Marwen Bouasker
email: marwen.bouasker@univ-orleans.fr

Nour El

Houda Khalifa

Pierre Mounanga

Ben Nabil

Kahla

Nabil Ben Kahla

Early-age deformation and autogenous cracking risk of slag-limestone filler-cement blended binders

Introduction and scientific background

In recent years, multi-component cementitious binders have received a renewed growing interest from the concrete science community . These binders are composed of a binary, ternary or even quaternary combination of Portland cement (PC) and supplementary cementitious materials (SCM) such as filler (quartzite filler -QF; limestone filler -LF) and industrial byproducts/ pozzolanic materials (fly ash -FA; calcined clay -CC; microsilica -lS; ground granulated blast furnace slag -BFS; silica fume -SF; metakaolin -MK; etc.). The interest for these alternate binders to ordinary PC is usually explained or justified by three principal reasons:

A reduction of the environmental impacts. The production of cement-based binders incorporating high volumes of recycled industrial waste or byproducts in substitution of ordinary PC is seen as one of the most promising way for the cement and concrete industry to decrease its CO 2 emissions [START_REF] Nehdi | Ternary and quaternary cements for sustainable development[END_REF][START_REF] Nehdi | Optimization of ternary cementitious mortar blends using factorial experimental plans[END_REF][START_REF] Mehta | Reducing the environmental impact of concrete[END_REF][START_REF] Malhotra | Reducing CO 2 emissions[END_REF]. This will allow the development of concrete compositions with lower environmental impact [START_REF] Damtoft | Sustainable development and climate change initiatives[END_REF] and also the reduction of landfill disposal.

An improvement of long-term performances. Numerous studies showed that the combination of cements with SCM exhibited significant advantages over binary binders and plain PC [START_REF] Thomas | Use of ternary cementitious systems containing silica fume and fly ash in concrete[END_REF]. Indeed, multi-component cement-based binders are well known for their improved long-term strength [START_REF] Thomas | Use of ternary cementitious systems containing silica fume and fly ash in concrete[END_REF][START_REF] Menéndez | Strength development of ternary blended cement with limestone filler and blast-furnace slag[END_REF][START_REF] Carrasco | Strength optimization of ''tailor-made cement'' with limestone filler and blast furnace slag[END_REF][START_REF] Antiohos | Improving the performance of ternary blended cements by mixing different types of fly ashes[END_REF][START_REF] Zelic | Synergistic action of a ternary system of Portland cement -limestone -silica fume in concrete[END_REF][START_REF] Güneyisi | Properties of self-compacting mortars with binary and ternary cementitious blends of fly ash and metakaolin[END_REF][START_REF] Erdem | Use of binary and ternary blends in high strength concrete[END_REF][START_REF] Gesog ˘lu | Properties of self-compacting concretes made with binary, ternary, and quaternary cementitious blends of fly ash, blast furnace slag, and silica fume[END_REF][START_REF] Moser | Assessment of binary and ternary blends of metakaolin and class C fly ash for alkali-silica reaction mitigation in concrete[END_REF][START_REF] De Weerdt | Synergy between fly ash and limestone powder in ternary cements[END_REF][START_REF] De Weerdt | Hydration mechanisms of ternary Portland cements containing limestone powder and fly ash[END_REF][START_REF] Radlinski | Investigation into the synergistic effects in ternary cementitious systems containing portland cement, fly ash and silica fume[END_REF] and durability [START_REF] Lane | Preventive measures for alkali-silica reactions (binary and ternary systems)[END_REF][START_REF] Thomas | Use of ternary cementitious systems containing silica fume and fly ash in concrete[END_REF][START_REF] Shehata | Use of ternary blends containing silica fume and fly ash to suppress expansion due to alkali-silica reaction in concrete[END_REF][START_REF] Pandey | Studies on high-performance blended/multiblended cements and their durability characteristics[END_REF][START_REF] Zelic | Synergistic action of a ternary system of Portland cement -limestone -silica fume in concrete[END_REF][START_REF] Gesog ˘lu | Properties of self-compacting concretes made with binary, ternary, and quaternary cementitious blends of fly ash, blast furnace slag, and silica fume[END_REF][START_REF] Radlinski | Investigation into the synergistic effects in ternary cementitious systems containing portland cement, fly ash and silica fume[END_REF][START_REF] Bagheri | Mechanical and durability properties of ternary concretes containing silica fume and low reactivity blast furnace slag[END_REF].

A higher potential cost/benefit ratio. The costs of BFS, FA and LF are significantly lower than that of PC and, when considering the material costs, price differences between the individual components may allow, in some cases, the ternary blended cement binders to compete with ordinary PC [START_REF] Thomas | Use of ternary cementitious systems containing silica fume and fly ash in concrete[END_REF]. However, the use of expensive mineral admixtures (SF for example) to increase the early-age mechanical properties of ternary binders can rapidly reverse this positive cost/benefit ratio [START_REF] Nehdi | Optimization of ternary cementitious mortar blends using factorial experimental plans[END_REF].

The mix-design principle of multi-component blended cement binders exploits the synergy that may exist between different types of SCM. This synergy, attributed to both chemical and physical phenomena [START_REF] Antiohos | Improving the performance of ternary blended cements by mixing different types of fly ashes[END_REF][START_REF] De Weerdt | Synergy between fly ash and limestone powder in ternary cements[END_REF][START_REF] Radlinski | Investigation into the synergistic effects in ternary cementitious systems containing portland cement, fly ash and silica fume[END_REF][START_REF] Bentz | Fine limestone additions to regulate setting in high volume fly ash mixtures[END_REF], is reflected in two main effects:

A complementary effect of mutual compensation of the shortcomings of each mineral addition (for example, in PC-SF--FA blended binder, SF improves the early-age performances of concrete while the later pozzolanic reactions of FA contribute to enhance the properties of the hardened concrete [START_REF] Thomas | Use of ternary cementitious systems containing silica fume and fly ash in concrete[END_REF][START_REF] Radlinski | Investigation into the synergistic effects in ternary cementitious systems containing portland cement, fly ash and silica fume[END_REF]).

And an interactive effect between PC and SCM which enables to obtain greater performances than those obtained with the individual effects of each addition used separately [START_REF] Shehata | Use of ternary blends containing silica fume and fly ash to suppress expansion due to alkali-silica reaction in concrete[END_REF][START_REF] Radlinski | Investigation into the synergistic effects in ternary cementitious systems containing portland cement, fly ash and silica fume[END_REF].

Several studies have been conducted to optimize the composition of ternary binders and various combinations of cement with SCMcm have been investigated (PC + BFS + SF [START_REF] Bágel | Strength and pore structure of ternary blended cement mortars containing blast furnace slag and silica fume[END_REF][START_REF] Lane | Preventive measures for alkali-silica reactions (binary and ternary systems)[END_REF][START_REF] Nehdi | Optimization of ternary cementitious mortar blends using factorial experimental plans[END_REF][START_REF] Erdem | Use of binary and ternary blends in high strength concrete[END_REF][START_REF] Gesog ˘lu | Properties of self-compacting concretes made with binary, ternary, and quaternary cementitious blends of fly ash, blast furnace slag, and silica fume[END_REF][START_REF] Bagheri | Mechanical and durability properties of ternary concretes containing silica fume and low reactivity blast furnace slag[END_REF]; PC + FA + SF [START_REF] Lane | Preventive measures for alkali-silica reactions (binary and ternary systems)[END_REF][START_REF] Thomas | Use of ternary cementitious systems containing silica fume and fly ash in concrete[END_REF][START_REF] Nehdi | Optimization of ternary cementitious mortar blends using factorial experimental plans[END_REF][START_REF] Shehata | Use of ternary blends containing silica fume and fly ash to suppress expansion due to alkali-silica reaction in concrete[END_REF][START_REF] Chen | Prediction of compressive strength and optimization of mixture proportioning in ternary cementitious systems[END_REF][START_REF] Erdem | Use of binary and ternary blends in high strength concrete[END_REF][START_REF] Gesog ˘lu | Properties of self-compacting concretes made with binary, ternary, and quaternary cementitious blends of fly ash, blast furnace slag, and silica fume[END_REF][START_REF] Radlinski | Investigation into the synergistic effects in ternary cementitious systems containing portland cement, fly ash and silica fume[END_REF]; PC + FA + LF [START_REF] Elkhadiri | Mechanical behaviour of various mortars made by combined fly ash and limestone in Moroccan Portland cement[END_REF][START_REF] Pandey | Studies on high-performance blended/multiblended cements and their durability characteristics[END_REF][START_REF] Mounanga | Improvement of the earlyage reactivity of fly ash and blast furnace slag cementitious systems using limestone filler[END_REF][START_REF] De Weerdt | Synergy between fly ash and limestone powder in ternary cements[END_REF][START_REF] De Weerdt | Hydration mechanisms of ternary Portland cements containing limestone powder and fly ash[END_REF][START_REF] Bentz | Fine limestone additions to regulate setting in high volume fly ash mixtures[END_REF]; PC + BFS + LF [START_REF] Menéndez | Strength development of ternary blended cement with limestone filler and blast-furnace slag[END_REF][START_REF] Carrasco | Strength optimization of ''tailor-made cement'' with limestone filler and blast furnace slag[END_REF][START_REF] Mounanga | Improvement of the earlyage reactivity of fly ash and blast furnace slag cementitious systems using limestone filler[END_REF]; PC + FA + BFS [START_REF] Douglas | Prediction of compressive strengths of mortars made with portland cement-blast furnace slag-fly ash blends[END_REF][START_REF] Wang | On predicting compressive strengths of mortars with ternary blends of cement, GGBFS and fly ash[END_REF][START_REF] Gesog ˘lu | Properties of self-compacting concretes made with binary, ternary, and quaternary cementitious blends of fly ash, blast furnace slag, and silica fume[END_REF][START_REF] Tan | Strengthening effects of finely ground fly ash, granulated blast furnace slag, and their combination[END_REF]; PC + FA + MK [START_REF] Pandey | Studies on high-performance blended/multiblended cements and their durability characteristics[END_REF][START_REF] Güneyisi | Properties of self-compacting mortars with binary and ternary cementitious blends of fly ash and metakaolin[END_REF][START_REF] Moser | Assessment of binary and ternary blends of metakaolin and class C fly ash for alkali-silica reaction mitigation in concrete[END_REF]; PC + SF + LF [START_REF] Zelic | Synergistic action of a ternary system of Portland cement -limestone -silica fume in concrete[END_REF]).

FA and BFS, which are available in large quantities, are the most used SCM in replacement of cement in concrete [START_REF] Malhotra | Reducing CO 2 emissions[END_REF]. Their low reactivity at early age can be mitigated by the incorporation of a third component, SF or LF, in moderate amount. The use of SF is increasingly limited due to its high cost [START_REF] Nehdi | Optimization of ternary cementitious mortar blends using factorial experimental plans[END_REF] while LF, as the main raw material of PC, is usually available in abundance near cement plants. Recent studies have shown that LF used in low or moderate amount (5-10%) may improve the early-age reactivity of ternary binders [START_REF] Mounanga | Improvement of the earlyage reactivity of fly ash and blast furnace slag cementitious systems using limestone filler[END_REF][START_REF] De Weerdt | Synergy between fly ash and limestone powder in ternary cements[END_REF][START_REF] De Weerdt | Hydration mechanisms of ternary Portland cements containing limestone powder and fly ash[END_REF][START_REF] Bentz | Fine limestone additions to regulate setting in high volume fly ash mixtures[END_REF][START_REF] Gurney | Reducing Set Retardation in High Volume Fly Ash Mixtures with the Use of Limestone: improving constructability for sustainability[END_REF] without compromising their mechanical properties [START_REF] Mounanga | Improvement of the earlyage reactivity of fly ash and blast furnace slag cementitious systems using limestone filler[END_REF][START_REF] De Weerdt | Synergy between fly ash and limestone powder in ternary cements[END_REF]. The adequate combination of PC, LF and BFS can even lead to higher performances when compared to the binary blended cements and plain PCs [START_REF] Menéndez | Strength development of ternary blended cement with limestone filler and blast-furnace slag[END_REF][START_REF] Pandey | Studies on high-performance blended/multiblended cements and their durability characteristics[END_REF][START_REF] Carrasco | Strength optimization of ''tailor-made cement'' with limestone filler and blast furnace slag[END_REF].

The great majority of research works carried out on ternary binders concerned the development of their mechanical properties and durability indicators. Very few studies have been dedicated to their risk of early-age cracking due to the physico-chemical interactions between PC and SCM [START_REF] Akkaya | Effect of supplementary cementitious materials on shrinkage and crack development in concrete[END_REF], while this issue is of great importance for a wider use of these types of binders in the concrete building industry. For example, Akkaya et al. found that ternary binder concretes, submitted to drying, cracked earlier than binary binder concretes, due to their lower strength [START_REF] Akkaya | Effect of supplementary cementitious materials on shrinkage and crack development in concrete[END_REF].

This study aims to investigate the early-age behavior of binary and ternary binders prepared with PC and various substitution rates of LF and BFS, focusing on the risk of early-age autogenous cracking. The autogenous cracking risk of 12 blended cement pastes prepared with the same water-to-cementitious materials (w/cm) ratio, equal to 0.32, and different dosages of PC, BFS and LF was analyzed using the ring test method. In parallel, the physico-chemical and mechanical evolutions of the matrices were characterized. The results were then used to correlate the early-age performances of the binders investigated and their resistance to early-age cracking.

Materials

A CEM I 52.5 N Portland cement (PC) was used (French standard NF EN 197-1 [START_REF]Cement -Part 1: composition, specifications and conformity criteria for common cements[END_REF]). Its Blaine fineness was 346 m 2 /kg and it contained 3.3% by weight of gypsum and 4.8% by weight of limestone filler. The mass fractions of the main phases of cement, as determined with Bogue formulas, were 70% of C 3 S; 9% of C 2 S; 3% of C 3 A and 13% of C 4 AF. The main constituents of cement and granulated ground blast furnace slag (BFS) are given in Table 1. The used limestone filler (LF) contained 97.7% of CaCO 3 and its density was 2714 kg/m 3 . The particle size distributions (PSD) of PC, BFS and LF are given in Fig. 1.

The pastes were prepared in a mixer of 20 L capacity. Solid constituents were first mixed for 30 s. Then, the mixing water was introduced and the mixing sequence was continued for 90 s at low speed and 90 s at high speed.

The compositions of the various binder pastes are given in Table 2. In the following, the term ''binder'' or ''cementitious materials'' refers to the binary or ternary combination of two or three solid constituents (PC, BFS and LF), respectively. The water-to-cementitious materials (w/cm) mass ratio was equal to 0.32 for all the studied mixtures. This low w/cm ratio was chosen in order to amplify the self-desiccation phenomenon at early-age and so the risk of autogenous cracking of the matrices.

Testing methods

An isothermal microcalorimeter TAM Air was used to measure the heat flow of reaction of the binders at early age. For each binder paste, 4 g specimens were taken at the end of mixing, accurately weighed (±0.01 g) and placed into two cylindrical flasks. The flasks were then sealed and loaded in the apparatus. The first measurement was acquired about 10 min after the first contact between the binder and the mixing water. The tests were conducted over the first 5 days of hydration. The curves reported in the article are average curves computed from the test results obtained on two parallel specimens.

The chemical shrinkage was determined using the hydrostatic weighing method [START_REF] Bouasker | Chemical shrinkage of cement pastes and mortars at very early age: effect of limestone filler and granular inclusions[END_REF]. At the end of mixing, two samples of 4-5 g were introduced into two different cylindrical flasks. The remaining volume of these flasks was then carefully filled with deaerated water, while avoiding disruption of the samples. Then, each flask was immersed in water and suspended with a nylon thread to a balance (accuracy: ±0.001 g). The test system was placed in an air-conditioned room at 20 ± 2 °C. The data acquisition was started 15 min after the first contact between the binder and the mixing water and was carried out automatically for 140 h. The autogenous shrinkage was measured according to the French standard NF P15-433 [START_REF] Nf P | Methods of testing cement -determination of shrinkage and swelling[END_REF] on 4 Â 4 Â 16 cm 3 prismatic specimens stored at 20 °C and wrapped with several layers of plastic film to avoid evaporation. The first strain measurement was made immediately after the demolding of the specimens, e.g. 24 h after their casting. For each binder paste, the tests were performed on three specimens.

A quasi-isothermal ring test system [START_REF] Mounanga | Early-age autogenous cracking of cementitious matrices: physico-chemical analysis and micro/macro investigations[END_REF] was used to study the cracking risk of the pastes. It allowed the monitoring of restrained shrinkage in thermally-controlled conditions. In the present work, the tests were carried out at 20 ± 1 °C. The experimental set-up was composed of:

À Two concentric rings. The central brass ring, which restrained the deformations of the cement matrix, had an inner diameter of 190 mm, a thickness of 10 mm and a height of 40 mm. A second outer PVC ring played the role of the external form. The section of the specimen was 40 Â 40 mm 2 .

À Four strain gauges, which measured the central ring deformations induced by the partially restrained autogenous shrinkage of the pastes, and four additional temperature compensation gauges, stuck on a metal plate attached to the inside face of the central ring.

À A thermal regulation system, made with a network of copper tubes welded to two aluminum plates, which completely covered the lower and upper surfaces of the sample. During the tests, the network of tubes was continuously fed by a thermostated water bath.

Before the beginning of the test, water was circulated through the tubes. When the target water temperature was stabilized, the fresh sample was cast between the two rings and covered with the aluminum top plate to keep it in autogenous conditions. From that moment, the data acquisition was initiated. It was stopped when a through crack appeared in the sample. This resulted in a sudden drop in the strain values of the central ring. For each binder paste, the tests were performed on three specimens.

Additionally, the pore size distribution and the mechanical properties of the pastes were determined [START_REF] Diamond | Mercury porosimetry -an inappropriate method for the measurement of pore size distributions in cement-based materials[END_REF]. The pore size distribution was measured by mercury intrusion porosimetry (MIP) on 28 day-old specimens (7-10 g) with an AutoPore IV apparatus (P max = 400 MPa) allowing the investigation of pore radii ranging from 3 nm up to 1000 lm. The compressive strength and the dynamic Young's modulus (E dyn ) (apparatus used: Grindosonic Ò device) were measured on 4 Â 4 Â 16 cm 3 -specimens stored in autogenous conditions in an air-conditioned room at 20 ± 2 °C until the time of testing. For each mix composition, three specimens were tested.

Result analysis

. Reaction heat flow

Fig. 2 presents the heat flow evolution of the different pastes, which was characterized by a hydration peak developing between about 8 h and 15 h after the first contact between cementitious materials and mixing water. For an ordinary cement paste, this peak corresponds to the hydration of C 3 S, the major phase of Portland cement [START_REF] Taylor | Cement chemistry[END_REF][START_REF] Odler | Hydration, setting and hardening of Portland cement[END_REF]. As expected, the increasing addition of SCM caused a progressive decrease in the intensity of the hydration peak. The systematic reduction in the reaction heat of binary and ternary binders, in comparison with that of the control binder, is clearly shown in Fig. 3, even if this reduction decreased over time, between 24 and 140 h (Fig. 4). The lower reaction heat of blended binders may be explained by the quasi-zero reactivity of LF and the lower reaction heat of BFS at very early age, when compared to that of PC [START_REF] Mounanga | Improvement of the earlyage reactivity of fly ash and blast furnace slag cementitious systems using limestone filler[END_REF][START_REF] Schindler | Heat of hydration models for cementitious materials[END_REF][START_REF] Ballim | The effects of supplementary cementing materials in modifying the heat of hydration of concrete[END_REF]. Besides, the need for a basic medium to initiate the hydration of slag makes it react with water more slowly than cement. The dissolution of BFS by the attack of OH-ions present in the pore solution becomes significant when the pH-value of the solution exceeds about 12 [START_REF] Taylor | Cement chemistry[END_REF]. Then the slag reacts with the portlandite produced by the cement hydration, following a pozzolanic process. These two phenomena explain the delayed reaction of the slag.

Regarding the effect of LF, for filler-cement systems, the following two observations can be distinguished: À A dilution effect before 24 h of setting (Fig. 2). This figure

shows that the substitution of cement by the limestone filler reduces the reaction heat flow [START_REF] Mounanga | Improvement of the earlyage reactivity of fly ash and blast furnace slag cementitious systems using limestone filler[END_REF]. The reaction heat is reduced by 16% and 27% by replacing 10% and 20% of cement by LF respectively.

À Beyond 24 h, LF begins to participate in the hydration reactions. Indeed, they will serve as additional nucleation sites for hydrates. This effect can be observed on the curve of PC0S10F at 24 h (Fig. 2B), compared with the PC0S0F at the same curing time (Fig. 2A), where it is noted a slightly increasing in the reaction heat. When the substitution rates reach 20% of LF (PC0S20F) we note that at 24 h of hydration, the reaction heat drops to less than 1 mW/g binder. This finding is explained by the dominance of the effect of dilution on the second effect (acceleration of the reaction by the additional new nucleation sites).

Regarding the ternary systems we note that the type of substituent (LF or S) has no major effects on the reaction heat flow. Rather, it is the substitution content of the (LF + S) that affects the reaction heat flow at very early age. This observation may support the hypothesis of the dilution effects of the limestone fillers and slag during the calorimeter test investigation.

Chemical shrinkage

The experimental curves of chemical shrinkage of the different cement pastes results are provided in Fig. 5. Chemical shrinkage develops because the absolute volume of the hydration products is lower than that of the reactants (cement, SCM and water). It is worth noting that research works carried out on the chemical shrinkage of multi-component binders are very rare [START_REF] De Weerdt | Hydration mechanisms of ternary Portland cements containing limestone powder and fly ash[END_REF][START_REF] Bouasker | Chemical shrinkage of cement pastes and mortars at very early age: effect of limestone filler and granular inclusions[END_REF].D e Weerdt et al. observed than LF-PC and LF-FA-PC systems had a slightly higher chemical shrinkage than their limestone free equivalents, demonstrating that in presence of LF, more hydration products were formed, or alternatively different hydrates were produced with less volume than the usual hydrates [START_REF] De Weerdt | Hydration mechanisms of ternary Portland cements containing limestone powder and fly ash[END_REF]. The authors also reported that PC blended with FA had a higher total chemical shrinkage per gram of PC, which was attributed to both the filler effect and the later pozzolanic reaction of FA. The results obtained in the present study confirmed that the partial substitution of cement with LF caused an increase of the early-age chemical shrinkage. PC0S10F and PC0S20F exhibited values of chemical shrinkage 17% and 24% higher than that of the control binder (PC0S0F) at 140 h of hydration, respectively (Fig. 4).

The effect of slag on chemical shrinkage depended on its dosage. For binary binder pastes with 0% and 30% of slag, the curves showed a rapid increase during the first 20 h, due to the hydration of PC, followed by a slow deformation phase. The shrinkage of pastes with 50% and 80% of slag presented a similar evolution to that of the paste with 30% of slag during the first hours. At 24 h, PC30S0F, PC50S0F and PC80S0F pastes exhibited chemical shrinkage values lower by 30%, 26% and 57% than that of the reference paste, respectively. Then (after 24 h), the chemical shrinkage evolution rate of the pastes with slag increased (Fig. 5). At 140 h, the difference with the reference paste was reduced to 14% and 7% for PC30S0F and PC80S0F pastes, respectively, while the PC50S0F paste even showed higher chemical shrinkage than that of the control binder (Fig. 4). This acceleration resulted in a curve crossing between 80 and 120 h of hydration and could be explained by the beginning of the slag reactions, which generated additional chemical shrinkage.

This trend was also observed for the ternary binder pastes. The combined effects of slag and filler caused a reduction in the chemical shrinkage of pastes compared to the control cement paste but this difference decreased over time: at 140 h, the chemical shrinkage of PC10S20F and PC30S20F pastes was equal or even higher than that of the control paste.

Pore size distribution

The third physico-chemical indicator measured in this study was the pore size distribution of the pastes determined by mercury intrusion porosimetry (MIP). The experimental curves, expressed as the incremental volume vs. pore diameter, are given in Fig. 6.

Two families of pore distributions were clearly highlighted: the pastes with a high slag content (PC80S0F, PC70S10F, PC60S20F) showed a bimodal distribution ranged between [0.009-0.02 lm] and [0.3-1 lm] respectively, while all other pastes had a monomodal distribution centered on a pore diameter of 0.050 lm. This monomodal distribution was also reported by Baroghel-Bouny et al. [START_REF] Baroghel-Bouny | Autogenous deformations of cement pastes -Part II: W/C effects, micro-macro correlations, and threshold values[END_REF] in the case of ordinary cement pastes with w/c = 0.25 and 0.35 and by Ishida et [START_REF] Ishida | Modeling of early age behavior of blast furnace slag concrete based on micro-physical properties[END_REF]. It has been widely reported that the pore size distribution of the BFS matrix was quite different from that of PC [START_REF] Ishida | Modeling of early age behavior of blast furnace slag concrete based on micro-physical properties[END_REF]. Generally speaking, at very early age, the BFS matrix has a coarse pore structure, while as cement and slag hydration goes on, the BFS matrix exhibits a denser structure than PC and the pore distribution curve of BFS matrices moves towards a much finer diameter. At 28 days, this effect was particularly significant for the higher dosage in slag (Fig. 6).

The addition of filler also tended to refine the porosity of binary binders, with a slightly modification of the total porosity volume, as seen in Fig. 7. Fig. 7 shows a similar evolution of total porosity for the pastes with 0% and 10% filler, regardless the slag content. For these pastes, the porosity remained virtually unchanged until 30% slag content. Between 30% and 50% slag, porosity decreased by more than 15%. Beyond 50% slag, the porosity increased again. For binders with 20% of limestone filler, an evolution of the porosity different from the binders at 0% and 10% limestone filler was observed. Indeed, for the pastes with 20% limestone filler, the addition of slag up to a dosage of 30% reduced the porosity; beyond this threshold, the porosity increased again to reach 32% for 60% of slag.

Synthesis on micro-indicators in relation with autogenous volume variations

The hydration rate, chemical shrinkage and pore size distribution are three key parameters, which determine the rate and amplitude of the autogenous deformations of cementitious systems, sometimes with opposed effects.

The hydration rate, measured by microcalorimetry, governs the kinetics of water consumption and therefore the rate of de-saturation of the porous network. Overall, the addition of SCM tended to increase the early-age reaction rate (quantified as the difference in the time of occurrence between the hydration peak of the blended binder pastes and that of the control paste) and would therefore accelerate the consumption of water, but the dilution effect induced by their presence also increased the effective w/c ratio, and therefore limited the effect of self-desiccation at early age. Even if the result of the competition between these two effects (increase of the binder reactivity and increase of the effective w/c ratio by dilution effect) depends on the degree of substitution of cement with SCM, it appears that the dilution effect seems predominant; indeed, the relative gain of reactivity caused by the presence of SCM remained low in comparison with the increase of w/c effective ratio due to the dilution effect. For example, the maximal increase in reactivity (reaction rate), observed for the PC70S10F mixture, is 33%, while the w/c ratio is multiplied by 5 with respect to that of the control paste. From this point of view, adding SCM will tend to slow down the creation of water menisci within the pores and thus to limit the early-age autogenous deformations.

0% of LF 10% of LF 20% of LF

The chemical shrinkage, the second driving mechanism of selfdesiccation, was also altered by the presence of SCM, as shown in Figs. 345. These effects could have two origins: first, the presence of SCM may modify the composition and so the volume occupied by the hydrates formed. Chen and Brouwers [START_REF] Chen | The hydration of slag, Part 2: reaction models for blended cement[END_REF] calculated that, for full hydration of reactants, the chemical shrinkage of slagblended cement hydration was higher (for 50% slag, about 12 ml/ 100 g of cement) than that of pure PC (around 8.7 ml/100 g of cement), mainly due to the consumption of portlandite by slag to form hydrates. This could explain the results of this study, showing the progressive increase of chemical shrinkage rate of slag-blended cement pastes. Secondly, by modifying the hydration rate, SCM also influence the chemical shrinkage rate of the matrices; De Weerdt et al. [START_REF] De Weerdt | Hydration mechanisms of ternary Portland cements containing limestone powder and fly ash[END_REF] and Bouasker et al. [START_REF] Bouasker | Chemical shrinkage of cement pastes and mortars at very early age: effect of limestone filler and granular inclusions[END_REF] observed higher chemical shrinkage for LF-blended cement matrices, which was attributed to the accelerating effect of LF on PC hydration and the fact that more free water was bound in Ettringite as a result of the influence of LF on cement hydration process [START_REF] De Weerdt | Hydration mechanisms of ternary Portland cements containing limestone powder and fly ash[END_REF][START_REF] Lothenbach | Influence of limestone on the hydration of Portland cements[END_REF].

In both cases, the acceleration of chemical shrinkage could lead to higher early-age autogenous deformation. This conclusion must be tempered by the fact that the continuous water supply of the chemical shrinkage samples facilitated their hydration and thus the development of their deformation, while in autogenous conditions, the hydration of the binder and so its chemical shrinkage were progressively slowed down as the initial mixing water was consumed. This difference is particularly significant for low w/c ratios [START_REF] Mounanga | Predicting Ca(OH) 2 content and chemical shrinkage of hydrating cement pastes using analytical approach[END_REF]. In our case, the curing effect was mitigated for binary and ternary binders given the partial replacement of cement with SCM: the effective w/c ratio, that is to say the amount of water available for the hydration of cement, was in fact much higher for the binary and ternary binders than for the control binder.

The refinement of porosity caused by the presence of SCM in cement-based matrices may also play a role in the development of autogenous deformation and therefore autogenous cracking. Indeed, according to Laplace law, higher tensile stress in the pore fluid develops in finer pores. It means that, considering the porosimetry results (Fig. 6), the blended binders and particularly those containing the higher dosages in slag will be more prone to develop higher autogenous shrinkage.

Macro-mechanical performances: resistance and stiffness

Before examining the effects of SCM on the autogenous cracking sensitivity of blended binders, the mechanical performances of each binder were analyzed. The evolution of compressive strength and dynamic Young's modulus of the different pastes as a function of BFS and LF mass contents are provided in Figs. 8 and9, respectively.

The partial substitution of PC with BFS and/or LF caused a global reduction of the mechanical performances of the pastes, throughout the whole period of investigation (1-90 days).

As for chemical shrinkage, the strength development of the slag-blended cement pastes was strongly depended on the dosage of BFS. The compressive strength of pastes with a slag dosage of 0% and 30% became almost constant beyond 28 days of maturation. For the two other binary slag binders (PC50S0F and PC80S0F), the strength continued to significantly increase between 28 and 90 days. This increase reached 30% for the cement paste with 80% of slag. It was explained by the slag contribution in the late hydration reactions [START_REF] Siddique | Waste materials and by-products in concrete[END_REF]. The filler-blended cement binders and the ternary binders (PC + BFS + LF) also showed systematically lower compressive strength and Young's modulus than those of the pure PC paste.

This reduction in early-age mechanical performances was attributed to the dilution effect induced by the replacement of cement with slag and/or filler. Additionally, the w/c ratio increased in binary and ternary binders due to the reduction of the cement dosage: it was 0.32 for the control binder, and 0.46, 0.64 and 1.60 for cement substitution rate of 30%, 50% and 80%, respectively. Considering the very little contribution of filler to produce hydrates and the low reactivity of slag at early age, the increase of the w/c ratio led to a higher porosity volume in blended binder pastes (Fig. 7), and therefore to a lower gain of strength [START_REF] Menéndez | Strength development of ternary blended cement with limestone filler and blast-furnace slag[END_REF].

In some cases, the addition of filler in slag-cement system enabled to enhance the early-age compressive strength of pastes, as reported by Menéndez et al. [START_REF] Menéndez | Strength development of ternary blended cement with limestone filler and blast-furnace slag[END_REF]: for example, at 30% of cement substitution, the pastes with 20% of BFS and 10% of LF (PC20S10LF) and 10% of BFS and 20% of LF (PC10S20LF) showed a 1-day compressive strength 43% and 19% higher than that of the corresponding binary binder paste (PC30S0LF), respectively. But this effect was only temporary since the compressive strength of PC30S0LF became 14% and 9% higher than those of PC20S10LF and PC10S20LF at 28 days. The same tendency was observed for the Young's modulus.

Effect of additions on early-age free and restrained autogenous shrinkage and cracking

Free autogenous shrinkage

For each studied mix composition, the free and partially restrained shrinkage evolutions were measured in autogenous and quasi-isothermal conditions (20 ± 1 °C). The free shrinkage curves, recorded from 1 to 36 days of hydration, are plotted in Fig. 10. The partial substitution of cement with slag caused an increase of autogenous shrinkage. This result is in agreement with previous studies [START_REF] Mounanga | Early-age autogenous cracking of cementitious matrices: physico-chemical analysis and micro/macro investigations[END_REF][START_REF] Tazawa | Influence of cement and admixture on autogenous shrinkage of cement paste[END_REF][START_REF] Lim | Autogenous shrinkage of ground-granulated blast-furnace slag concrete[END_REF][START_REF] Lura | Effect of curing temperature and type of cement on early-age shrinkage of high-performance concrete[END_REF][START_REF] Jiang | Autogenous relative humidity change and autogenous shrinkage of high performance cement pastes[END_REF][START_REF] Lee | Autogenous shrinkage of concrete containing granulated blast-furnace slag[END_REF]. Tazawa and Miyazawa [START_REF] Tazawa | Influence of cement and admixture on autogenous shrinkage of cement paste[END_REF], and Lee et al. [START_REF] Lee | Autogenous shrinkage of concrete containing granulated blast-furnace slag[END_REF] found an increase of autogenous shrinkage as the percentage of cement substituted by slag increased up to 90% and up to 50%, respectively. Lim and Wee [START_REF] Lim | Autogenous shrinkage of ground-granulated blast-furnace slag concrete[END_REF] observed that a replacement percentage of 50% BFS gave larger autogenous shrinkage and that an increase (up to 80%) or decrease (down to 30%) in the replacement percentage reduced the autogenous shrinkage of concrete [START_REF] Lim | Autogenous shrinkage of ground-granulated blast-furnace slag concrete[END_REF]. According to the authors, the maximal value of autogenous shrinkage obtained for the 50% BFS replacement level may be due to a higher degree of hydration, and therefore, a greater degree of self-desiccation.

The increase of autogenous shrinkage of slag-blended cement paste as compared with that of control cement paste, is clearly correlated to the micro-physico-chemical and macro-mechanical properties of the pastes: the higher chemical evolution rate at early-age (recorded between 24 and 140 h), the finer porosity (particularly for the higher slag replacement levels) and the lower Young's modulus simultaneously induced a greater self-desiccation of the pore network and a higher capacity of the slag-cement matrix to deform when submitted to self-induced stress. The increase of the effective w/c ratio due to the replacement of cement with slag, which could limit the self-desiccation phenomenon, did not compensate the effect of slag on chemical shrinkage, pore size, and Young's modulus.

The addition of LF to the slag-cement system had a triple effect on the autogenous shrinkage of ternary binders. The first effect was to slow down the evolution of autogenous shrinkage of the pastes containing the higher dosages in slag, at very early age: indeed, during the first ten days of hydration, the shrinkage of PC40S10F and PC70S10F was lower than that of PC0S10F and PC20S10F. The same observation was made for the PC30S20F and PC60S20F curves, when compared with the PC0S20F and PC10S20F curves. This lower shrinkage rate is probably linked to the higher w/c ratio of the systems containing more SCM, which delayed the development of the self-desiccation in the pore network at early-age. The second effect of limestone filler was a progressive reduction of the gap between the shrinkage curves of the ternary binders. It means that, beyond the first ten days of hydration, the autogenous shrinkage of pastes with high dosage of slag increased more rapidly than that of Portland cement paste, due to the later reactions of slag and the development of a finer pore structure. Similar results were observed by Zhou et al. [START_REF] Zhou | Autogenous deformation of Portland cement paste blended with blast furnace slag measured by mini-TSTM[END_REF] on slag-blended cement pastes after about the first 48 h of hydration and by Lee et al. [START_REF] Lee | Autogenous shrinkage of concrete containing granulated blast-furnace slag[END_REF] and Darquennes et al. [START_REF] Darquennes | Effect of autogenous deformation on the cracking risk of slag cement concretes[END_REF] on BFS concretes after the first 7 days of hydration. However, at the end of the period of investigation, the relative position of the ternary binder shrinkage curves remained the same as the one observed for the binary pastes, the higher dosage of slag inducing the greater autogenous shrinkage.

The third effect of LF was to increase the ''final'' amplitude of autogenous shrinkage of the ternary binders, in comparison with the corresponding binary binders. This increase was attributed, as previously mentioned, to the acceleration of chemical shrinkage evolution, the refinement of the porosity and the diminution of the Young's modulus.

Early-age restrained autogenous shrinkage and cracking

Free autogenous shrinkage measurements are not sufficient to estimate the sensitivity of the binder to autogenous cracking. Indeed, the autogenous cracking tendency of a cement-based material is the result of the competition between the gain of mechanical resistance to tensile stress, the early-age self-induced stress development due to the partial or total restraint of autogenous deformations, and the capacity of the matrix to relax these stress without significant damage. In order to investigate and compare the risk of early-age autogenous cracking of the binary and the ternary binders, ring tests were performed. The evolutions of the maximal tensile stress, provided in Fig. 11, were obtained from the deformations of the central brass ring, measured during the tests [START_REF] Hossain | Assessing residual stress development and stress relaxation in restrained concrete ring specimens[END_REF]. The moment at which the cracking started was detected by the sharp drop in the ring strain-time curve.

A general observation of the ring test curves reveals that the presence of SCM delayed, to a more or less extent, the age of the first autogenous through crack. Darquennes et al. also observed that the cracking susceptibility of slag cement concretes kept in autogenous conditions was delayed in comparison with Portland cement concrete [START_REF] Darquennes | Effect of autogenous deformation on the cracking risk of slag cement concretes[END_REF], the higher dosage of slag inducing the higher delay in cracking. They attributed this behavior to the slower hydration rate, the larger capacity to relax tensile stresses and the early-age expansion of slag cement concrete.

The current results show that the cracking age of the matrices depended on the dosage in SCM. For a given dosage in LF, the pastes with the lower slag content (PC30S0F, PC20S10F and PC10S20F) always cracked later. It indicates that for these three mixtures, despite a higher autogenous shrinkage than that of the reference paste (PC0S0F), the combined effects of a reduced Young's modulus and likely higher relaxation capacity delayed the development of internal stresses and thus the age of cracking (from 35% up to 149%, depending on the slag and filler contents) of the matrices in comparison with those of the reference paste. The maximum tensile stress levels reached at the moment of cracking demonstrated that the tensile strength of the material cannot be considered as a reliable indicator of the autogenous cracking risk. For example, the PC30S0F paste cracked later that the PC10S20F paste, but for a lower stress level. In other words, a higher early-age tensile strength does not guarantee a later age of cracking.

When the content in SCM increased up to 50% of replacement rate, the cracking age of the blended binder pastes (PC50S0F, PC40S10F and PC30S20F) became close to that of the corresponding reference paste (PC0S0F, PC0S10F and PC0S20F, respectively), while remaining later. The amplification of the deformations associated with the higher dosage in SCM probably accelerates the development of early-age self-induced stresses and explains this shortening of the cracking age.

Increasing the dosage of SCM up to 80% significantly altered the shape of the ring strain curves, which were characterized by a first increasing phase followed by a decreasing phase indicating a reduction of the pressure exerted on the metal ring. Then, the curves showed an increasing and quasi-linear evolution until the moment of cracking. This phase of decreasing stress indicates either a swelling or a microcracking of the matrix, which could re- duce the pressure exerted by the paste, and so the metal ring strain. The rapid growth of strain after the decreasing phase suggests a regime change in the development of the autogenous deformations and corresponds well with both the acceleration of chemical shrinkage observed between 24 and 140 h and the increasing autogenous shrinkage rate of the matrices containing the higher dosages in SCM. It is worth noting that these binders exhibited also a different and unsystematic behavior concerning their cracking age. For a given LF dosage, they sometimes cracked before the corresponding reference binders (PC0S20F: 230.2 h; PC60S20F: 193.0 h), sometimes after (PC0S0F: 164.8 h; PC80S0F: 229.3 h), or almost at the same age (PC0S10F: 165.7 h; PC70S10F: 169.7 h) for quite similar stress levels.

For these pastes (PC80S0F, PC70S10F and PC60S20F), the maximal tensile stress reached at the moment of cracking was significantly lower than the control paste: it is 33%, 29% and 41% lower than that of the PC0S0F paste, respectively, indicating their particularly weak mechanical performances at early age. Further research works at the micro-scale are needed to highlight the microstructural characteristics of these binders: MIP measurement already showed their specific pore size distribution in comparison with the binders with low or moderate SCM dosages but this micro-indicator remains insufficient to clearly understand the earlyage cracking sensitivity of high slag blended cementitious systems.

The substitution of cement with filler also tended to delay the age of the first crack of filler-cement binder. This effect was particularly significant for the paste with 20% of filler, for which a delay of about 65 h of the age of cracking was registered, when compared to PC0S0F (age of cracking: 164.8 h) and PC0S10F (age of cracking: 165.7 h). Considering the higher early-age autogenous shrinkage of LF-PC-cement pastes and the relatively close values of Young's modulus of PC0S0F, PC10S0F and PC20S0F, the explanation to the later cracking of PC20S0F may lie in its higher capacity of stress relaxation, which probably induced a slower evolution of self-induced stress. The first crack occurred at a close stress level for the three pastes considered (PC0S0F, PC0S10F and PC0S20F). The effect of filler on the stress development was therefore primarily a delaying effect: for the substitution rate investigated here, LF did not significantly modify the level of early-age mechanical resistance to tensile stress of the binder.

Conclusions

The result analysis of this study on the early-age behavior of binary and ternary binders highlighted the following points:

À The partial replacement of Portland cement (PC) with blast furnace slag (BFS) and/or limestone filler (LF) caused a decrease in early-age reaction heat and chemical shrinkage, due to the lower reactivity of the supplementary cementitious materials (SCM). After a few hours of hydration, the filler effect and the starting of the slag reactions tended to accelerate the evolution of both heat of reaction and chemical shrinkage, as indicated by the progressive reduction of the gap between the binary and ternary binder curves and the reference binder one (free of slag and filler).

À As previously reported, the substitution of PC with BFS and/or LF resulted in a decrease in mechanical strength and Young's modulus, when compared to the control binder. For ternary binders with 30% of cement substitution rate, the addition of filler in slag-cement system does not affect the compressive strength of pastes at later ages.

À The combination of PC, BFS and LF in binary and ternary binders yielded, in most cases, a delay of the cracking ztime compared to the corresponding binary binder paste.

The increase in the dosage of LF from 10% to 20% resulted in delaying the appearance of the first crack in the ternary binders. The best results in terms of crack delaying were obtained for the binders with the lowest concentration of slag. The higher was the slag substitution, the earlier the first cracking of ternary binders tended to occur.

4. 1 .

 1 Microphysico-chemical indicators 4.1.1

Fig. 2 .

 2 Fig. 2. Reaction heat flow; (A) without LF; (B) with 10% of LF and (C) with 20% of LF.

Fig. 3 .

 3 Fig. 3. Relative percentage differences in cumulative heat of reaction and chemical shrinkage at 24 h with respect to the control mortar.

Fig. 4 .

 4 Fig. 4. Relative percentage differences in cumulative heat of reaction and chemical shrinkage at 140 h with respect to the control mortar.

Fig. 5 .

 5 Fig. 5. Chemical shrinkage; (A) without LF; (B) with 10% of LF and (C) with 20% of LF.

Fig. 6 .

 6 Fig. 6. Mercury porosimetry curves; (A) without LF; (B) with 10% of LF and (C) with 20% of LF.

Fig. 7 .

 7 Fig. 7. Total measured MIP vs.BFS content.

Fig. 8 .

 8 Fig. 8. Compressive strength of the binders vs. BFS content; without LF; (B) with 10% of LF and (C) with 20% of LF.

Fig. 9 .Fig.

 9 Fig. 9. Dynamic Young's modulus of the binders vs. BFS content; (A) without LF; (B) with 10% of LF and (C) with 20% of LF.

Fig. 11 .

 11 Fig. 11. Cracking ring test curves; (A) without LF; (B) with 10% of LF and (C) with 20% of LF.

Table 1

 1

	Mass composition (%) and density of cement (PC) and blast furnace slag (BFS) (Data
	provided by the supplier).
	Constituents	PC	BFS
	SiO 2	21.39	34.49
	Al 2 O 3	3.66	13.19
	Fe 2 O 3	4.25	0.40
	CaO	64.58	41.03
	MgO	0.96	8.21
	MnO	0.13	0.40
	TiO 2	0.16	0.88
	K 2 O	0.28	0.54
	Na 2 O	0.10	0.43
	SO 3 Density, kg/m 3	2.63 3200	0.10 2890

Fig. 1. Particle size distributions for PC, BFS and LF measured by laser granulometry. Results are the average of two individual measurements.

Table 2

 2 Mass proportion of binary and ternary binders.

	Labels	PC	BFS	LF	w/cm a	w/c b
	PC0S0F	1	0	0	0.32	0.32
	PC30S0F	0.7	0.3	0	0.32	0.46
	PC50S0F	0.5	0.5	0	0.32	0.64
	PC80S0F	0.2	0.8	0	0.32	1.60
	PC0S10F	0.9	0	0.1	0.32	0.36
	PC20S10F	0.7	0.2	0.1	0.32	0.46
	PC40S10F	0.5	0.4	0.1	0.32	0.64
	PC70S10F	0.2	0.7	0.1	0.32	1.60
	PC0S20F	0.8	0	0.2	0.32	0.40
	PC10S20F	0.7	0.1	0.2	0.32	0.46
	PC30S20F	0.5	0.3	0.2	0.32	0.64
	PC60S20F	0.2	0.6	0.2	0.32	1.60

a Water-to-cementitious materials mass ratio. b Water-to-cement mass ratio.


Anton Rudenko

Prof Jean-Philippe Colombier

Dr Tatiana E Itina

Dr Razvan Stoian

Genesis of nanogratings in silica bulk via multipulse interplay of ultrafast photo-excitation and hydrodynamics

Keywords: Laser materials processing, Ultrashort pulse, Fused silica, Nanostructuring, Nanogratings, Self-organization

Introduction

Matter redistribution under the influence of optical fields is a prominent field of research ranging from optical trapping to additive manufacturing and laser material processing. Particularly in the field of laser structuring, this process is at the origin of intriguing forms of self-organization reaching extreme sizes [1,2]. Topography patterns with characteristic scales well below the optical wavelength can be obtained, creating new shape and size-dependent material functions and application fields in mechanics, optics, and life sciences. The generation of regular periodic material patterns on surfaces with close-towavelength and deep sub-wavelength periodicities has been under scrutiny since more than five decades, with the most recent models advancing theories of dissipative self-organization and material rearrangement under a synergistic light action [1]. The observation of a similar phenomenon in the bulk of transparent materials, the so-called nanogratings [2], has led to the development of inclusive electromagnetic and electron plasma kinetics theories [3][4][5] to describe a generalized phenomenon of light-induced generation of regular patterns in two and three dimensions aligning with respect to the laser polarization [6,7].

Commonly created after multipulse femtosecond laser irradiation of transparent glasses and crystals [2,3,[8][9][10][11][12][13], the nanogratings emerge under a feedback action required to guide, amplify, and stabilize order. A gradual arrangement of matter under optical fields, reassembling in turn the optical patterns, matches the self-limited evolution towards complexity observed in dissipative non-equilibrium open thermodynamic systems [14]. The incipient transition to order was observed in laser-irradiated glasses by 3D-reconstruction of scanning electron microscopy and X-ray scattering images [12]. The formation of layered nanogratings has been demonstrated to generate strong birefringence [3,15], with potential applications in high-density optical data storage [16], geometric phase optical manipulation [17,18], and information processing [13]. Very recently, equally interesting nanovoid domains of scatterless birefringence were observed in the intermediate irradiation stages [19]. These structures are important for optical systems that optimally couple losses and anisotropy for light transport and manipulation. In view of a wide range of emerging applications, it is of interest to determine the specific drives and paths leading to the observed self-organization of matter in nonlinearly excited materials under the action of intense and repetitive ultrashort laser pulses. Particularly, predictive tools able to describe the properties of the patterns at different levels of their organisation are urgently needed.

Owing to the high complexity of the numerical problem, the previously reported simulations in the bulk of transparent materials were mostly limited to single pulse excitation, considered simplified damage criteria or implied reduced geometries [4][5][6][7], leaving open the questions regarding the feasibility of threedimensional multipulse arrangement with high order and regularity. A full description of a multipulse feedback mechanism should implicitly take into account not only electron plasma kinetics in spatially variable ultrafast optical fields, but also glass heating, melt flow driven by temperature gradients, culminating with local cavitation and growth of failure spots.

The present model describes the complex multiscale dynamics coupling self-consistently nonlinear propagation, electronic excitation and electron-ion thermalization, melt flow, and compressible modifications to elucidate the emergence of periodic patterns of dense and void layers in fused silica on scales below the laser wavelength. In order to investigate the nanostructure evolution upon multipulse irradition, we include both intra-pulse and inter-pulse feedbacks, considering optical transient and permanent modifications respectively. We show that the inter-pulse feedback, commonly neglected in previously proposed models, is crucial in order to achieve the regular and highly periodic nanogratings. Within the proposed model, we also validate the intermediate irradiation regimes that, via material regular structures, generate form birefringence while minimizing scattering losses.

Modeling details

The model consists of two coupled parts relevant for the excitation of electron and ion sub-systems. Thus, the first part includes nonlinear full-vector Maxwell propagation solver and electron plasma kinetics equations for momentum, energy and free carrier density. The second part considers compressible fluid dynamics described by Navier-Stokes equations with the equation-of-state for fused silica. If the electromagnetic models were already used to describe three-dimensional patterns of light in the context of periodic laser nanostructuring [4,5], the thermomechanical evolution of matter driven by the temperature gradients is a recent addition that was successfully applied for laser-irradiated surfaces [20,21] and will be here validated for bulk 3D environments.

Nonlinear propagation and energy deposition

The numerical model is based on the three-dimensional nonlinear Maxwell equations coupled with a rate equation for the nonlinear production of free carriers for energy deposition, written as follows

                                   ∂ E ∂t = ∇ × H 0 ∞ - 1 0 ∞ ( J p + J pi + J Kerr ) ∂ H ∂t = - ∇ × E µ 0 ∂ J p ∂t = - J p τ e + e 2 N e m e E ∂N e ∂t = w pi + w av - N e τ rec C e ∂T e ∂t = ∇ • (k e ∇T e ) -γ ei (T e -T i ) + J p • E -E g w av , (1)
where E is the electric field, H is the magnetic field, 0 and µ 0 are the permittivity and the permeability of free space, ∞ is the permittivity of the non-excited fused silica. J p is the polarization current describing the electron heating by classical Drude model, J pi is the photo-ionization depletion current, and J Kerr introduces the Kerr effect. The expressions for the currents and the numerical method for coupling the nonlinearities with full-vector Maxwell solver can be found in Ref. [22]. The last two equations are written for the time-dependent electron density N e and temperature T e . e and m e are the electron charge and mass, τ e and τ rec are the electron collision and recombination times respectively. The electrons in the conduction band are firstly generated by photo-ionization described by the Keldysh formula w pi [23].

The secondary electrons are produced by the avalanche ionization, when the electrons gain the critical threshold energy required for energy and momentum conservation ≈ 3/2E g [24][25][26]:

J p • E = 3/2E g w av ,
where E g is fused silica electron bandgap. Dealing with the electronic excitation well below the complete ionization of fused silica, we omit the negligible pre-factor Nv-Ne Nv (N v being the electron density in the valence band) for ionization rates, losses, valence band permittivity, and Kerr response. In Equation (1), we use a simplistic single rate equation for carrier excitation limited by extreme computational memory and time requirements for three-dimensional simulations. More accurate quantitative description of energy deposition and ionization processes can be achieved by considering multiple rate equations [25,26] and energy-resolved Bloch-Boltzmann approaches [24,27], but occurs to be outside of the scope of the current discussion.

The equation for the electron temperature includes electron diffusion, electron-ion coupling term, Joule heating and losses due to avalanche ionization. The electron heat capacity is approximated by

C e = 3k B n e /2,
where k B is the Boltzmann constant. The electron heat conductivity is k e = 2k B 2 µ e n e T e /e, where µ e is the electron mobility. The electron-ion coupling factor is related to the electron capacity as γ ei = C e /τ ei . The parameters for fused silica are used as in Ref. [28].

Hydrodynamic equations

A major development of the code with respect to the electromagnetic description is the accountability of fluid dynamics permitting the spatial evolution of laser-induced structures. To take into account the melt flow in fused silica heat-affected regions, compressible Navier-Stokes equations are solved, written in the form of the conservation laws for energy, momentum and mass as follows

                   ρC i ∂T i ∂t + u • ∇T i = ∇ • (k i ∇T i ) + γ ei (T e -T i ) ∂(ρ u) ∂t + ( u • ∇)(ρ u) + (ρ u)∇ • u = = -∇P i + µ∇ 2 u + 1 3 µ∇(∇ • u) ∂ρ ∂t + ∇ • (ρ u) = 0, ( 2
)
where u is the fluid velocity, ρ, T i and P i are the density, temperature and pressure of fused silica respectively. The dependence P i (ρ, T i ) is evaluated from the equation-of-state for fused silica [29]. µ(T i ) is the fused silica viscosity, which decays exponentially with the increasing temperature and here is evaluated according to Ref. [30]. For the reference, the viscosity is as high as µ ≈ 10 8 Pa•s near the softening point T melt = 1875 K and decreases down to ≈ 10 3 Pa•s at the highest relevant temperatures of T i ≈ 3000 K. Additionally, heat capacity C i (T i ) and thermal conductivity k i (T i ) dependencies are taken into account, based on Refs. [31,32].

Glass decomposition criteria

After each pulse, irreversible modifications occur in the bulk of silica, resulting in the appearance of void structures. The next pulse is considered to interact with newly arranged inhomogeneous distribution of void-like structures with the permittivity of air/gas = 1. We imply two criteria to define the established rarefaction regions: one for the appearance of random nucleation scattering centers or nanopores and the other one is for localized cavitation processes in liquid phase discussed in details in Ref. [33]. The first criterion is required for the initial perturbation of the system, where the probability is related to the temperature as in the classical nucleation theory ∝ exp(k B T i /W ), where W = 4πγr 2 /3 is the free energy of the critical nucleus of r = 20 nm (equal to the mesh cell size) and γ is the surface tension.

The minimum probability is set to be 10 -4 for liquid fused silica at T melt = 1875 K. We consider the temperature dependence of surface tension γ = γ 0 (1 -T i /T cr ) 1.25 with γ 0 = 0.3 N/m and the critical temperature T cr = 5400 K for fused silica. The second criterion for cavitation is the Grady's criterion for spall in Newtonian liquids derived from the viscoelastic energy conservation law [34]. Such criteria have been routinely applied for sub-surface cavitation in metals, using the critical negative pressures and the strain rates within material as the indicators of the mechanical failure [21,35]. Following similar approach, the critical negative pressure for surface-energy spall is |P | ≥ (6ρ 2 c 3 s γζ) 1/3 and for viscous-dissipation spall is |P | ≥ (2ρc s 2 µζ) 1/2 , where c s ≈ 5.9 • 10 3 m/s is the longitudinal speed of sound in fused silica and ζ = δρ/ρδt is the strain rate due to rarefaction δρ during the exposure time δt.

These two criteria are applied to every point of bulk silica as soon as the conditions are met and the structure topography changes according to these criteria at the beginning of the next pulse. For simplicity, we do not consider the possibility of void replenishment by denser material or its movement in melt flow as soon as the void structure is organized by previous pulses. Modeling of these processes would require knowledge of precise intrinsic material properties/multi-component chemistry in the damage regions and significantly more refined mesh. Note that the involvement of chemical processes including Si -O bonds decomposition was reported and supported by the observations of the molecular oxygen content in the void-like structures [10,36]. To a first approximation, the void content is considered here as the material with ≈ 1, negligibly low electronic and material density (compared to fused silica). Additionally, the increase of the refractive indices in the densified regions is not taken into account but is discussed in the next sub-section.

Results and Discussion

The formation of quasi-periodic nanoplasmas with periodicities λ/2n, where λ is the laser wavelength and n is the refractive index of the material, starting from initial inhomogeneous refractive index distributions (related to rough interface [6,7], presence of intrinsic voids or defects [4,5], or refractive index perturbations [37]) was reported in several works. Independently on the nature of the initial perturbations, the interference of the incident and the inhomogeneity-scattered waves prioritizes the arrangement with periods being a fraction of the propagating laser wavelength in medium. Ordering occurs upon nanoplasma (intra-pulse feedback) or nanovoid structure (inter-pulse feedback) growth perpendicular to the laser polarization, both enhancing the scattering effects. In this work, these feedback mechanisms supported by cumulative generation and evolution of structures driven by light are combined together via multipulse simulations indicating stronger convergence to regular patterns. The proposed scenario is motivated by the observations of laser-induced hollow nanocavities and nanopores as integral parts in the nanogratings genesis [9,10]. These results suggest already an intrication of near-field effects (hence eventual periodicities below the half wavelength in medium) and material fracture effects (void scales in the 10 nm-range) [3]. The present model sustains a perspective where ultrashort laser interacts with distributed intrinsic and laser-induced scattering centers. Polarization-dependent local field enhancement near the individual nanovoids contributes to the optical anisotropy of the system. More particularly, the orientation of the enhanced field occurs to be perpendicular to the laser polarization as a consequence of the optical response of a small inhomogeneity with a lower refractive index (void structure) inside transparent medium with higher refractive index (non-excited glass). Local field enhancement near the individual inhomogeneities results in enhanced nonlinear absorption and localized optical breakdown. The ionization process locally transforms the dielectric material into an absorbing plasma with quasi-metallic properties. The electrons in the conduction band are heated by the laser field and transfer their energy to the matrix. As a result of rarefaction processes driven by negative pressures, the localized nanovoids are extended in the direction of higher thermal gradients. Upon the next pulse, ultrashort light interacts with the modified nanostructures, resulting in partial symmetry breaking in the silica bulk. The repetitive interaction contributes to the growth of nanoplanes, scattering efficiently light in the direction perpendicular to laser polarization. The interference of the incident light with the waves scattered by these elongated nanostructures results in a standing light pattern inducing enhanced nonlinear absorption in quasi-periodic nanoplanes perpendicular to laser polarization. After each pulse, the established temperature and pressure gradients contribute to material rearrangements that assist in creating a higher level of complexity and order in the incoming light redistribution, determining a gradual evolution to order.

The laser irradiation conditions in silica bulk are chosen to be below the ablation threshold and microexplosion regimes in a pure sample, with a pulse energy of 250 nJ, 200 fs pulse duration and moderate focusing N A ≈ 0.65 of a Gaussian beam. Starting with few nucleation scattering centers, Fig. 1(a,c) shows the maximum free carrier density and lattice temperature distributions upon single-pulse irradiation. The typical densities are sub-critical (N cr ≈ 1.74 • 10 27 m -3 being the critical density in vacuum for the respective laser wavelength); upon multipulse irradiation only localized hot spots reach higher values. The estimated maximal temperatures lie in the 2000 -2500 K interval enabling low viscosity states. For comparison, the snapshots of electron density and temperatures are also shown for the case of higher number of applied pulses just before the onset of the periodic structures in Fig. 1(b,d). Once formed through local cavitation, the nanovoids are considered as non-ionizing medium and, therefore, they appear as points with reduced densities and temperatures. The periodic arrangement of the electronic modification starts with the number of pulses smaller than required for the establishment of continuous permanently inscribed nanovoids. In fact, the nanoplasmas affect the energy deposition with already established asymmetrical response as shown in Fig. 1(e). Nevertheless, Fig. 1(f) shows that much higher regularity and contrast can be achieved within several pulses with the considered inter-pulse feedback.

Three-dimensional void morphologies created in bulk silica, corresponding to different number of applied pulses, are illustrated in Fig. 2. At each pulse, light interacts with these complex structures that evolve upon multipulse laser irradiation. First pulses would encounter random isolated structures, slightly extended in the direction of laser propagation. They evolve into the oriented nanoplanes in Fig. 2(b) and finally, form continuous well-ordered gratings in Fig. 2(c). Because of high complexity, the two-dimensional snapshots in the plane perpendicular to laser propagation are further discussed in details. The results of multipulse simulations with the increasing number of applied pulses from left to right are summarized in Fig. 3. The upper part of the figure shows how light interacts with inhomogeneous silica bulk during the ultrashort pulse excitation in terms of fluence. The central part stands for viscosity of the melt flow which underlines the regions affected by softening and transitions to the liquid phase. Finally, the bottom part of the figure highlights the final void structure established due to irreversible damage. During first pulses (for instance, Fig. 3(a,e,i)) the interaction is limited to localized hot spots randomly distributed along almost homogeneous Gaussian section. These hot spots originate from local field enhancement near nanoscopic nucleation centers and lead to local cavitation and growth of nanovoid structures perpendicular to laser polarization. As a result of such a feedback, the ellipsoidal nanovoids are pre-formed in Fig. 3(j,k). These structures interact much stronger with the incident light, and the interference effects result in well-defined profiles of periodic energy deposition in Fig. 3(c). The region with melt flow expands and the thermal gradients are pronounced on the viscosity maps in Fig. 3(g), indicating that the hotter regions are separated by the regions with extremely high viscosity in almost solid state. The gradients originate from contrasted nanoplasmas that absorb efficiently light but are surrounded by nearly transparent silica bulk. This feature is different from the mechanisms predicted numerically on the laser-irradiated metal surfaces [21]. In case of metals, the viscous dissipation is much weaker due to lower viscosity and its weaker dependency on the temperature. As a result, the melt flow is actively driven by pressure gradients and Marangoni forces through the laser-affected regions. In glass, the melt flow is confined between solid regions, and the relaxation occurs mostly mechanically, through the dissipation of pressure waves in the surrounded regions. The emergence of the continuous void structures in Fig. 3(l) requires few additional pulses, during which ones the structures become regular, adapting their periods to a fraction of the laser wavelength in medium. Interestingly, when fully established, the structures resonantly enhance scattering and absorption as seen in Fig. 3(d). Larger number of pulses is expected to melt larger areas, including in between the structures, and create additional damage. Melting the whole domain above temperatures ≈ 2500 K might result in the erasure of self-organized nanogratings [33]. Fig. 4 shows the magnified silica density snapshots taken 50 ps after ultrashort pulse excitation by (a) N = 3 and (b) N = 7 pulses (the time delay is given after the last pulse exposure). Here, the white colored regions are voids; therefore, the first snapshot corresponds to the situation where only localized random voids appear; the pre-formed perpendicularly oriented structures are already established in the second one. Apart from these patterns, the transient densities below and above the pristine silica density are clearly seen. The first ones correspond to the electronic plasma patterns established during laser pulse excitation and heated above the softening temperature, subject to cavitation if significantly negative pressures are reached. The second ones are transiently densified regions between these plasmas, regions where the compressive stresses are accumulated due to shock waves propagating from the plasmas. This accumulation might result in the permanent plastic deformations and positive refractive index changes [29,38]. The index contrast of order 10 -4 -10 -3 was predicted by thermo-elasto-plastic simulations for the regions with tensile stress exceeding the critical yield strength [39].

-2 2 0 -1 1 X, µm -2 2 0 -1 1 X, µm
The timescales of nanopattern relaxation and void formation by cavitation are detailed by dynamic snapshots of the negative pressures P i (ρ, T i ) inside silica bulk in Fig. 5. The response is strongly inhomogeneous following the complex temperature distribution. For instance, first voids appear from the hot spots immediately after the electron-ion thermalization ≈ 15 ps in Fig. 5(a). However, the larger elongated structures with a pronounced polarization-dependent response necessitate longer timescales, in between 30 ps and 50 ps as underlined in Fig. 5(b,c). The critical negative pressures required for cavitation also vary dependent on the attained temperatures and effective relaxation time from -3 GPa to -100 MPa. In addition to void formation and elasto-plastic effects, an alternative pathway for positive density changes in fused silica is caused by electronic excitation and bond breaking [36,40]. These are a consequence of electron self-trapping [41] and occur dominantly in the solid phase. Their level corresponds to a gentle process of densification in the range of 10 -4 per pulse and its role is minor in the present discussion compared to the strong changes occurring via cavitation and melt flow. The process occurs at relatively low carrier densities that keep the solid cold, where exciton self-trapping is accompanied by a stabilizing atomic displacement and structural distortion, locally densifying the material. It is to be noted that, with stronger excitation, fast vibrational activation will decrease the yield of structural densification by lowering the probability of carrier-self-trapping (with a complete arrest in the softening phase), limiting thus the index contrast achievable by this path [42,43]. Thermomechanical effects will then kick-in. The cooling cycle may equally determine soft densifications via a change of the fictive temperature providing the process is sufficiently long. Adding to the electronically assisted structural densification, for a range of temperatures approaching the softening value with enough molecular mobility in the low viscosity glass, rapid cooling may induce a structurally denser phase [44], particularly for the anomalous thermal behavior of fused silica. The quantitative estimation of such refractive index changes is not discussed here and should rely on the realistic estimation of the number of the required pulses or on long-time processes of lattice cooling and relaxation freezing new structural arrangements. Small refractive index perturbations 0.01 do not have a strong effect on nonlinear pulse propagation at the nanoscale, whereas scattering originates mostly from void-like domains suggesting thus the dominance of the thermomechanical scenario.

Given the importance of thermally driven material changes, potential regimes of thermal accumulation may be of interest. Thus, the question of laser repetition rate becomes relevant for multipulse irradiation. The experimental observations conclude that melting enhanced by heat accumulation during high repetition rate processing prevents nanogratings formation or erases the created structures [45]. Importantly, the formation of nanogratings is commonly observed for low repetition rates (< 200 kHz, when heat accumulation can be safely avoided), and our simulations are performed neglecting heat accumulation effects to emphasize the pure role of interpulse feedback solely driven by intrinsic topography and optical refractive index modifications. The potential contribution of heat accumulation to nanogratings erasure in terms of the attained temperature threshold has been discussed in a recent work [33]. Simulations in the current work (see Fig. 3(l)) indicate that high temperatures (that are reachable as well by high repetition rate processing) would produce larger void-like modifications with sizes comparable to the spacing ≈ 250 nm between the created nanostructures, resulting in merging with separate structures to form a single micrometer disrupted region. The generation of nanostructures was associated with optical functions emerging from phase and polarization sensitivity [46]. The recent report [19] of low-loss birefringence raises the interest in the intermediate stages in the nanogratings formation. We have tested qualitatively the optical properties of the nanovoid structures created at different stages of their multipulse evolution by simulating the passage of a continuous wave beam (plane wave) with a particular orientation of the polarization vector with respect to the grating vector. As expected, the structures exhibit strong birefringence during their genesis towards regular nanostructured domains. The higher the number of pulses is, the more compact structures become as shown in Fig. 2. The numerical results for plane wave propagation through the void structures detailed in Fig. 6 confirm that the scattering losses increase as well with the increasing number of pulses. This dependency is in agreement with the experimental observations in Ref. [19].

Two last points should be finally addressed.

The experiments report the formation of nanogratings after higher number of applied pulses (thou-sands) [2,3,12,45] than in the current simulations. This discrepancy implies that the inter-pulse feedback should be much weaker. One possible reason is that a higher number of pulses is required to promote the appearance of initial scattering centers (inhomogeneities). This might be related also to a much more delicate and complex intrinsic evolution from initial defects to nanoscale damage inside transparent materials [8]. Although this point is not yet well understood in the literature and the inter-pulse feedback in the current work is likely overestimated in order to make a problem still computationally feasible, we provide an essential improvement comparing to single pulse models [4,5,7], where no discussion regarding the involved hydrodynamics and the potential impact on the next pulse evolution was given. It is worth noting that much slower evolution (hundreds of pulses instead of 10 pulses) towards well-organized nanostructures can be achieved even within the same numerical model, by considering much refined spatial resolution (sub-nm instead of 20 nm) and, consequently, the nucleation centers of few nanometer size that are produced by heterogenous nucleation. This would result in a weaker scattering but still does not exclude the pronounced role of local field surface effects on a few-nanometer scale. In this case, the growth rate of nanoplasmas and void nanostructures is expected to be slower, resulting in higher number of pulses incubation effects and much thinner nanogratings, similar to the ones observed experimentally [3]. This way, we believe that the better quantitative description in terms of the number of applied pulses is rather a technical detail than the missing physical mechanism.

The nanograting period reduction with the increasing number of applied pulses reported in Refs. [2,45] is another intriguing dependency yet to be clarified. For instance, the nanoplasmas with periods smaller than λ/2n were reported to originate in systems with a higher concentration of inhomogeneities, enhanced by multiple scattering [5]. Intuitively, a mechanism similar to the one reported on laser-irradiated metal surfaces with a blueshift caused by collective response of random nanoholes and consequent period reduction [47] can be applicable to describe the observed dependency. However, the smooth successive transition from already created regular void nanostructures with larger periods towards the structures with lower periods is challenging to describe inside bulk material without consideration of possible void replenishment by denser material. Thus, an additional inter-pulse feedback based on readjustment of irregular void structure interfaces by melt flow driven by surface tension effects [21] together with irreversible damage effects considered in the current work might be relevant to further improve the proposed model for fused silica.

Conclusion

In conclusion we have performed multipulse simulations to describe the interplay between ultrafast light and matter in the formation of light-driven self-organized nanostructures in bulk silica glass. Uniquely mixing light and matter dynamics, the model couples full-vector nonlinear propagation in inhomogeneous medium, electronic excitation by ionization processes, energy transfer to lattice, and fluid dynamics. Each laser pulse results in the appearance of new regions exposed to irreversible localized damage and void formation. New arrangement generates inhomogeneous field distributions, affecting the electron plasma kinetics and fluid dynamics after electron-phonon thermalization. In this scenario, the anisotropy is set by the electromagnetic field and the degree of order facilitated by material topography evolution. Light acts as both the generator and the stabilizer of the structures. Our simulations indicate that better order and anisotropic refractive index contrast are achieved after multipulse irradiation, during which the modification passes through the stages of disorder with random nanovoid distribution, polarization-dependent deformations resulting in the formation of elongated ellipsoidal voids, and regulation into connected nanogratings with deeply sub-wavelength periodicity. The model facilitates predictions for the laser-induced formation of optical elements optimizing losses and vectorial properties.

Figure 1 :

 1 Figure 1: (a-d) Electron density and temperature snapshots of the irradiated regions subject to one pulse N = 1 and few pulses N = 3 irradiation. The maximum values are plotted. The electron density is normalized to the critical value N cr . (e-f) Energy deposition snapshots (in terms of fluence) showing the effect of the number of applied pulses on the ordering of periodic nanoplasmas in the chosen half-Gaussian spots. The pulse energy is 250 nJ, the pulse duration is 200 fs. The number of pulses N is indicated in each image.

Figure 2 :

 2 Figure 2: Three-dimensional void structures ( = 1) (a) at lower number of applied pulses (individual nanopores); (b) intermediate number (ellipsoidal nanoplanes); (c) high number (nanogratings). The colors are applied along the propagation direction k for better visibility. The direction of laser polarization E and the number of pulses N are indicated in each image.

Figure 3 :

 3 Figure 3: Multipulse snapshots corresponding to (a-d) the deposited energy density during the laser pulse excitation inside the bulk; (e-h) viscosity maps underlying the material under transitions to the liquid phase after pulse excitation; (i-l) final structure where 1 stands for undamaged material and 0 for a void structure. The pulse energy is 250 nJ, the pulse duration is 200 fs. The number of pulses N is indicated in each image.

Figure 4 :

 4 Figure 4: Silica density snapshots corresponding to 50 ps after irradiation by (a) N = 3 and (b) N = 7 pulses. The pulse energy is 250 nJ, the pulse duration is 200 fs. The density of pristine silica ρ 0 ≈ 2200 kg/m 3 is indicated on the scale.

Figure 5 :

 5 Figure 5: Snapshots of negative pressures as precursors of laser-induced cavitation inside bulk silica at the times (a) 15 ps; (b) 30 ps, and (c) 50 ps after excitation by N = 5 pulse. The pulse energy is 250 nJ, the pulse duration is 200 fs.

Figure 6 :

 6 Figure 6: Scattering losses upon propagation of plane continuous waves through the nanovoid structures created (a) by N = 3 and (b) N = 10 pulse irradiations. The intensity is averaged over the period and normalized to the incident value I 0 . The regions limited by dashed lines indicate the nanostructured domains.

Acknowledgements

This work was supported by an Air Force Office of Scientific Research (AFOSR) award FA9550-19-1-0032 and by ADEME: Agence de la transition écologique via the project IMOTEP. This work has equally been funded by a public grant from the French National Research Agency (ANR) under the Investments for the Future Program (PIA), which has the reference EUR MANUTECH SLEIGHT -ANR-17-EURE-0026.

We also acknowledge the support of LABEX MANUTECH-SISE (ANR-10-LABX-0075) of the Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007).

Conflict of interest

The authors declare no conflict of interest. Nonlinear light-matter interaction driven by ultrashort laser pulses enables inscribing a variety of sub-wavelength void-like structures inside silica bulk, serving as optical elements with unique anisotropic and scattering properties. 3D modeling of the nanostructure genesis, evolution and self-organization to nanogratings is pioneered here by original coupled simulations considering both nonlinear propagation and material arrangement upon multipulse irradiation.