Sudip Chakraborty

Shuvankar Gupta

Vidha Bhasin

Santanu Pakhira

Céline Barreteau

Jean-Claude Crivello

Shambhu Nath

Dibyendu Bhattacharyya

Maxim Avdeev

Valérie Paul-Boncour

Jean-Marc Greneche

Eric Alleno

Chandan Mazumdar

Observation of charge transfer induced large enhancement of magnetic moment in a structurally disordered inverse Heusler alloy Fe 2 RuGe

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I. INTRODUCTION

Heusler alloys (HA) are known to be a series of enigmatic compounds that are often known to exhibit high ferromagnetic transition temperatures, even when all individual constituents are nonmagnetic [1,[START_REF] Felser | Heusler alloys[END_REF]. HAs have a general chemical formula of X 2 Y Z, where X and Y are transition metal atoms and Z is generally a main group element atom. They crystallize in the Cu 2 MnAl-type or L2 1 -type structure (F m 3m). Most HAs are highly ordered cubic intermetallic compounds with three crystallographic positions in their crystal lattice, viz. 4a (0,0,0), 4b ( 1 2 , 1 2 , 1 2 ) and 8c ( 1 4 , 1 4 , 1 4 ) [1]. It is generally seen that the occupancy of an atom at a particular site is determined by its number of valence electrons. Those with more valence electrons (X) tend to occupy the 4c and 4d positions, while atoms with fewer valence electrons (Y ) tend to occupy the 4b position, which is generally * chandan.mazumdar@saha.ac.in known as the valence electron number rule [START_REF] Mondal | [END_REF]. However, there is also a subclass of HAs, where Y and one of the X atoms interchange their occupancy, and such systems are known as inverse HA, forming in the XA-type structure, also known as the Hg 2 CuTi structure [4,5]. This latter crystallises in F 43m space group with a splitting of 8c sites from F m 3m into two individual 4c and 4d sites. Another fascinating feature of HA system is the structural tunability, as many different combinations of 3d, 4d and 5d transition metal elements can be used in the X and Y positions. Interestingly, one may realize that the choice of constituent elements and their occupancies determines of the electronic band structure, which in turn controls most of the physical properties of these materials. As a result, HAs remain a very attractive system for appropriate crystal engineering [6][7][8][9].

The high Curie temperature and large saturation magnetic moment displayed by Heusler alloys recently got renewed attention due to their multi-functional properties viz. Half metallic ferromagnetism (HMF) [10][11][12], magnetic shape memories [13,14], magnetic spin valve ef-fects [15], magnetic skyrmions [16,17], spin-gapless semiconductors [18,19], etc., as all these properties could be used in a large number of technological devices operated at room temperature. For example, spintronics devices are considered to have huge advantages over conventional electronic devices due to their high speed for data processing, non-volatile nature and reduced power consumption rate [20]. It is generally seen that HA with the combination of both Co and Fe is particularly good for obtaining a high magnetic moment and elevated Curie temperature. A substantial number of Co-based systems are particularly known to exhibit HMF behaviour and could be used for spintronic-related applications [11] [21]. On the other hand, although Fe-based HAs are rarely known to show such features, they have an enormous potential to be used as economically viable rare-earth free permanent magnet. In the quest for such new permanent magnetic material, the iron-rich compound, Fe 3 Ge turns out to be one of the most remarkable systems [22]. The compound could be considered as the binary equivalent of Heusler alloy, where both the X and Y atoms are identical. Very interestingly, the compound is found to be stable at room temperature in two polymorphic crystal structures, viz., a cubic L2 1 phase (Cu 3 Au type, P m 3m, space group no. 221) formed by annealing at low temperatures (< 1073 K) and a hexagonal D0 19 phase (Mg 3 Cd type, P 6 3 /mmc, space group no. 194) stabilized when the system is annealed at higher temperatures (>1073 K) [22]. Although both phases exhibit high Curie temperatures (655 K for the hexagonal phase and 755 K for the cubic phase) and large magnetic moments (∼ 6µ B /f.u.) at room temperature, the anisotropic magnetic properties of the hexagonal phase have generated considerable interest in its use as a permanent magnet. A lot of attempts have been made to modify the magnetic anisotropy by partially replacing Fe atoms with other 3d elements, viz., V, Cr, Mn, Co and Ni [4,[23][24][25]. It has been found that depending on the use of heavier or lighter 3d element substitution, the structural as well as magnetic properties can vary widely. Both Fe 2 CoGe and Fe 2 NiGe form in cubic inverse Heusler alloy structure [4], while Fe 3-x Cr x Ge (x < 0.70) and Fe 2 MnGe retain the hexagonal crystal structure [24] [25]. Fe 3-x V x Ge remains hexagonal for x < 0.125, but changes to cubic for 0.125 < x < 0.75 [23]. The ferromagnetic Curie temperature for Fe 2 CoGe (T C = 925 K) and Fe 2 NiGe (T C = 760 K) is also higher than that of both the hexagonal as well as cubic phases of the parent compound, Fe 3 Ge. In addition, although Co and Ni are considered magnetic elements, the magnetic moment is confined only to Fe in Fe 2 NiGe, while both Fe and Co carry magnetic moment in Fe 2 CoGe. On the other hand, the Curie temperature decreases in case of substitution by 3d elements lighter than Fe [4,[23][24][25].

In light of such contrasting magnetic properties of Fe 3-x T x Ge depending on the electronic configuration of 3d T -element, it would be interesting to understand the role of the valence electron and the electronic band structure in this system. The substitution of isoelectronic elements belonging to the 4d (Ru) or 5d (Os) series would be highly helpful, despite the fact that both are nonmagnetic and isoelectronic to Fe, and are also susceptible to structural disorder. In this work, we report the successful synthesis of a new inverse Heusler alloy Fe 2 RuGe and explored its structural and physical properties through different experimental and theoretical techniques. Two different spectroscopic techniques, viz., 57 Fe Mössbauer spectrometry and Extended X-ray Absorption Fine Structure (EXAFS) have been adopted to investigate the local structural disorders, While neutron diffraction studies have been carried out to investigate the magnetic spin arrangements. The electronic band structure calculation is also presented to complement the experimental results.

II. METHODS

A. Experimental details

The Fe 2 RuGe polycrystalline ingot was prepared by the standard arc melting method in argon atmosphere on water-cooled Cu hearth. A stoichiometric amount of Fe chunk (>99.9%), Ru powder (>99.9%) and Ge lump (>99.999%) were used as starting materials. All the elements were melted and re-melted together for 5 times after flipping each time to improve homogeneity. A negligible amount (<0.6%) of weight loss was recorded after the melting process. X-ray diffraction (XRD) measurement at room temperature was carried out using a commercial diffractometer (rotating Cu anode, 9 kW, Model: TTRAX-III, Rigaku Corp., Japan). The single-phase nature of the as-cast sample was confirmed by Rietveld refinement using FULLPROF software [26]. Microstructural analysis and compositional homogeneity were further investigated using a wavelength dispersive electron probe microanalysis (EPMA) spectrometer [Model: SX 100, Cameca, France].

Extended X-ray Absorption Fine Structure (EXAFS) experiments on Fe 2 RuGe were carried out at the Indus-2 Synchrotron Source (2.5 GeV, 100 mA) at the Energy-Scanning EXAFS beamline (BL-9) at Raja Ramanna Centre for Advanced Technology (RRCAT), Indore, India which operates in the energy range of 4 -25 keV. Both transmission and fluorescent modes can be used to perform EXAFS measurements in this beamline. A Rh/Pt coated collimating meridional cylindrical mirror is used and the collimated beam is reflected by a mirror that is monochromatized by a double crystal monochromator (DCM) of Si(111) (2d = 6.2709 Å). For horizontal focusing, a sagittal cylinder (the second crystal of DCM) is used, and for vertical focusing of the beam, a Rh/Pt coated bendable post mirror facing down at the sample position is employed. The higher harmonics content of the X-ray beam is rejected by detuning the second crystal of DCM. For EXAFS measurements, we have used the fluorescence mode. In this method, the incident Xray beam angle is 45 degrees to the sample position, and a fluorescence detector, positioned at 90 degrees to the in-cident X-ray beam, is used to collect the signal. To measure the incident flux (I 0 ), an ionization chamber detector is placed before the sample, and fluorescence intensity (I f ) is measured by a fluorescence detector. The relation, µ = (I f /I 0 ), is used to calculate the X-ray absorption coefficient of the sample. The spectrum (as a function of energy) was acquired by scanning the monochromator over a particular range. In order to extract qualitative information about the local structure, the oscillations of the normalized absorption spectra (µ(E) vs. E) were transformed to absorption function χ(E) using the relation:

χ(E) = µ(E) -µ 0 (E) ∆µ 0 (E 0 ) (1)
here, E 0 is the absorption edge energy, µ 0 (E 0 ) is the background of exposed atom and ∆µ 0 (E 0 ) is the step in µ(E) value at the absorption edge. The absorption coefficient as a function of energy χ(E), was changed to the absorption coefficient as a function of wave number χ(K) by the following equation,

K = 2m(E -E 0 ) ℏ 2 (2)
here, m is the mass of the electron. To intensify the oscillation at high χ(K), it is multiplied by k 2 and then to obtain the χ(R) vs. R plots, a Fourier transformation of χ(k)k 2 functions into R space, regarding to the real distances calculated from the centre of the absorbing atom is done. The set of EXAFS data was analyzed by the program available in the Demeter software package. Background reduction, Fourier transformation of the absorption spectra to derive χ(R) vs. R plots (using ATHENA code) [27], simulation of the theoretical plots from the assumed crystallographic structure, and finally the fitting of experimental data using the theoretically generated spectra (by ARTEMIS code) were also included in this package [27].

Isothermal magnetisation measurements at low temperatures were performed in commercially available SQUID VSM (Quantum Design Inc., USA). Magnetic measurements in the temperature range 300 -900 K were done in a high-temperature VSM equipped with an electromagnet (Model EV9, MicroSense, LLC Corp., USA).

Room temperature, as well as high-temperature neutron diffraction experiments (λ = 2.4395 Å), were performed at ECHIDNA beam line in ANSTO, Sydney, Australia [28]. The details of the crystal structure as well as the analysis of the magnetic structure were performed by Rietveld refinement of neutron diffraction data using the FULLPROF software.

57 Fe transmission Mössbauer spectrometry was used to study the hyperfine structure at Fe sites. The spectra were obtained at 300 K and 77 K in a bath cryostat and using an electromagnetic transducer with a triangular velocity nature and a 57 Co source in a Rh matrix. The sample consists of a thin powdered and homogeneous layer containing about 5 mg-Fe/cm 2 . The least-squares fitting method, which assumes quadrupolar doublets and/or magnetic sextets involving Lorentzian lines, has been applied to model the hyperfine structures using the MOSFIT program. The refined isomer shift values are corrected to that of α-Fe at 300 K, and an α-Fe standard was used to calibrate the velocity.

Resistivity experiments using a standard four-probe method were performed in the temperature range 2 -300 K using a PPMS Evercool-II instrument, (Quantum Design Inc., USA).

B. Computational methods

For the modelling part, the L2 1 , inverse XA and disordered structures of Heusler alloys have been described in the same F 43m space group having both 4c and 4d positions (splitting of 8c site in F m 3m), for a fuller discussion of site comparison.

The calculations of enthalpy of formation, electronic structure and spin polarisation at 0 K were carried out using density functional theory (DFT). They were conducted using the projector augmented wave (PAW) method [29] implemented in the Vienna ab initio simulation package (VASP) [30,31]. The exchange-correlation was described by the generalized gradient approximation modified by Perdew, Burke and Ernzerhof (GGA-PBE) [32]. Energy bands up to a cutoff of E = 600 eV were used in all calculations and the convergence tolerance for the calculations was selected as a difference on the total energy within 1 × 10 -6 eV/atom. For each structure, volume and ionic (for disordered compounds) relaxation steps were performed and the tetrahedron method with Blöchl correction [33] was applied. Spin-polarization calculations were considered for all the structures. In order to statistically simulate the chemical disorder in Fe 2 RuGe, unit cells based on the concept of special quasirandom structure (SQS) [34] were generated for different possible disorder schemes. To generate the SQS, the cluster expansion formalism for multicomponent and multisublattice systems [35] was used as implemented in the Monte-Carlo (MCSQS) code contained in the Alloy-Theoretic Automated Toolkit (ATAT) [36,37]. Subsequent DFT calculations were performed in order to test the quality of the SQS and to see how reliable the DFT results are. The root mean square (rms) error on correlation functions was used as another quality criterion in addition to the calculations including a different order of interactions. The rms error describes the deviation of the correlation function of the SQS (Π k SQS ) from the correlation function of a fully random structure (Π k md ) for all clusters k.

rms = k (Π k SQS -Π k md ) 2 (3)
Several tests on the dependence of the type and number of clusters were performed to generate the disordered structure: Ge at 4a (0,0,0), Fe at 4b ( 12 , 1 2 , 1 2 ) and Fe = 0.5/Ru = 0.5 at 4c ( 1 4 , 1 4 , 1 4 ) and Fe = 0.5 & Ru = 0.5 at 4d ( 34 , 3 4 , 3 4 ). Finally, 7 pairs, 5 triplets and 11 quadruplets interactions were considered to obtain reliable results. Using these parameters, a disordered quaternary SQS cell of 28 atoms was generated. The powder XRD data taken at room temperature is presented in Fig. 1. With the exception of very few small peaks (<2% of main peak intensity), all the peaks in the XRD pattern can be well indexed with a Hg 2 CuTi-type (space group F 43m, No -216) inverse Heusler (XA-type) crystal structure with lattice parameter a = 5.871(4) Å. It may be noted that Heusler alloys are prone to structural disorder, and despite the formation in cubic structure, such atomic disorders are known to affect the intensity of the ( 111) and ( 200) superlattice Bragg peaks in the XRD patterns. For example, in A2-type disorder (all atoms mixed on a single site), both (111) and (200) peaks are absent, while in B2-type disorder (atoms mixed on 2 sites), only the (200) peak is present [START_REF] Mondal | [END_REF] [12] [38]. The occurrence of both (111) and (200) lines in Fig. 2 allows discarding B2 or A2 type of disorder. Our attempt to describe the crystal structure with an ordered variant (Ge occupy 4a position, Fe at 4b, Fe at 4c and Ru in 4d site) strongly undermined the experimentally observed (111) peak intensity (Fig. 1, Inset), suggesting a disordered structure of different variant. Accordingly, we tried various combinations of site-disorders and obtained the best result by considering a 50% permutation between Fe and Ru in the tetrahedral 4c and 4d sites (Fig. 2). The Rietveld analysis, considering the above model, can fit the XRD pattern quite well (Fig. 1). The trace amount of the minority phase turns out to be that of FeGe 2 of less than 2% of the weight fraction of the primary phase. The structural disorder is further confirmed by the EXAFS and neutron diffraction data analysis which will be discussed in later sections. This result is also in conformity with the theoretical calculations establishing that the disordered XA structure is more stable than the ordered one.

B. EXAFS analysis

The normalized EXAFS (µ(E) vs. E) spectra of Fe 2 RuGe at the Fe and Ru edges, following the treatment presented in Eq. 1 and Eq. 7, are shown in Fig. 3. The χ(R) vs. R plots (Fourier transformed EXAFS spectra) generated by the crystallographic information and the EXAFS equation of the Fe and Ru edge is shown in Fig. 4. Simultaneous fitting with several edges of various data sets is used in this approach. The χ(R) vs. R plots calculated at the Ru and Fe edges are fitted at the same time with common fitting parameters. The statistical significance of the fitting is improved by reducing the number of independent parameters below the Nyquist criterion. The value of R f actor was used to determine the goodness of fit, which is calculated by:

R f actor = [Im(χ dat (r i ) -χ th (r i )] 2 + [Re((χ dat (r i ) -χ th (r i )] 2 ] 2 [Im(χ dat (r i ) 2 ] + [Re(χ dat (r i ) 2 ]
(4) where χ th and χ dat are the theoretical and experimental χ R values, respectively. Re and Im are the real and imaginary components of the respective quantities. To theoretically simulate the EXAFS spectra of Fe 2 RuGe, the structural information (lattice parameters and nearest neighbour numbers) have been taken from the XRD From the fitting of Fe edge of the Fourier transformed spectra, we found that the main peak near Å has a contribution from all Fe-Fe (2.48 Å), Fe-Ru (2.53 Å) and Fe-Ge (2.48 Å) distances. The second intense peak near 3 Å arises due to the contribution of Fe-Ru (2.89 Å) and Fe-Fe (2.89 Å) and the peak near 4 Å consists of the contribution of Fe-Fe (4.07 Å) and Fe-Ru (4.17 Å). From the coordination number and bond length analysis, we found occupancy of the 4b, 4c and 4d sites between Fe and Ru is nearly 71%:29%, close to 66%:33%. Similarly, we analysed the Ru-edge Fourier transformed spectra, where the main peak near 2 Å arises due to the contribution of scattering paths of Ru-Ge (2.53 Å) and Ru-Ru (2.53 Å). The second peak consists of the scattering paths of Ru-Ru (2.88 Å) and Ru-Fe (2.88 Å) and the third peak near 4 Å consists of Ru-Fe (4.07 Å) and Ru-Ru (4.07 Å). From these data we also calculated the intermixing between 4c and 4d sites to be 58:42. This data is consistent with the Fe edge data also. From the XRD analysis in Sec. III A we found that the disorder between Fe and Ru in 4c and 4d sites is about 50-50. Our EXAFS analysis is also in agreement with this.

C. DC Magnetization Study

To measure the magnetic ordering temperature and magnetic moment of Fe 2 RuGe, the magnetization as a function of temperature as well as magnetic field was measured. The isothermal magnetic measurements at room temperature show a soft ferromagnetic character with a rather large magnetic moment (∼4.71 µ B /f.u.) (Fig. 5), suggesting ferromagnetic ordering at a temperature above 300 K. Accordingly, we performed magnetic susceptibility measurements in a VSM with electromagnet in the temperature range 300 -900 K under a magnetic field of 100 Oe. Very interestingly, the system exhibits ferromagnetic ordering at ∼860 K (estimated from dM/dT curve) (Fig. 6, Inset), much higher than its binary parent compound, Fe 3 Ge (T C = 755 K) [22]. It may be noted here that the minor phase of FeGe 2 detected from our XRD analysis are known to exhibit a ferromagnetic ordering at a much lower temperature, ∼ 290 K [39], and hence the observed ordering at ∼ 860 K must arise from the main phase. The large magnetic moment in the isothermal magnetic measurement at 300 K also confirms the ferromagnetic ordering of the primary phase, Fe 2 RuGe. Substituting a magnetic Fe atom with a nonmagnetic Ru atom, having a random mixed site occupancy increases T C even in comparison to the case where 3d atoms like V, Cr, Mn, and Ni are substituted [4,[23][24][25]. The isothermal magnetic measurement was also extended to lower temperatures to compare it to the theoretically estimated moments. The data taken at 5, 50 and 300 K are shown in Fig. 5. Even at the lowest measured temperature, 5 K, the coercive field retains its soft magnetic character (H C = 130 Oe), and the saturation moment is only slightly enhanced to ∼4.92 µ B /f.u.. It may be pointed out here that the well-known Slater-Pauling (S-P) rule provides a theoretical limit of the magnetic moments in Heusler alloy systems. According to the S-P rule, the saturation magnetic moment (M ) can be expressed as (N V -24)µ B /f.u. where N V is the valence electron number [1]. The atomic disorder present in the system is known to reduce the experimental value in comparison to the S-P-rule prediction [12]. Since Fe and Ru are randomly distributed in 4c and 4d positions in Fe 2 RuGe, one thus expects a considerably diminished value of magnetic moment. Surprisingly, the experimentally observed saturation magnetic moment (∼4.92 µ B /f.u.) for Fe 2 RuGe is found to be much higher than that theoretically predicted (4 µ B /f.u.). Although a few Fe-based HA are already known to exhibit saturation moment higher than that predicted by the SP-rule [4], Fe 2 RuGe occupies a special place because it exhibits such a large value despite its inherent atomic disorder involving the moment carrying Fe-atoms. As up to now all studied HMF systems obey the S-P rule [12], the specific behaviour of Fe 2 RuGe needs other experimental measurements (neutron diffraction and Mössbauer spectrometry) as well as theoretical calculations to be more clearly understood.

-4 0 -2 0 0 2 0 4 0 -4 -2 0 2 4 M ( µ B / f . u ) H ( k O e ) 5 K 5 0 K 3 0 0 K -0 . 1 0 . 0 0 . 1 -0 . 2 0 . 0 0 . 2 M ( µ B / f . u ) H ( k O e )

D. Neutron Diffraction

Neutron powder diffraction measurements have been carried out on Fe 2 RuGe at 300 K and 950 K, respectively, below and above its Curie temperature (T C ∼ 860 K) to analyze the nuclear structure at 950 K and the long-range magnetic order at 300 K (Fig. 7). The diffraction pattern at 950 K, i.e., in the paramagnetic region, can be well refined in the cubic space group F 43m with lattice parameter as a = 5.936(2) Å, while the Fe and Ru occupy the 4c and 4d positions with occupation rates of 55% and 45%, respectively. This agrees with the XRD data analysis described earlier in Sec. III A and confirms the larger stability of the disordered XA structure compared to Heusler or ordered XA structure. We may, however, note that the intensity of ( 111) and (200) Bragg peaks, which are generally considered as a signature of perfect crystalline ordering, have much-reduced intensity in the ND spectra in comparison to XRD data, which can be explained due to the different atomic scattering factors of neutron and X-ray. The small peak at 2 θ = 33.9°c an be refined with 0.6% of FeGe 2 impurity. The NPD pattern measured at 300 K, in the magnetically ordered state, appears to be nearly like that at 950 K, except for a moderate increase in the intensity of the (111) and (311) crystal Bragg peaks. Assuming the structural model refined in the paramagnetic region (950 K) remains similar at 300 K, the absence of additional peaks beyond the allowed crystal Bragg positions ruled out the antiferromagnetic type of order in this system. Rietveld refinement of the 300 K data yields a refined cell parameter a = 5.8787(2) Å close to the XRD value. A good refinement was obtained assuming a ferromagnetic alignment of the Fe sublattice in agreement with the magnetization data. In a powder pattern, all the axes are equivalent to a cubic structure, and it is not possible to specify a preferred orientation of the magnetic moments. Since the intensity of only a few Bragg peaks is related to magnetic ordering, with a small intensity compared to the nuclear contribution, it was not possible to refine independently each Fe moment without a divergence of the fit. A unique Fe moment was therefore assumed for all sites (i.e. 4b, 4c and 4d ) and the refinement of the Fe moment intensity lead to 2. [START_REF] Rossiter | The electrical resistivity of metals and alloys[END_REF] As the analysis of the Fe 2 RuGe ND spectra does not allow the determination of site-specific Fe moments, 57 Fe Mössbauer spectrometry was used to check the relative population of Fe atoms and their respective magnetic moments (determined appropriately from the magnetic hyperfine fields of the individual components) in the three crystallographic positions, namely 4b, 4c and 4d. The Mössbauer spectra taken at 300 K and 77 K (shown in Fig. 8) are quite similar and show complex magnetic structures consisting of well-resolved magnetic hyperfine structures with broadened and asymmetrical lines. Initial inspection of the spectra reveals that the outermost lines belong to the major magnetic sextet that must be described using a discrete distribution of hyperfine fields (ranging from about 270 to 340 kOe and 290 to 360 kOe at 300 and 77K, respectively), common values of isomer shift and quadrupole shift (see the mathematical procedure discussed in Varret et al. [START_REF] Varret | Proceedings of the International Workshop Mössbauer Spectroscopy[END_REF] and Campbell et al. [START_REF] Campbell | Mössbauer spectroscopy applied to inorganic chemistry[END_REF]). The rest of the hyperfine structure can be described by another, but narrower, distribution of hyperfine fields (from about 210 to 240 kOe and 230 to 270 kOe at 300 and 77K, respectively), common values of isomer shift and quadrupole shift. But the two values of isomer shift are different. Several models can be proposed to describe each spectrum: the first description consists therefore of two magnetic components with broad and Lorentzian lines characterized by two different values of isomer shift attributed to the two Fe 4b and 4d sites. The Fe, Ru and Ge disorder explains why only two components are not able to describe perfectly the hyperfine structures observed at 300 and 77 K. Indeed, the second description for both spectra involve three magnetic components, by splitting the component with the lowest values of hyperfine fields into two components: each results from the superposition of several magnetic sextets to describe the asymmetry and width of the lines, in order to take into account the disordered atomic environments. The corresponding refined mean values of the hyperfine parameters are listed in Table II.

The relative absorption areas are estimated at 55%, 23% and 22% for the three sites Fe-4b, Fe-4c and Fe-4d, respectively. Assuming the same values of their respective Lamb-Mössbauer factors, they directly give rise to the proportions of Fe atoms that match quite well with our analysis of ND and XRD patterns (Sec. III A, Sec. III D). Considering the fact the larger hyperfine field value corresponds to the 4b site in inverse Heusler alloys [4], the mean hyperfine field values at 300 K for the three magnetic components as 306 kOe, 233 kOe and 218 kOe are assigned to 4b, 4c and 4d sites, respectively. The individual Fe moments corresponding to the Wyckoff positions 4b, 4c and 4d in Fe 2 RuGe can be estimated from the three different hyperfine field components, provided that the magnetic hyperfine field values can be properly scaled with the respective magnetic moments. Usually, α-Fe with a magnetic moment of 2.2 µ B yields a hyperfine field of ∼330 kOe, and most often this reference is used as the calibration factor. Using this approach, it was concluded in a previous study on the structurally similar compound Fe 3-x Ru x Si that Ru atoms contains a magnetic moment of about ∼1.3 µ B for x = 0.75, while the proposed moment in Ru is slightly reduced to 1 µ B in Fe 2 RuSi [START_REF] Mishra | [END_REF]. This result is really surprising, as only a handful of materials are known where Ru carries magnetic moments [43]. If we implement the same calibration factor in Fe 2 RuGe as well, and compare the result with isothermal magnetisation data, we also would have to assign a magnetic moment of 0.7 µ B on Ru atoms in our sample of Fe 2 RuGe. However, the neutron diffraction experiment presented above ruled out the presence of any significant magnetic moment at the Ru site. In this context, we may like to point out that the relationship between the magnetic hyperfine field and the magnetic moment are not so straight-forward as elaborated earlier in literature for many different Fe-containing DO 3 -type alloys [44], [45] as well as for other binary systems [46]. In some other Fe-based Heusler compounds too, it has also been suggested that a magnetic moment of 2.2 µ B /Fe would correspond to 275 kOe [4]. Such a change is usually caused by the presence of a large anisotropic hyperfine field involving a dipolar field, a non-cubic distribution of spin density in the iron atom, an anisotropic g-factor, etc [45]. For our calculation, we have thus utilized the reference of Fe 3 Ge, which can be regarded as the parent compound of our studied Heusler system, Fe 2 RuGe, where a magnetic hyperfine field value of 220 kOe had been associated with 2 µ B /Fe atom [45]. If we use this calibration factor for Fe 2 RuGe, we find the Fe magnetic moment values at 4b, 4c and 4d sites as 2.78, 2.12 and 1.98 µ B , respectively, giving a resulting magnetic moment of <4.83> µ B , that matches quite well with the isothermal magnetisation measurement and theoretical calculations.

F. Theoretical analysis

In order to theoretically establish the most stable crystal structure, several crystal configurations were studied by DFT calculations. We considered the ordered Cu 2 MnAl-type corresponding to the full Heusler structure (L2 1 ) and the Hg 2 CuTi-type known as the XA structure. For both structures, the optimized crystal structure was obtained from DFT calculations and the enthalpies of formation are summarized in Table III. Our calculations show that the Cu 2 MnAl-type structure is less stable than the XA structure which is in good agreement with the structural analysis (Sec. III.A.). Moreover, a structural disorder of Fe and Ru on the 4c and 4d positions, in the XA structure, leads to a more stable compound, thus confirming the XRD, ND and EXAFS data. Fig. 9(a-c) shows the calculated spin-polarized band structure and the calculated density of states (DOS) of the ordered XA structure. As it can be seen, the DOS shows no band gap at the Fermi level (E F ) for either the majority or minority spin population. This explains a rather low value of the spin polarization, with P (XA) = DOS ↑ (EF)-DOS ↓ (EF) DOS ↑ (EF)+DOS ↓ (EF) =-29.9%, and P (Heusler structure)=-33.3%. As in many other Heusler compounds, the spin polarization drastically decreases when the disorder increases, P drops to -2.7% in the disordered XA inverse Fe 2 RuGe too. As in Fig. 9(a-c), Fig. 9(df) shows the calculated spin-polarized band structure and the associated DOS of the disordered XA structures where no semiconducting behaviour can be noticed because both spin directions correspond to a metallic ground state. The calculated total magnetic moment, for all configurations, is in good agreement with the experimental magnetic moment, always around 5 µ B /f.u.. Although all calculated total magnetic moments are almost the same for the three configurations, only the ordered and disordered XA types show significant differences in atomic moment of Fe compared to the full Heusler configuration. It may be noted that the magnetic moment is shared between the Fe and Ru elements for the Heusler type. In contrast to this, in the XA structure type, the magnetic moment of the Ru element is considerably decreased whereas the magnetic moment carried by the Fe atom in 4b positions is strongly increased (Table IV).

In the full Heusler configuration, the Fe-8c site is surrounded by 4 Ge and 4 Ru atoms, while the nearest Fe neighbours are at a large distance and the mean Fe moment is 1.98 µ B /Fe. In the ordered and disordered 4 Fe and 4 Ge atoms retain a moment close to 1.9 µ B /Fe. The spin-polarized DOS projected on each site for the XA ordered structure clearly shows a different contribution of the Fe site to the spin-polarized-DOS (Fig. 10), with a stronger interaction of Ru orbitals with Fe-4b than with Fe-4c. The calculation of the Bader charges, as shown in Table V, reveals a larger electronic charge transfer from Fe-4b (-0.35) to Ru-4d (+0.47) in the disordered XA structure compared to the direct structure, -0.13 to +0.26, for both Fe and Ru sites, respectively. In fact, the charge transfer from Fe-4d is less important in XA structure since its atomic environment is surrounded by Fe and Ge. Due to the charge transfer from Fe to Ru, the number of unpaired electrons for the Fe-4b atom increases, explaining the enhancement of its magnetic moment in comparison with Fe-4d and the low value for the Ru moment. Such charge transfer is also responsible for the enhancement of the magnetic moment of the Fe at 4b site, compared to the average moment on Fe in the parent compound Fe 3 Ge.

The observed enhancement of magnetic moment (4.92 µ B /f.u.) from the expected S-P value (4 µ B /f.u.) in Fe 2 RuGe (VEC 28) is indeed quite rare as among the known inverse HA's. Only a handful of such material are known to exists, primarily in Fe-based systems only. One such system is Fe 2 CoGe (VEC 29) that exhibit a magnetic moment (5.40 µ B /f.u.), instead of expected 5 µ B /f.u. The enhancement of magnetic moment in Fe 2 CoGe (0.40 µ B ) is also smaller than that observed in the present case of Fe 2 RuGe (0.92 µ B ). Nevertheless, in order to make an enhanced comprehension of the distinction between Fe 2 RuGe (VEC = 28) and Fe 2 CoGe (VEC = 29), we have additionally carried out band structure computations for Fe 2 CoGe within the identical disordered XA configuration. In this structure, only Fe is present in the 4b site, while Co (in place of Ru) and Fe share the same 4c:4d sites with a 50% : 50% statistic occupation. The outcomes of these DFT computations for Fe 2 CoGe are given in Table VI. Firstly, we can compare the calculated values of magnetic moments, both overall and site-specific, with the experimental values. While the experimental value is approximately 5.0 µ B /f.u. in both compounds, the two types of total moment values-calculated in the Ru-and Co-compounds, respectively, are in good agreement. As can be seen below, the computed site-specific Fe moments likewise agree very well with the experimental ones (in parenthesis). M(Fe-4b) = 2.74 (2.78) µ B /atom and M(Fe-4c:4d) = 1.98 (2.12) µ B /atom are the values for Fe 2 RuGe, while M(Fe-4b) = 2.67 (2.68) µ B /atom and M(Fe-4c:4d) = 1.56 (1.51) µ B /atom are the values for Fe 2 CoGe. When comparing the computed Fe moments of Fe 2 RuGe and Fe 2 CoGe, it can be observed that the 4b site of both compounds has a greater Fe moment (∼2.7 µ B /atom). A significant charge transfer of about -0.3 electrons per Fe atom is associated with this moment. Therefore, although the enhancement of larger Fe-4b moment is not unique to Fe 2 RuGe, nevertheless the Fe atom at the 4c:4d site is actually what makes Fe 2 RuGe special. Fe 2 RuGe (VEC = 28) has a much larger moment of ∼2 µ B /atom, while Fe 2 CoGe (VEC = 29) has a moment of ∼1.5 µ B /atom. The charge transfer that Fe-4c:4d experiences in the first compound is negative (-0.06), whereas in the second compound, it is positive (+0.03). While Co only receives +0.18 electrons and still bears 1 µ B /atom, all of the Fe electrons in Fe 2 RuGe are mostly transferred to Ru (+0.47), which is almost nonmagnetic. The positive Bader charge transfer of Ge (+0.06) in Fe 2 CoGe compared to Fe 2 RuGe (-0.07) is also likely to play a crucial role. Fe 2 RuGe is therefore unique to this effect for Fe at the 4c:4d site, which helps explain why its total magnetic moment exceeds the S-P limit. In conclusion, we have discovered a novel effect in Fe 2 RuGe and have successfully linked it to calculated charge transfer between the atoms that make up the material.

G. Resistivity study

In sec. III F, it is predicted that Fe 2 RuGe has density of states in both up and down spin configuration at the Fermi level. To check its validity, we have performed resistivity experiments. Fig. 11 represents the temperature-dependent electrical resistivity (ρ(T )) behaviour of Fe 2 RuGe measured in the absence of magnetic field (H = 0 kOe) in both heating and cooling cycles. We could not observe any irreversibility between these data: thus we ruled out any possibility of a structural transition in the system. In the case of a ferromagnetic material, the temperature dependence of electrical resistivity can be attributed to three different types of scattering factors. According to Matthiessen rule, all these contributions arise due to different types of factors such as, a) contribution due to scattering of conduction electrons by the lattice defects, ρ 0 , b) phonon scattering, ρ P , c) magnon scattering and electron-electron interaction, ρ M , are additive in nature. From Fig. 11 we can see that the residual resistivity ratio (RRR) of Fe 2 RuGe (ρ 300K /ρ 5K ) is around 1.625, which clearly indicates the existence of substantial structural disorder in the sample [47,48]. We can say that resistivity of any ferromagnetic material is

ρ(T ) = ρ 0 + ρ P (T ) + ρ M (T ) (5)
The phonon scattering term can be written as [12] [49]

ρ P = C T Θ D 5 Θ D T 0 x 5 (e x -1)(1 -e -x ) dx (6)
and the magnon and electron contribution as BT 2 . Here Θ D is the Debye temperature and C is scattering constant [12]. As the T C is quite high, we have fitted the data using Eq. 5 From the fitted parameters, phonon contribution was found much higher compared to the magnon contribution. However, Eq. 5 fits the data well within the region 60 < T < 300 K only, but is unable to fit the low temperature region properly. From the fitted results we get Θ D = 360 K. Generally, electron-electron (e-e) and electron-magnon (e-m) lead to a quadratic temperature dependence of resistivity. However, between these two, the dominant contribution can be inferred from the magnitude of the coefficient, B. Normally, B is of the order of 10 -2 nΩcm.K 2 for e-e interaction while it is normally two orders higher for e-m interaction. From the fitting, we got the value of B (e-e interaction coefficient) to be 4.57×10 -5 µΩcm.K 2 which falls within the accepted range for electron-electron scattering, indicating the very weak presence of a single-magnon-scattering mechanism. We have tried to fit the low temperature resistivity data by using the equation

ρ(T ) = ρ 0 + ρT n (7)
From the fitting, we have found the value of n = 2.2, from which we can confirm that at low temperatures also there is a dominant magnon contribution, which is quite surprising and calls for further investigations of magnetic dynamics in this material. Previously, several authors have obtained different power (n) values depending on the temperature range considered. The value of n above 2 gives some signs of the weak-metallic character even at higher temperatures [12,48].

IV. CONCLUDING REMARKS

To summarize, we have synthesized a new Fe-based Heusler alloy Fe 2 RuGe through the arc melting technique. The combined XRD, ND and EXAFS study re-veals that the material crystallizes in a disordered structure, which is also supported by the lower formation ground state energy of the disordered structure over the ordered one, calculated by SQS+DFT. 57 Fe Mössbauer spectrometry confirms the inverse Heusler XA disorder with different sextets, strongly suggesting different Fe positions. From neutron diffraction, we confirm that the disorder between Fe and Ru in the 4c and 4d sites is 50:50 in nature. This leads to the mixing of Fe and Ru in the same plane. All these results validate that there are two different Fe environments compared to the Heusler structure. The compound exhibits a ferromagnetic to paramagnetic transition at a significantly high Curie temperature of 860 K and the saturation moment at 5 K is estimated to be 4.90 µ B /f.u., which is higher than the expected S-P value of 4 µ B /f.u.. Such enhancement of the magnetic moment above the predicted S-P value is observed for the first time. The neutron diffraction experiments reveal that only Fe, distributed over different sites, contributes to the net magnetic moment while no moment could be detected on Ru site. Both theoretical calculation and the Mössbauer experiment support that there is a larger moment on Fe-4b site, in comparison with the other disordered Fe-(4c -4d) sites. This enhanced magnetic moment is explained by a large electronic charge transfer from Fe-4b to Ru, as calculated by DFT. The resistivity experiment confirms the presence of electron-electron behaviour at the high-temperature range and a weak phonon contribution at low temperature compared to the magnon contribution.

FIG. 1 .

 1 FIG. 1. Room-temperature powder XRD data along with Rietveld refinement. Insets (a) and (b) display enlarged views of superlattice reflection peaks fitted by ordered and disordered models, respectively.

FIG. 2 .

 2 FIG. 2. Crystal structure of Fe2RuGe in disordered form in F 43m, mixing 4c and 4d sites with a 50:50 composition.

2 F e 2 FIG. 4 .

 224 FIG. 3. Normalized EXAFS spectra of Fe2RuGe taken at (a) Fe edge (b) Ru edge.

5 KFIG. 5 .FIG. 6 .

 556 FIG. 5. Isothermal magnetization plot at various temperatures. Inset represents the hysteresis phenomenon at T = 5 K

C r y s t a l B r a g g p o s i t i o n M a g n e t i c B r a g g p o s i t i o n IFIG. 7 .

 n7 FIG. 7. Neutron diffraction pattern along with full Rietveld refinement of paramagnetic (upper panel) and magnetically ordered temperature (lower panel)

  FIG.8. 57 Fe Mössbauer spectra of Fe2RuGe taken at 300 K (lower panel) and at 77 K (upper panel), respectively.

FIG. 9 .

 9 FIG. 9. Spin-polarized band structure and density of states of Fe2RuGe in ordered Hg2CuTi-type structure: (a) minority (spin-down) band (b) density of states, (c) majority (spin-up) band. Spin-polarized band structure and density of states of Fe2RuGe in disordered Hg2CuTi-type structure: (d) minority (spin-down) band (e) density of states, (f) majority (spin-up) band. The energy axis zero point has been set at the Fermi level and the spin-up (minority) and spin-down (majority) electrons are represented by positive and negative values of the DOS, respectively.

FIG. 10 .

 10 FIG. 10. Projected spin-polarized DOS on each site for the XA-ordered structure.

4 E x p e r i m e n t a l D a t a F i t t e d w i t h e q u a t i o n 6 E x p e r i m e n t a l d a t a F i t t e d u s i n g e q u a t i o n 6 F i t t e d u s i n g e q u a t i o n 7 FIG. 11 .

 466711 FIG. 11. Zero field electrical resistivity measured at a function of temperature.

TABLE I .

 I Extracted values of Bond length (R), co-ordination number (N), and Debye-Waller or disorder factor σ obtained from EXAFS fitting for Fe2RuGe at Fe and Ru edge.

		Fe edge				Ru edge
	Path	R ( Å)	N	σ 2	Path	R ( Å)	N	σ 2
	Fe-Ru 2.53 ±0.01 4	0.0250 ±0.0023	Ru-Ge 2.53 ±0.01 4	0.0082 ±0.0003
	Fe-Fe 2.48±0.01 4	0.0164 ±0.0004	Ru-Fe 2.53 ±0.01 4	0.0082 ±0.0003
	Fe-Ge 2.48±0.01 3	0.0164 ±0.0004	Ru-Ru 2.88 ±0.01 2.3	0.0073 ±0.0014
	Fe-Ru 2.89±0.01 1.7	0.0034 ±0.0004	Ru-Fe 2.88 ±0.01 3.7	0.0073 ±0.0014
	Fe-Fe 2.88±0.01 4.3	0.0080 ±0.0004	Ru-Ru 4.07±0.03 5.1	0.0075 ±0.0047
	Fe-Ge 3.11±0.01 6	0.0247 ±0.0017	Ru-Fe 4.07±0.03 6.9	0.0075 ±0.0047

  (4) µ B /Fe or 4.98 µ B /f.u (RB nucl = 0.65 % and R M ag =7.78%). This value agrees quite well with the isothermal magnetization measurements (Sec. III C) with M = 4.69 µ B /f.u at 300 K and M = 4.92 µ B /f.u at 5 K. In order to check if a Ru magnetic contribution had to be taken into account, a fit was performed by fixing the values of Fe and Ru moment to the values calculated by DFT: M (Fe-4b) = 2.74 µ B /Fe, M (Fe-4d) = 1.92 µ B /Fe and M (Ru) = 0.33 µ B /Ru (See Sec. III F). This lead to higher values of the refinement's factors (RB nucl = 1.25% and R M ag =15%). To conclude this part, we consider that the larger total Fe moment in the XA ordered or disordered structure is related to the Fe:Ru 4b charge transfer.

E. 57 Fe Mössbauer Spectrometry

TABLE II .

 II Refined values of hyperfine parameters estimated from the Mössbauer spectra at 300 and 77 K: δ, 2ϵ and B hf correspond to the isomer shift, quadrupolar shift and hyperfine field, respectively.

	T (K) Site	δ mm/s ±0.01	2ϵ mm/s ±0.01	B hf kOe ±0.5	ratio (%) ±1
		Fe-4b <0.17> <0.01> <306>	55
	300 K	Fe-4c <0.39> <-0.01> <233> Fe-4d <0.41> <0.02> <218>	23 22
			<0.28> <0.01> <269>
		Fe-4b <0.28> <-0.01> <330>	52
	77 K	Fe-4c <0.50> <0.01> <252> Fe-4d <0.53> <0.01> <234>	24 24
			<0.40> <0.01> <288>

TABLE III .

 III Calculated enthalpy of formation ∆ f H and total magnetic moment for each ordered type of Fe2RuGe, and one disordered case.

		4a 4b 4c	4d ∆ f H (kJ/mol -1 ) Magnetic Moment (µ B /f.u.)
	Heusler (Cu 2 MnAl)	Ge Ru Fe	Fe	2.79	5.0
	XA structure (Hg 2 CuTi) Ge Fe Ru	Fe	-18.94	5.0
	Disordered XA structure Ge Fe Fe:Ru Fe:Ru	-20.24	4.9

TABLE IV .

 IV Calculated magnetic moment for each ordered type of Fe2RuGe, and one disordered case. Fe and 4 Ru atoms have a enhanced moment close to 2.8 µ B /Fe while Fe-4c(d) atoms surrounded by

	4a (µ B /f.u.) 4b (µ B /f.u.)	4c (µ B /f.u.)	4d (µ B /f.u.)	P (%)
	L2 1 (Cu 2 MnAl) Ge = -0.05 Ru = 1.3	Fe = 1.94	Fe = 1.94	-33.3 %
	XA (Hg 2 CuTi) Ge = -0.04 Fe = 2.76	Ru = 0.33	Fe = 1.92	-29.9 %
	Disordered XA Ge = -0.04 Fe = 2.74 Fe:Ru with Ru = 0.16 Fe:Ru with Fe =1.98 -2.7 %
	XA structures, it can be observed that Fe-4b atoms sur-
	rounded by 4

TABLE VI .

 VI Bader charge transfer in Fe2CoGe (considering disordered XA-type structure)

	Fe 2 CoGe	4a	4b 4c:4d 4d:4c
	Occupancy	Ge	Fe Fe:Co Fe:Co
	Magnetic moment (µ B /f.u.) -0.05 2.67 Co: 1 Fe: 1.56
	Total magnetic moment		5.18 (µ B /f.u.)
	Bader Charge (electron) +0.06 -0.27 +0.18 +0.03

ACKNOWLEDGMENTS

S.C. and S.G. would like to sincerely acknowledge UGC, India, and SINP, respectively, for their fellowship. DFT calculations were performed using HPC resources from GENCI-CINES (Grant No. 2021-A0100906175). Work at the Ames National Laboratory (in part) was supported by the Department of Energy-Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DEAC02-07CH11358.


Ph.D Aylin Nouri
email: aylin.nouri@enpc.fr

Associate Professor, Ph.D Ali Noorzad
email: a_noorzad@sbu.ac.ir

Professor, Ph.D Jean-Michel Pereira
email: jean-michel.pereira@enpc.fr

Anh Minh Tang

MSc Candidate

Small-scale cyclically thermally-activated pile under inclined mechanical loads

Keywords: Thermo-mechanical behavior, Energy pile, Physical model, Inclined mechanical load, Cyclic thermal load

Small-

Introduction

In the last few decades, to preserve the future generations from energy crises, significant effort has been accomplished to collect energy from renewable sources, including shallow geothermal energy. Geothermal energy piles are one of the most common and efficient systems of shallow geothermal energy, in which geothermal loops are integrated into the foundation elements to extract/inject the heat from/into the ground with the purpose of meeting the building heating and/or cooling demands. Since the mid-1980s, when the first energy piles were installed in Austria, the use of energy piles has increased rapidly in many countries, including Canada, Australia, Europe, UK, and China [START_REF] Brandl | Energy foundations and other thermo-active ground structures[END_REF][START_REF] Laloui | Experimental and numerical investigations of the behaviour of a heat exchanger pile[END_REF][START_REF] Adam | Energy from earth-coupled structures, foundations, tunnels and sewers[END_REF][START_REF] Loveridge | Performance of piled foundations used as heat exchangers[END_REF][START_REF] Loveridge | Temperature response functions (G-functions) for single pile heat exchangers[END_REF][START_REF] Loveridge | Long term monitoring of CFA energy pile schemes in the UK[END_REF][START_REF] Loveridge | Energy geostructures: a review of analysis approaches, in situ testing and model scale experiments[END_REF]. Even though lots of successful energy pile projects have been implemented in a variety of important structures such as high rise buildings, underground transport projects and earth retaining structures in the world, the application of this technology is still limited in the energy industry and the true potential for adoption of energy piles is yet to be realized in highway bridges for deck de-icing and offshore platforms for combined exploitation of offshore wind, wave and geothermal energy. In such applications, energy piles could be subjected not only to axial loads, but also to cyclic horizontal loads and moments due to heavy wind, earthquakes, earth pressure, slope failure, lateral spread induced by liquefaction and wave and current forces on offshore structures.

In the current design practice, the response of conventional pile under combined axial and horizontal loading is separately analyzed and then superposed. This approach neglects the coupling effect while the optimum design of pile foundations requires consideration of the influence of axial loads on their horizontal response. Most of previous studies have investigated the behavior of conventional piles under pure horizontal loads. Only a limited number of studies have investigated the response of conventional piles subjected to inclined loading using physical modelling under single gravity [START_REF] Jain | Effect of vertical load on flexural behavior of piles[END_REF][START_REF] Lee | Experimental investigation of the combined load response of model piles driven in sand[END_REF][START_REF] Lee | Influence of axial loads on the lateral capacity of instrumented steel model piles[END_REF][START_REF] Mu | Influence of vertical loads on lateral behaviour of monopoles in sand[END_REF][START_REF] Xu | Investigation of single pipe pile behavior under combined vertical and lateral loadings in standard and coral sands[END_REF][START_REF] Zhang | Model test study on horizontal bearing behavior of pile under existing vertical load[END_REF] or multiple gravities [START_REF] Lu | Influence mechanism of vertical-horizontal combined loads on the response of a single pile in sand[END_REF] and field-scale tests [START_REF] Bartolomey | Experimental Analysis of Pile Groups under Lateral Loads[END_REF][START_REF] Karasev | Investigation of the Work of Single Situ-Cast Piles under Different Load Combinations[END_REF][START_REF] Zhukov | Investigation of the Effect of a Vertical Surcharge on Horizontal Displacements and Resistance of Pile Columns to Horizontal Loads[END_REF]. Early studies, using physical model, presented by Jain et al [START_REF] Jain | Effect of vertical load on flexural behavior of piles[END_REF] and Lee et al [START_REF] Lee | Experimental investigation of the combined load response of model piles driven in sand[END_REF][START_REF] Lee | Influence of axial loads on the lateral capacity of instrumented steel model piles[END_REF] suggested an increase in pile head horizontal displacement in the presence of axial loading. That was in contrast to the findings of more recent studies presented by Mu et al [START_REF] Mu | Influence of vertical loads on lateral behaviour of monopoles in sand[END_REF],

Lu & Zhang [START_REF] Lu | Influence mechanism of vertical-horizontal combined loads on the response of a single pile in sand[END_REF], Xu et al [START_REF] Xu | Investigation of single pipe pile behavior under combined vertical and lateral loadings in standard and coral sands[END_REF] and Zhang et al [START_REF] Zhang | Model test study on horizontal bearing behavior of pile under existing vertical load[END_REF]. There is still a lot of complexities and uncertainties pertinent to the coupling effects even on the conventional pile behavior. That might be intensified in the case of energy piles because the thermal variations could affect the energy pile-soil interaction behavior, e.g., causing ratcheting phenomena in case of cyclic thermal loads. Therefore, it is necessary to identify the influence mechanism of axial compression loads on the horizontal behavior of energy piles.

As for traditional piles, the studies conducted so far have concentrated on the separate investigation of axial and horizontal responses of energy piles neglecting the coupling effects on the thermally-induced displacements in both axial and horizontal directions. Many researchers have put a lot of effort to better understand the thermo-mechanical behavior of energy piles during monotonic heating or cooling and one or multiple thermal cycles. The works of Vitali et al [START_REF] Vitali | Centrifuge modelling of the use of discretely-spaced energy pile row to reinforce unsaturated silt[END_REF] and Zhao et al [START_REF] Zhao | Thermally induced ratcheting of a thermo-active reinforced concrete pile in sand under sustained lateral load[END_REF] could be considered as the only available studies investigating the influence of monotonic heating and heating-cooling cycles on the flexural behavior of horizontally-loaded energy piles, respectively. Several studies have been performed to assess the behavior of axially-loaded energy piles during multiple thermal cycles through field scale tests [START_REF] Wang | Posttemperature effects on shaft capacity of a full-scale geothermal energy pile[END_REF][START_REF] Mccartney | Investigation of potential dragdown/uplift effects on energy piles[END_REF][START_REF] Faizal | Axial and radial thermal responses of a field-scale energy pile under monotonic and cyclic temperature changes[END_REF][START_REF] Faizal | Effects of cyclic temperature variations on thermal response of an energy pile under a residential building[END_REF][START_REF] Sutman | Full-scale in-situ tests on energy piles: Head and base-restraining effects on the structural behaviour of three energy piles[END_REF][START_REF] Jiang | Thermo-mechanical behavior of driven energy piles from full-scale load tests[END_REF], 1-g small-scale physical model tests [START_REF] Kalantidou | Preliminary study on the mechanical behaviour of heat exchanger pile in physical model[END_REF][START_REF] Yavari | Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling[END_REF][START_REF] Yavari | Mechanical behaviour of a small-scale energy pile in saturated clay[END_REF][START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF][START_REF] Nguyen | Long-term thermo-mechanical behaviour of energy piles in clay[END_REF][START_REF] Wang | Different types of energy piles with heating-cooling cycles[END_REF][START_REF] Wu | Thermo-mechanical behavior of energy pile under different climatic conditions[END_REF][START_REF] Fei | Experimental and numerical study on the behavior of energy piles subjected to thermal cycles[END_REF][START_REF] Liu | Ultimate bearing capacity of energy piles in dry and saturated sand[END_REF][START_REF] Bao | Investigation on thermo-mechanical behavior of reinforced concrete energy pile with large cross-section in saturated sandy soil by model experiments[END_REF][START_REF] Kong | Thermal induced horizontal earth pressure changes of pipe energy piles under multiple heating cycles[END_REF] and centrifuge model tests [START_REF] Stewart | Centrifuge modeling of soil-structure interaction in energy foundations[END_REF][START_REF] Ng | Centrifuge modelling of energy piles subjected to heating and cooling cycles in clay[END_REF][START_REF] Ng | Centrifuge modelling of heating effects on energy pile performance in saturated sand[END_REF][START_REF] Ng | Centrifuge modelling of displacement and replacement energy piles constructed in saturated sand: a comparative study[END_REF][START_REF] Ng | Scaling effects on the centrifuge modelling of energy piles in saturated sand[END_REF]. Dry sand was the most common type of soil used in these small-scale physical model tests. The above-mentioned studies indicated that imposing thermal cycles upon the axially-loaded semi-floating energy piles results in cumulative irreversible settlement, which has been identified qualitatively similar in 1-g small-scale physical model tests and in centrifuge testing, even though quantitative differences have been observed. Therefore, and 40% of the ultimate axial load); in the subsequent stage, horizontal static load was incrementally applied [START_REF] Nguyen | Long-term thermo-mechanical behaviour of energy piles in clay[END_REF][START_REF] Feia | Changes in permeability of sand during triaxial loading: effect of fine particles production[END_REF], and 70% of the ultimate horizontal load), while the axial load was kept constant. At each level of horizontal load, to simulate the actual operating condition of energy piles, repeated ten thermal cycles with temperature variation in the range of 1  °C were applied to the pile while the mechanical loads were maintained constant. The obtained results, including pile temperature, soil temperature, horizontal and axial displacements of pile head were finally analyzed and discussed.

despite

Experimental approach

Experimental setup

The schematic view of the experimental setup is depicted in Fig. 1. To obtain a correct physical modeling, the material type and dimensions of the model pile are selected by maintaining the dimensionless ratio of

EI GL 4 1 
 identical in the model and the prototype piles (G= soil stiffness; E =elastic modulus; I = moment of inertia; L=length of pile). Since the soil stiffness scales as

       n 1
in 1-g model testing (  = 0.5 for sandy soils; n = length scaling factor), the bending stiffness, EI, would scale as [START_REF] Wood | Geotechnical modelling[END_REF]. In the present study, a closed-end aluminum tube having an outer diameter (D) of 20 mm, inner diameter of 18 mm, embedded length of 600 mm, and thermal expansion coefficient of was selected as the model pile with a length scaling factor of 20. This is used to simulate the prototype pile of 570 mm diameter solid section made of reinforced concrete with a compressive strength of 30 MPa. Since the scaling of pile diameter depends on the scaling of pile bending stiffness, the diameter and length of the pile could not be scaled in the same way. According to Das [START_REF] Das | Principle of Foundation Engineering[END_REF], for the properties of sand and pile selected in this study, model pile having the length to diameter ratio (L/D) of 30 behaves as a long flexible pile during horizontal loading at 50% relative density of the sand. Therefore, in response to horizontal loading, the model pile is expected to bend from the top. A cylindrical steel tank with a diameter of 548 mm (  27D) and a height of 980 mm was used as a soil tank, in which the distance between the pile toe and the base of the model container was equal to 340 mm (  17D). It is inferred from the literature that with a tank-to-pile diameter ratio of 10D and a soil cushion with a depth of 3-4D below the pile toe, boundary effects of the tank could be considered negligible while testing the model pile under a combination of axial, horizontal and thermal loads [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF][START_REF] Kraft | Performance of axially loaded pipe piles in sand[END_REF][START_REF] Boominathan | An experimental study on static and dynamic bending behaviour of piles in soft clay[END_REF][START_REF] Leblanc | Response of stiff piles in sand to long-term cyclic lateral loading[END_REF][START_REF] Reddy | Experimental Studies on Behavior of Single Pile under Combined Uplift and Lateral Loading[END_REF][START_REF] Kramer | Laboratory Thermal Performance Tests on a Model Heat Exchanger Pile in Sand[END_REF][START_REF] Arshad | Model Studies on Monopile Behavior under Long-Term Repeated Lateral Loading[END_REF]. In order to mimic the roughness of the prototype pile surface, the surface of the model pile was coated with sand. It is to be noted that the attached sand layer would not change the axial and flexural stiffness of the pile.

5 . 4 1       n
Expanded polystyrene sheets were wrapped around the soil tank to insulate it against heat exchange between the soil and the ambient air.

The soil used for this study was dry Fontainebleau NE34 sand with the following physical properties [START_REF] Feia | Changes in permeability of sand during triaxial loading: effect of fine particles production[END_REF] . In the developed model, the ratio between the pile diameter (20 mm) and the mean grain size (0.21 mm) was equal to 95. The mentioned ratio was greater than the suggested limit by Fioravante [START_REF] Fioravante | On the shaft friction modelling of non-displacement piles in sand[END_REF], thereby the grain-size scaling effect could be considered negligible. A wooden tamper was used to compact the dry sand to a density of 1.54 Mg/m 3 (that corresponds to a relative density of 50%). Before installation of the model pile, the sand was placed and compacted in seven 50-mm-thick layers in the tank. After the compaction of these layers, a steel bar was mounted and bolted to the upper surface of the soil tank as a temporary support for installing the model pile at the center of the tank. Compaction of the remaining soil around the fixed pile was then continued by 50-mm-thick layers except for the top layer, which had a thickness of 40 mm. The density was controlled by the mass of soil being compacted and the thickness of each layer. The above-mentioned experimental setup and method of sand samples preparation have already been adopted by Kalantidou et al [START_REF] Kalantidou | Preliminary study on the mechanical behaviour of heat exchanger pile in physical model[END_REF], Yavari et al [START_REF] Yavari | Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling[END_REF] and Nguyen et al [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF].

The repeatability of these studies confirms the uniformity of sand samples prepared by this method. To control the pile temperature, model pile was equipped with an aluminum U-shaped tube (2 mm inner diameter and 3 mm outer diameter) linked to a temperature-controlled water bath and a peristaltic pump. The annulus between the pile and the aluminum U tube was filled with water to improve the heat transfer. Yavari et al [START_REF] Yavari | Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling[END_REF] indicated that the temperature changes measured at different depths of soil and at the same distance from the pile are quite similar. Hence, it could be concluded that the temperature of the shallow soil layers is not influenced by the ambient temperature, even though the soil surface is not insulated against heat exchange. Therefore, in the present study, pile and soil temperatures were only measured by the temperature sensors (S1-S5) placed at a depth 300 mm below the soil surface and at distances of 30 mm (  1.5D) and 50 mm (  2.5D), respectively, from the pile axis (as shown in Fig. 1).

The loading system, which had been previously adopted by Kalantidou et al [START_REF] Kalantidou | Preliminary study on the mechanical behaviour of heat exchanger pile in physical model[END_REF], Yavari et al [START_REF] Yavari | Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling[END_REF], and Nguyen et al [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF], was modified to consider the horizontal load. The static axial compressive load was applied to the model pile by placing dead weights on the pile head and the static horizontal load was applied to the pile in increments by allowing water flow in the plastic bucket linked to the pile head through a piece of rope over a pulley. The flow rate was controlled by a valve attached to the water tank. The applied horizontal load and pile head displacements were measured accurately using a load cell and displacement transducers (V1-V4, H1-H2), respectively.

Test program

In the present work, nine experiments were performed (Table 1), each one corresponds to a soil sample. In the test ID, notations of E and T denote the experiment (E) performed on one soil mass, and subtests (T) of the main experiment, respectively. Notations of M and TM after the first number denote loading type in experiments, i.e. mechanical loading (M), and thermo-mechanical loading (TM), respectively. The number after notations of E or T is the amount of pre-applied axial load (percent compared to ultimate axial load), and the number after notations of M or TM is the amount of applied horizontal load (percent compared to ultimate horizontal load).

Actually, for experiment E40M (and test T40M), after the installation of the setup, axial load (F v ) was first applied to 40% of the ultimate axial load (Q v , which was estimated at 500 N by Nguyen et al [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF] using the same system and the same soil). Afterward, the horizontal load (F h ) was increased progressively until failure (assumed to occur when pile head horizontal displacement exceeds 20%D). This value is in the range of pile horizontal displacements (at the sand bed surface level) often used to estimate the ultimate horizontal load capacity value [START_REF] Arshad | Model Studies on Monopile Behavior under Long-Term Repeated Lateral Loading[END_REF][START_REF] Sawwaf | Lateral resistance of single pile located near geosynthetic reinforced slope[END_REF]. The aim of experiment E40M (and test T40M) was to determine the mechanical behavior (and the ultimate horizontal load Q h ) of the pile under the increase of horizontal load while the axial load was maintained at 40% Q v . Experiment E40M_R (and test T40M_R) is the replicate of experiment E40M (and test T40M). Experiments E20M (and test T20M) and E10M (and test T10M) are similar to E40M (and test T40M) but with F v equal to 20% and 10% Q v , respectively. Experiments E20M_R and E10M_R are their replicates. In order to simulate typical load combinations of energy piles implemented in high-rise buildings, highway bridges, earth-retaining structures and those located on sloping ground, the loading scheme of model tests in the present study comprised pre-axial static loading followed by horizontal static loading before subsequent heating-cooling cycles. In such a loading scheme, the additional rotational restraint induced by pile cap, group effects and the cyclic nature of horizontal loading were not taken into consideration to isolate the coupling effects on the energy pile behavior during cyclic thermal loading. Therefore, for experiment E40TM, F v was first increased to 40% Q v , followed by an increase of F h to 30% Q h . Afterward, under this inclined mechanical load, thermal cycles were applied (test T40TM_30). Owing to the fact that the pile temperature was controlled manually in the experiments, a duration of 2 h was adopted for the heating and cooling phases, which was long enough for the soil temperature to reach equilibrium according to the temperature history of soil obtained by Nguyen et al [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF] using identical pile and soil under the same temperature change applied to the pile. Therefore, in each thermal cycle, pile temperature was manually increased from an ambient temperature of 22 to 23 °C over a 2-h heating phase prior to being decreased to 21 °C over a 2-h cooling phase. Finally, during the recovery phase, it was rapidly increased to an ambient temperature of 22 and maintained over 20 h prior to the subsequent thermal cycle. For the tests continued during the weekends, the duration of the recovery phase of some thermal cycles was increased to more than 20 h.

Table 1. Test program.

Experiment Test

v Q v F / (%) h Q h F / (%)

Number of thermal cycle

To scale the heat diffusion time in thermal cycles, Fourier's number could be used [START_REF] Kramer | Laboratory Thermal Performance Tests on a Model Heat Exchanger Pile in Sand[END_REF]:

(

Where , , and are soil thermal diffusivity, heat diffusion time, and pile diameter, respectively. The subscripts "m" and "p" mean model and prototype, respectively. Since the same sand was considered in model and prototype scale, the scaling factor for soil thermal diffusivity is one. Hence, the heat diffusion time must be scaled by .

As already noted by Zhao et al [START_REF] Zhao | Small-scale modeling of thermomechanical behavior of reinforced concrete energy piles in soil[END_REF], thermal strains ( ) should be scaled by the same scaling factor as mechanical strains (i.e.

). Hence, the temperature changes in the prototype-scale concrete pile ( ) are given by:

(2)

Since the model-scale aluminum pile has a thermal expansion coefficient ( ) of , which is 2.2 times that ( ) of a prototype-scale concrete pile, temperature changes of ( ) during 2-h heating and cooling phases in the model-scale pile could simulate temperature changes of during 2.25-month heating and cooling phases in the prototype-scale pile. This temperature variation range of the prototype pile is within the range of 3-37 °C of field-scale energy piles [START_REF] Jiang | Thermo-mechanical behavior of driven energy piles from full-scale load tests[END_REF][START_REF] You | Experimental study on structural response of CFG energy piles[END_REF].

four hours of temperature changes of in the model-scale pile ( ) could simulate five months of temperature changes of in the prototype-scale pile.

After performing test T40TM_30, F h was increased to 50% and 70% Q h prior to the application of the thermal cycles in tests T40TM_50 and T40TM_70, respectively. Experiments E20TM and E10TM are similar to E40TM but with F v equal to 20% and 10% Q v , respectively. Normally, in each thermo-mechanical test (TM), model pile was subjected to 10 heating-cooling cycles over a period of two weeks. There were two reasons to simulate the cyclic thermal load using 10 heating-cooling cycles. First, each heating-cooling cycle required about one day for completion and hence, in order to investigate different loading conditions, the number of thermal cycles should be optimized. Second, the results obtained from the first thermo-mechanical test (test T10TM_30) indicated that the increment rate of irreversible displacement in both axial and horizontal directions is unsteady during the first thermal cycles and, as the number of thermal cycles increased, it tended to be stable.

Results and discussions

Load-displacement response of the model pile subjected to purely mechanical load

In the mechanical experiments, the data collected in terms of axial load and settlement of the model pile while being subjected to pure axial loading are plotted in Fig. 2. The load-settlement curves corresponding to the previous studies conducted using identical pile and soil are drawn in the same figure for comparison purpose [START_REF] Yavari | Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling[END_REF][START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF]. It is clearly seen that the measured settlements in the present study is similar to those reported in previous works, confirming the repeatability of the model preparation and loading system. is equal to 86 -90 N. An increasing pre-applied axial load from 10% to 20% Q v causes a negligible reduction in pile head horizontal displacement, which agrees with the findings of previous studies using similar soil conditions and experimental set-up [START_REF] Mu | Influence of vertical loads on lateral behaviour of monopoles in sand[END_REF][START_REF] Xu | Investigation of single pipe pile behavior under combined vertical and lateral loadings in standard and coral sands[END_REF][START_REF] Zhang | Model test study on horizontal bearing behavior of pile under existing vertical load[END_REF][START_REF] Lu | Influence mechanism of vertical-horizontal combined loads on the response of a single pile in sand[END_REF]. On the contrary, with an increase of pre-applied axial load to 40% Q v , pile head horizontal displacement increases rather than decreases further so that the horizontal load-horizontal displacement curve is almost the same as the case of the pre-applied axial load of 10% Q v . Overall, where axial load varies between 10% and 40% Q v , the horizontal behavior of the pile is almost independent of the axial load. It is likely that small pre-applied axial loads (F v ≤ 40%Q v ) have negligible influence on the horizontal soil resistance. ) are ignored, it could be observed that normalized pile head settlement increases at a reducing rate with increasing horizontal load, and tends to stabilize at 0.35%, 0.50%, and 0.70% at high horizontal load under constant axial load of 10% Q v (E10M, E10M_R), 20% Q v (E20M), and 40% Q v (E40M), respectively. This behavior is similar to that obtained in the experimental study of Lu & Zhang [START_REF] Lu | Influence mechanism of vertical-horizontal combined loads on the response of a single pile in sand[END_REF]. This can be explained by the fact that when the pile has not moved sufficiently in the horizontal direction, the mobilization of passive earth pressure in front of the pile does not compensate for the loss of active earth pressure behind the pile. Thereby, the resulting shaft resistance loss and interface slip lead to the transfer of axial compressive load from the shaft to the pile toe and causes the increase in the pile toe settlement and resistance.

Influence of cyclic thermal loading on the behavior of the model pile subjected in advance to inclined mechanical loading

Fig. 4 illustrates the histories of measured temperature of model pile and surrounding soil at various distances from the pile axis for the first thermal cycle of Test T40TM_30. As shown in Fig. 4, when the pile temperature rises up from 22 to 23 during the heating phase and decreases to 21 during the subsequent cooling phase, the variation of soil temperature recorded at 30 mm (S1 and S4) and 50 mm (S3 and S5) from the pile axis have a smaller amplitude, ±0.5 and ±0.2 , respectively. The same phenomenon was also observed by Ng et al [START_REF] Ng | Centrifuge modelling of displacement and replacement energy piles constructed in saturated sand: a comparative study[END_REF] and Nguyen et al [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF]. It is important to note that for all thermal cycles in the thermo-mechanical tests, the measured temperatures in the model pile and surrounding soil follow the same trend as observed for the first thermal cycle of Test T40TM_30. Additionally, during the recovery phase, the temperatures of the model pile and the surrounding soil return gradually to the ambient temperature. As can be seen from Fig. 5, during the first thermal cycle, the heating phase did not lead to axial displacement at the pile head, while the cooling phase causes a continuous pile head settlement of up to 0.13%D. With increasing the number of thermal cycles, the pile head tends to move slightly upward with increasing temperature to 23 in the heating phase. Meanwhile, during cooling the pile temperature to the ambient temperature (i.e. 22 ), the pile head does not move axially but with a further decrease in pile temperature to 21 , the pile head begins to move downward with a settlement of approximately 0.06%D. Eventually, during the recovery phase of all thermal cycles, there is no axial movement of the pile head. In the cooling phase of each thermal cycle, the settlement/temperature slope is similar to that of the free thermal expansion/contraction curve (i.e. equal to ), which corresponds to the thermally-induced axial displacement of a fully toe-restrained pile being free to move in other directions. This trend is consistent with those obtained from previous experimental studies on dry sand [START_REF] Kalantidou | Preliminary study on the mechanical behaviour of heat exchanger pile in physical model[END_REF][START_REF] Yavari | Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling[END_REF][START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF]. In Fig. 6, generally, it can be observed that the pile head horizontal displacement increases continuously throughout each heating-cooling cycle. However, the rate of increase of the pile head horizontal displacement due to the cooling phase is negligible and could be ignored compared to that due to the heating phase. When the number of thermal cycles increases, the model pile tends to move less in the horizontal direction during the recovery phase, so that for the last few thermal cycles, the horizontal displacement could be neglected when compared to the one taking place during the heating phase. As can be seen from Fig. 6, for the first thermal cycle, the pile head initially moves horizontally by about 0.063%D during the heating phase, and then it continues to move horizontally for another 0.007%D during the subsequent cooling phase. Afterward, during the recovery phase, the pile head horizontal displacement continues to increase, reaching a peak value of 0.22%D. Correspondingly, for the tenth thermal cycle, pile head moves horizontally to 0.053%D during the heating phase while it moves marginally during the subsequent cooling phase. Afterward, during the recovery phase, the pile head exhibits no horizontal displacement and stabilizes at 0.06%. This kind of phenomenon is similarly observed in available centrifuge observations for horizontally-loaded energy pile [START_REF] Zhao | Thermally induced ratcheting of a thermo-active reinforced concrete pile in sand under sustained lateral load[END_REF], where the pile head movement in the horizontal direction increases clearly during the heating cycle and it remains approximately unchanged during the subsequent cooling phase. It can be also noticed from Figs. 5 and 6 that although the pile has been subjected to some constant temperature for a long time in some thermal cycles due to continuing tests during weekends, its settlement and horizontal displacement are nearly stabilized. By the end of each thermal cycle, the model pile keeps settling and accumulating horizontal movement instead of returning to its initial position. This irreversible phenomenon may occur as a result of the cooling-induced radial contraction and constrained heating-induced downward expansion of the model pile accompanied by the thermally-induced volumetric contraction of surrounding sandy soil. When the surrounding soil experiences a volumetric contraction under the heating/cooling cycle (evidence of this phenomenon is available in previous works [START_REF] Kong | Thermal induced horizontal earth pressure changes of pipe energy piles under multiple heating cycles[END_REF][START_REF] Ng | Centrifuge modelling of heating effects on energy pile performance in saturated sand[END_REF]) or when the model pile contracts radially under decreasing temperature, the lateral pressure acting on the pile shaft decreases, resulting in a reduction of the passive soil resistance as well as the shaft resistance. Since the surrounding soil is less resistant against the inclined mechanical loads, the amount of pile head horizontal displacement and pile toe settlement would increase to further mobilize the passive soil resistance in front of the pile and the base resistance at the pile toe.

The accumulated irreversible settlement and horizontal displacement of pile head are plotted against the number of thermal cycles in Fig. 7. In Fig. 7(a), the results show a general trend with a quick increase of normalized horizontal displacement during the first cycles and a continued increase at a smaller rate during the remaining cycles, which reaches 1.1-1.25%, 1.2-1.65% and 1.8-2.3% after ten cycles for the cases with F h =30% Q h , 50% Q h and 70% Q h , respectively. In Fig. 7(b), the results of Nguyen et al [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF], using identical pile and soil, under axial load only (F h = 0) are also shown for comparison purposes. The results show that, for the cases with

F v = 10% Q v , irreversible
normalized pile head settlement increases continuously and reaches 0.4% after ten cycles for

F h = 30% Q h (T10TM_30); for F h = 50% Q h (T10TM_50) and F h = 70% Q h (T10TM_70)
, it increases during the first three cycles and stabilizes at 0.13%. For the cases with F v = 20% Q v , irreversible normalized pile head settlement increases continuously and reaches 0.43%, 0.23% and 0.2% after ten cycles for F h = 0 (i.e. T20TM_0 [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF]), F h =50% Q h (T20TM_50) and F h = 70% Q h (T20TM_70), respectively, while for F h = 30% Q h (T20TM_30), it rapidly increases during the first three cycles and tends to stabilize at 0.47%. Finally, for the cases with

F v = 40% Q v , irreversible
normalized pile head settlement increases continuously and reaches 0.61%, 0.41% and 0.35% after ten cycles for F h = 30% Q h (T40TM_30), F h = 50% Q h (T40TM_50) and F h = 70% Q h (T40TM_70), respectively. For the pure axial loading case with F v = 40% Q v (i.e. T40TM_0 [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF]), the accumulation rate of the irreversible settlement during the first two cycles is much higher than that in the cases of inclined loading; however, it decreases significantly during subsequent cycles and the accumulated irreversible normalized settlement stabilizes at 0.62% after ten cycles.

What should be noted from Fig. 7 is that for all the nine thermo-mechanical tests, regardless of the magnitude of the applied mechanical loads, the observed ratcheting pattern for axial and horizontal displacements is characterized by two features: first, the largest increment of irreversible settlement and horizontal displacement are induced by the first thermal cycle; second, after a fast accumulation of irreversible displacement in the first thermal cycle, the accumulation rate initially decreases slightly, and then almost remains constant when increasing the number of thermal cycles. The tendency for a model pile to exhibit less settlement and horizontal displacement with an increase in the number of thermal cycles is commonly explained by the strengthening of surrounding soil due to the thermally-induced gradual densification (which is a phenomenon observed in previous works [START_REF] Blanc | Intrinsic creep of a granular column subjected to temperature changes[END_REF]). This kind of ratcheting response was similarly observed for axially-loaded energy piles reported by Nguyen et al [START_REF] Nguyen | Long-term thermomechanical behavior of energy pile in dry sand[END_REF], Yavari et al [START_REF] Yavari | Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling[END_REF] and Ng et al [START_REF] Ng | Centrifuge modelling of heating effects on energy pile performance in saturated sand[END_REF][START_REF] Ng | Centrifuge modelling of displacement and replacement energy piles constructed in saturated sand: a comparative study[END_REF][START_REF] Ng | Scaling effects on the centrifuge modelling of energy piles in saturated sand[END_REF], and for horizontally-loaded energy pile reported by Zhao et al [START_REF] Zhao | Thermally induced ratcheting of a thermo-active reinforced concrete pile in sand under sustained lateral load[END_REF]. As shown in Fig. 8, for the same horizontal load, imposing ten thermal cycles at an axial load higher than 10% Q v induces a higher accumulated irreversible settlement of up to 228% but a lower accumulated irreversible horizontal displacement of up to 25.8%. For the same axial load, imposing ten thermal cycles at a horizontal load higher than 30% Q h induces a lower accumulated irreversible settlement of up to 68.8% but a higher accumulated irreversible horizontal displacement of up to 86.6%. This possibly occurs because of the influence of mechanical loading condition on the soil-pile stiffness before the application of thermal loading. In general, it could be stated that at a specific axial load, the axial stiffness of the soil-pile system increases with an increase in horizontal load due to the increase in mobilized skin friction stresses, which result from increasing horizontal stresses and upward-directed movement of passive earth pressure wedge in front of the pile. Moreover, at a specific horizontal load, the horizontal stiffness of the soil-pile system increases with the increasing axial load. This could be explained by the increase in mobilized passive earth pressure, which arises from increasing level of confinement provided by the surrounding soil due to the axial load-induced settlement of pile.

Coupling effects on the thermally-induced mechanical response of model pile

These results agree with those obtained for purely mechanical loading, in which the increase of axial load at the same horizontal load leads to a reduction in horizontal displacement, but an increase in the settlement; Moreover, the increase of horizontal load at the same axial load leads to an increase in horizontal displacement. Only the reduction of the accumulated irreversible settlement with the increase of horizontal load at the same axial load is contrary to that observed for purely mechanical loading. Since for the same axial load, the horizontal load increases in three steps, and ten thermal cycles are imposed to the pile at the end of each step (as described in section 2.2), the accumulated thermally-induced irreversible settlement under the horizontal loads of 50% and 70% Q h might be influenced by the accumulated thermally-induced irreversible settlement induced by the horizontal loads of 30% and 50% Q h .

Load-displacement response of model pile subjected to thermo-mechanical load

In order to investigate the influence of thermal loading on the pile response, the results obtained from the mechanical and thermo-mechanical experiments are presented in terms of normalized pile head horizontal displacement and settlement versus normalized horizontal load (i.e. divided by pile's ultimate horizontal load for the mechanical tests) in Fig. 9. As shown in Fig. 9, during the initial increase of F h to 30% Q h prior to the application of thermal loading, the settlement and horizontal displacement of pile head in thermo-mechanical tests are similar to those in mechanical ones. In the subsequent increments of the horizontal load to 50%, 70%, and 100% Q h after the application of thermal loading, pile head horizontal displacement remains unchanged for a while and then increases again with increment rates equal to those in mechanical tests. Meanwhile, pile head settlement almost does not change with horizontal load increments after having been thermally loaded. When comparing the horizontal loaddisplacement response of the pile in mechanical experiments to those in thermo-mechanical ones, it must be pointed out that the thermal loading does not affect the horizontal response of the soil-pile system. The reason for this is that the large extent of reduction in the horizontal stress and mobilized skin friction is recovered by the subsequent reloading phase. Therefore, it could be concluded that the total axial and lateral resistance of the pile is affected only slightly by the thermal loading. By comparing the horizontal load at a pile head horizontal displacement of 4 mm (i.e. 20% pile diameter), the ultimate horizontal bearing capacity of pile may remain unchanged after ten heatingcooling cycles. However, due to the gradual accumulation of the irreversible pile head horizontal displacement over thermal cycles, it is recommended that the long-term performance of the energy pile is controlled by horizontal displacement rather than ultimate horizontal bearing capacity.

Conclusions

The thermo-mechanical behavior of a model energy pile subjected to inclined mechanical loads and temperature variations was experimentally investigated in dry sand. Ten heating-cooling cycles were applied to the pile under various combination of axial and horizontal mechanical loading (axial loads equal to 10, 20, and 40% of the ultimate axial load; horizontal loads equal to 30, 50, and 70% of the ultimate horizontal load). The main conclusions that can be drawn from this study are the following:

 For Fv ≤ 40%Qv, effect of Fv on the horizontal response of the pile under horizontal loading could be considered negligible. Moreover, additional settlement occurs at pile head due to the horizontal loading.

 The application of temperature variations along with inclined mechanical loads results in irreversible settlement and horizontal displacement at the pile head, whose largest increment takes place during the first thermal cycle. After a fast accumulation of irreversible displacement in the first thermal cycle, the increments of irreversible settlement and horizontal displacement, accumulating after each thermal cycle, initially decrease slightly and then almost remain constant with an increase in the number of heating-cooling cycles. By the end of the tenth thermal cycle, the amount of accumulated irreversible settlement and horizontal displacement are generally in the range of 0.1-0.6%D and 1.1-2.3%D, respectively.

 Under the same horizontal load, thermal cycles at a higher axial load induce a higher irreversible settlement but a lower horizontal displacement at the pile head.

 Under the same axial load, thermal cycles at a higher horizontal load induce a lower settlement but a higher horizontal displacement at the pile head.

 Thermal loading did not affect the subsequent horizontal load-displacement response of the pile.

Likewise, by comparing the horizontal load at a pile head horizontal displacement of 4 mm (i.e.

20%D), the ultimate horizontal bearing capacity of the pile remained barely unchanged after ten heating-cooling cycles. However, due to the accumulation of irreversible horizontal displacement during the cyclic thermal loading, it is vital to ensure that the long-term cyclic thermal loading does not degrade the safety and durability of the energy piles for the service life of the building. Therefore, it is highly recommended that the long-term performance of the energy pile is controlled by horizontal displacement rather than ultimate horizontal bearing capacity.

The results of 1-g model tests carried out in this study could be helpful to gain insights into the qualitative influence of inclined mechanical loading on the thermally-induced displacements in both axial and horizontal directions; however, in order to provide quantitative confirmation of these initial findings, further studies are required to be conducted using centrifuge and field-scale tests.

D

  Outer diameter of model pile L Length of pile Thermal strain n length scaling factor (prototype divided by model) Thermal expansion coefficient of the prototype-scale pile Thermal expansion coefficient of the model-scale pile Temperature change in the prototype-scale pile Temperature change in the model-scale pile

  the inherent limitations of 1-g small-scale physical model tests compared to the field-scale and centrifuge model tests, qualitative results obtained from the former could be used to gain an insight into the behavior of energy piles under thermo-mechanical loading and the mechanism involved. Overall, model tests to analyze the performance of energy piles subjected to combined mechanical and cyclic thermal loads are still limited and there is a necessity to deeply investigate the potential effects of multiple thermal cycles on the energy pile-soil interaction mechanism.The objectives of the present research are twofold: (1) investigating the influence of multiple heating-cooling cycles on the geotechnical responses of energy piles; (2) evaluating the coupling effects on the thermally-induced mechanical response of energy piles. Therefore, a series of 1-g model experiments was carried out on a single model energy pile embedded in dry sand. The model pile was initially subjected to axial static compressive load(10, 20,

Fig. 1 .

 1 Fig. 1. Schematic view of experimental setup.

  To measure pile head axial displacement, in all experiments except E20M_R and E40M_R, axial displacement sensors V1 and V2 were mounted in the perpendicular direction to horizontal load and opposite to each other at a distance of 40 mm from the pile axis. Conversely, in experiments E20M_R and E40M_R, axial displacement sensors V3 and V4 were mounted in the horizontal load direction and opposite to each other at a distance of 40 mm from the pile axis. In all experiments, pile head horizontal displacement was measured at a height of 40 mm above the soil surface by two horizontal displacement sensors (H1 and H2) mounted directly opposite to each other at a distance of 50 mm from the pile axis (see Fig.1).

Fig. 2 .

 2 Fig. 2. Pile head settlement versus axial load measured in mechanical tests without horizontal loading.

Fig. 3 .

 3 Fig. 3. Variation of (a) pile head horizontal displacement; (b) pile head settlement with horizontal load measured under constant axial load.

Fig. 4 .

 4 Fig. 4. Soil and pile temperature versus the elapsed time during the first thermal cycle of Test T40TM_30.

Fig. 5 .

 5 Fig. 5. Thermally-induced pile head settlement versus (a) temperature changes and (b) elapsed time during ten heating-cooling cycles of test T40TM_30.

Fig. 6 .

 6 Fig. 6. Thermally-induced pile head horizontal displacement versus (a) temperature changes and (b) elapsed time during ten heating-cooling cycles of test T40TM_30.

Fig. 7 .

 7 Fig. 7. (a) Irreversible horizontal displacements; (b) irreversible settlement of pile head versus the number of heating-cooling cycles.

Fig. 8

 8 Fig. 8 demonstrates the coupling effects on the irreversible settlement and horizontal displacements accumulated over ten heating/cooling cycles at the pile head.

Fig. 8 .

 8 Fig. 8. Coupling effects on the irreversible settlement and horizontal displacement accumulated over ten heating/cooling cycles at the pile head.

Fig. 9 .

 9 Fig. 9. Temperature-induced change in pile head response to horizontal load under a constant axial load of (a) 10% (b) 20% and (c) 40% of the axial pile resistance.

The first and second authors would like to express their gratitude to the Niroo Research Institute (NRI) for funding the present study, which is a part of the research project entitled, "Safety assessment of energy piles" (Project No. 99/51304/178). The first author is also funded as a visiting scholar by the Iranian Ministry of Science, Research and Technology, and the French Foreign Ministry. The financial support from these funding sources is greatly appreciated.

Data availability and materials

The data that support the findings of this study are available from the corresponding author on reasonable request.

Declarations

Conflict of Interest

The authors declare that they have no known competing for financial interests or personal relationships that could have appeared to influence the work reported in this paper.