 and 1.4 with a non-frustrated ferrimagnetic order, the temperature dependence of the spontaneous magnetization Ms(T) obeys to Bloch's law with exponent T 3/2 . For x = 1.5 and 1.6, compounds with frustrated ferrimagnetic order, a deviation from Bloch's

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

law was seen, the Ms(T) curves being described using Dyson approximation (exponents T 3/2 and T 5/2 ). Spin wave stiffness parameters were determined for each composition from the fits of Ms(T) using Bloch's law. This study will be very useful to understand the magnetic properties of Ga x Mn (3-x) O 4 compounds.

Cell parameter

Cell parameter a(Å)

x (Ga)

Highlights

• Ga x Mn (3-x) O 4 (1.2 ≤ x ≤ 1.6) compounds prepared by solid-state reaction.

• Cation distribution and crystallographic parameters have been determined using Rietveld method and O'Neill and Navrotsky model.

• Spin wave stiffness parameters were determined for each composition

• Compounds x = 1.2-1.4 present a non-collinear ferrimagnetic order.

• Compounds x = 1.5-1.6 present a frustrated non-collinear ferrimagnetic order.

  magnetization measurements from 0T up to 9T at different temperatures using Physical Property Measurement System (PPMS) from Quantum Design. The spontaneous magnetizations Ms(T) were determined by extrapolation to H = 0T of the linear variation of M (H) near saturation. M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 4

  four models are shown in figure (SI-4) with their corresponding reliability factors.

Figure 1 (

 1 d) shows the occupancy variation of the different cations located at the tetrahedral and octahedral sites. The occupation of Mn 3+

Figure 2 (

 2 Figure 2(a) displays the change of the inverse magnetic susceptibility as a function of temperature recorded under a magnetic field of 0.1T of Ga x Mn (3-x) O 4 powders (1.2 ≤ x ≤ 1.6).

Figure 3 (

 3 Figure 3 (b) displays the hysteresis loops as a function of the applied magnetic field at 2K for Ga x Mn 3-x O 4 (1.2 ≤ x ≤ 1.6) compounds. The change of the coercive field Hc as a function of x(Ga 3+ ) is displayed in the inset Fig. 3(b). The magnetization curves show a hysteresis typical

Figure 1 :

 1 Figure 1: (a) X-ray diffraction patterns for Ga x Mn (3-x) O 4 (x=1.2-1.6) at room temperature, (b) refined diagram by the Rietveld method using a4 model, (c) evolution of the lattice parameter (a) as function of composition x(Ga 3+ ), (d) occupancy of different cations as a function of x(Ga 3+ ) in tetrahedral and octahedral sites.

Figure 2 :Figure 3 :

 23 Figure 2: (a) Inverse magnetic susceptibility 1/χ as a function of temperature recorded under a magnetic field of 0.1T for all samples of the Ga x Mn 3-x O 4 system (1.2 ≤ x ≤ 1.6). (b) 1/χ fit using Curie-Weiss equation in the temperature range from 150 to 300K.

Figure 4 :

 4 Figure 4: First magnetization curves as a function of magnetic field up to 9T at different temperatures.

Figure 5 :

 5 Figure 5: (a) Evolution of the angle φ(H) as a function of the magnetic field, together with the fit of φ(H) curves obtained using the equation: ߮ሺܪሻ = ߮ + ߮ ଵ ݁ షಹ ಹ బ . (b) angle φ 0 of the magnetic structure at strong magnetic field ( H→∞), and the φ 0 + φ 1 angle of the magnetic structure at H=0T of each compound.

Figure 6 :

 6 Figure 6: Temperature dependence of spontaneous magnetization Ms (T) determined by extrapolation of the linear part of M(H) (fig. 4) to H = 0T.

Figure 7 :

 7 Figure 7: Fitting results of Ms(T) curves using equations (8) and(10).

  1.2 Mn 1.8 O 4 composition, taken as an example, are the following: a1 Model with (Ga) A [Ga 0.2 Mn 1.8 ] B O 4 , a2 Model with (Mn 0.5 Ga 0.5 ) A [Ga 0.7 Mn 1.3 ] B O 4 , a3 Model with (Mn) A [Ga 1.2 Mn 0.8 ] B O 4 and a4 Model with (Mn 0.8 Ga 0.2 ) A [GaMn] B O 4 . The results of Rietveld

Table 1 :

 1 Crystal

											2											1.3							1.4	1.5	1.6
	a(Å)			8.4868(3)						8.4818(2)							8.4775(2)	8.4729(2)	8.4675(2)
	O(32e) : u			0.2625(2)						0.2629(2)							0.2634(2)	0.2636(2)	0.2638(2)
	Cation	(Mn 2+	0.80(6)Ga	3+	0.20(6))A	(Mn 2+	0.79(1)Ga	3+	0.21(1))A	(Mn 2+	0.76(1)Ga	3+	0.24(1))A	(Mn 2+	0.77(2)Ga	3+	0.23(2))A	(Mn 2+	0.84(2)Ga	3+	0.16(2))A
	distribution	[Mn 2+	0.20(6)Mn	3+ 0.80(6)Ga	3+ ]B	[Mn 2+	0.21(1)Mn	3+ 0.70(1)Ga	3+	1.09(1)]B	[Mn 2+	0.24(1)Mn	3+ 0.60(1)Ga	3+	1.16(1)]B	[Mn 2+	0.23(2)Mn	3+ 0.50(2)Ga	3+	1.27(2)]B	[Mn 2+	0.16(2)Mn	3+ 0.40(2)Ga	3+	1.44(2)]B
	Rietveld
	RP(%)					10.2											8.8										8.6	9.5	9.1
	Rwp (%)					15.8										13.9										13.5	16.8	14.0
	Rexp (%)					14.7										13.6										13.3	16.2	13.7
	RBragg(%)					4.4											3.5										3.4	5.3	4.7
	RF (%)					3.9											3.0										3.1	3.6	3.7
	2					1.10										1.03										1.02	1.08	1.05
	Cation
	distribution	(Mn 2+	0.84Ga	3+	0.16)A			(Mn 2+	0.83Ga	3+	0.17)A			(Mn 2+	0.82Ga	3+	0.18)A	(Mn 2+	0.81Ga	3+	0.19)A	(Mn 2+	0.80Ga	3+	0.20)A
	O'Neill	[Mn 2+	0.16Mn	3+	0.80Ga	3+	1.04]B	[Mn 2+	0.17Mn	3+	0.70Ga	3+	1.13]B	[Mn 2+	0.18Mn	3+	0.60Ga	3+	1.22]B	[Mn 2+	0.19Mn	3+	0.50Ga	3+	1.31]B	[Mn 2+	0.20Mn	3+	0.40Ga	3+	1.40]B
	Model
	a(Å)
	Shannon					8.488									8.482									8.477	8.470	8.462
	and
	Rietveld
	a(Å)
	Shannon					8.487									8.481									8.475	8.469	8.463
	and
	O'Neill
															structures (Fd-3m), cell parameters (a), oxygen atomic coordinates (u),
		cation distribution and reliability factors for Ga x Mn (3-x) O 4 (x=1.2-1.6) determined from
		Rietveld refinements using the a4 model. The cation distribution was calculated using O'Neill
		and Navrotsky's model. Bottom: Theoretical cell parameters calculated using Shannon ionic
		radii, chemical occupation (determined from Rietveld refinements) and cation distribution
		(O'Neill Model).

Table 2 :

 2 Results of fits: C Curie-Weiss constant; µ eff experimental magnetic moment, µ theo

	x(Ga	3+ ) M s (µ B /f.u.)	M s (µ B /f.u.)	ϕ 0	ϕ 0 + ϕ 1	H 0 (T) B (x10	-3 K	3/2 ) D (mev.Å 2 )
			Exp	Theo (Néel)	(deg)	(deg)
	1.2	0.61(3)	1.8	19	47	17.6	1.9(1)	53
	1.4	0.45(2)	2.6	47	64	10.3	3.5(4)	40
	1.5	0.43(2)	3.0	50	71	12.6	1.3(3)	82
	1.6	0.32(1)	3.4	53	79	17.7	0.9(1)	135

theoretical magnetic moment, Tc transition temperature, θ Curie-Weiss temperature; f frustration parameter.

Table 3 :

 3 Ms(µ B /f. u.) exp experimental values of the spontaneous magnetization determined at

	2 K, Ms(µ B /f. u.) theo theoretical values of the spontaneous magnetization calculated using
	collinear Néel model, φ 0 canting angles at H = ∞, φ 0 + φ 1 canting angles at H = 0T, H 0

magnetic interaction parameter, B Bloch's constant, D Spin wave stiffness parameter determined from results of Ms (T) using Bloch's and Dyson equations.

Acknowledgements

In memory of Arlei B. Antunes (1967-2010), whose invaluable comments concerning the magnetic properties, helped to carry this work to term.

Conflicts of interest

There are no conflicts of interest to declare.

Appendix A. Supplementary data

Supplementary data related to this article can be found at XXXX


Brissot Pierre

Cavey Thibault

Guggenbuhl Pascal

Loréal Olivier

Title. Genetic hemochromatosis: Pathophysiology, Diagnostic and Therapeutic Management

Le terme d'hémochromatose (HC) correspond à plusieurs affections caractérisées par une surcharge en fer systémique d'origine génétique, affectant qualité et espérance de vie. Les importantes avancées récentes dans la compréhension du métabolisme du fer permettent de diviser ces affections en deux grandes catégories physiopathologiques. Pour la plupart des HC (types1, 2, 3, et 4B) la surcharge en fer est la conséquence d'un manque cellulaire en hepcidine à l'origine d'une hypersidérémie puis de l'apparition de fer non lié à la transferrine plamsatique. En contraste, dans l'HC de type 4A, l'excès en fer est la conséquence d'un défaut de passage dans le courant sanguin du fer macrophagique. Quel que soit le type d'HC, le diagnostic repose désormais sur une stratégie non invasive combinant données cliniques, biologiques et d'imagerie. La base du traitement demeure les saignées avec la perspective, dans les HC par déficit en hepcidine, de la supplémentation en cette hormone. La prévention de l'HC est cruciale à l'échelon de la famille et, dans le cas de l'HC de type1, demeure un objectif majeur, quoiqu'encore débattu, au niveau de la population.

of hepcidin supplementation for hepcidin-deprivation related HC. Prevention of HC is critical at the family level and, for type 1 HC, remains a major goal, although still debated, at the population level. t

Genetic hemochromatosis: Pathophysiology, Diagnostic and Therapeutic management

The term genetic hemochromatosis (HC) has become a generic one, encompassing a variety of disorders corresponding to systemic iron overload of genetic origin. Therefore, today, one should now think in terms of « hemochromatoses » rather than « hemochromatosis ».

Numerous mutations, located on different chromosomes, are involved, leading to varying phenotypes according to clinical expression and severity. The present review will focus on HFE-related (type 1) HC (chromosome 6), by far the most frequent form in Caucasians, and on the non-HFE related HC, rare diseases involving mutations of the hemojuvelin(1) (HFE2 or HJV) (chromosome 1) , hepcidin(2) (HAMP) (chromosome 19), transferrin receptor2(3) (chromosome 7) (TFR2), ferroportin(4, 5) (SLC40A1) (chromosome 2) and ceruloplasmin (CP) (chromosome 3) genes, and corresponding to types 2A, 2B, 3, 4 HC, and to hereditary aceruloplasminemia(6) (HA), respectively [START_REF] Brissot | Iron disorders of genetic origin: a changing world[END_REF][START_REF] Pietrangelo | Genetic Testing, and Management of Hemochromatosis: 15 Years Since Hepcidin[END_REF]. Essentially produced by the hepatocytes [START_REF] Pigeon | A new mouse liverspecific gene, encoding a protein homologous to human antimicrobial peptide hepcidin, is overexpressed during iron overload[END_REF], this 25 aminoacid peptide decreases plasma iron by a double mechanism [START_REF] Ganz | Systemic iron homeostasis[END_REF]. On the one hand, it limits digestive iron absorption, on the other hand it decreases iron release from the spleen into the plasma (this splenic iron originates from the normal erythrophagocytotic process). Hepcidin modulates the amount of iron release into the plasma by targeting ferroportin, the only known cellular iron exporter, [START_REF] Drakesmith | Resistance to hepcidin is conferred by hemochromatosis-associated mutations of ferroportin[END_REF]. Schematically, after hepcidin binding to ferroportin, the complex is internalized and leads to intracellular ferroportin degradation which, in turn, decreases the iron export capacity mediated by the residual ferroportin at the membrane level [START_REF] De Domenico | The molecular mechanism of hepcidin-mediated ferroportin down-regulation[END_REF]. Therefore, every physiological or pathological situation increasing hepcidin synthesis will decrease plasma iron, and conversely.

The development of iron overload in hepcidin deprivation-related HC is mediated by plasma iron increase (hypersideremia), through two mechanisms.

The most frequent one is hypohepcidinemia. It is the case for types 1 (HFErelated), 2A (HFE2 or HJV-related), and type 3 (TFR2 -related) HC. In these settings, the causal mutations, through alteration of molecular cascades that are increasingly dissected, and involve especially the BMP-SMAD signaling pathway and/or ERK1/2 patways [START_REF] Ruchala | The pathophysiology and pharmacology of hepcidin[END_REF], lead to abnormally decrease hepatic synthesis of hepcidin with respect to iron status, and subsequently to decrease levels of plasma hepcidin.

The other situation implicated in hepcidin cellular « deprivation » is hepcidin resistance. It occurs during type B ferroportin disease, due to very specific mutations and characterized by an impaired capacity of ferroportin to interact with hepcidin. Hepcidin being then unable to decrease ferroportin expression, the cellular consequences are equivalent to those observed during plasma hepcidin deficiency with a resulting increase efflux of iron from the enterocytes and from the splenic macrophages, and therefore increased plasma iron levels.

Pathophysiological consequences of hepcidin cellular deprivation.

The key primary biochemical event is increased plasma iron concentration which leads to increased saturation of transferrin, the physiological carrier protein of plasma iron (corresponding to transferrin saturation -TfSat-levels over 45%). As a result, novels forms of circulating iron may appear in the plasma, named nontransferrin bound iron (NTBI). NTBI, in contrast with transferrin-iron that targets essentially the bone marrow, is very avidly taken up by parenchymal cells, first and foremost the hepatocytes(15) but also cardiomyocytes and. pancreatic cells. Therefore, NTBI is the major iron species accounting for cellular (and tissue) iron deposition in HC. Moreover, whenever TfSat exceeds 75% [START_REF] Lan | Redox active plasma iron in C282Y/C282Y hemochromatosis[END_REF], a novel NTBI form appears, defined by its capacity to produce reactive oxygen species (ROS), and called labile plasma iron (LPI) [START_REF] Cabantchik | LPI-labile plasma iron in iron overload. Best practice & research[END_REF] or reactive plasma iron (RPI). LPI is considered as the main culprit for cellular iron toxicity in HC, through damaging cellular plasma membranes as well as intracellular organelles . The resulting tissue alterations underly the clinical organ damage developed in HC, such as hepatic, pancreatic and cardiac lesions.

Pathophysiological consequences of ferroportin deficiency

As a consequence of altered cellular iron egress, plasma iron does not increase and may even decrease (corresponding to normal or decreased TfSat, respectively). Therefore, no plasma NTBI is present, implying that parenchymal cells are only moderately affected by iron deposition, especially as ferroportin activity is particularly pronounced in macrophages. The sites of cellular iron overload are therefore mainly the spleen (particularly rich in macrophages) and, at a lesser degree, the liver (kupffer cells). The absence of NTBI also means absence of LPI and, therefore, less damaging capacity of excessive stored iron (especially as macrophages are less sensitive to iron-related damage than parenchymal cells). These data likely explains why type 4A HC seems a relatively begnin disease as compared to the hepcidin deprivation-related forms of HC [START_REF] Lan | Sex and acquired cofactors determine phenotypes of ferroportin disease[END_REF]. However, long-term studies remain to be conducted.

1.4.Hemochromatosis of not fully solved pathophysiology

It is the case for HA (19). The proposed explanation for iron overload is iron retention due loss of ferroxidase activity normally exerted by ceruloplasmin [START_REF] De Domenico | Ferroxidase activity is required for the stability of cell surface ferroportin in cells expressing GPI-ceruloplasmin[END_REF]. Indeed, this ferroxidase property is required for plasma transferrin to take up the iron released, under the ferrous form, from the cells (iron oxidation into its ferric form being needed for transferrin uptake). As an upstream consequence, ferroportin activity for cellular iron export would be altered, leading to cellular iron retention (as in type 4 A ferroportin disease). This would fit with the decreased plasma iron levels (and TfSat) observed in HA. However, this mechanism cannot not explain why, in HA, iron overload spares the spleen and affects essentially the hepatocytes (like in hepcidin deprivation-related HC) [START_REF] Brissot | Iron metabolism and related genetic diseases: A cleared land, keeping mysteries[END_REF]. Moreover, HA is the sole HC form where iron overload is significantly present in the brain, accounting for neurological manifestations of the disease. Further studies are therefore needed to fully elucidate the mechanisms whereby systemic (including brain) iron overload develop in this disease.

1.5.The issue of penetrance variability. It has become clear that genetic predisposition does not mean clinical expression. This is particularly clear in type 1 HC where it has been estimated that 1% of women and less than 30% of C282Y/C282Y men would develop the full-blown disease [START_REF] Allen | Iron-overload-related disease in HFE hereditary hemochromatosis[END_REF]. Many studies are underway to determine the environmental and host factors likely to account for phenotypic variability, which concerns not only the amount of body iron excess, but also, for an equivalent amount of iron overload, the organ targeting of iron excess. Among environmental factors, dietary iron content, physiological iron losses (menstruations [START_REF] Warne | C282Y homozygosity predisposes to rapid serum ferritin rise after menopause: a genotypestratified cohort study of hemochromatosis in Australian women[END_REF], pregnancies, breastfeeding), body weight( 23) have been identified. Among host factors, the role of male gender (through the hepcidin decreasing effect of testosterone [START_REF] Latour | Testosterone perturbs systemic iron balance through activation of epidermal growth factor receptor signaling in the liver and repression of hepcidin[END_REF][START_REF] Bachman | Testosterone suppresses hepcidin in men: a potential mechanism for testosterone-induced erythrocytosis[END_REF].has been proposed for favoring greater higher stores as compared to females, and genetic factors have been reported for explaining visceral complications, especially PCSK7 polymorphism for favoring hepatic fibrosis [START_REF] Stickel | Evaluation of genome-wide loci of iron metabolism in hereditary hemochromatosis identifies PCSK7 as a host risk factor of liver cirrhosis[END_REF]) have been reported.

Diagnostic management

It is based on a non invasive strategy, i.e. not requiring in most cases to perform a liver biopsy. Five main diagnostic steps can be individualized(27) (Fig. 3). 2.1.2. From the biochemical viewpoint, the most frequent abnormality leading the clinician to suggest iron overload is, by far, hyperferritinemia (usually defined by plasma ferritin levels over 300µg/L in men, and over 200 µg/L in women). It is critical, however, to remember that hyperferritinemia may be due to other causes than iron excess [START_REF] Ong | How should hyperferritinaemia be investigated and managed?[END_REF]. The main differential diagnosis is the metabolic syndrome. Dysmetabolic hyperferritinemia( 29) is probably the most frequent cause of hyperferritinemia worldwide. It should be suspected in any patient with an increase of weight (or waist circumference), blood pressure, glycemia, lipidemia, or uricemia. Plasma TfSat is normal and hepatic iron overload (when assessed by magnetic resonance imaging -MRI-) is normal or only moderately increased(30) (less than three times the upper normal limit). Two other possible causes of hyperferritinemia should be ruled out, inflammation and alcoholism [START_REF] Moirand | Increase in glycosylated and nonglycosylated serum ferritin in chronic alcoholism and their evolution during alcohol withdrawal[END_REF]. It is only after having excluded these three major causes, that increased plasma ferritin levels can be considered as reliably reflecting body iron excess.

With regard to plasma iron or TfSat, it is important to recall that it can be normal or even low, despite significant body iron excess, in HC forms such as type 4A ferroportin disease and HA.

To confirm iron overload

It is valuable to get a direct visualization of tissue iron overload. For this purpose, hepatic MRI has replaced liver biopsy. Some techniques corespond to relaxometry approaches [START_REF] Wood | Estimating tissue iron burden: current status and future prospects[END_REF][START_REF] St Pierre | Noninvasive measurement and imaging of liver iron concentrations using proton magnetic resonance[END_REF], defining indices such as T2* or R2*. A simple and reliable method is based on the signal intensity ratio [START_REF] Gandon | Non-invasive assessment of hepatic iron stores by MRI[END_REF]. The decreased T2 hepatic signal (as compared the spinal muscle signal which serves as a reference) is inversely correlated with the increase in hepatic iron concentration (the darker the liver, the higher the hepatic iron concentration). «Iron-MRI» also allows to assess the iron status of the spleen and pancreas (and, with relaxometry techniques, of the heart).

A further important MRI information is provided by comparing the liver and spleen signals [START_REF] Brissot | Iron metabolism and related genetic diseases: A cleared land, keeping mysteries[END_REF]. Schematically a «black» liver together with a «white» spleen orientates toward a type of HC with hepcidin deprivation, whereas a «black» spleen together with a «grey» liver favours the usual (type A) form of ferroportin disease. Therefore, iron-MRI not only ascertains and quantifies iron overload but, by showing the iron balance between liver and spleen, provides a valuable indication on the pathophysiology of iron overload development, an important clue for approaching the HC type.

2.3.

To suspect the genetic nature of iron overload 2.3.1. An acquired form of iron overload is usually easily ruled out. Transfusional iron overload is obvious in the context of chronic anaemia such as haemoglobinopathies (thalassaemias [START_REF] Saliba | Iron overload in transfusion-dependent thalassemia[END_REF][START_REF] Musallam | Non-transfusion-dependent thalassemias[END_REF], sickle cell disease(37)), myelodysplastic syndromes [START_REF] Steensma | When is iron overload deleterious, and when and how should iron chelation therapy be administered in myelodysplastic syndromes?[END_REF] or aplastic anaemia related to bone marrow transplantation procedure [START_REF] Sirvent | Prevalence and risk factors of iron overload after hematopoietic stem cell transplantation for childhood acute leukemia: a LEA study[END_REF]. Similarly, iron overload due to excessive parenteral iron supplementation( 40) is diagnosed by the detailed patient's history.

Family data indicating problems of iron excess is another important clue in

favor of a genetic disease.

2.4.To orientate toward the pathophysiological category of HC

Combining plasmaTfSat and imaging data is here essential.

MRI is also, as previously mentioned, an interesting indicator by

establishing an iron balance between liver and spleen, thus suggesting hepcidin deficiency or decreased macrophage iron release.

2.5.To definitely identify the genetic HC type

Guided by the combination of clinical, biological, and imaging data, the final diagnostic step is appropriate genetic testing.

HFE-related HC

It corresponds, in the vast majority of cases, to C282Y (new nomenclature p.Cys.282Tyr) homozygosity (C282Y/C282Y). As to the other HFE mutations, the following statements can be proposed : i) The H63D (His63Asp) mutation is a simple polymorphism ; ii) Compound heterozygosity (C282Y/H63D) or H63D homozygosity are not susceptible to cause significant body iron overload unless they are associated with factors such as alcoholism, the metabolic syndrome, or other mutations impacting iron metabolism gene (digenism) [START_REF] Porto | EMQN best practice guidelines for the molecular genetic diagnosis of hereditary hemochromatosis (HH)[END_REF] ; iii) The S65C mutation has no diagnostic interest ; iv) Exceptional profiles of compound heterozygosity can be responsible for clinically overt forms of HC.

Non-HFE HC(42)

They are rare diseases, with a reserve for type 4A HC (type A ferroportin disease) that may be more frequent than initially thought (probably related to its dominant mode of transmission) [START_REF] Wallace | The global prevalence of HFE and non-HFE hemochromatosis estimated from analysis of next-generation sequencing data[END_REF]. The corresponding specific genetic testing requires duly accredited laboratories [START_REF] Porto | EMQN best practice guidelines for the molecular genetic diagnosis of hereditary hemochromatosis (HH)[END_REF]. It should be noticed that, for HA, it is good clinical practice to check that plasma ceruloplasmin levels are very low or not detectable and/or ferroxidase activity is decreased before performing specific genetic testing. The new technical approach resorting to high throughput sequencing (NGS: next generation sequencing) offers the advantage of its power but should not lead to forget the need for a preliminary clinical orientation, at best managed by clinical reference centers. Moreover, it presents the drawback to identify an increasing number of new mutations whose deleterious nature is often difficult to establish and requiring additional family and/or functional studies(44) .

Therapeutic management

It will be confined here to the management of iron removal(27) (Fig. 4) 3.1.Treatment of HFE (type 1) HC 3.1.1. Venesections (phlebotomies) remain the key procedure. By removing total blood, they remove red blood cells which contain half the total quantity of body iron (2g), and lead the body to pump iron into its reserves in order to produce new erythrocytes. The induction phase usually consists of weekly venesections (7mL/kg body weight without exceeding 550 mL) until plasma ferritin reaches approximately 50µg/L(45), provided haemoglobin levels remain superior to 11g/dL (or do not fall more than 2 g from the baseline levels). Thereafter starts the maintenance treatment, theoretically for life, whose goal is to prevent recurrence of iron overload by maintaining ferritin levels around 50µg/L. It usually requires one venesection every one to 3 months. Checking plasma TfSat has no interest during the major part of the induction phase since this parameter, in contrast with plasma ferritin levels, does not fall until the very end of this phase. During maintenance therapy, it may be advised to monitor TfSat for instance twice a year in order to ensure that the patient does not exhibit a biological profile permanently marked by the contrast between satisfactory ferritin levels and a strong rise in transferrin saturation (especially over 75%, a threshold that may correspond to some risk of iron toxicity due to the presence of LPI). In terms of global results, venesection therapy is simple, cheap, efficient, and well tolerated. Some limitations, however, should be pointed out: i) efficiency may only be partial when organ lesions were too severe when starting the treatment (arthropathy, liver cirrhosis with the persistent risk of liver cancer despite appropriate iron removal) ; ii) tolerance is not devoid of side effects affecting the quality of life (discomfort of the needle puncture especially) [START_REF] Brissot | Hereditary hemochromatosis: patient experiences of the disease and phlebotomy treatment[END_REF].

Erythocytapheresis;

This method is to remove only red blood cells. Rarely used, it is more complex and expensive than venesections, but more efficient, and globally well accepted by the patients [START_REF] Rombout-Sestrienkova | Erythrocytapheresis versus phlebotomy in the maintenance treatment of HFE hemochromatosis patients: results from a randomized crossover trial[END_REF]. It can be particularly suitable for people whose professional activity (frequent travelers) is not conducive to frequent repeated bleedings.

3.1.3. Iron chelation. It can be discussed in the rare situations where phlebotomies are not possible either for psychological or technical (poor venous access) reasons.

Although desferrioxamine is the only approved drug in this indication, its modalities of administration (prolonged subcutaneous infusions by a portable pump, twelve hours a day and 5 days a week) are rather dissuasive and explain why an oral chelator (such as deferasirox ,may be preferred despite its status of off label medication and some possible side effects (leading to a prescription under the clinician responsibility and with an informed written consent by the patient).

Therapeutic perspective

The improved mechanistic knowledge of iron overload development in HC opens the road for applying an innovative approach consisting in hepcidin supplementation. Two main ways are theoretically possible, exogenous administration of hepcidin (minihepcidins [START_REF] Ramos | Minihepcidins prevent iron overload in a hepcidin-deficient mouse model of severe hemochromatosis[END_REF], full hepcidin, or hepcidin agonists) or endogenous stimulation of hepcidin synthesis by targeting one of the molecular steps involved in the hepcidin synthetic pathway. Normalizing plasma hepcidin levels would restore normal iron homeostasis, and could be indicated as an adjunct to venesections during the induction phase (in order to shorten this phase) or for totally replacing maintenance venesections.

3.2.Treatment of non-HFE HC

Types 2, 3 ad 4B HC

Venesection treatment is fully indicated given the phenotype of hepcidin deprivation. Chelation therapy may be associated in case of massive iron overload such as in juvenile HC (type 2A(49, 50) and 2B). Hepcidin supplementation is also a logical perspective (except for type 4B HC characterized by hepcidin resistance).

Type 4 A HC

Venesections remain indicated although their tolerance is less satisfactory than in the group of hepcidin deprivation-related HC. Indeed, given the impairment of cellular iron export, the iron recycling process induced by the venesection procedure is less efficient and exposes to the risk of anemia if the phlebotomy schedule is too strong. Therefore, it is advised to alleviate this schedule and, usually, one venesection every two weeks is feasible and efficient [START_REF] Lan | Sex and acquired cofactors determine phenotypes of ferroportin disease[END_REF]. It should be noticed that the plasma ferritin levels reflecting « de-ironing » may be significantly higher than in type 1 HC (the correlation between plasma ferritin concentrations and tissue iron overload being different) so that iron-MRI can be helpful to get an objective assessment of residual body iron stores. Restoring ferroportin activity in its specific iron export property would represent the future therapeutic approach but still seems a distant prospect.

In conclusion, hemochromatoses are potentially severe diseases, especially because their diagnosis can be ignored during a long asymptomatic period or misdiagnosed due to frequently aspecific clinical expression. Diagnosing

1 .

 1 It will consider four main aspects(9) (Figs. 1 and 2) . 1.2. Hemochromatoses with iron overload due to enhanced cellular iron influx related to deprivation in hepcidin 1.2.1. Mechanisms of hepcidin cellular deprivation. Hepcidin (encoded by the HAMP gene) is the iron hormone governing systemic iron homeostasis.

1. 3 .

 3 Hemochromatoses with iron overload due to decreased cellular iron efflux related to ferroportin deficiency 1.3.1. Mechanisms of ferroportin deficiency. The involved mutations of the ferroportin gene affect the cellular iron export function and not the domain interacting with hepcidin, . As a consequence, cellular iron egress is impaired, leading to increased intracellular iron stores. Such a situation is present in type 4A HC, which is the most frequent form of the ferroportin disease(4, 5).

2. 1 .

 1 To suspect iron overload 2.1.1. From the clinical viewpoint, many symptoms, more or less associated, can reflect HC. Chronic fatigue, joint pains, hyperpigmentation (melanodermia), impotence, diabetes, osteoporosis, hepatic features (mild increase of plasma transaminase activities, hepatomegaly, sometimes cirrhosis or hepatocellular carcinoma), cardiac symptoms (rhythm disturbances, heart failure). Anemic syndrome and neurological symptoms (extrapyramidal syndrome, cognitive dysfunction) can express HA. When comparing the clinical expression of the various HC types, the following remarks can be proposed : i) Type 1 HC is most often a delayed disease, with a long clinically asymptomatic phase until the age of approximately 30-40 years in men and 40-50 in women ; ii) Types 2A and 2B (and sometimes type 3) HC correspond to much rarer but also more severe diseases with clinical expression before the age of 30, and often before 20. They are characterized by severe lesions of the liver (cirrhosis), heart (cardiac failure), and endocrines (hypothalamic-pituitary insufficiency) ; iii) type 4A ferroportin disease is only clinically mildly symptomatic despite strong iron overload.

2. 4 . 1 .

 41 Tfsat is a pivotal diagnostic parameter, since increased TfSat favours hepcidin deprivation-related HC, whereas normal or low values are observed in the usual form of ferroportin disease and in HA.

  ABBREVIATION GLOSSARY

FIGURE 1 .

 1 FIGURE 1. From mutations to hypersideremia ; molecular and biochemical

FIGURE 2 .

 2 FIGURE 2. From mutations to cellular iron excess ; biological cascade.

FIGURE 3 .

 3 FIGURE 3. Diagnostics steps for HFE and non-HFE haemochromatosis.

FIGURE 4 .

 4 FIGURE 4. Present and future therapeutic approaches for HFE and non-

4

 4 Figure 1 Click here to download high resolution image

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ACKNOWLEDGEMENTS

The authors wish to thank the FFAMH, EFAPH, and AFeMERS associations for financial support.

DISCLOSURE OF INTEREST

PB has received honoraria for occasional consulting and lectures from Novartis laboratories.