Shuyin Yu

Qingfeng Zeng

Artem R Oganov

Chaohao Hu

Gilles Frapper

Litong Zhang

Exploration of stable compounds, crystal structures, and superconductivity in the Be-H system

Using first-principles variable-composition evolutionary methodology, we explored the high-pressure structures of beryllium hydrides between 0 and 400 GPa. We found that BeH 2 remains the only stable compound in this pressure range. The pressure-induced transformations are predicted as Ibam → P 3m1 → R 3m → Cmcm → P4/nmm, which occur at 24, 139, 204 and 349 GPa, respectively. P 3m1 and R 3m structures are layered polytypes based on close packings of H atoms with Be atoms filling all octahedral voids in alternating layers. Cmcm and P4/nmm contain twodimensional triangular networks with each layer forming a kinked slab in the ab-plane. P 3m1 and R 3m are semiconductors while Cmcm and P4/nmm are metallic. We have explored superconductivity of both metal phases, and found large electron-phonon coupling parameters of λ=0.63 for Cmcm with a T c of 32.1-44.1 K at 250 GPa and λ=0.65 for P4/nmm with a T c of 46.1-62.4 K at 400 GPa. The dependence of T c on pressure indicates that T c initially increases to a maximum of 45.1 K for Cmcm at 275 GPa and 97.0 K for P4/nmm at 365 GPa, and then decreases with increasing pressure for both phases.

INTRODUCTION

The search for new high-temperature superconductors has attracted great enthusiasm in both fundamental and applied research. Owing to its low mass and high electron density, "metallic hydrogen" has been predicted to possess a high superconducting transition temperature (T c > 200 K). [1][2][3] However, hydrogen remains insulating at extremely high pressure (>320 GPa 4 ), which are too high for any applications. Another feasible method of obtaining the properties of metallic hydrogen is to form hydrogen-rich alloys with other elements. 5 Due to "chemical precompression," the pressure of metallization may be reduced significantly.

Inspired by the elusive state of matter, theoretical and experimental research has made considerable progress towards exploring superconductivity in hydrogen-rich compounds, e.g. for group IVa hydrides, calculations predicted that SiH 4 , [6][7][8][9] SiH 4 (H 2 ) 2 , 10 GeH 4 , [11][12][13] SnH 4 14,15 and PbH 4 16 may become superconductors at high (yet lower than pure H) pressure. The origin of high-pressure superconductivity can be derived from the particular "H 2 " units, which are a feature common to a Electronic address: yushuyin2014@gmail.com 2158-3226/2014/4 ( hydrides of alkali metals, 17 alkaline earth metals 18,19 and group IVa elements. 12,15 Experiments suggested metallization of SiH 4 at ∼60 GPa 20 and its superconducting transition temperature (T c ) is 17 K at 96 and 120 GPa, 21 though debates remain. In addition, the superconductivity of group IIIa hydrides (BH, 22 AlH 3 23,24 and GaH 3 25 ) and alkaline earth metal hydrides (CaH n , 26 SrH n 19 and BaH n 18 ) have also been extensively explored.

Beryllium hydrides can be an interesting subject of study, because low atomic mass of Be may lead to very high T c values. The only known beryllium hydride is BeH 2 . The ground-state structure of BeH 2 is body-centered orthorhombic with Ibam 27 symmetry. At ambient conditions, BeH 2 is an insulator with a pronounced band gap of 5.5 eV. 28 Vajeeston et al. 29 proposed that BeH 2 undergoes a series of phase transitions α → β → γ → δ → ϵ at pressures of 7, 51, 87 and 98 GPa, respectively, and reported that BeH 2 remains insulating up to 100 GPa. Zhang et al. 30 systematically investigated the pressure-induced metallization of alkaline earth hydrides, and found the metallization pressure of Pnma-BeH 2 to be greater than 300 GPa. Wang et al. 31 predicted that BeH 2 reaches a metallic state by a R 3m → Cmcm phase transition, instead of a direct band gap closure in R 3m phase.

METHOD

First-principles variable-composition evolutionary simulations were performed at 0, 50, 100, 150, 200, 250, 300 and 400 GPa using the USPEX code, [32][33][34][35] which has the capability of discovering possible stoichiometries and the corresponding stable and metastable structures at given pressuretemperature conditions, and has successfully predicted a large number of stable structures. [36][37][38] The initial generation of structures and compositions was produced randomly with the use of space groups picked randomly from the total list of 230 groups. 50% of the lowest-enthalpy structures were used as parents for the next generation. In addition, 20% of structures in each new generation were produced by lattice mutation, 15% by atomic transmutation and 15% were produced randomly. Each generation contained 60 structures and runs proceeded for up to 50 generations.

The underlying structure relaxations were carried out using the Vienna Ab-initio Simulation Package (VASP) code, 39 in the framework of density functional theory (DFT) 40,41 within the Perdew Burke Ernzerhof generalized gradient approximation (PBE-GGA). 42 The frozen all-electron projected augmented wave approach (PAW) 43 was adopted to describe the core electrons and their effects on valence orbitals. A plane-wave kinetic energy cutoff of 600 eV and dense Monkhorst-Pack k-point grids 44 with a resolution higher than 2π × 0.06 Å -1 were used for all structures. The most stable structures were studied further at increased accuracy using a reciprocal-space grid better than 2π × 0.03 Å -1 .

Phonon calculations were carried out using the supercell approach as implemented in the PHONOPY code. 45 Electron-phonon coupling (EPC) calculations were explored using the pseudopotential plane-wave method within PBE-GGA, as implemented in the Quantum-Espresso package. 46 In these calculations, we used the kinetic energy cutoff of 60 Ry and Monkhorst-Pack k-point grids of 20 × 20 × 12 for the Cmcm phase and 16 × 16 × 8 for the P4/nmm phase with a Methfessel-Paxton 47 smearing factor of 0.05 Ry. Additionally, q-meshes of 5 × 5 × 3 for Cmcm and 4 × 4 × 2 for P4/nmm were used to calculate the electron-phonon coupling matrix elements, respectively. We used the Allen-Dynes-modified McMillan equation 48 to estimate T c , as follows:

T c = ω log 1.2 exp  - 1.04(1 + λ) λ -µ * (1 + 0.62λ)  (1)
where ω l og is the logarithmic average frequency, λ is the electron-phonon coupling constant and µ * is the Coulomb pseudopotential, which is assumed to be between 0.10-0.13. 5

RESULTS AND DISCUSSIONS

Fig. 1 shows the convex hull phase diagrams for the Be-H system at selected pressures. The ground-state enthalpy of formation ∆H f is defined as ∆H f (Be x H y ) = ∆H(Be x H y ) -x∆H(Be) -y∆H(H). A compound is thermodynamically stable if it has lower enthalpy than any isochemical mixture of the elements or other compounds. Such stable compounds form the convex hull. Based on our evolutionary searches, elemental Be adopts the P6 3 /mmc structure below 390 GPa and bcc Im 3m structure above 390 GPa. Our findings are in good agreement with previous calculations. 49 Hydrogen undergoes a series of phase transitions: P6 3 /m (P < 105 GPa), C2/c (105 < P < 207 GPa), Cmca-12 (270 < P < 385 GPa), Cmca (P > 385 GPa), 50 in addition to the experimentally known Ibam, 27 structure, we found a series of pressure-induced structural transformations (Ibam → P 3m1 → R 3m → Cmcm → P4/nmm) with increasing pressure. Notably, we did not find other stable compounds besides BeH 2 over the entire pressure range 0-400 GPa. The detailed structural parameters of these predicted phases are summarized in Table I. At ambient conditions, BeH 2 crystallizes in the orthorhombic Ibam structure. This structure consists of a three-dimensional network of distorted tetrahedra with Be atoms sitting at the center of the tetrahedra and H atoms at the corner in a bridged position between two Be atoms. The orthorhombic phase transforms to a CdI 2 -type structure (P 3m1; Fig. 2(a)) at 24 GPa, then it transforms to a related CdCl 2 -type structure (R 3m; Fig. 2(b)) at 139 GPa (Fig. 3(a)). Both structures are made We found a similar high-pressure structure in the B-H system: 22 at P > 168 GPa, the P6/mmm-BH structure is the most stable phase, and may be described as stacking BH-layers with planar closely-packed arrays of boron atoms. On-top H atoms locate symmetrically between the boron layers. Note that if one assigns a formal charge of -1 to H (hydride-like), both the boron atoms in BH and beryllium atoms in BeH 2 have a formal ns 2 valence electron configuration. Notably, the structural transformation from Ibam to P 3m1 is accompanied by a large density jump of 9.81% while only 0.79% increase occurs at the transition from P 3m1 to R 3m (Fig. 3(b)). The structures in Ref. 27 are metastable with respect to the P 3m1 structure.

At 204 GPa, the layered R 3m structure transforms into an orthorhombic Cmcm structure (Fig. 2(c)). In this structure, Be atoms are coordinated by eight hydrogens, whereas hydrogens are in the fourfold coordination (H1 atoms -in planar square coordination, H2 atoms -in tetrahedral coordination). Note that H1 atoms form flat pure-hydrogen rectangular layers with shortest H-H distance of 1.42 Å at 250 GPa. The tetragonal P4/nmm structure (PbClF-type) becomes stable at 349 GPa. In this structure, Be atoms are coordinated by nine hydrogen atoms (forming a capped tetragonal antiprism); H1 atoms are in a fourfold (planar square) coordination and H2 atoms in a fivefold (square pyramid) coordination. The structure can be viewed as layered, with double layers formed by Be and H2 atoms, alternating with square layers formed by H1 atoms. The Be-Be distances at 400 GPa are 1.901 and 1.906 Å within the double layers, and 2.328 Å between these layers, reinforcing cohesion of the highly delocalized covalent three-dimensional BeH 2 structure. The shortest H-H distance is between H1 atoms, i.e. in the pure-hydrogen square layer -at 400 GPa this distance is 1.345 Å. At such distances overlap of atomic orbitals is strong enough to make the material metallic. This is very similar to the Pbcn-SiH 4 9 with the closest H-H distance of 1.35 Å. Fig. 4 shows electronic densities of states (DOS) for the P 3m1 and R 3m structures, from which it can be clearly seen that both structures are insulting. As we know, GW approximation can precisely estimate the materials band gaps in contrast to the GGA and LDA methods. For the P 3m1 and R 3m phases, the gaps are 3.12 eV at 50 GPa and 1.80 eV at 150 GPa, respectively, indicating that both structures can be viewed as wide band gap semiconductors. In addition, it is clear that there is substantial hybridization of the Be-p states and H-s states, suggesting large degree of covalency. The covalent bonds are mainly from the intralayer BeH 6 octahedra while the interlayer interactions are mainly van der Waals forces. Fig. 5 shows the band structures, partial DOS and electron localization function (ELF) for the Cmcm phase at 250 GPa and P4/nmm phase at 400 GPa, respectively. The band structures reveal that both structures are metallic with several bands crossing the Fermi level, and a pseudogap. The dispersed valence and conduction bands near the Fermi level signify a relatively large DOS at the Fermi level (0.098 and 0.107 electrons/eV/f.u., respectively), which may favor superconducting behavior. The valence band widths are greater than in the low-pressure phases, which indicates enhanced electron delocalization, thus, more electrons participate in bonding interactions, which promotes structural stability.

Distributions of the electron localization function (ELF) reveal electron accumulation on the H atoms. For the P4/nmm phase, the ELF between H atoms in the square H-layer is close to 0.5 (Fig. 5(e)), which equals to the value for the electron gas. This indicates that the square H-layer is metallic, which we think it is the origin of the superconductivity. In the Cmcm phase, Bader [START_REF] Bader | Atoms in molecules: a quantum theory[END_REF] analysis reveals that Be atoms have charge +1.58 and the charges of H1 and H2 atoms are -0.82 and -0.76, respectively. The charges of Be, H1 and H2 atoms of the P4/nmm phase are +1.57, -0.94 and -0.63, respectively. It is obvious that there are large charge transfer from Be atoms to H atoms for both structures, indicating the ionic character of the bonds. Together with the DOS and ELF analysis, the bonding nature can be characterized as mixed metallic, covalent and ionic bonds.

The calculated phonon spectra for the Cmcm and P4/nmm phases establish dynamical stability, as there are no imaginary phonon frequencies anywhere in the Brillouin zone (Fig. 6). We further explored the superconductivity for both structures by performing electron-phonon coupling (EPC) calculations. For the Cmcm structure at 250 GPa, the electron-phonon coupling parameter λ is 0.63, indicative of quite strong EPC. Using the calculated ω l og of 1670.7 K and the commonly accepted values of the Coulomb pseudopotential µ * (0.1-0.13), 5 we obtained T c in the range of 32.1-44.1 K using the modified Allen-Dynes-modified McMillan equation. 48 Our results are similar to those of Wang et al., 31 the differences being due to different pseudopotentials. From Fig. 7(c), it is clear that T c of the Cmcm structure first increases and then decreases with increasing pressure, and reaches a maximum (45.1 K) at ∼275 GPa. Fig. 7 shows the total and partial phonon density of states together with the Eliashberg phonon spectral function α 2 F(ω) and electron-phonon integral λ(ω) as a function of frequency for the P4/nmm structure at 400 GPa. Low-frequency (<35 THz) vibrations are mostly related to Be atoms, while higher-frequency (>45 THz) modes mainly come from the vibration of H1 and H2 atoms. At 400 GPa, The calculated EPC parameter λ is 0.65, indicating rather strong EPC in the P4/nmm structure. Using the calculated ω l og of 2170 K and µ * (0.1-0.13), we obtained T c in the range of 46.1-62.4 K. The vibrations of Be below 35 THz contribute about 44.3% of total λ, while the vibrations of H1 and H2 above 45 THz contribute about 55.7% with no obvious difference between H1 and H2 vibrations to λ. In addition, the pressure dependence of T c displays the same trend as observed in the Cmcm phase and reaches a maximum of 97.0 K at 365 GPa. This is one of the highest T c values predicted in the literature. Note that the Allen-Dynes formula is expected to be reliable when λ is less than 1-1.5, 52 which is the case here.

CONCLUSIONS

In summary, using variable-composition evolutionary simulations for crystal structure prediction, we investigated the high-pressure phases of solid beryllium hydrides in the pressure range of 0-400 GPa. BeH 2 is found to be the only stable beryllium hydride. The pressure-induced transformations are predicted to be Ibam → P 3m1 → R 3m → Cmcm → P4/nmm, which occur at 24, 139, 204 and 349 GPa, respectively. The layered P 3m1 and R 3m structures belong to the well-known CdI 2 and CdCl 2 types, respectively. The Cmcm and P4/nmm phases contain 8-and 9-coordinate Be atoms, respectively, and layers of H atoms with short H-H distances, responsible for metallic conductivity. The entire phase transformations are first-order with volume shrinkage values of 9.81%, 0.79%, 2.71% and 0.43%, respectively. The P 3m1 and R 3m structures are semiconductors while the Cmcm and P4/nmm phases are metallic. Electron-phonon coupling calculations show that the Cmcm and P4/nmm structures are phonon-mediated superconductors, with large electron-phonon coupling parameters of 0.63 for the Cmcm phase with a T c of 32.1-44.1 K at 250 GPa and 0.65 for the P4/nmm phase with a T c of 46.1-62.4 K at 400 GPa. Dependence of T c on pressure indicates that T c will increase initially to a maximum value of 45.1 K for the Cmcm phase at 275 GPa and 97.0 K for the P4/nmm phase at 365 GPa, respectively, and then decrease with increasing pressure for both structures.

107118- 3 Yu

 3 FIG.1. Convex hull phase diagrams for the Be-H system at 0, 50, 150, 250 and 400 GPa.

FIG. 2 .

 2 FIG. 2. Extended crystal structures of solid BeH 2 for (a) the P 3m1 structure at 50 GPa; (b) the R 3m structure at 150 GPa; (c) the Cmcm structure at 250 GPa; and (d) the P4/nmm structure at 400 GPa. The large blue spheres represent Be atoms, while the small red and green spheres indicate two symmetrically inequivalent H atoms.

107118- 5 Yu

 5 FIG. 3. (a) Enthalpy per atom for various BeH 2 structures as a function of pressure with the P 3m1 structure taken as the reference; (b) Computed equations of state of BeH 2 (solid lines) and shortest H-H distance (dotted lines).

FIG. 4 .

 4 FIG. 4. Total and Partial density of states (DOS) for the (a) P 3m1 phase at 50 GPa and (b) R 3m phase at 150 GPa.

107118- 7 Yu

 7 FIG. 5. (a) and (b) band structures and partial DOS for Cmcm phase at 250 GPa and P4/nmm phase at 400 GPa, respectively; (c), (d) and (e) electron localization function (ELF) through specific surfaces.

FIG. 6 .

 6 FIG. 6. Calculated phonon spectra along selected high symmetry points for (a) the Cmcm phase at 250 GPa and (b) P4/nmm phase at 400 GPa.

TABLE I .

 I Optimized structural parameters for the predicted BeH 2 structures at selected pressures.

	107118-4	Yu et al.
	Pressure			Lattice parameters			Wyckoff positions
	(GPa)	Space group	No.	(Å, deg)	Atom	Sites	x	y	z
	50	P 3m1	164	a = 2.085	Be	1a	0	0	0
				c = 3.104	H	2d	0.667	0.333	0.721
	150	R 3m	166	a = 1.886	Be	1b	0	0	0.5
				c = 8.316	H	2c	0	0	0.732
	250	Cmcm	63	a = 1.796	Be	4c	0	0.139	0.75
				b = 5.503	H1	4b	0	0.5	1
				c = 2.840	H2	4c	0	0.819	0.75
	400	P4/nmm	129	a = 1.906	Be	2c	0.5	0	0.707
				c = 3.240	H1	2a	0	0	0
					H2	2c	0.5	0	0.327

AIP Advances 4, 107118 (2014)

107118-9 Yu et al. AIP Advances 4, 107118 (2014) We thank the Natural Science Foundation of China (Grants No. 51372203, No. 11164005 and No. 51332004), the National Basic Research Program of China (973 Program, Grant No. 2014CB643703), the Basic Research Foundation of NWPU (Grant No. JCY20130114), the Foreign Talents Introduction and Academic Exchange Program (Grant No. B08040), the National Science Foundation (Grants No. EAR-1114313 and No. DMR-1231586), DARPA (Grants No. W31P4Q1310005 and No. W31P4Q1210008), and the Government of the Russian Federation (Grant No. 14.A12.31.0003) for financial support. The authors also acknowledge the High Performance Computing Center of NWPU, Shanghai Supercomputer Centre, and the National Supercomputing Center in Shenzhen and the GENCI-CINES (France) for the allocation of computing time on their machines.


Hamza B Mahamat

Mathieu Le Coz

Hamit Abderamane

Paul Sardini

Moumtaz Razack

Hydrochemical and Isotopic Characteristics of the Basement Aquifer in the Wadi Fira Area, Eastern Chad

Keywords: Basement Aquifer, Hydrochemistry, Stable Isotopes

The Wadi-Fira region in eastern Chad is facing dramatic water supply problems, related to the climatic semi-arid context and the reception of refugees from the Darfour, which has increased the local population by 22% these last years. Expansion of agglomerations (temporary new towns), development of agricultural and pastoral practices together with the augmentation of the population have led to dramatic water needs. The basement aquifer of Wadi-Fira constitutes the main source of water supply. However, little is known about this system. Within this context, this work aims at better understanding and identifying hydrogeochemical processes and their relations to groundwater quality within this complex environment, and groundwater recharge mechanisms. 31 groundwater samples were collected at two sites, Am Zoer and Guereda-Iriba, from hand dug wells and deep wells. Major chemical elements were analyzed on all samples and stables isotopes (oxygen-18 and deuterium) on 17 samples. Various methods were used to interpret the hydrochemical data (descriptive and multivariate statistics, Piper and Schoeller diagrams, scatter plots, minerals saturation indices). The stable isotopes were interpreted using conventional IAEA methods. The results permitted to differentiate the laterite reservoir from the deep fractured reservoir. The main process controlling groundwater mineralization is water-rocks interaction and natural minerals dissolution. Ion exchanges, evaporation and anthropogenic activities have also a moderate impact on groundwater quality. Based on isotopes data, it is concluded that groundwater in the basement aquifer is related with modern rainfall. These results provide further insights into this basement aquifer, which is a vital resource for the region of Wadi-Fira.

Introduction

The Wadi-Fira region in eastern Chad, adjacent to Sudan (Figure 1), is located in an arid environment, exposed to the climate changes, where crystalline basement is mainly exposed. This region is regularly faced with recurring problems of water supply. This situation is linked to the climatic context of this region with a rather low rainfall, but also to the lack of knowledge about the basement aquifer.

However, the basement aquifer of Wadi-Fira constitutes the main source of water supply for the populations of this region. The aquifer system has two main types of reservoirs, the alterites reservoir and the fractured reservoir. Most of the underground water resources exploited by deep wells and hand dug wells are located in alterites and basement fractured rocks. Sedimentary formations play a negligible role.

In 2003, the Wadi-Fira region hosted ≈201,000 refugees from Darfur out of a total of ≈924,000 residents that is 22% of the population. This migratory flow led to an expansion of agglomerations (temporary new towns), an increase in agricultural and pastoral practices. The groundwater of the crystalline system is thus now heavily exploited to meet the dramatically increasing water requirements in recent years.

The rational exploitation of this vital resource requires a prior assessment of the processes of mineralization of the groundwater in order not to degrade its quality by a disorderly overexploitation. Within this framework, the present investigation aims at better understanding and identifying hydrogeochemical processes and their relations to groundwater quality within this complex environment, and groundwater recharge mechanisms.

The geological formations encountered in the study area are mainly granitoids, schists, migmatites and volcano-sedimentary formations (basalts and alluvium) covering the crystalline basement. Two regions were sampled to conduct this work, the Am Zoer region and the Guereda-Iriba region.

Geological and Hydrogeological Framework

The study area lies between latitudes 14˚ and 16˚North, and longitudes 21˚ and 23˚East. It covers an area of approximately 50,000 km². It is characterized by a Sahelo-Saharan climate, with a great spatial and temporal variability in precipitation, i.e. 150 to 400 mm of rain per year, between the North and the South.

Most of the rainfall is concentrated over two months, between July and August.

The Am Zoer site is located in the south-west, and that of Guereda-Iriba in the northeast (Figure 1). The particularities of these two contexts will be analyzed from the hydrogeochemical point of view related to the aspect of the water resource.

The geological context of the study area (Figure 1) was elaborated from the geological map of Niéré at 1/500,000 [START_REF] Sonet | Explanatory Booklet on the Niéré Sheet[END_REF].

The formations of the Precambrian basement identified in Chad, of which the Ouaddaï massif forms part, covers between 15% and 20% of the territory of the country [START_REF] Isseini | Crustal Growth and Differentiation during the Neoproterozoic Example of the Pan-African Domain of Mayo Kebbi in Southwestern Chad[END_REF]. The formations encountered are granitoids, metamorphic rocks (schists, quartzites, micaschists, gneiss, green rocks and migmatites) and volcano-sedimentary formations. The granitoids are composed of granodiorites and granites that are exposed on most parts of the basement of the Ouaddaï. The volcanic formations occur in basaltic flows along the wadi Absounout near Iriba, or in isolated pitons with circular base about 200 m in diameter and with steep slope. The sedimentary formations consist of the Palaeozoic (Cambrian) sandstones, the Continental Terminal sandstones and alluvial formations (sand, clay, silt).

From recent results, it is observed that in basement hard rocks, aquifers are located within the first tens of meters in the rocks [START_REF] Wyns | Application of SNMR Soundings for Groundwater Reserves Mapping in Weathered Basement Rocks (Brittany, France)[END_REF] [4] [START_REF] Maréchal | Review of Specific Methods for the Evaluation of Hydraulic Properties in Fractured Hard-Rock Aquifers[END_REF]. The typical vertical profile comprises from top to bottom: i) The laterite layer with a few meters thickness, ii) The alterite (or regolith) layer, a few tens of meters thick, derived from the weathering of the basement rocks; iii) The fractured layer which consists of the massive rocks. The fracture network mainly results from the tectonic activity in the region, but also from the weathering process itself [START_REF] Acworth | The Development of Crystalline Basement Aquifers in a Tropical Environment[END_REF] [START_REF] Cho | Relationship between the Permeability of Hard-Rock Aquifers and Their Weathered Cover Based on Geological and Hydrogeological Observation in South Korea[END_REF].

In the Wadi-Fira study area, groundwater is exploited by shallow large-diameter wells (average depth ≈10 m) dug in the alterites and deeper wells penetrating the fractured aquifer (mean depth ≈45 m). The piezometric map is reported in Figure 2. This map does not differentiate the laterite reservoir from the fractured rocks reservoir. Given the scale of the study area, a continuous system can be assumed. Interpretation of the map indicates that groundwater is mainly drained towards rivers beds. [START_REF] Piper | A Graphic Procedure in the Geochemical Interpretation of Wa-H. B. Mahamat et al[END_REF] and dug wells [START_REF] Cho | Relationship between the Permeability of Hard-Rock Aquifers and Their Weathered Cover Based on Geological and Hydrogeological Observation in South Korea[END_REF]. The chemical and isotopic analyzes were carried out at the Center of Hydrogeology and Geothermics (CHYN) of the University of Neuchâtel in Switzerland.

Sampling and Analytical Procedures

During both field missions, the physical parameters (electrical conductivity, pH and temperature) of the groundwater were measured in situ. The data of the conductimeter during these two campaigns proved unfortunately wrong.

Other complementary parameters were also measured, the location and altitude of the water points using a Garmin GPS, the piezometric level and the depth of the wells respectively by a piezometric probe and a decametric tape.

Analyzes of the major ions, cations and anions were carried out respectively by ion chromatography Dionex DX-120 and Dionex-ICS-1600. The determination of the bicarbonate ion ( 3 HCO -) was carried out by the titrimetry method using an apparatus of the Metrohm 805 Dosimat type. The quality of the analyses was verified by the calculation of the ion balance.

The isotopic analyzes were carried out only on the samples collected during the 2 nd campaign in 2015. The stable isotopes contents of the water molecule are measured by the Picarro L2140-i analyzer, which performs simultaneous measurements of δ 18 O and δ 2 H with an accuracy of ±0.0015‰.

All stable isotopic composition ( 18 O and ²H) are reported in standard δ‰ notation (part per thousand versus VSMOW (Vienna Standard Mean Ocean Water)) as follows:

( )

‰ Rsample Rstandard 1 1000 δ = -×    
where Rsample and Rstandard represent the ratio of heavy to light isotopes of the samples and standard, respectively [START_REF] Craig | Isotopic Variations in Meteoric Waters[END_REF].

Interpretative Methods

The results of the physico-chemical and isotopic analyzes carried out on the 31 groundwater samples are interpreted using statistical, graphical and hydrogeochemical methods. Statistical interpretations were performed using box-plots, correlation matrice and Principal Component Analysis (PCA). The hydrochemical classification of water is developed using Piper's trilinear diagram [START_REF] Piper | A Graphic Procedure in the Geochemical Interpretation of Wa-H. B. Mahamat et al[END_REF]. The study of hydrochemical processes is based on the calculation of the saturation indices and scatter diagrams of chemical elements.

The Phreeqc geochemical program allowed to evaluate the saturation indices, to characterize the geochemical processes at the origin of the mineralization of groundwater.

Isotopic data on stable isotopes (oxygen-18 and deuterium) in groundwater have been interpreted using conventional IAEA methods [START_REF]Global Network of Isotopes in Precipitation (GNIP) Database IAEA/WMO[END_REF].

The application of all these different methods to the hydrochemical and isotope data allowed to characterize the mechanisms of mineralization of ground-DOI: 10.4236/jwarp.2017.913105 1693 Journal of Water Resource and Protection water and the recharge processes in the basement aquifer of the Wadi-Fira area.

Groundwater Chemistry

Descriptive Statistics

The physico-chemical data of the groundwaters samples are reported in Table 1.

Table 1. Hydrochemical data from samples collected in the field at the 2 sites, Am-Zoer (AZ) and Guereda-Iriba (GI). P: hand dug wells; F: deep wells.

Name Long E Lat N Depth (m) T˚C pH Ca 2+ Mg 2+ Na + K + 3 HCO - Cl - 2 4
SO -F - The descriptive statistics (average, variance, coefficient of variation) are reported in Table 2. The groundwater samples are of low overall mineralization. The average mineralization is 336 mg/l and is in the range of 106 to 628 mg/l, showing that the groundwater in the study area is fresh. The pH of the groundwater, for both hand dug wells and deep wells ranges between 4.6 and 8.9 with an average of 7.0. More than half of the pH values (51%) are in the range 5.5 -7.5. Such intermediate natural-water pH values implies a balance between the production of H + ions from the dissociation of weak acids, and H + (and CO 2 ) consumption by weathering reactions, as the weathering of albite (Na-feldspar) to kaolinite [START_REF] Langmuir | Aqueous Environmental Geochemistry[END_REF].

( )

3 8 2 2 2 2 5 4 4 3 4 2NaAlSi O 2CO 11H O Al Si O OH 2Na 4H SiO 2HCO + - + + → + + + (1)
The weak acids involved in these processes are carbonic acid and organic acids such as fulvic acid [START_REF] Langmuir | Aqueous Environmental Geochemistry[END_REF]. These weak acids are the cause which provokes the weathering of silicate and alumino-silicate minerals within such basement environment.

Higher pH values are also observed in the study area with values in the range 7.5 -8.5 common in groundwaters in hard rocks (basalt and granite). The maximum observed pH value for groundwaters is 8.9. High pH values occur in waters whose composition is dominated by minerals such as silicates and aluminosilicates, which tend to raise the pH [START_REF] Langmuir | Aqueous Environmental Geochemistry[END_REF]. Groundwaters with pH values greater than 9.0 are classified as'rock-dominated' [START_REF] Langmuir | Aqueous Environmental Geochemistry[END_REF], meaning that they are likely not to be recharged very fast. All pH values higher that 7.5 characterize deep wells in the study area, showing that groundwater recharge in such sites is slower.

The groundwater temperature varies from 16˚C to 33˚C with an average of 28˚C. These temperatures are close to the air temperature in the region of 29˚C,

showing that recharge takes place by infiltration of rainfall, in the absence of An analysis of the hydrochemical data, carried out using Box-plots, is shown in Figure 3. The purpose of this plot is to demonstrate a possible differentiation between subsurface groundwater sampled in wells dug in alterites and the deep groundwater sampled in wells penetrating the fractured crystalline reservoir.

The mean values of the variables are also reported in Table 3.

The box-plot (Figure 3) compares the parameters of waters from the boreholes and dug wells. This results in significant differences in the values of T˚C, pH, Ca 2+ , Na + , K + , Cl -,

3 HCO -, 2 4
SO -, and F -. NO -. This highlights the increasing mineralization of infiltrating waters and that mineralization processes are more pronounced in fractured rock. The average mineralization of dug wells water is lower (average TDS = 235 mg/l) than that of deep wells (average TDS = 357 mg/l).

Correlation Matrice

Pearson correlation matrice [START_REF] Swan | Introduction to Geological Data Analysis[END_REF] was calculated between hydrochemical variables to display their respective statistical relationships (Table 4). Significant correlation coefficients, at a level of 0.05 (p < 0.05), are highlighted in the table.

Strong correlations are found between Ca 2+ and Fluoride content is rather an important issue regarding potability of groundwater. According to the World Health Organization [START_REF] Who | Guidelines for Drinking Water Quality[END_REF], water with a content higher than 1.5 mg/lis unsuitable for drinking. In the Wadi-Fira area, F -content ranges between 0.1 mg/l and 2.9 mg/l, with an average of 1.0 mg/l, indicating that at some places, the groundwater is unsuitable for drinking. It is thus important to understand the origin of F -in groundwater.

The high correlation between F -and Na + should be noticed, providing an indication on the possible source of F -. Dissolution of fluoride-bearing minerals ) was depicted as a source of F-in hard rocks groundwater [START_REF] Furi | Hydrochemical Characterization of Complex Volcanic Aquifers in a Continental Rifted Zone: The Middle Awash Basin, Ethiopia[END_REF]. However further investigations are still required to deepen this issue in the Wadi-Fira area.

Cations that can exchange through ion exchange processes exhibit moderate correlation (Na + -Ca 2+ : R = 0.45; Na + -Mg 2+ : R = 0.51). This indicates that cation exchange processes can affect the groundwater chemical composition, but are not dominant processes.

Principal Component Analysis

Principal Component analysis is a well-established and widely used multivariate method in hydrochemical studies. As groundwater mineralization is a multivariate concept, analyzing the hydrochemical parameters pairwise, may lead to ignore relevant relationships [START_REF] Steinhorst | Discrimination of Groundwater Sources using Cluster Analysis, MANOVA, Canonical Analysis and Discriminant Analysis[END_REF]. Thus, a Principal Component analysis (R mode factor analysis, [16] [17] was undertaken in this work in order to extract significant information about analyzed data set and better display the inter-relations between the variables. A PCA may also contribute to understand the underlying geochemical reaction and hydrochemical evolution processes. The data processed by the ACP consists of 12 hydrochemical elements measured on 31 samples from the Am Zoer and Guéréda-Iriba sites. The eigenvalues and the percentages of variance explained by each Principal Component (PC) are shown in Table 5.

The PC1 component with an expressed variance of 37.2% is the most important of all the factorial axes. The PC2 component expresses the greatest residual variance, i.e. 18.6% of the total variance. The factor plane PC1-PC2 expresses 58.8% of the cumulative variance. As can be seen on the screeplot (Figure 4), the first 2 components are sufficient to explain the variability of the data set. Thus, this PC1-PC2 plan incorporates enough significant information to highlight and explain the general trends of the studied system. The loadings of the variables are reported in Table 5 and reported in Figure 3.

The results of the PCA are shown in Figure 5 (Projection of the hydrochemical parameters on the plane associated to components PC1 and PC2, and in Figure 6 (Projection of the samples).

The component PC1, which has the highest variance (37.2%), is strongly associated with major chemical elements (Ca 2+ , Mg 2+ , Na + , 3 HCO -, Cl -). Correlations with the other elements (F -and 2 4 SO -) also remain significant. It is noted that the physical parameters (temperature, pH, depth) are also well associated with this axis. The second component PC2 is positively associated with F -(0.71), and negatively with potassium (-0.86).

The analysis of the projection of the variables on the factor plane (PC1-PC2) reveals that the factorial axis PC1 gathers almost all the elements in the positive pole with the exception of potassium (K + ) and 3 NO -. These two elements have no significant correlation with the set of variables represented in the correlation matrix. The axis CP2 is negatively correlated with the variables; Ca 2+ , Cl -,

2 4
SO -, pH, T˚C, and K + , the positive pole is represented by the variables; 3 HCO -, Na + , Mg 2+ , F -.

The spatial analysis of the variables of the PC1-PC2 plane makes it possible to classify, according to the affinities of the ions, two groups of variables. The first group is determined by On the other hand, certain discrimination can be observed on the deep waters between the two sites. Accordingly, it can be noted that most of the deep wells at Am Zoer site have warmer, more basic waters, differenciated by SOand Cl - ions. Guereda-Iriba waters are more associated with Na + and 3 HCOelements, and especially with F -.

The alkaline earths (Ca 2+ , Mg 2+ ) are present in both sites and do not discriminate between these two sites.

Groundwater Types

The analysis of the data from the 31 water samples shows the order of abundance of major ions as follows: calcium (51%) and bicarbonate (80%) are respectively the main cation and anion in the groundwater. The relative abundance in descending order for cations in groundwater is Ca 2+ > Na + > Mg 2+ > K + while that of the anions is SOions play a minor role in the mineralization of the basement aquifer groundwater.

Hydrogeochemical Processes

Scatter Plots

Interpretation of ionic relations in the form of scatter plots can greatly help to understand the origin of solutes and the various hydrogeochemical processes involved in the groundwater chemistry. These scatter plots are reported in Figure 9. The plot Na + vs. Cl -(Figure 9 shows that in all samples these elements are very weakly correlated. All samples display an enrichment with Na + compared to Cl -, indicating that these elements are not derived from the same source. The Na + /Cl -molar ratio is higher than 1

(1.2 < Na + /Cl -< 13.8), reflecting that silicate weathering can be the main contributor for Na + [START_REF] Meybeck | Global Chemical Weathering of Surficial Rocks Estimated from River Dissolved Loads[END_REF]. For example albite weathering contributes Na + (see equation 01). The relation of Na + associated to base exchanges process is discussed below.

The presence of Cl -can be attributed to another source for this ion than the dissolution of halite and could be associated, at least partly, to anthropogenic sources (agricultural fertilizers).

The source for alkaline earth elements (Ca 2+ and Mg 2+ ) may be dissolution of silicate minerals (e.g., plagioclase feldspar, chlorite, or biotite), carbonates (dolomite or calcite), gypsum, and/or cation exchange of Na + for Ca 2+ and Mg 2+ on clay minerals.

3 HCOvs. Ca 2+ (Figure 9(b)) displays a significant linear trend (R = 0.75). Samples from Am Zoer site display an excess of Ca 2+ while those from Guereda-Iriba plot close to 1:1 line. An essential point is that mineralization processes in the study area, are not homogeneous but display a noteworthy spatial variability.

The scatter plot 3 HCOvs. Mg 2+ (Figure 9(c)) is characterized by a significant correlation (R = 0.68), but also shows a deficit in Mg 2+ . These relations indicate that dissolution of carbonates (dolomite or calcite) is not the main source for these elements. Other sources for these ions are discussed below.

In crystalline rocks, Ca 2+ is found in the feldspar network, associated with sodium and potassium, while Mg 2+ is associated with iron in ferromagnesian materials (micas, amphiboles, pyroxenes, peridots). Thus excess of Ca 2+ in granitic rocks (Figure 9

Figure 1 .

 1 Figure 1. Location and geological setting of the study site. Wadi-Fira region (Eastern Chad).

Figure 3 . 3 HCO

 33 Figure 3. Box plots representation of the hydrochemical parameters sampled in hand dug wells and in deep wells.

3 HCO- 3 HCO

 33 (R = 0.77), Mg 2+ and 3 HCO -(R = 0.68), Na + and 3 HCO -(R = 0.78), Ca 2+ and Cl -(R = 0.73), Na + and F -(R = 0.73). Strong relationships between Ca 2+ , Mg 2+ , Ca 2+ and Cl -, Na + and 3 HCOwould result from complex processes discussed below.

Figure 4 .

 4 Figure 4. Principal components analysis (PCA) screeplot.

3 NO

 3 and K + are poorly represented on this axis. The component PC1 thus expresses the mineralization of the water in the study region.

3 HCO

 3 -, Na + and F -. The second group contains the variables pH, T˚C, DOI: 10.4236/jwarp.2017.913105 1699 Journal of Water Resource and Protection

Figure 5 .

 5 Figure 5. Principal Components Analysis (PCA). Hydrochemical variables loading plot on PC1 vs. PC2.

Figure 6 .

 6 Figure 6. Plot of groundwater samples on PC1 vs. PC2.

3 HCO

 3 are not significantly correlated with any other element (indicating anthropogenic origin), they ae not considered in the Piper diagram (Figure7).The Piper diagram shows that the dominant anion is at both sites. For the waters of most deep wells at Am Zoer site, the dominant cation is Ca 2+ .Waters from dug wells and some boreholes at Guereda-Iriba, are marked by the poles Ca 2+ and Mg 2+ . A single well (F23) at Guereda-Iriba, is characterized by the Na + pole.The Piper diagram thus shows the following hydrochemical types:-bicarbonate-calcium type secondary bicarbonate-sodium and bicarbonatemagnesium -bicarbonate calcium type secondarily magnesium -bicarbonate sodium type secondary bicarbonate-calcium and magnesium These hydrochemical types are also represented on a semi-logarithmic Schoeller diagram[START_REF] Schoeller | Geochemistry of Groundwater. An International Guide for Research and Practice[END_REF] (Figure8) on 10 selected samples. This diagram also shows that the Ca 2+ and 3 HCOions are preponderant in groundwater chemical composition and reveals more clearly that Cl -and 2 4

  (a)) H. B. Mahamat et al. DOI: 10.4236/jwarp.2017.913105 1701 Journal of Water Resource and Protection

Figure 7 .

 7 Figure 7. Trilinear Piper plot of the groundwater samples.

Figure 8 .

 8 Figure 8. Plot on the Schoeller semi-logarithmic diagram of some selected groundwater samples.

H

  . B. Mahamat et al. DOI: 10.4236/jwarp.2017.913105 1702 Journal of Water Resource and Protection

Figure 9 .

 9 Figure 9. Scatter plots between chemical elements.

  Two sampling campaigns were conducted in 2011 and 2015 for a total of 31 Figure2. Piezometric map of the study area.

	H. B. Mahamat et al.
		groundwater samples. The first campaign involved 15 deep wells. The analyses
		were carried out at the National Laboratory of Water Analysis (LNAE) in Ndja-
		mena (Chad). The second field mission in July 2015 resulted in the sampling of
		16 water samples from boreholes
	DOI: 10.4236/jwarp.2017.913105	1692	Journal of Water Resource and Protection

Table 2 .

 2 Descriptive statistics of the hydrochmical parameters. CV: coefficient of variation; SD: standard deviation.

	Parameter	Minimum	Maximum	Average	S.D.	CV %	WHO Standard
	Ca 2+ (mg/l)	10.6	88.8	42.6	20.4	47.9	-
	Mg 2+ (mg/l)	0.5	30.0	9.0	6.3	69.7	50 -500
	Na + (mg/l)	6.3	92.1	28.5	16.1	56.5	150 -200
	K + (mg/l)	0.8	9.0	3.5	2.0	58.2	No-12
	Cl -(mg/l)	2.7	45.0	14.9	10.9	72.6	200 -250
	2 4 SO -(mg/l)	2.0	54.0	13.4	11.5	86.4	250
	3 HCO -(mg/l)	53.4	430.1	196.2	99.1	50.5	-
	3 NO -(mg/l)	2.1	113.1	20.7	21.7	105.2	50
	F -(mg/l)	0.1	2.9	1.0	0.6	58.7	1.5
	T˚ (˚C)	16.5	32.9	28.0	3.0	10.6
	pH	4.6	8.9	7.0	1.3	18.0

DOI: 10.4236/jwarp.2017.913105 1695 Journal of Water Resource and Protection very deep circulations.

  All box-plots show that concentrations of the elements are higher in deep wells than in wells dug in the alterites except for K + and

			3
			2 4 SO -F -	3 NO -TDS
	DW.	45.1 28.5 7.4 47.3 9.5 32.0 3.0 210.5 17.7 14.9 1.2 21.3 357
	HDW.	10.2 26.3 5.8 26.3 7.4 16.7 5.3 147.1 5.3	8.1 0.5 18.4 235

DOI: 10.4236/jwarp.2017.913105 1696 Journal of Water Resource and Protection

Table 4 .

 4 Correlation matrix between variables.

	Variable Depth T˚C	pH Ca 2+ Mg 2+ Na +	K +	3 HCO -Cl -	2 4 SO -	F -	3 NO -
	Depth	1.00
	T˚C	0.23	1.00
	pH	0.40	0.37 1.00
	Ca 2+	0.35	0.44 0.61 1.00
	Mg 2+	0.02	0.09 0.18 0.47 1.00
	Na +	0.31	0.28 0.21 0.45 0.51 1.00
	K +	-0.28 -0.05 -0.12 -0.19 0.05 -0.34 1.00
	3 HCO -	0.21	0.32 0.33 0.77 0.68 0.77 -0.29 1.00
	Cl -	0.43	0.45 0.56 0.73 0.30 0.16 0.19	0.31	1.00
	2 4 SO -	0.31	0.22 0.40 0.42 0.45 0.31 0.42	0.28	0.61 1.00
	F -	0.31	0.06 0.03 0.38 0.27 0.73 -0.65 0.59	0.05 0.01 1.00

DOI: 10.4236/jwarp.2017.913105 1697 Journal of Water Resource and Protection such as cryolite (Na 3 AlF 6

Table 5 .

 5 Physicochemical variables loadings on principal components.

		PC1	PC2	PC3
	T˚C	0.480	0.130	-0.077
	pH	0.776	0.095	-0.335
	Ca 2+	0.812	0.426	0.064
	Mg 2+	0.403	0.339	0.640
	Na +	0.285	0.787	0.288
	K +	0.192	-0.726	0.300
	Cl -	0.855	-0.079	0.143
	2 4 SO -	0.668	-0.132	0.397
	3 HCO -	0.513	0.748	0.186
	3 NO -	-0.157	0.009	0.545
	F -	0.015	0.862	0.087

DOI: 10.4236/jwarp.2017.913105 1698 Journal of Water Resource and Protection

NO - -0.06 0.02 -0.20 0.07 0.10 0.01 -0.12 -0.16 0.11 0.00 0.07 1.00

4SOand Cl -. The Ca 2+ , Mg2+ and Depth variables are intermediate to these 2 groups.

Weathering of ferromagnesian minerals such as biotite may be responsible for the release of Mg 2+ in groundwater in basement rocks (reaction 3):

Additional geochemical processes such as the Ca 2+ ↔ Mg 2+ exchanges during precipitation reactions or calcite recrystallization [START_REF] Edmunds | The Origin of Saline Groundwaters in the Carnmenellis Granite, Cornwall (UK): Further Evidence from Minor and Trace Elements[END_REF] may contribute to excess of Ca 2+ compared to Mg 2+ (Figure 9(d)). Figure 9(e) shows the scatter plot

SOvs. Ca 2+ . This plot displays a large deficit in SOvs. Mg 2+ . The absence of any significant correlation indicates that the main source of these elements is not the dissolution of gypsum or any Mg-sulfate mineral. Concentrations of K + are low in Wadi-Fira groundwater (average 3.5 mg/l), which can be expected as there are no important mineral sources of K + in these aquifers.

Mineral Saturation Indices

Saturation indices of minerals indicate to which extent water mineralization is controlled by equilibrium with solid phases [START_REF] Appelo | Geochemistry, Groundwater and Pollution[END_REF]. When this indice is negative, the water is undersaturated with respect to the concerned mineral. A positive SI means that water is oversaturated regarding the mineral. When the SI value is close to 0, water is in equilibrium with the mineral.

The software PHREEQC [START_REF] Parkhurst | User's Guide to PHREEQC (Version 2)-A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations[END_REF] was used to determine mineral saturation indices using the specific ionic concentrations in the water.

The saturation index of a mineral is obtained from Equation (5) [START_REF] Appelo | Geochemistry, Groundwater and Pollution[END_REF].

( )

where IAP is the ion activity product of the dissociated chemical species in solution, Kt is the equilibrium solubility product for the chemical involved at the sample temperature.

The saturation indices of the following minerals in all water samples were evaluated: calcite, dolomite, gypsum and halite. The average values of the SI for each mineral are given in Table 6.

The saturation indices regarding calcite and dolomite have high and negative values, expressing that the groundwater is undersaturated with these minerals.

The evaporitic minerals (gypsum, halite) also have negative SI values. These results show that the minerals in question (calcite, dolomite, gypsum and halite)

are not the main source of the groundwater mineralization. This is in agreement with the conclusions derived above.

Role of Evaporation

As the study is located in a semi-arid climatological context, it may expected that evaporation could also affect groundwater mineralization. The role of evapora tion has been assessed using the Gibbs diagrams [START_REF] Gibbs | Mechanism Controlling World River Water Chemistry[END_REF].

Gibbs diagrams represent the ratios of (Na + + K + )/(Na + + K + + Ca 2+ ) and

Cl -/(Cl -+ 3 HCO -) as a function of TDS. They assume that evaporation increases salinity by increasing Na + and Cl -contents in relation with increasing TDS.

The diagram differentiates 3 areas highlighting various mechanisms: precipitation dominance, rocks dominance, evaporation dominance.

The plots of the hydrochemical data in Gibbs diagram are reported in Figure 10.

This figure shows that chemical weathering of rock-forming minerals is the most important functional source of dissolved elements in almost all groundwater samples. A few samples fall in the evaporation dominance area. These samples were collected from hand dug wells.

We may thus conclude that evaporation does not represent a major hydrochemical process in the study area.

Ions Exchanges Processes

Ions exchanges processes between the groundwater and its host rocks during its flow, can be analyzed using the plot of (Ca 2+ + Mg 2+ ) versus (

In this scatter diagram, the points close to the 1:1line (Ca 2+ + Mg 2+ = 2 4 SO -+ 3 HCO -) suggest that these ions have resulted from minerals dissolutions [START_REF] Fisher | Hydrochemical Evolution of Sodium-Sulfate and Sodium-Chloride Groundwater beneath the Northern Chihuahuan Desert, Trans-Pecos, Rexas, USA[END_REF].

When groundwater has been in contact with clayey materials able to release the interchangeable alkaline-earth ions easily, then Na + contained in groundwater can exchange with these alkaline-earth ions (Ca 2+ and Mg 2+ ) sorbed on the exchangeable sites. In such cases, groundwater is enriched with Ca 2+ and Mg 2+ and depleted in Na + . This process is called reverse ion exchange. Direct ion exchange may also occur (exchange between adsorbed Na + or K + with Mg 2+ or Ca 2+ in the groundwater). The fact that ions exchanges processes between groundwater and the crystalline aquifer are relatively limited, is well in agreement with the previous findings.

Isotopes Analysis

The environment isotopes of oxygen δ 18 O and hydrogen δ 2 H are excellent tracers for determining the origin of groundwater and widely used in studying the natural water circulation and groundwater movement. The groundwater has δ 18 O values in the range of -5.06‰ to -0.39‰ and δ²H from -30.18‰ to +6.0‰ (Table 7). The average values of δ 18 O and δ²H in the groundwater are -3.6‰ and -18.9‰ respectively.

The local meteoric water line (LMWL) is defined at the Geneina station (capital of West Darfur in Sudan). Its equation is: The stable isotopes values are plotted in Figure 12. The global meteoric water line (GMWL) [START_REF] Craig | Isotopic Variations in Meteoric Waters[END_REF] is also given as reference. The GMWL is written as: This diagram shows that the groundwater data are close to the GMWL meaning that the groundwater is in relation to modern rainfall.

This finding indicates that the groundwater recharge resource is mainly from precipitation and is weakly affected by evaporation.

Suc result is quite important since we can deduce that the renewal of groundwater is sufficiently rapid. Dating using C isotopes ( 13 C, 14 C) would help to determine the residence time of water in the aquifer system.

Summary and Conclusions

Groundwater is a vital resource for the Wadi-Fira region in eastern Chad The aquifer system exploited in this region is represented by the rocks of the crystalline basement. Groundwater is exploited using wells dug in the alterites and deep wells penetrating the fractured rocks. However, the available knowledge about the hydrogeology and the water quality of this system is still very low.

The objective of this work was to study the processes of groundwater mineralization and recharge mechanisms. Hydrochemical and isotopic analyses were carried out on water samples collected during two field campaigns organized in 2011 and 2015. The results of the analyses and their interpretations have shown that groundwater is on the whole fairly gentle. However, the mineralization of the deep waters of the fractured crystalline reservoir is more important than that of the waters of the alterites. The predominant process of mineralization is the interaction between water and rock and the solution of minerals. Other processes intervene (basic exchanges, precipitation, evaporation), but their impact is moderate. The isotopic data have shown that the groundwater of this system is related to modern precipitation. Recharging the system is relatively fast.

This study has allowed to significantly improve knowledge on this complex system and laid the bases to consider a more rational exploitation of the resource.