T Martinez

M Espanol

C Charvillat

O Marsan

M P Ginebra

C Rey

Stéphanie Sarda
email: stephanie.sarda@univ-tlse3.fr

α-tricalcium phosphate synthesis from amorphous calcium phosphate: structural characterization and hydraulic reactivity

Keywords: Amorphous calcium phosphate, -Tricalcium phosphate, Rietveld refinements, Calcium phosphate cement, Bone substitute

In the present study, amorphous tricalcium phosphate (TCP) has been synthetized by a wet route to obtain low temperature -TCP at 650 °C (LT-TCP) and compare its structural, physical-chemical and thermal properties with those of -TCP obtained by the conventional solid-state reaction method at 1400°C (HT-TCP). Even if no significant differences were observed concerning the values of lattice parameters measured by Rietveld refinement, LT-TCP presented lower crystallinity and higher crystal strains than HT-αTCP. The reactivity in water of the -TCP obtained by the two different routes was assessed. Both raw samples appeared relatively inert in solution and did not favour the nucleation of calcium deficient apatite (CDA); the LT-TCP and HT-TCP were converted into apatite only after milling. The mechanical process leads to a decrease in crystallinity and the formation of an amorphous phase, which is supported in this work by Raman spectroscopy.

The faster rate of conversion of milled LT-TCP compared to HT-TCP can be assigned to its higher specific surface area, lower crystallinity and higher residual crystal strain; these favour the dissolution of the -TCP phase. Finally, the setting properties of -TCP based bone cements were compared regarding their synthesis route. Although the synthesis route does not significantly affect the setting times, the kinetic of conversion into CDA was faster for LT-TCP than for HT-TCP. Thus, the modulation of the dissolution rate of -TCP based cement determined by the preparation route and the grinding process allows control of the overall setting reaction.

Introduction

Alpha tricalcium phosphate (α-TCP) is especially interesting as a bioactive material because of its ability to react with water and set at low temperatures to give calcium deficient apatites (CDA) with a composition close to human bone mineral. For these reasons, α-TCP is currently used in several biomaterials such as hydraulic bone cements for filling bone defects [START_REF] Ginebra | New processing approaches in calcium phosphate cements and their applications in regenerative medicine[END_REF][START_REF] Carrodeguas | α-Tricalcium phosphate: Synthesis, properties and biomedical applications[END_REF].

The phase equilibrium diagram of the CaO-PO5 system exhibits three polymorphs corresponding to the tricalcium phosphate composition Ca3(PO4)2: -TCP, -TCP and '-TCP phases, depending on the temperature [START_REF] Elliott | Structure and chemistry of the apatites and other calcium orthophosphates[END_REF], (Fig. 1). The '-TCP phase exists only at temperatures above 1430 °C and, at this time, it does not present any practical interest as it has not been stabilized at room temperature.

-TCP is stable up to 1120 °C with a rhombohedral structure (space group R3c), [START_REF] Dickens | Crystallographic studies of the role of Mg as a stabilizing impurity in β-Ca3(PO4)2. The crystal structure of pure β-Ca3(PO4)2[END_REF] and, above this temperature, it transforms to monoclinic -TCP (space group P21/a), [START_REF] Mathew | The crystal structure of α-Ca3(PO4)2[END_REF]. The synthesis of -TCP, generally obtained through a phase transition reaction, is rather difficult as this phase, thermodynamically stable only between 1120 and 1470 °C, has to be quenched to avoid the formation of -TCP impurities [START_REF] Mathew | The crystal structure of α-Ca3(PO4)2[END_REF]. Moreover, due to the sintering and crystal growth occurring at the high temperatures corresponding to the stability domain of the -TCP phase, it is not possible to obtain particles of -TCP with a high specific surface area by this conventional and most used preparation route. That reduces the chemical and biological reactivity of the prepared -TCP phase.

However, α-TCP can also be obtained as a metastable compound by heating amorphous tricalcium phosphate (ATCP), which exhibits the appropriate Ca/P ratio, between 600 and 800 °C, even though the maximum temperature of this formation process is far below the stability domain of -TCP (Fig. 1), [START_REF] Kanazawa | Thermal crystallisation of amorphous calcium phosphate to αtricalcium phosphate[END_REF]. Above 800 °C, the metastable -TCP phase, thus obtained is converted into the stable -TCP one [START_REF] Somrani | Thermal evolution of amorphous tricalcium phosphate[END_REF][START_REF] Maciejewski | Phase transitions in amorphous calcium phosphates with different Ca/P ratios[END_REF][START_REF] Eanes | Thermochemical studies on amorphous calcium phosphate[END_REF][START_REF] Rey | 15 -Tricalcium phosphate-based ceramics[END_REF]. ATCP can be obtained by two main routes: in aqueous medium at low temperature (wet route), [START_REF] Heughebaert | Conversion of amorphous tricalcium phosphate into apatitic tricalcium phosphate[END_REF][START_REF] Somrani | Physico-chemical and thermochemical studies of the hydrolytic conversion of amorphous tricalcium phosphate into apatite[END_REF][START_REF] Rodrigues | Influence of ethanol in the precipitation medium on the composition, structure and reactivity of tricalcium phosphate[END_REF] or by using high energy processing or high temperatures (dry route), [START_REF] Combes | Amorphous calcium phosphates: synthesis, properties and uses in biomaterials[END_REF]. Several authors have reported the synthesis of ATCP by flame spray synthesis [START_REF] Maciejewski | Phase transitions in amorphous calcium phosphates with different Ca/P ratios[END_REF][START_REF] Döbelin | Thermal Treatment of Flame-Synthesized Amorphous Tricalcium Phosphate Nanoparticles[END_REF][START_REF] Loher | Fluoro-apatite and calcium phosphate nanoparticles by flame synthesis[END_REF], but the resulting -TCP obtained after heating at 600 °C exhibits a lower reactivity than the product classically obtained at high temperature [START_REF] Bohner | Effect of thermal treatments on the reactivity of nanosized tricalcium phosphate powders[END_REF].

In the present study, we synthesized ATCP by the wet route developed by Heughebaert et al. [START_REF] Heughebaert | Conversion of amorphous tricalcium phosphate into apatitic tricalcium phosphate[END_REF][START_REF] Heughebaert | Contribution à l'étude de l'évolution des othophosphates de calcium précipités amorphes en orthophosphates apatitiques[END_REF].

The conversion of ATCP into -TCP was first shown by Eanes [START_REF] Eanes | Thermochemical studies on amorphous calcium phosphate[END_REF] and then studied on thermodynamic basis by Somrani et al. [START_REF] Somrani | Thermal evolution of amorphous tricalcium phosphate[END_REF]. However, despite the fact that this route entails a significant reduction in the cost of production and opens a rather large low temperature formation domain, limiting grain growth and sintering, the low-temperature -TCP has been barely exploited to produce cements, contrary to that obtained by the usual high temperature process. Therefore, the objectives of this work were as follows: (i) to compare the structural, physic-chemical and thermal properties of α-TCP obtained by the two different available routes (by conventional solid state reaction at 1400 °C and from ATCP conversion at 650 °C) and (ii) to examine the effect of the synthesis route on the hydraulic conversion of the -TCP into apatite and the reactivity, setting and final properties of the cements in view of bone filling applications.

Materials and Methods

Powders synthesis

Amorphous tri-calcium phosphate (ATCP, Ca/P=1.5) was synthesized by double decomposition of calcium and phosphate salts dissolved in aqueous solutions at room temperature and pH close to 10 [START_REF] Somrani | Thermal evolution of amorphous tricalcium phosphate[END_REF][START_REF] Heughebaert | Conversion of amorphous tricalcium phosphate into apatitic tricalcium phosphate[END_REF][START_REF] Combes | Amorphous calcium phosphates: synthesis, properties and uses in biomaterials[END_REF][START_REF] Heughebaert | Contribution à l'étude de l'évolution des othophosphates de calcium précipités amorphes en orthophosphates apatitiques[END_REF]. A calcium nitrate solution, Ca(NO3)2•4H2O (43.6 g in 550 mL of water containing 40 mL of NH4OH 30%),was mixed quickly with a phosphate-containing solution, (NH4)2HPO4 (27.3 g in 1300 mL of water containing 40 mL of NH4OH 30%). After filtration, the precipitate was washed and lyophilized during 48 h. Two α-TCP synthesis routes have been studied: (i) a low temperature route (named LT-TCP) using thermal treatment of the ATCP obtained by wet double decomposition method at 650 °C for 30 min;

(ii) a high temperature dry route (named HT-TCP) using a solid state reaction at 1400 °C (based on a referenced method) by mixing calcium hydrogen phosphate CaHPO4 and calcium carbonate CaCO3 [START_REF] Ginebra | New processing approaches in calcium phosphate cements and their applications in regenerative medicine[END_REF]. The sintered raw HT-TCP was lightly ground manually in an agate mortar. -TCP powders were milled using a Pulverisette 6 (Fritsch GmbH): 35.5 g α-TCP powder was processed in a 10 cm diameter agate bowl (6 agate beads, Ø = 3 cm,) at 450 rpm for 15 min.

Solid samples characterization

X-ray diffraction (XRD) analysis was carried on a BRUKER D8 Advance diffractometer (CuK radiation, 40 mA, 40 kV). The 2 range was 10°-80° (step size of 0.01°, time/step of 1s). The -TCP lattice parameters were determined by least square Rietveld refinement from the well-determined positions of the most intense reflections using the Thompson-Cox-Hastings pseudo-Voigt peak shape function (Fullprof program). Apparent sizes (d) were calculated using Scherrer Formula [START_REF] Scherrer | Estimation of the size and internal structure of colloidal particles by means of röntgen[END_REF]. Max strains (in %%) correspond to 1/4 of the apparent strain defined by Stokes and Wilson (Eq. 1), [START_REF] Stokes | The diffraction of X rays by distorted crystal aggregates-I[END_REF]:

Strain= e = 1/2 *  * d (Eq.1)
with  being the integral breadths given in reciprocal lattice units (1/Å) x 1000.

The specific surface area was measured by nitrogen adsorption (Brunauer-Emmett-Teller method) using ASAP 2020 equipment (Micromeritics). Before measurement the powder was outgassed at 100 °C.

Raman analyses were carried out using a confocal Raman microscope Horiba Labram HR 800 Jobin Yvon. The samples were exposed to a continuous laser radiation provided by an Argon diode laser at 532 nm (8 mW). A macrospot module was used to obtain a spot size of 100x100 µm. Raman spectra were acquired through a grating of 1800 lines per mm (spectral resolution of 1 cm -1 ) with a quantum well detector cooled to -60 ° C (Synapse CCD). Each spectrum was recorded between 900-1100 cm - 1 (integration time of 240 s, 3 accumulations). A certified silicon standard allowed frequency equipment to be calibrated using the silicon line at 520.7 cm -1 . A baseline correction and fitting processing were realized using Labspec 5 software (Horiba Jobin Yvon) by varying parameters (position and width of phosphate bands) to provide the best curve fit. The baseline was linearized, and the band shape was considered to be Gaussian-Lorentzian.

Differential thermal analysis (DTA) of ATCP and -TCP was performed using a SetSys Evolution 1600 SETARAM apparatus with a heating rate equal to 10°C/min.

Hydraulic reactivity profiles consist of an evaluation of -TCP reactivity and transformation ability using only pH variations in solution. To preserve of the sensitivity of this technique no buffer can be used. These profiles were obtained at constant temperature in a regulated bath (37 ± 1 °C) with external circulation connected to a double wall cell. The experiments were carried out in triplicate by dispersing -TCP powders (25 mg) in deionized water (20 mL) with a liquid-to-powder ratio (L/S) equal to 80 mL/g under stirring. The pH, temperature and conductivity were measured every 20 sec.

The powders were added to water approximately 2 min after the start of the measurements, removed by filtration of the solution at 8, 15, 18, 24, 30 h, quenched in acetone to stop the reaction, and dried.

Setting properties of the cement

The cement samples were obtained by mixing -TCP powders with an aqueous solution containing 2.5 wt % of disodium hydrogenphosphate as an accelerant with an L/P ratio equal to 0.45 mL/g. The initial (I) and final (F) setting times, determined with Gillmore needles (ASTM-C266-89 standard method), are defined as the time a small needle (113.4 g, Ø=2.13 mm, 0.3 MPa) and a large needle (453.6 g, Ø=1.06 mm, 5 MPa) no longer leave a visible print on the surface of the cement paste. The cement pastes were placed in Teflon moulds (Ø = 6 mm, h = 12 mm) and immersed in Ringer's solution at 37°C. The samples were removed from their moulds at 0, 18, 24, 48, 168 h, and dropped in acetone to stop the setting reaction, dried, ground to powder, and characterized by XRD. The apparent crystallite size was calculated from the (002) lines by applying Scherrer's formula [START_REF] Scherrer | Estimation of the size and internal structure of colloidal particles by means of röntgen[END_REF]. The relative intensity for each component was calculated by indexing the peaks using JCPDS-9-348 for α-TCP and JCPDS-9-432 for CDA. The compressive strength was measured using a mechanical testing machine (HOUNSFIELD H25KS Model, 25kN) with a crosshead speed of 1 mm/min.

Scanning electron microscopy (SEM) observations were performed using an FEG JEOL JSM 6700F.

Results

Characterization of the powders

Thermal evolution of ATCP into LT-TCP

The X-ray diffraction diagram of the ATCP powder (Fig. SI1) shows the characteristic features of an amorphous compound with broad humps around 30° and 50° and no additional peak of a crystalline phase. Moreover, after heating the sample at 900 °C for 2 h, no apatite was observed by XRD and no pyrophosphate groups by FTIR spectroscopy (data not shown). According to Heughebaert [START_REF] Heughebaert | Preparation de l'orthophosphate tricalcique pur[END_REF], this is indicative of pure amorphous tricalcium phosphate (Ca/P=1.5, above 98%).

The DTA curve of ATCP powders from 25 to 1200 °C (Fig. SI2) shows an asymmetric endothermic peak with a minimum at about 190 °C that is associated with water loss and an intense exothermic peak at about 680 °C which was attributed by Somrani et al. [START_REF] Somrani | Thermal evolution of amorphous tricalcium phosphate[END_REF] to the crystallization of the amorphous phase.

The structural evolution of ATCP was characterized by XRD after heating 1g of the amorphous powder in an oven at different constant temperatures from 25 to 850 °C for 30 min (Fig. 2).

Considering the phase diagram of the P2O5-CaO system [START_REF] Elliott | Structure and chemistry of the apatites and other calcium orthophosphates[END_REF], -TCP is normally thermally stable up to its phase transition into -TCP at a temperature of 1120 °C, then -TCP is stable between 1120 and 1470 °C but metastable at room temperature [START_REF] Carrodeguas | α-Tricalcium phosphate: Synthesis, properties and biomedical applications[END_REF]. According to Fig. 2, ATCP remained amorphous until 550 °C, and its crystallization into -TCP occured between 550 and 650 °C; this was at a lower temperature than the crystallization peak observed on the thermal analysis, a difference usually observed between dynamic and static heating modes. Then the metastable -TCP begins to recrystallise into stable β-TCP, and the α and β phases coexist between 750 and 850°C. Thus, the thermodynamically unstable phase at these temperatures forms first, which is in agreement with the Ostwald step rule [START_REF] Van Santen | The Ostwald step rule[END_REF].

Structural properties of -TCP

Influence of synthesis route

SEM observations of -TCP powders produced at low and high temperature after 15 min of milling are presented in Fig. 3. Particle agglomerates with a dimension of few m are observed for both powders. HT-TCP appears compact due to the high temperature process, whereas LT-αTCP appears as looser agglomerates. Specific surface area values are about 5 times lower for -TCP obtained by conventional synthesis: 2.0  0.2 and 11  1 and m 2 /g for HT-TCP and LT-TCP, respectively. It can be noted that the results of specific surface area for HT-TCP are in accordance with those published in the literature [START_REF] Yashima | Determination of Precise Unit-Cell Parameters of the α-Tricalcium Phosphate Ca3(PO4)2 Through High-Resolution Synchrotron Powder Diffraction[END_REF][START_REF] Kolmas | Alpha-tricalcium phosphate synthesized by two different routes: Structural and spectroscopic characterization[END_REF][START_REF] Camiré | Correlating crystallinity and reactivity in an α-tricalcium phosphate[END_REF][START_REF] Hurle | Calorimetry investigations of milled α-tricalcium phosphate (α-TCP) powders to determine the formation enthalpies of α-TCP and X-ray amorphous tricalcium phosphate[END_REF]. TCP and HT-TCP were successfully performed in the monoclinic system P21/a (Fig. 4). The lattice parameters, apparent crystal size and maximal strain calculated by Rietveld refinement are presented in Table 1 [START_REF] Mathew | The crystal structure of α-Ca3(PO4)2[END_REF][START_REF] Yashima | Determination of Precise Unit-Cell Parameters of the α-Tricalcium Phosphate Ca3(PO4)2 Through High-Resolution Synchrotron Powder Diffraction[END_REF][START_REF] Yashima | High-temperature neutron powder diffraction study of the structural phase transition between α and α′ phases in tricalcium phosphate Ca3(PO4)2[END_REF]. The structural parameters obtained agreed with those published (Table 2) but significant differences were observed concerning the apparent crystal size and strain depending on the synthesis route and mechanical treatment. LT-αTCP powder presents a smaller apparent crystal size (about 675  30 and 3585  500 Å for unmilled LT-αTCP and HT-TCP, respectively), lower crystallinity and higher maximum strain than HT-TCP.

Influence of mechanical treatment

Structural analysis

Figure 5 shows XRD diagrams of the LT-TCP phase obtained from ATCP powder at 650 °C, unmilled and after 15 min of ball milling time. Milling leads to broad XRD peaks with low intensity.

In addition, the broad hump around 30° in milled samples can be related to an amorphization of the -TCP phase due to milling, in agreement with data already reported [START_REF] Camiré | Correlating crystallinity and reactivity in an α-tricalcium phosphate[END_REF][START_REF] Nakano | Variation in crystallinity of hydroxyapatite and the related calcium phosphates by mechanical grinding and subsequent heat treatment[END_REF].

The two types of α-TCP studied in this work exhibit similar lattice dimensions, and the milling process does not have any significant consequences on these values (Table 1). Moreover, the crystal size calculated for HT-TCP powder decreases strongly after 15 min of milling (from 359 nm  50 to 191 nm  6), while this value appears slightly larger for LT-TCP after 15 min of milling (from 68 nm  3 to 84 nm  3). This can be due to a bias in the determination of the average size excluding the amorphized part of the sample and the smaller crystals participating only to the base enlargement of the diffraction lines excluded by the background corrections. Moreover, a significant increase of maximum crystal strain parameter was observed after 15 min of milling, whatever the synthesis route.

Thermal evolution

The DTA curves from 250 to 650 °C for the LT-TCP and HT-TCP powders before and after milling are presented in Fig. 6. A broad exothermic peak was observed at about 530 °C after 15 min of milling whatever the synthesis route. This peak could be associated to the crystallization of an amorphous phase related to grinding because it is not observed in the unmilled samples; such a recrystallization phenomenon after milling has also been reported by Camiré et al. [START_REF] Camiré | Correlating crystallinity and reactivity in an α-tricalcium phosphate[END_REF] for milled HT-TCP at slightly lower temperatures (400-450 °C).

Raman investigations

Raman spectra of LT-TCP et HT-TCP with and without milling (15 min) are presented in Fig. 7.

Factor group analysis predict that the primitive cell of -TCP should exhibit 216 Raman bands for internal modes of the PO4 3-ion [START_REF] Jillavenkatesa | The infrared and Raman spectra of β-and α-tricalcium phosphate (Ca3(PO4)2)[END_REF], but fewer vibration bands than predicted are observed in Raman spectra. The most prominent bands of -TCP are present between 900-1000 cm -l , as published by previous authors [START_REF] Rey | Characterization of calcium phosphates using vibrational spectroscopies[END_REF]. There are attributed to the  symmetric P-O stretching vibration of the phosphate ion. The presence of a medium intensity line at 984 cm -1 has been assigned to the v3 fundamental vibrational mode corresponding to the triple-degenerate asymmetric P-O stretching mode [START_REF] Jillavenkatesa | The infrared and Raman spectra of β-and α-tricalcium phosphate (Ca3(PO4)2)[END_REF]; other bands corresponding to this mode are found at 998, 1012, 1027, 1058 and 1077 cm - 1 . The most obvious difference between milled and unmilled samples is line broadening and the existence of a prominent broad band on the low wavenumber side of the 1 PO4 vibrational domains.

This broad line centred at 951 cm -1 is related to the milling process, whatever the synthesis route, and it can be assigned to the  PO4 line of an amorphous phase [START_REF] Rey | Characterization of calcium phosphates using vibrational spectroscopies[END_REF][START_REF] Demnati | Suppl 1-M3: Comparison of Physical-chemical and Mechanical Properties of Chlorapatite and Hydroxyapatite Plasma Sprayed Coatings[END_REF]. To evaluate the proportion of this phase, a curve fitting was performed, and the relative band integrated intensities were defined as the ratio of  PO4 vibration band area of ATCP to the total area of PO4 bands in the 900-1000 cm -1 range. This value was close to zero for unmilled -TCP, and it increased considerably after 15 min of milling (above 0.3) for both HT-TCP and LT-TCP. These results provide evidence for the formation of an amorphous calcium phosphate phase with rather similar amounts in the milled samples whatever the synthesis route.

Reactivity of -TCP powders

Reactivity assessment of -TCP powders was performed at 37 °C in deionized water by pH measurements during about 20 h (Fig. 8). The hydrolysis reaction was stopped after 8, 15, 18, 24, 30 h by immersion in ethanol, and the powders were characterized by XRD analysis (Fig. 9). In all cases the first event detected is powder dissolution associated with an uptake of protons and a sharp pH increase that is due to the hydrolysis of dissolved PO4 3-ions into HPO4 2-and H2PO4 -ions. Without ball milling, no transformation into CDA was detected by XRD during the test period whatever the synthesis route (Figure SI3). As seen in Figs. 8a and8c, after a sharp pH increase related to the powder dissolution, the values remain stable and neutral (7.6 for LT-TCP and 8 for HT-TCP). There is no significant pH decrease, which in agreement with the extremely low rate of hydrolysis reported for unmilled -TCP first by Monma and Kanazawa [START_REF] Monma | Millennial Special Leading Papers on Ceramics in the 20th Century: the Best of JCerSJ The Hydration of α-Tricalcium Phosphate[END_REF].

For milled powders, after the initial pH increase related to the dissolution of -TCP, the pH kinetics exhibited several decrease events that are related to the transformation of the -TCP into CDA (Fig. 9). The addition of HT-TCP to water led to a rapid increase of the pH value, which reaches a maximum of 9.6 in few sec before decreasing continuously during the test. The rate of decrease is not constant, and it can be divided into several regions; after about 5 h, a rapid pH decrease is followed by a slower decrease. The XRD study of the powders shows that CDA becomes detectable at only 18 h of HT-TCP hydrolysis, and no -TCP phase is detected at 30 h (Fig. 9). Comparatively, mixing LT-TCP with water leads to a rapid increase in pH up to 8.8 in few sec before decreasing. As with HT-TCP, the rate of decrease can be divided in several steps showing two fast decrease periods at 8.5 and 14 h. The pH reaches lower values (pH 6.4) than those of HT-TCP at the end of the test.

The XRD diagrams of the powders show that the observation of CDA is delayed. At 8 h no CDA is observed, and a small amount is seen at 15 h. These data indicate that the formation of CDA occurs only after an important lag time, but once this phase has nucleated, the hydrolysis reaction is completed in a few hours and, only CDA is observed at 24 h (Fig. 9). Nevertheless, the transformation reaction of -TCP into CDA appears globally faster for LT-αTCP. This observation can be related to the higher specific area and the lower crystallinity of LT-αTCP compared to HT-TCP. Additionally, the XRD peaks of the CDA formed appear less resolved for LT--TCP, suggesting the formation of an apatitic phase with a lower crystallinity. HT-TCP in red) hydrolyzed for increasing time periods (L/S = 80 mL/g, 37 °C).

Bone cement applications

Setting properties

Setting properties of the α-TCP based cements obtained by the two different routes and milled for 15 min were studied with a L/S equal to 0.45 mL/g and 2.5 wt.% Na2HPO4 as accelerant in the liquid phase. These experimental conditions are clearly different from those used in the previous paragraph but correspond closely to those of α-TCP cement [START_REF] Fernandez | Comparative study of the setting reaction kinetic of several apatitic calcium phosphate bone cements[END_REF]. The initial and final setting times of the cement formulated with LT-TCP were similar to those obtained with HT-TCP: I was equal to 24  2 min and 22  1 min for LT-TCP and HT-TCP, respectively; F was 75  5 min for both. Whereas the reaction transformation of -TCP into CDA was not achieved before 48 h for HT-TCP, as seen in Fig. 10a and Table 3, full conversion was reached in less than 24 h for LT-TCP (Fig. 10b). These results are in agreement with the hydrolysis data (see 3.1.2) despite the rather different reaction conditions. The crystal size of the CDA formed seems slightly smaller for LT-αTCP than HT-αTCP.

As usually observed [START_REF] Fernandez | Comparative study of the setting reaction kinetic of several apatitic calcium phosphate bone cements[END_REF][START_REF] Sarda | Rheological properties of an apatitic bone cement during initial setting[END_REF], there is no clear correlation between the setting times determined by the Gillmore needles and the advancement of the hydrolysis reaction determined by XRD.

Table 3. Weight percent of conversion of LT-TCP and HT-TCP based cements into CDA and L(002)

apparent crystallite size calculated from the (002) XRD lines of CDA obtained at different hardening times.

Compressive strength

The final compressive strengths (Cs) of cement cylinders after immersion in Ringer's solution for 18, 24, 40 h, and 7 days are presented in Fig. 11a. Cs increased until 24 h for both cements and then remained stable after 48 h. The best values obtained for both cements were around 10-15 MPa. These values are significantly higher for the cement formulated from HT-TCP. This is in accordance with crystal size (Table 3), and previous work has shown that the evolution of the growth of the apatitic crystals is responsible for the mechanical properties [START_REF] Fernández | High-strength apatitic cement by modification with superplasticizers[END_REF]. However, no difference in size and morphology of CDA crystals was detected by SEM up to 48 h (Fig. 11).

Discussion

The setting reaction and the role of grinding in α-TCP based cements have been the object of several studies [START_REF] Carrodeguas | α-Tricalcium phosphate: Synthesis, properties and biomedical applications[END_REF][START_REF] Camiré | Correlating crystallinity and reactivity in an α-tricalcium phosphate[END_REF][START_REF] Ginebra | Compliance of an apatitic calcium phosphate cement with the short-term clinical requirements in bone surgery, orthopaedics and dentistry[END_REF][START_REF] Monma | Preparation of octacalcium phosphate by the hydrolysis of α-tricalcium phosphate[END_REF]. Several articles have pointed out a loss of crystallinity and the formation of an amorphous phase on grinding [START_REF] Camiré | Correlating crystallinity and reactivity in an α-tricalcium phosphate[END_REF][START_REF] Bohner | Combining particle size distribution and isothermal calorimetry data to determine the reaction kinetics of α-tricalcium phosphate-water mixtures[END_REF] that is associated with an increase in the conversion reaction rate [START_REF] Bohner | Combining particle size distribution and isothermal calorimetry data to determine the reaction kinetics of α-tricalcium phosphate-water mixtures[END_REF]. Isothermal calorimetry following the hydrolysis reaction suggests that two heat releases occur at different setting times in mixed amorphous-TCP obtained by milling (200-300s and 5000s), [START_REF] Camiré | Correlating crystallinity and reactivity in an α-tricalcium phosphate[END_REF]. The study of the setting reaction of -TCP obtained by thermal conversion of an amorphous calcium phosphate produced by flame spray synthesis revealed a slower rate of conversion that mainly resulted in an increase of the induction time [START_REF] Bohner | Effect of thermal treatments on the reactivity of nanosized tricalcium phosphate powders[END_REF]. Generally, the induction time corresponds to the time needed for the first nuclei of CDA to form. In the case of heterogeneous nucleation, it is related to the interfacial tension between the nucleating substrate and the forming nucleus [START_REF] Burke | Relation of lattice ion solution composition to octacalcium phosphate dissolution kinetics[END_REF][START_REF] Bohner | A physical approach to modify the hydraulic reactivity of α-tricalcium phosphate powder[END_REF].

In the present study, XRD analysis of ATCP at different heating temperatures (Fig. 2) show that thermodynamically unstable -TCP occurs first between 550 and 650 °C and it recrystallizes into stable β-TCP between 750 and 850 °C, in accordance with previous studies [START_REF] Carrodeguas | α-Tricalcium phosphate: Synthesis, properties and biomedical applications[END_REF][START_REF] Somrani | Thermal evolution of amorphous tricalcium phosphate[END_REF]. The formation of crystalline metastable phases during heating of amorphous compounds has been explained by the Ostwald's step rules or the law of successive reactions [START_REF] Van Santen | The Ostwald step rule[END_REF]. It states that in metastable systems, the closer phase in terms of free energy often crystallizes first, followed by solid state transitions to thermodynamically more stable phases. Even if no significant differences were observed concerning the values of lattice parameters measured by Rietveld refinement, LT-TCP presents lower crystallinity and higher maximal crystal strains than HT-αTCP. The conventional high temperature process of -TCP synthesis favours crystal growth and the relatively low temperature involved in the conversion of ATCP to LT-TCP implies lower ion mobility, preserving smaller particles. However, the high temperatures also favour the formation of thermal defects which might be preserved in the final HT-TCP due to the quenching.

The ball milling process leads to a decrease in crystallinity and the formation of an amorphous phase (mATCP) as evidenced by DTA, Raman spectroscopy and, with lower sensitivity, by XRD. Thus the starting material is converted into a biphasic powder. Without affecting lattice parameters, ball milling of the powders for only 15 min also involves a significant increase in the maximum crystal strain, creating high energy fracture faces with a high reactivity that determine the behaviour of the powder in solution. The events occurring when -TCP is dipped in water were investigated in relation to the synthesis method using a simple pH follow-up (Fig. 8). The main events are a dissolution reaction associated with an initial sharp pH increase, the possible re-equilibration of the solutions due to milling, and the CDA nucleation and growth.

The initial pH increase corresponds to the dissolution of the powders, more precisely, it is related to the amount of phosphate ions dissolved. The difference in the amount dissolved between the nonmilled LT-TCP and HT-TCP is revealed by the maximum value reached by the pH. This could be due to thermodynamic reasons and/or to differences in surface-solution reactions. Such differences in dissolution have already been reported by Bohner et al. [41] between raw -TCP and -TCP reheated at 500 °C, using isothermal calorimetry, and the difference in solubility was assigned to dissolution inhibition. Such inhibition of dissolution reactions in under-saturated media has been described and by Tang and Nancollas for octacalcium phosphate and other sparingly soluble salts, and attributed to the lack of active surface defects on the crystals faces [START_REF] Tang | Abnormal dissolution of octacalcium phosphate crystals at constant undersaturation[END_REF]. The absence of surface defects in the unmilled LT-TCP would thus lead to a pseudo-equilibrium of solubility lower than that reached by HT-TCP. Another possible explanation would be the difference in the dissolution enthalpy of LT-TCP and HT-TCP determined by Somrani et al. [START_REF] Somrani | Thermal evolution of amorphous tricalcium phosphate[END_REF], (-536.3±1.5 and -512.4±1.8 J/g, respectively), indicating that LT-TCP is more stable regarding dissolution.

Without milling, the α-TCP phases (LT and HT) do not transform into CDA (at least during 20 h, Fig. SI3). This observation is in agreement with the data initially reported by Monma et al. [START_REF] Monma | Properties of hydroxyapatite prepared by the hydrolysis of tricalcium phosphate[END_REF][START_REF] Monma | Composition and properties of hydroxyapatite prepared by the hydration of tricalcium phosphate[END_REF].

After the first short period of dissolution (a few min), the pH remains quasi-stable for the non-milled LT-TCP; for non-milled HT-αTCP, a slow very small decrease is observed during the 20 h of the experiment. This phenomenon reveals the absence of spontaneous nucleation sites for CDA on unmilled -TCP as there is for -TCP [START_REF] Campion | Microstructure and chemistry affects apatite nucleation on calcium phosphate bone graft substitutes[END_REF][START_REF] Kotani | Bone bonding mechanism of β-tricalcium phosphate[END_REF], which implies the need for a higher supersaturation regarding CDA nuclei formation and the start-up of hydrolysis.

Whatever the synthesis route, this lack of reactivity is swept out after milling. For both milled samples the initial increase of pH is higher than that observed for the raw powders, confirming that mechanical grinding favours sample dissolution overpassing the solubility products. Moreover, the milling decreases the crystallinity of -TCP whatever the synthesis route, and involves the formation of a potentially more soluble amorphous phase (mATCP). The higher dissolved amounts of milled α-TCPs, compared to unmilled ones, do not however allow CDA nucleation according to XRD. The very slow pH decrease which follows the dissolution is similar to that obtained for unmilled α-TCP.

This can be assigned to surface re-equilibration of particles with solution. However, the fast pH decreases of the two samples at about 5 and 8.5 h for HT-αTCP and LT-αTCP, respectively (Fig. 8), testify to a nucleation of a Ca-P phase with a lower solubility product than the initial phases. For both LT-and HT-TCP, a small CDA amount is clearly observed on XRD diagrams at 15 and 18 h, respectively (Fig. 9); it cannot be excluded that an amorphous Ca-P hydrated phase forms first from the hydrolysis of -TCP or mATCP both present in these biphasic powders. Such a neo-formed amorphous precursor could be a necessity due to the difficulty to nucleate CDA on the α-TCP and the requirement of high supersaturation [START_REF] Wei | Hydrolysis of α-Tricalcium Phosphate in Simulated Body Fluid and Dehydration Behavior During the Drying Process[END_REF]. Precipitated ATCP can hydrolyze easily into CDA through an autocatalytic hydrolysis reaction as shown by Eanes [START_REF] Eanes | Thermochemical studies on amorphous calcium phosphate[END_REF]. The difference in induction times between the milled HT-TCP (5 h) and LT-TCP (8.5 h) can be related to the higher supersaturation reached in the HT-TCP solution, as it is well established that induction times for nucleation decrease as the supersaturation increases. The slowdown in the pH after this first fast pH decrease indicates the installation of the dissolution-reprecipitation process at a lesser ion activity product in solution.

A second fast decrease with the milled LT-αTCP occurs at around 14 h, corresponding to CDA detection by XRD with a second adjustment to a new inferior ionic product of solution. The HT-αTCP curve shows only one major event in solution, possibly because the formation of apatite appears slower. These two conversion steps, clearly observed in the pH variation/evolution for LT-TCP, have also been observed by Camire et al. in -TCP cements using isothermal calorimetry, although at much earlier times [START_REF] Camiré | Correlating crystallinity and reactivity in an α-tricalcium phosphate[END_REF]. Once apatite nucleation has occurred, the dissolution-reprecipitation reaction is active and it is the dissolution rate of the initial α-TCP phases, related to their specific surface area, which is the limiting factor of the conversion reaction into CDA. Another fact to consider regarding the hydrolysis rate is that LT-TCP induces a larger pH drop and thus facilitates the dissolution process; this could be related to differences in the composition of formed CDAs depending on the initial powder which have to be analyzed, but essentially to the higher specific surface area of LT-TCP which makes it more reactive.

Regarding the trials on -TCP based cements, the synthesis route of the initial powders does not significantly affect the setting times. The Cs values remained low (around a maximum of 10-15 MPa) but suitable for filling non-load-bearing bone defects. However, XRD data show that LT-αTCP presents faster conversion kinetics into CDA than HT-αTCP. This is in agreement with the reactivity study of the powders in water which was performed at a much higher L/S ratio (80 instead of 0.45 mL/g in setting experiments) and in different conditions (Na2HPO4 as accelerator in the cement). The reaction rate seems to be mainly controlled by the dissolution rate of the -TCP/mATCP biphasic sample, once the nucleation of CDA has occurred, with induction periods similar to those observed in the testing of the powders' reactivity. Thus the preparation route and grinding allows the control of the overall setting reaction. Although the powder reactivity assessment was performed at high L/S, they appear nicely related to the cements conversion reaction including the induction time. Therefore, simple tests such as monitoring the pH evolution could be used to understand the behaviour of cement mixtures.

Conclusion

In the present study, it appears that the milling process acts on the -TCP reactivity. It not only favours the dissolution rate of the powder through increased surface area but also the formation of an amorphous phase and surface instabilities. The synthesis route acts on the structure stability of -TCP based cement by modifying the rate of CDA nucleation.

Figure 1 .

 1 Figure 1. Domain of formation (dark red) and existence (light blue) of amorphous calcium phosphate(ATCP), -tricalcium phosphate (-TCP) and -tricalcium phosphate (-TCP), (inspired from[START_REF] Rey | 15 -Tricalcium phosphate-based ceramics[END_REF]).

Figure 2 .

 2 Figure 2. XRD diffraction of ATCP after heating in a range of temperature between 450 and 850 °C ( and  for -TCP and -TCP main XRD peaks, respectively).

Figure 3 .

 3 Figure 3. SEM observations of -TCP powders milled 15 min (a), (c) HT-TCP; (b), (d) LT-TCP.

Figure 4 .

 4 Figure 4. XRD diagrams and Rietveld refinement of milled (15 min) -TCP: (a) LT-TCP) and (b) HT-TCP. The black lines (Ycalc) are calculated intensities and the red points (Yobs) the observed intensities. The difference between the observed and calculated intensities (Yobs-Ycalc) is plotted in blue line below the profile. The short vertical green lines show the position of Bragg reflections.

Figure 5 .

 5 Figure 5. XRD diagrams of: (a) unmilled and (b) milled (15 min) LT-TCP. The Y axis corresponds to the standardized intensity relative to maximum intensity (normalized intensity in %).

Figure 6 .

 6 Figure 6. DTA curve of unmilled (a) HT-TCP, (b) LT-TCP; and of milled (c) HT-TCP, (d) LT-TCP.

Figure 7 .

 7 Figure 7. Raman spectra of (a) unmilled and (c) milled HT-TCP, (b) unmilled and (d) milled LT-TCP; (e) Decomposition of Raman spectrum of milled LT-TCP in the domain of 900-1000 cm -1 .

Figure 8 .

 8 Figure 8. Kinetics of pH of -TCP powders suspensions (L/S = 80 mL/g, 37 °C): (a) LT-TCP without milling; (b) milled LT-TCP; (c) HT-TCP without milling and (d) milled HT-TCP.

Figure 9 .

 9 Figure 9. XRD diagrams of milled -TCP obtained by the two different routes (LT-TCP in blue;

Figure 10 .

 10 Figure 10. XRD diagrams of cement obtained with (a) HT-αTCP and (b) LT-TCP powders at different hardening times in Ringer's solution (L/S = 0.45 mL/g, 2.5 wt.% Na2HPO4).

Figure 11 .

 11 Figure 11. (a) Compressive strength (Cs) of cement formulated from LT-TCP and HT-TCP at different hardening times in Ringer's solution (L/S = 0.45 mL/g, 2.5 wt.% Na2HPO4); SEM observations of cement formulated from (b) HT-TCP and (c) LT-TCP after 48 h of hardening.

Table 1 .

 1 Lattice

		Milling	a (Å)	b (Å)	c (Å)	β (°)	App-size	Max-strain
	powder	time					(Å)	(%%)
		0 min	12.8598(2)	27.2241(2)	15.1863(1)	126.201(1)	675  30	10.5  0.8
	LT-TCP	15 min	12.8740(3)	27.2808(3)	15.2098(2)	126.220(2)	842  30	20  2
		0 min	12.84247(8)	27.33254(9)	15.21115(5)	126.3083(5)	3585  500	2.7  0.7
	HT-TCP	15 min	12.8414(2)	27.3274(2)	15.2087(2)	126.3086(1)	1905  60	9.0  0.3

parameters, apparent crystal size and maximal strain obtained by Rietveld refinement from XRD data of -TCP powders, as synthesized (LT-TCP and HT-TCP) and milled.

-TCP

Table 2 .

 2 Structural

	Reference	a (Å)	b (Å)	c (Å)	β(°)
	Mathew et al. [5]	12.887(2)	27.280(4)	15.219(2)	126.20(1)
	Yashima and Sakai [28]	12.859(2)	27.354(2)	15.222(2)	126.35(1)
	Yashima et al. [23]	12.87271(9)	27.28034(8) 15.21275(12) 126.2078(4)

data of -TCP reported in the literature obtained by Rietveld refinement from X-ray or neutron diffraction data

[START_REF] Mathew | The crystal structure of α-Ca3(PO4)2[END_REF][START_REF] Yashima | Determination of Precise Unit-Cell Parameters of the α-Tricalcium Phosphate Ca3(PO4)2 Through High-Resolution Synchrotron Powder Diffraction[END_REF][START_REF] Yashima | High-temperature neutron powder diffraction study of the structural phase transition between α and α′ phases in tricalcium phosphate Ca3(PO4)2[END_REF]

. All the values were determined on α-TCP obtained by solid state reaction at 1400 °C.

Acknowledgements

M.P.G. acknowledges the support provided by the Spanish Government through Project MAT2015-65601-R (MINECO/FEDER, UE), and the "Generalitat de Catalunya" for the 2017 SGR11-65 and the Icrea Academia Award. M.E. acknowledges the Serra Hunter Fellowship. This project was supported by Inca-Cancéropôle GSO under the DOXOSARCOME project.

Conflict of interest

The authors declare that they have no conflict of interests in this paper.


Pedro H Albuquerque

Sophie Albuquerque

Social Implications of Technological Disruptions: A Transdisciplinary Cybernetics Science and Occupational Science Perspective

Keywords: technological disruptions, technological innovations, cybernetics science, occupational science, labor and nonlabor occupations

In this article we argue that the disruptive social implications of skill-replacing technological innovations are determined neither by human characteristics, such as "low skills" or "low cognition," nor by task characteristics, such as "routine," as it is typically assumed in the predominant economics and management science literature, but by the cybernetic characteristics of the innovations. We also propose that the negative effects of technological disruptions on human well-being cannot be fully understood without the use of a transdisciplinary approach involving cybernetics science and occupational science, and that it is urgent that policymakers look beyond their narrow effects on productivity and on the labor force, and consider instead the complexity of the interactions between cybernetic technologies and meaningful human occupations. We offer as an example the case of the fast adoption of online food delivery services and of remote work technologies during the COVID-19 pandemic. Ethical implications are derived from the arguments.

I. INTRODUCTION

In this article we employ a transdisciplinary cybernetics science and occupational science perspective to argue that the social implications of technological disruptions due to skill-replacing technological innovations are defined by the cybernetic characteristics of the innovations, and not by human characteristics, such as "low skills" and "low cognition," nor by task characteristics, such as "routine," as it is usually assumed in predominant economics and management science approaches. We also propose that it is of the essence to broaden the study of the effects of skill-replacing technologies beyond a productivist and economistic approach by considering their effects on the form, function and meaning of labor and nonlabor human occupations. We propose therefore that implications of technological disruptions on human well-being cannot be fully understood without the use of a transdisciplinary approach involving cybernetics science and occupational science. We ask the reader to keep in mind that, in the context of this article and when used alone, the term "occupation" means, as defined in the occupational science literature, any kind of labor or nonlabor human occupation.

The article is organized as follows: in the "Human Skills, Cybernetics and Occupations" section, we present our thesis' arguments. In the "Online Food Delivery and Remote Work: A COVID-19 Pandemic Case Study" section we offer applications of our thesis. In the "The Future of Technology and of Occupations" section, we speculate on the dangers of a limited and narrow understanding of the social implications of technological disruptions, and derive ethical implications. Finally, we summarize the contributions of the article and perspectives for future research in the "Conclusions" section.

II. HUMAN SKILLS, CYBERNETICS AND OCCUPATIONS

A. Automatic and Autonomous Systems

Among the latest contributions to the understanding of technological change, one that we believe to have been somewhat overlooked in the economics and management science literature is the importance of cybernetics science in the analysis of the social implications of technological innovations and technological disruptions. The existing economics and management science literature is unquestionably aware of the developments in robotics, machine learning and artificial intelligence [START_REF] Brynjolfsson | Artificial Intelligence and the Modern Productivity Paradox: A Clash of Expectations and Statistics[END_REF]. We think however that a more careful look into cybernetics is necessary to improve the understanding of how skill-replacing technologies affect societies.

We adopt here a broad definition of cybernetics that includes all fields of study related to automatic or autonomous systems, therefore encompassing subjects such as automation, machine learning and artificial intelligence. All these fields, even though sometimes following different epistemological approaches, are equivalent in what concerns their effects on social phenomena. That is because they are all related to the study and creation of self-governing technological innovations that, due to their automatic or autonomous nature and accelerated development pace, have been associated with increasingly disruptive socio-economic effects [START_REF] Grinin | The cybernetic revolution and the future of technologies[END_REF]. These technologies typically follow algorithms, which can range from static to adaptive, and simple (e.g. automation) to complex (e.g. artificial intelligence).

As examples, consider a standard elevator that embodies static and simple cybernetics (automatic technologies), and a self-driving vehicle that embodies adaptive and complex cybernetics (autonomous or intelligent technologies). Both are capable of disrupting the socio-economic fabric, but the latter, due to its decision-making capabilities, must be designed and certified following uniquely broad and stringent ethical standards [START_REF] Havens | From principles and standards to certification[END_REF]. Notice also from these examples that technological disruptions are assumed here to always have the potential to impact society positively or negatively, the outcome being a function not of the technology itself, but of how it is utilized and managed: an automatic elevator and a self-driving vehicle can suppress the jobs of operators, but can also extend the availability of services to a large range of contexts and users.

B. Cybernetic Characteristics of Technological Innovations

The predominant economics and management science literature on skill-replacing technologies sees in human characteristics ("low skills," "low cognition") or in task characteristics ("routine") the determinants of technological impacts on society [START_REF] Autor | The skill content of recent technological change: An empirical exploration[END_REF], [START_REF] Acemoglu | Skills, tasks and technologies: Implications for employment and earnings[END_REF], [START_REF] Violante | Skill-biased technical change[END_REF], [START_REF] Cortes | Disappearing routine jobs: Who, how, and why?[END_REF], [START_REF] Acemoglu | Robots and jobs: Evidence from US labor markets[END_REF], [START_REF] Jaimovich | Job polarization and jobless recoveries[END_REF]. We disagree with these predominant perspectives. For us, it is the cybernetic characteristics of skill-replacing technologies (their ability to self-govern in order to replace human skills) that determine their socio-economic effects.

Most of the current economics and management scholarship on the socio-economic effects of technological innovations turns around the disputes between so-called skill-biased technical change (SBTC) and routine-biased technical change (RBTC) approaches [START_REF] Staccioli | The present, past, and future of labor-saving technologies[END_REF]. Both approaches were however developed in hindsight as explanations to changes in data patterns that previous theories could not predict. They also suffer from reductionism and poorly defined core concepts, as they try to fit qualitative concepts to available quantitative data instead of admitting that quantitative data that fit the qualitative concepts can only be obtained by excessive proxying. This happens because, in those fields, research based on quantitative methodologies are frequently seen as superior to those employing qualitative methodologies [START_REF] Lenger | The rejection of qualitative research methods in economics[END_REF]. In the cases of SBTC and RBTC, skills tend to be measured merely through quantifiable dimensions of training, education or experience, while task routinization tends to be measured using data from narrowly defined sources based on industry and labor government surveys designed to achieve objectives not necessarily related to technology studies. Take NASA's Perseverance rover, a self-governed, complex, adaptive and learning-capable cybernetic system [START_REF] Abcouwer | Machine learning based path planning for improved rover navigation[END_REF] as an example of the problems mentioned above. The rover does not replace hypothetical astronauts in the exploration of Mars because astronauts have low skills or low cognition, or because of the routine nature of the tasks they perform. It does it because Perseverance embodies a broad range of cybernetic characteristics that fully and adequately replace specialized human skills needed for the tasks involved in planetary exploration, and despite the fact that those tasks are arguably of a routine nature. In reality, due to their breadth and complexity, those routine tasks do not fit well into typical measures of task routinization based on categorical proxying for labor, as used in economics and management studies. This point is driven home using as an example the recent rise of large language models (LLM) that deliver cognitive automation [START_REF] Korinek | Language models and cognitive automation for economic research[END_REF]. One could argue convincingly that these models only perform routine tasks. But routine and complex, although being two different characteristics of tasks, can easily coexist. Many of the routine tasks a LLM perform can be daunting for the average human due to their complexity, for example, text translation in unusual languages, or rewriting a text competently in different styles. Because core concepts such as task routinization are poorly defined in the economics and management literature, they cannot adequately represent rigorously defined cybernetics-based concepts, such as algorithmic routine, measuring instead some misleadingly similar concept, for example, task simplicity, which is then inappropriately used as a proxy for the measurement of task routinization.

Moreover, human and task characteristics specify the context that precedes a technological innovation, therefore they cannot be the determinants of the skill-replacement process. A skillreplacing technological innovation, on the other hand, is the new element in a preexistent context, therefore its cybernetic (self-governing) characteristics must be the determinants of the skillreplacement process. In summary, we propose the following:

Proposition 1: the replacement of human skills by a skill-replacing technology is not caused by human characteristics (such as low skills) nor by task characteristics (such as routine or simplicity) but by the cybernetic (self-governing) characteristics of the skill-replacing technology in a given context.

C. Human Skills, Tasks, and Occupations

Another contribution of this article is that we introduce knowledge from occupational science into the analysis. The broadest meaning of the word occupation is that it is an activity in which one engages. Collectively, occupations are defined as "the combination of everything that people do throughout their lives" [START_REF] Wilcock | An occupational perspective of health, 3rd ed[END_REF], p. 117. As such, they constitute the fabric of everyday living and determine the way in which humans occupy their space-time continuum and use their skill set to accumulate experiences over a life course. Furthermore, they provide personal and social meaning and identities through humans' interactions with their environment [START_REF] Christiansen | Defining lives: Occupation as identity: An essay on competence, coherence, and the creation of meaning[END_REF].

For instance, occupations can be categorized as maintenance occupations (structuring everyday life), work occupations (production-based occupations resulting in a compensation), play occupations (exploratory and cultural activities), and recreational occupations (involving relaxation and rest) [START_REF] Persson | Value dimensions, meaning, and complexity in human occupation -A tentative structure for analysis[END_REF].

What do we mean by that? Firstly, consider that labor is just one type of occupation among many types of occupations, meaning that occupational choice studies need to consider how humans allocate their time between labor and nonlabor occupations. Secondly, consider also how improvements in skill-replacing technologies will render many meaningful labor occupations forever out of reach of most humans, and that, under a well-being perspective, the time freed up because of the disappearance of these occupations shall be reallocated not only among other labor occupations, but also among nonlabor occupations.

For example, consider a dishwasher. It replaces human skills related to dish washing, reducing the amount of time humans devote to housekeeping as an occupation. By doing so, it allows humans to devote more time to other nonlabor occupations, such as watching movies or sleeping.

Notice that human skills, and the tasks and occupations that they support, are environment and meaning-making dependent [START_REF] Rowles | Place in occupational science: A life course perspective on the role of environmental context in the quest for meaning[END_REF]. As examples of nonlabor occupation technological disruptions, consider how senior people may remain unable to use smartphones for the rest of their lives, while young people may find themselves in an embarrassing situation when asked to use a vintage rotary phone. In both cases, technological characteristics are alien to humans' contextual skills, differently disrupting human occupations.

In addition, an occupational science perspective allows us to go beyond the productivist perspective about "how much output is obtained" with labor occupations, e.g. [START_REF] Syverson | What determines productivity?[END_REF], p. 329. Keeping in mind that skills are needed to perform tasks [START_REF] Autor | The skill content of recent technological change: An empirical exploration[END_REF], and that occupations refer to groups of tasks [START_REF] Law | Core concepts of occupational therapy[END_REF], p. 34, this broader approach allows for a better understanding of how technological innovations can create supportive or disruptive environments for humans as life resources [START_REF] Wilcock | An occupational perspective of health, 3rd ed[END_REF], [START_REF] Rowles | Place in occupational science: A life course perspective on the role of environmental context in the quest for meaning[END_REF], and how they affect their well-being. Therefore, with the help of the occupational substrates taxonomy [START_REF] Clark | Occupational science: Academic innovation in the service of occupational therapy's future[END_REF], we state the following:

Proposition 2: technological innovations destruct, disrupt, or create human occupations depending on the characteristics of the technologies, altering the form (how it is done), function (purpose) and meaning (human experience) of these occupations.

As an example, consider target shooting as a labor occupation (producing nourishment) or as a nonlabor occupation (leisure). Some humans may find meaning in those occupations. Under a labor occupation perspective, a rifle is a technological innovation when compared to a crossbow, and the invention of a cyber-shooter (a shooting robot) may lead to the disappearance of target shooting as a labor occupation. Nonetheless, under an existing leisure perspective, the crossbow and the rifle are just different technological artifacts used in different sports, and in a sports context a cyber-shooter is useless as a technological innovation. In addition, target shooting for nourishment could still be performed as a labor occupation, as long as it provides meaning or function to the human shooter, despite the availability of cyber-shooters. At the same time, cyber-shooting could become a new sport, as humans may play and compete using shooting robots as proxies.

In summary, in order to better understand the socio-economic effects of technological innovations, it is essential to look beyond their effects on productivity and on the labor force, and to consider the complexity of the interactions between cybernetic technologies and human occupations. In particular, skill-replacing technologies allow artifacts and processes to perform increasingly complex tasks as alternatives to humans, disrupting the form, function and meaning of human occupations, with the potential, if unmanaged, to reduce human well-being.

III. ONLINE FOOD DELIVERY AND REMOTE WORK: A COVID-19 PANDEMIC CASE STUDY

As an application of Proposition 1, consider how the previous availability of online food delivery (OFD) services before the COVID-19 pandemic [START_REF] Khan | Technological disruptions in restaurant services: Impact of innovations and delivery services[END_REF] created the right conditions for the explosive growth of OFD services during the pandemic, as lockdowns were imposed. The pandemic was naturally a major factor concerning the disruption of dine out restaurant services, but the availability of OFD services also contributed to the intensity and speed of the disruption [START_REF] Gavilan | Innovation in online food delivery: Learnings from COVID-19[END_REF]. Using the predominant economics and management paradigm, one would propose that the contribution of technological innovations such as OFD services to the disruption of dine out restaurants was caused or by low-skill workers (according to the SBTC approach) or by the routine nature of the tasks involved in dine out restaurants (according to the RBTC approach). It is nonetheless clear that the intensity of the disruption was not caused by either (think gourmet restaurants as a clear example). Proposition 1 offers an alternative answer to the source of the disruption: OFD technologies were disruptive because of the cybernetic characteristics of these skill-replacing technologies that were well adapted to the context of the COVID-19 pandemic. Now, as an application of Proposition 2, consider the fast adoption of remote work technologies during the pandemic. It provides a good example of how important it is to look beyond labor when studying technological disruptions. Analysis of available survey data about the phenomenon in the US indicated that: (a) there was a significant increase in the number of employees using technology to work from home during the pandemic; (b) commuting to work was negatively correlated to remote work, as expected; (c) remote work was more prevalent where COVID-19 infection rates where higher; (d) young employees were more likely to remote work; (e) remote work was more prevalent in information sectors of the economy; and (f) industries that adopted remote work more intensely were also the ones that recurred the least to layoffs or furloughs [START_REF] Brynjolfsson | COVID-19 and remote work: An early look at US data[END_REF].

Although the study as usual concentrates most of its attention on labor, it is evident from its results that nonlabor occupations have played a role during the pandemic. For example, younger employees were probably more exposed to remote technologies and remote nonlabor occupations (consider as an example remote dating) before the pandemic started, making the transition to remote work more natural than for older employees.

The COVID-19 pandemic has also been associated with broad social phenomena that has deeply changed perceptions about the role of work in the ensemble of human occupations. Stylized examples of social shifts in perceptions are the Great Resignation [START_REF] Cohen | How to quit your job in the great post-pandemic resignation boom[END_REF], [START_REF] Klotz | The Great Resignation Is still here, but whether it stays Is up to leaders[END_REF], which represents a rising trend of more highly valuing meaningful nonlabor and labor occupations independently of pay, and the quiet quitting [START_REF] Lord | Quiet quitting is a new name for an old method of industrial action[END_REF], a loss of motivation at work due to decreasing levels of occupational meaning. These trends are believed to have started before the pandemic, but remote work seems to have triggered mass reevaluation of meaning and an acceleration of the trends, due in large part to the effects of remote work on the reevaluation of the importance of nonlabor activities.

Periods of remote work have also put in evidence human social needs embedded in meaningful work activities that are only indirectly connected to productivity or financial compensation but that lead to improvements in well-being, for example, socialization routines at the workplace (such as informal brainstorming by the coffee machine) or the need for physical interactions with coworkers. On the other hand, remote working can create labor and nonlabor occupational benefits such as reduced hours of tedious commuting and flexible schedules that allow for health-related activities such as workout routines and home cooking. Some studies have identified trade-offs that favor flexible arrangements combining some remote work with some physical interactions at the workplace as the most beneficial under a well-being perspective for the employee but also under a productivist perspective for the firm [START_REF] De Klerk | Is working from home the new workplace panacea? Lessons from the COVID-19 pandemic for the future world of work[END_REF].

IV. THE FUTURE OF TECHNOLOGY AND OF OCCUPATIONS

In this section we offer a few arguments of a speculative and ethical nature. We beg to disagree with the typical optimistic neoliberal economics and management perspective on the future of technological disruptions [START_REF] Brynjolfsson | Artificial Intelligence and the Modern Productivity Paradox: A Clash of Expectations and Statistics[END_REF], [START_REF] Eichengreen | Secular stagnation: The long view[END_REF]. We believe instead that the development of cybernetic technologies will continue to accelerate, and that the social implications of skill-replacing technologies may become, if unmanaged, increasingly detrimental to well-being, as it becomes humanly impossible to continuously adapt to broader, faster and more frequent technological disruptions. Even if disruptions can have many positive effects, it will not compensate for the asymmetric nature of the negative effects, as humans are normally risk averse, assigning more weight to losses than to equivalent gains [START_REF] Kahneman | The psychology of preferences[END_REF].

In addition, in the words of Economics Nobel laureate Robert Solow, "if a small class of owners of wealth -and it is small -comes to collect a growing share of the national income, it is likely to dominate the society in other ways as well" [START_REF] Solow | Thomas Piketty is right[END_REF]. There is by now ample evidence that this is happening, as technological control is held by a few cyber-entrepreneurs, suggesting that we should heed Solow's alert. And the wealth concentration resulting from the ownership of skill-replacement technologies is paired with the disruption or destruction of ever larger amounts of meaningful occupations, at an accelerating speed, without necessarily or always providing meaningful labor or nonlabor occupations as alternatives to humans, therefore with increasingly negative consequences for their well-being.

Finally, attributing the malaise caused by unregulated technological innovations to hard-to-define human characteristics (such as low skills) or occupational components (such as routine tasks) is dangerous, as this argument can be ideologically appropriated to turn attention away from the necessary regulation of cybernetic technologies towards the unfair characterization of the victims of negative disruptions as the only ones responsible for their own unfortunate fate. If this is true, we should not be surprised if the result is widespread rage against the machine and the resurrection of Luddism.

V. CONCLUSIONS

In this article we introduced knowledge from cybernetics science and occupational science into the analysis of technological disruption to broaden its scope beyond the predominant productivist and economistic labor paradigms and towards a comprehensive meaningful occupations framework. We offered two propositions: the first one establishes that it is the cybernetic (self-governing) characteristics of skill-replacing technologies that drive technological disruptions, and not human characteristics (such as low skills) or task characteristics (such as routine). The second one states that technological innovations affect form, function and meaning of all types of human occupations. To illustrate the two propositions, we presented a case study based on the growth of online food delivery services and of remote work during the COVID-19 pandemic. Finally, we suggested that the current state of social affairs may not be politically and socially sustainable. As disruptions seem to happen at an accelerating pace, policymakers may need to urgently broaden their perspectives with the help of a transdisciplinary cybernetics science and occupational science approach. We plan to address this matter in more details in our future investigations.

The project leading to this publication has received funding from the French government under the "France 2030" investment plan managed by the French National Research Agency (reference: ANR-17-EURE-0020) and from the Excellence Initiative of Aix-Marseille University -A*MIDEX.